%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP292^3 : 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 : n001.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 09:19:17 AM UTC 2026
% Result : Theorem 54.91s 14.51s
% Output : Refutation 54.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 34 unt; 0 typ; 1 def)
% Number of atoms : 182 ( 67 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 252 ( 40 ~; 21 |; 8 &; 177 @)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 211 ( 210 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 1999 (1996 usr; 83 con; 0-8 aty)
% Number of variables : 46 ( 6 ^; 40 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
real: $tType ).
thf(type_def_6,type,
int: $tType ).
thf(type_def_8,type,
rat: $tType ).
thf(type_def_9,type,
assn: $tType ).
thf(type_def_10,type,
produc3658429121746597890et_nat: $tType ).
thf(type_def_11,type,
list_VEBT_VEBTi: $tType ).
thf(type_def_12,type,
vEBT_VEBT: $tType ).
thf(type_def_13,type,
array_VEBT_VEBTi: $tType ).
thf(type_def_14,type,
produc2732055786443039994et_nat: $tType ).
thf(type_def_15,type,
nat: $tType ).
thf(type_def_16,type,
num: $tType ).
thf(type_def_17,type,
word_N3645301735248828278l_num1: $tType ).
thf(type_def_18,type,
code_integer: $tType ).
thf(type_def_19,type,
uint32: $tType ).
thf(type_def_20,type,
produc6271795597528267376eger_o: $tType ).
thf(type_def_21,type,
produc8923325533196201883nteger: $tType ).
thf(type_def_22,type,
set_nat: $tType ).
thf(type_def_23,type,
set_set_nat: $tType ).
thf(type_def_24,type,
set_int: $tType ).
thf(type_def_25,type,
set_real: $tType ).
thf(type_def_26,type,
complex: $tType ).
thf(type_def_27,type,
filter_real: $tType ).
thf(type_def_28,type,
product_prod_int_int: $tType ).
thf(type_def_29,type,
product_prod_nat_nat: $tType ).
thf(type_def_30,type,
filter_nat: $tType ).
thf(type_def_31,type,
set_o: $tType ).
thf(type_def_32,type,
set_set_o: $tType ).
thf(type_def_33,type,
set_Code_integer: $tType ).
thf(type_def_34,type,
set_set_Code_integer: $tType ).
thf(type_def_35,type,
set_complex: $tType ).
thf(type_def_36,type,
set_set_complex: $tType ).
thf(type_def_37,type,
set_set_int: $tType ).
thf(type_def_38,type,
set_set_set_nat: $tType ).
thf(type_def_39,type,
set_list_o: $tType ).
thf(type_def_40,type,
set_li6976499617229504675nteger: $tType ).
thf(type_def_41,type,
set_list_complex: $tType ).
thf(type_def_42,type,
set_list_int: $tType ).
thf(type_def_43,type,
set_list_list_nat: $tType ).
thf(type_def_44,type,
set_list_nat: $tType ).
thf(type_def_45,type,
set_list_real: $tType ).
thf(type_def_46,type,
set_list_set_nat: $tType ).
thf(type_def_47,type,
set_list_literal: $tType ).
thf(type_def_48,type,
set_list_VEBT_VEBT: $tType ).
thf(type_def_49,type,
set_num: $tType ).
thf(type_def_50,type,
set_Numeral_num0: $tType ).
thf(type_def_51,type,
set_Product_unit: $tType ).
thf(type_def_52,type,
set_rat: $tType ).
thf(type_def_53,type,
set_literal: $tType ).
thf(type_def_54,type,
set_VEBT_VEBT: $tType ).
thf(type_def_55,type,
set_set_real: $tType ).
thf(type_def_56,type,
set_set_VEBT_VEBT: $tType ).
thf(type_def_57,type,
list_nat: $tType ).
thf(type_def_58,type,
extended_enat: $tType ).
thf(type_def_59,type,
set_VEBT_VEBTi: $tType ).
thf(type_def_60,type,
literal: $tType ).
thf(type_def_61,type,
list_o: $tType ).
thf(type_def_62,type,
vEBT_VEBTi: $tType ).
thf(type_def_63,type,
heap_Time_Heap_nat: $tType ).
thf(type_def_64,type,
option_nat: $tType ).
thf(type_def_65,type,
heap_T2636463487746394924on_nat: $tType ).
thf(type_def_66,type,
heap_Time_Heap_o: $tType ).
thf(type_def_67,type,
heap_T8145700208782473153_VEBTi: $tType ).
thf(type_def_68,type,
list_int: $tType ).
thf(type_def_69,type,
option_set_o: $tType ).
thf(type_def_70,type,
option_set_int: $tType ).
thf(type_def_71,type,
option_set_nat: $tType ).
thf(type_def_72,type,
produc827990862158126777uint32: $tType ).
thf(type_def_73,type,
set_Pr958786334691620121nt_int: $tType ).
thf(type_def_74,type,
set_uint32: $tType ).
thf(type_def_75,type,
list_real: $tType ).
thf(type_def_76,type,
list_VEBT_VEBT: $tType ).
thf(type_def_77,type,
list_list_o: $tType ).
thf(type_def_78,type,
list_list_nat: $tType ).
thf(type_def_79,type,
list_list_real: $tType ).
thf(type_def_80,type,
list_list_VEBT_VEBT: $tType ).
thf(type_def_81,type,
list_Code_integer: $tType ).
thf(type_def_82,type,
list_complex: $tType ).
thf(type_def_83,type,
list_set_nat: $tType ).
thf(type_def_84,type,
list_num: $tType ).
thf(type_def_85,type,
list_rat: $tType ).
thf(type_def_86,type,
list_P7333126701944960589_nat_o: $tType ).
thf(type_def_87,type,
list_P3521021558325789923at_int: $tType ).
thf(type_def_88,type,
list_P6011104703257516679at_nat: $tType ).
thf(type_def_89,type,
list_P3644420460460130531t_real: $tType ).
thf(type_def_90,type,
list_P2320588648998582380_VEBTi: $tType ).
thf(type_def_91,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(type_def_92,type,
list_assn: $tType ).
thf(type_def_93,type,
list_uint32: $tType ).
thf(type_def_94,type,
set_Product_prod_o_o: $tType ).
thf(type_def_95,type,
set_Pr6227168374412355847list_o: $tType ).
thf(type_def_96,type,
set_Pr765067013931698361st_int: $tType ).
thf(type_def_97,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(type_def_98,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(type_def_99,type,
set_Pr6218003697084177305l_real: $tType ).
thf(type_def_100,type,
set_Pr611352295856513593t_real: $tType ).
thf(type_def_101,type,
set_Pr1773385645901665561uint32: $tType ).
thf(type_def_102,type,
set_Pr2258164808687509945uint32: $tType ).
thf(type_def_103,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(type_def_104,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(type_def_105,type,
set_Pr2227491710730465451_VEBTi: $tType ).
thf(type_def_106,type,
set_Pr4797120415438012619_VEBTi: $tType ).
thf(type_def_107,type,
list_literal: $tType ).
thf(type_def_108,type,
product_prod_o_o: $tType ).
thf(type_def_109,type,
list_P4002435161011370285od_o_o: $tType ).
thf(type_def_110,type,
product_prod_o_int: $tType ).
thf(type_def_111,type,
list_P3795440434834930179_o_int: $tType ).
thf(type_def_112,type,
product_prod_o_nat: $tType ).
thf(type_def_113,type,
list_P6285523579766656935_o_nat: $tType ).
thf(type_def_114,type,
product_prod_int_o: $tType ).
thf(type_def_115,type,
list_P5087981734274514673_int_o: $tType ).
thf(type_def_116,type,
list_P5707943133018811711nt_int: $tType ).
thf(type_def_117,type,
product_prod_int_nat: $tType ).
thf(type_def_118,type,
list_P8198026277950538467nt_nat: $tType ).
thf(type_def_119,type,
product_prod_nat_o: $tType ).
thf(type_def_120,type,
product_prod_nat_int: $tType ).
thf(type_def_121,type,
list_P3069071885182933823uint32: $tType ).
thf(type_def_122,type,
list_P7985473006766602707_nat_o: $tType ).
thf(type_def_123,type,
set_Pr4532377907799695533_nat_o: $tType ).
thf(type_def_124,type,
list_list_int: $tType ).
thf(type_def_125,type,
list_P362550909693114634et_nat: $tType ).
thf(type_def_126,type,
set_Pr8536935166611901872et_nat: $tType ).
thf(type_def_127,type,
list_P2321686559999237006et_nat: $tType ).
thf(type_def_128,type,
set_Pr3286484037609594932et_nat: $tType ).
thf(type_def_129,type,
list_P9062070895058802706et_nat: $tType ).
thf(type_def_130,type,
set_Pr3948176798113811640et_nat: $tType ).
thf(type_def_131,type,
set_Pr903927857289325719_int_o: $tType ).
thf(type_def_132,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(type_def_133,type,
list_P6863124054624500543t_real: $tType ).
thf(type_def_134,type,
set_Pr3538720872664544793t_real: $tType ).
thf(type_def_135,type,
list_P7524865323317820941T_VEBT: $tType ).
thf(type_def_136,type,
set_Pr8044002425091019955T_VEBT: $tType ).
thf(type_def_137,type,
set_Pr7995236796853374141at_int: $tType ).
thf(type_def_138,type,
list_P4344331454722006975al_int: $tType ).
thf(type_def_139,type,
set_Pr1019928272762051225al_int: $tType ).
thf(type_def_140,type,
list_P8689742595348180415l_real: $tType ).
thf(type_def_141,type,
list_P877281246627933069T_VEBT: $tType ).
thf(type_def_142,type,
set_Pr6019664923565264691T_VEBT: $tType ).
thf(type_def_143,type,
list_P6254988961118846195et_nat: $tType ).
thf(type_def_144,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(type_def_145,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(type_def_146,type,
set_Pr3175402225741728619VEBT_o: $tType ).
thf(type_def_147,type,
list_P4547456442757143711BT_int: $tType ).
thf(type_def_148,type,
set_Pr5066593544530342725BT_int: $tType ).
thf(type_def_149,type,
list_P7037539587688870467BT_nat: $tType ).
thf(type_def_150,type,
set_Pr7556676689462069481BT_nat: $tType ).
thf(type_def_151,type,
list_P2623026923184700063T_real: $tType ).
thf(type_def_152,type,
set_Pr7765410600122031685T_real: $tType ).
thf(type_def_153,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(type_def_154,type,
produc3925858234332021118et_nat: $tType ).
thf(type_def_155,type,
list_P785718909624839377_VEBTi: $tType ).
thf(type_def_156,type,
produc3777764054643897931_VEBTi: $tType ).
thf(type_def_157,type,
list_P5988454224134618948T_VEBT: $tType ).
thf(type_def_158,type,
produc2810682830582626868T_VEBT: $tType ).
thf(type_def_159,type,
list_P735349106241217576_VEBTi: $tType ).
thf(type_def_160,type,
produc3625547720036274456_VEBTi: $tType ).
thf(type_def_161,type,
produc8243902056947475879T_VEBT: $tType ).
thf(type_def_162,type,
produc679980390762269497t_real: $tType ).
thf(type_def_163,type,
list_P4447955379000644808_VEBTi: $tType ).
thf(type_def_164,type,
produc2062302194595185346_VEBTi: $tType ).
thf(type_def_165,type,
produc1531783533982839933T_VEBT: $tType ).
thf(type_def_166,type,
produc7716430852924023517t_real: $tType ).
thf(type_def_167,type,
produc214224863196444774_VEBTi: $tType ).
thf(type_def_168,type,
produc8025551001238799321T_VEBT: $tType ).
thf(type_def_169,type,
list_P8833571063612306856EBTi_o: $tType ).
thf(type_def_170,type,
produc5014006835512566296EBTi_o: $tType ).
thf(type_def_171,type,
list_P7392757774524453448Ti_int: $tType ).
thf(type_def_172,type,
produc8927069083091599426Ti_int: $tType ).
thf(type_def_173,type,
list_P8536626330812492744i_real: $tType ).
thf(type_def_174,type,
produc6680258955013199682i_real: $tType ).
thf(type_def_175,type,
list_P5232166724548748803o_real: $tType ).
thf(type_def_176,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(type_def_177,type,
list_P3595434254542482545real_o: $tType ).
thf(type_def_178,type,
list_P6834414599653733731al_nat: $tType ).
thf(type_def_179,type,
option4927543243414619207at_nat: $tType ).
thf(type_def_180,type,
option2860828798490689354et_nat: $tType ).
thf(type_def_181,type,
option5190343406534369742et_nat: $tType ).
thf(type_def_182,type,
option4624381673175914239nt_int: $tType ).
thf(type_def_183,type,
option3972171592325465343uint32: $tType ).
thf(type_def_184,type,
option_int: $tType ).
thf(type_def_185,type,
option_num: $tType ).
thf(type_def_186,type,
option_rat: $tType ).
thf(type_def_187,type,
option_real: $tType ).
thf(type_def_188,type,
char: $tType ).
thf(type_def_189,type,
heap_e7401611519738050253t_unit: $tType ).
thf(type_def_190,type,
produc7102631898165422375list_o: $tType ).
thf(type_def_191,type,
produc1186641810826059865st_int: $tType ).
thf(type_def_192,type,
produc1828647624359046049st_nat: $tType ).
thf(type_def_193,type,
produc478978216448986841t_real: $tType ).
thf(type_def_194,type,
produc823665806539077721uint32: $tType ).
thf(type_def_195,type,
produc3089554586268799851_VEBTi: $tType ).
thf(type_def_196,type,
produc9211091688327510695T_VEBT: $tType ).
thf(type_def_197,type,
produc5657529347773406293et_nat: $tType ).
thf(type_def_198,type,
produc6830853553727218525et_nat: $tType ).
thf(type_def_199,type,
produc1219242969750017639nt_int: $tType ).
thf(type_def_200,type,
produc859450856879609959at_nat: $tType ).
thf(type_def_201,type,
produc8822557026176459367uint32: $tType ).
thf(type_def_202,type,
produc8786904178792722361al_int: $tType ).
thf(type_def_203,type,
produc2422161461964618553l_real: $tType ).
thf(type_def_204,type,
produc3757001726724277373T_VEBT: $tType ).
thf(type_def_205,type,
produc7819656566062154093et_nat: $tType ).
thf(type_def_206,type,
produc334124729049499915VEBT_o: $tType ).
thf(type_def_207,type,
produc4894624898956917775BT_int: $tType ).
thf(type_def_208,type,
produc9072475918466114483BT_nat: $tType ).
thf(type_def_209,type,
produc5170161368751668367T_real: $tType ).
thf(type_def_210,type,
set_Pr3444600963470892981et_nat: $tType ).
thf(type_def_211,type,
set_Pr7928877670098842301et_nat: $tType ).
thf(type_def_212,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(type_def_213,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(type_def_214,type,
set_Pr3773659940955823943uint32: $tType ).
thf(type_def_215,type,
itself_Numeral_num0: $tType ).
thf(func_def_0,type,
set_Pr3444600963470892981et_nat: $tType ).
thf(func_def_1,type,
produc5657529347773406293et_nat: $tType ).
thf(func_def_2,type,
set_Pr7928877670098842301et_nat: $tType ).
thf(func_def_3,type,
produc6830853553727218525et_nat: $tType ).
thf(func_def_4,type,
option2860828798490689354et_nat: $tType ).
thf(func_def_5,type,
list_P362550909693114634et_nat: $tType ).
thf(func_def_6,type,
set_Pr8536935166611901872et_nat: $tType ).
thf(func_def_7,type,
produc2732055786443039994et_nat: $tType ).
thf(func_def_8,type,
option5190343406534369742et_nat: $tType ).
thf(func_def_9,type,
list_P2321686559999237006et_nat: $tType ).
thf(func_def_10,type,
set_Pr3286484037609594932et_nat: $tType ).
thf(func_def_11,type,
produc3925858234332021118et_nat: $tType ).
thf(func_def_12,type,
word_N3645301735248828278l_num1: $tType ).
thf(func_def_13,type,
set_Pr3773659940955823943uint32: $tType ).
thf(func_def_14,type,
produc8822557026176459367uint32: $tType ).
thf(func_def_15,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(func_def_16,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(func_def_17,type,
set_Pr4797120415438012619_VEBTi: $tType ).
thf(func_def_18,type,
list_P7985473006766602707_nat_o: $tType ).
thf(func_def_19,type,
set_Pr4532377907799695533_nat_o: $tType ).
thf(func_def_20,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(func_def_21,type,
produc859450856879609959at_nat: $tType ).
thf(func_def_22,type,
produc1219242969750017639nt_int: $tType ).
thf(func_def_23,type,
list_P9062070895058802706et_nat: $tType ).
thf(func_def_24,type,
set_Pr3948176798113811640et_nat: $tType ).
thf(func_def_25,type,
produc3089554586268799851_VEBTi: $tType ).
thf(func_def_26,type,
produc9211091688327510695T_VEBT: $tType ).
thf(func_def_27,type,
set_Pr2258164808687509945uint32: $tType ).
thf(func_def_28,type,
produc3658429121746597890et_nat: $tType ).
thf(func_def_29,type,
list_P785718909624839377_VEBTi: $tType ).
thf(func_def_30,type,
set_Pr2227491710730465451_VEBTi: $tType ).
thf(func_def_31,type,
set_Pr611352295856513593t_real: $tType ).
thf(func_def_32,type,
list_P735349106241217576_VEBTi: $tType ).
thf(func_def_33,type,
list_P5988454224134618948T_VEBT: $tType ).
thf(func_def_34,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(func_def_35,type,
set_Pr765067013931698361st_int: $tType ).
thf(func_def_36,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(func_def_37,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(func_def_38,type,
list_P6254988961118846195et_nat: $tType ).
thf(func_def_39,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(func_def_40,type,
produc823665806539077721uint32: $tType ).
thf(func_def_41,type,
produc3777764054643897931_VEBTi: $tType ).
thf(func_def_42,type,
produc478978216448986841t_real: $tType ).
thf(func_def_43,type,
list_P8536626330812492744i_real: $tType ).
thf(func_def_44,type,
list_P7392757774524453448Ti_int: $tType ).
thf(func_def_45,type,
list_P2320588648998582380_VEBTi: $tType ).
thf(func_def_46,type,
list_P4447955379000644808_VEBTi: $tType ).
thf(func_def_47,type,
produc3625547720036274456_VEBTi: $tType ).
thf(func_def_48,type,
produc2810682830582626868T_VEBT: $tType ).
thf(func_def_49,type,
list_P2623026923184700063T_real: $tType ).
thf(func_def_50,type,
list_P877281246627933069T_VEBT: $tType ).
thf(func_def_51,type,
produc1828647624359046049st_nat: $tType ).
thf(func_def_52,type,
produc1186641810826059865st_int: $tType ).
thf(func_def_53,type,
set_Pr7765410600122031685T_real: $tType ).
thf(func_def_54,type,
set_Pr6019664923565264691T_VEBT: $tType ).
thf(func_def_55,type,
list_P7037539587688870467BT_nat: $tType ).
thf(func_def_56,type,
list_P4547456442757143711BT_int: $tType ).
thf(func_def_57,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(func_def_58,type,
list_P7524865323317820941T_VEBT: $tType ).
thf(func_def_59,type,
set_Pr6227168374412355847list_o: $tType ).
thf(func_def_60,type,
produc8243902056947475879T_VEBT: $tType ).
thf(func_def_61,type,
option3972171592325465343uint32: $tType ).
thf(func_def_62,type,
set_Pr7556676689462069481BT_nat: $tType ).
thf(func_def_63,type,
set_Pr5066593544530342725BT_int: $tType ).
thf(func_def_64,type,
set_Pr8044002425091019955T_VEBT: $tType ).
thf(func_def_65,type,
produc7819656566062154093et_nat: $tType ).
thf(func_def_66,type,
produc8923325533196201883nteger: $tType ).
thf(func_def_67,type,
list_P3069071885182933823uint32: $tType ).
thf(func_def_68,type,
list_P8833571063612306856EBTi_o: $tType ).
thf(func_def_69,type,
set_Pr1773385645901665561uint32: $tType ).
thf(func_def_70,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(func_def_71,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(func_def_72,type,
set_Pr3175402225741728619VEBT_o: $tType ).
thf(func_def_73,type,
produc6680258955013199682i_real: $tType ).
thf(func_def_74,type,
option4927543243414619207at_nat: $tType ).
thf(func_def_75,type,
option4624381673175914239nt_int: $tType ).
thf(func_def_76,type,
list_P8689742595348180415l_real: $tType ).
thf(func_def_77,type,
set_Pr6218003697084177305l_real: $tType ).
thf(func_def_78,type,
produc8927069083091599426Ti_int: $tType ).
thf(func_def_79,type,
produc214224863196444774_VEBTi: $tType ).
thf(func_def_80,type,
produc2062302194595185346_VEBTi: $tType ).
thf(func_def_81,type,
list_P6834414599653733731al_nat: $tType ).
thf(func_def_82,type,
list_P4344331454722006975al_int: $tType ).
thf(func_def_83,type,
list_P3644420460460130531t_real: $tType ).
thf(func_def_84,type,
list_P6863124054624500543t_real: $tType ).
thf(func_def_85,type,
produc5170161368751668367T_real: $tType ).
thf(func_def_86,type,
produc3757001726724277373T_VEBT: $tType ).
thf(func_def_87,type,
set_Pr1019928272762051225al_int: $tType ).
thf(func_def_88,type,
set_Pr3538720872664544793t_real: $tType ).
thf(func_def_89,type,
produc7102631898165422375list_o: $tType ).
thf(func_def_90,type,
list_P6011104703257516679at_nat: $tType ).
thf(func_def_91,type,
list_P3521021558325789923at_int: $tType ).
thf(func_def_92,type,
list_P8198026277950538467nt_nat: $tType ).
thf(func_def_93,type,
list_P5707943133018811711nt_int: $tType ).
thf(func_def_94,type,
produc9072475918466114483BT_nat: $tType ).
thf(func_def_95,type,
produc4894624898956917775BT_int: $tType ).
thf(func_def_96,type,
produc8025551001238799321T_VEBT: $tType ).
thf(func_def_97,type,
produc1531783533982839933T_VEBT: $tType ).
thf(func_def_98,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(func_def_99,type,
set_Pr7995236796853374141at_int: $tType ).
thf(func_def_100,type,
set_Pr3448869479623346877nt_nat: $tType ).
thf(func_def_101,type,
set_Pr958786334691620121nt_int: $tType ).
thf(func_def_102,type,
heap_T2636463487746394924on_nat: $tType ).
thf(func_def_103,type,
produc827990862158126777uint32: $tType ).
thf(func_def_104,type,
heap_T8145700208782473153_VEBTi: $tType ).
thf(func_def_105,type,
produc5014006835512566296EBTi_o: $tType ).
thf(func_def_106,type,
list_P3595434254542482545real_o: $tType ).
thf(func_def_107,type,
list_P5232166724548748803o_real: $tType ).
thf(func_def_108,type,
list_list_VEBT_VEBT: $tType ).
thf(func_def_109,type,
set_list_list_nat: $tType ).
thf(func_def_110,type,
list_P7333126701944960589_nat_o: $tType ).
thf(func_def_111,type,
list_P5087981734274514673_int_o: $tType ).
thf(func_def_112,type,
list_P6285523579766656935_o_nat: $tType ).
thf(func_def_113,type,
list_P3795440434834930179_o_int: $tType ).
thf(func_def_114,type,
set_list_VEBT_VEBT: $tType ).
thf(func_def_115,type,
produc334124729049499915VEBT_o: $tType ).
thf(func_def_116,type,
set_Pr903927857289325719_int_o: $tType ).
thf(func_def_117,type,
set_list_set_nat: $tType ).
thf(func_def_118,type,
set_li6976499617229504675nteger: $tType ).
thf(func_def_119,type,
produc6271795597528267376eger_o: $tType ).
thf(func_def_120,type,
set_set_VEBT_VEBT: $tType ).
thf(func_def_121,type,
set_set_set_nat: $tType ).
thf(func_def_122,type,
set_set_Code_integer: $tType ).
thf(func_def_123,type,
produc2422161461964618553l_real: $tType ).
thf(func_def_124,type,
produc8786904178792722361al_int: $tType ).
thf(func_def_125,type,
produc7716430852924023517t_real: $tType ).
thf(func_def_126,type,
produc679980390762269497t_real: $tType ).
thf(func_def_127,type,
heap_e7401611519738050253t_unit: $tType ).
thf(func_def_128,type,
product_prod_nat_nat: $tType ).
thf(func_def_129,type,
product_prod_nat_int: $tType ).
thf(func_def_130,type,
product_prod_int_nat: $tType ).
thf(func_def_131,type,
product_prod_int_int: $tType ).
thf(func_def_132,type,
list_P4002435161011370285od_o_o: $tType ).
thf(func_def_133,type,
set_list_complex: $tType ).
thf(func_def_134,type,
set_Product_prod_o_o: $tType ).
thf(func_def_135,type,
set_list_literal: $tType ).
thf(func_def_136,type,
set_set_complex: $tType ).
thf(func_def_137,type,
array_VEBT_VEBTi: $tType ).
thf(func_def_138,type,
option_set_nat: $tType ).
thf(func_def_139,type,
option_set_int: $tType ).
thf(func_def_140,type,
list_VEBT_VEBTi: $tType ).
thf(func_def_141,type,
list_list_real: $tType ).
thf(func_def_142,type,
set_VEBT_VEBTi: $tType ).
thf(func_def_143,type,
set_list_real: $tType ).
thf(func_def_144,type,
list_list_nat: $tType ).
thf(func_def_145,type,
list_list_int: $tType ).
thf(func_def_146,type,
list_VEBT_VEBT: $tType ).
thf(func_def_147,type,
heap_Time_Heap_nat: $tType ).
thf(func_def_148,type,
set_set_real: $tType ).
thf(func_def_149,type,
set_list_nat: $tType ).
thf(func_def_150,type,
set_list_int: $tType ).
thf(func_def_151,type,
product_prod_nat_o: $tType ).
thf(func_def_152,type,
product_prod_int_o: $tType ).
thf(func_def_153,type,
product_prod_o_nat: $tType ).
thf(func_def_154,type,
product_prod_o_int: $tType ).
thf(func_def_155,type,
list_set_nat: $tType ).
thf(func_def_156,type,
list_Code_integer: $tType ).
thf(func_def_157,type,
set_VEBT_VEBT: $tType ).
thf(func_def_158,type,
set_set_nat: $tType ).
thf(func_def_159,type,
set_set_int: $tType ).
thf(func_def_160,type,
set_Code_integer: $tType ).
thf(func_def_161,type,
set_Product_unit: $tType ).
thf(func_def_162,type,
set_Numeral_num0: $tType ).
thf(func_def_163,type,
option_set_o: $tType ).
thf(func_def_164,type,
list_list_o: $tType ).
thf(func_def_165,type,
itself_Numeral_num0: $tType ).
thf(func_def_166,type,
list_complex: $tType ).
thf(func_def_167,type,
list_assn: $tType ).
thf(func_def_168,type,
heap_Time_Heap_o: $tType ).
thf(func_def_169,type,
set_list_o: $tType ).
thf(func_def_170,type,
product_prod_o_o: $tType ).
thf(func_def_171,type,
list_literal: $tType ).
thf(func_def_172,type,
set_complex: $tType ).
thf(func_def_173,type,
option_real: $tType ).
thf(func_def_174,type,
list_uint32: $tType ).
thf(func_def_175,type,
filter_real: $tType ).
thf(func_def_176,type,
set_literal: $tType ).
thf(func_def_177,type,
set_set_o: $tType ).
thf(func_def_178,type,
set_uint32: $tType ).
thf(func_def_179,type,
option_rat: $tType ).
thf(func_def_180,type,
option_num: $tType ).
thf(func_def_181,type,
option_nat: $tType ).
thf(func_def_182,type,
option_int: $tType ).
thf(func_def_183,type,
filter_nat: $tType ).
thf(func_def_184,type,
vEBT_VEBTi: $tType ).
thf(func_def_185,type,
list_real: $tType ).
thf(func_def_186,type,
set_real: $tType ).
thf(func_def_187,type,
list_rat: $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_integer: $tType ).
thf(func_def_197,type,
extended_enat: $tType ).
thf(func_def_198,type,
list_o: $tType ).
thf(func_def_199,type,
complex: $tType ).
thf(func_def_200,type,
assn: $tType ).
thf(func_def_201,type,
literal: $tType ).
thf(func_def_202,type,
set_o: $tType ).
thf(func_def_203,type,
uint32: $tType ).
thf(func_def_204,type,
char: $tType ).
thf(func_def_205,type,
real: $tType ).
thf(func_def_206,type,
rat: $tType ).
thf(func_def_207,type,
num: $tType ).
thf(func_def_208,type,
nat: $tType ).
thf(func_def_209,type,
int: $tType ).
thf(func_def_210,type,
archim7802044766580827645g_real: real > int ).
thf(func_def_211,type,
archim3151403230148437115or_rat: rat > int ).
thf(func_def_212,type,
archim6058952711729229775r_real: real > int ).
thf(func_def_213,type,
archimedean_frac_rat: rat > rat ).
thf(func_def_214,type,
archim2898591450579166408c_real: real > real ).
thf(func_def_215,type,
rep_assn: assn > produc3658429121746597890et_nat > $o ).
thf(func_def_216,type,
entails: assn > assn > $o ).
thf(func_def_217,type,
ex_ass463751140784270563_VEBTi: ( list_VEBT_VEBTi > assn ) > assn ).
thf(func_def_218,type,
ex_assn_VEBT_VEBT: ( vEBT_VEBT > assn ) > assn ).
thf(func_def_219,type,
pure_assn: $o > assn ).
thf(func_def_220,type,
snga_assn_VEBT_VEBTi: array_VEBT_VEBTi > list_VEBT_VEBTi > assn ).
thf(func_def_221,type,
times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_222,type,
times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
thf(func_def_223,type,
bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
thf(func_def_224,type,
bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
thf(func_def_225,type,
bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
thf(func_def_226,type,
bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_227,type,
bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
thf(func_def_228,type,
bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
thf(func_def_229,type,
bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
thf(func_def_230,type,
bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_231,type,
bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
thf(func_def_232,type,
bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_233,type,
bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
thf(func_def_234,type,
bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
thf(func_def_235,type,
bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
thf(func_def_236,type,
bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
thf(func_def_237,type,
bNF_re7364608769721783435num1_o: ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > ( ( word_N3645301735248828278l_num1 > $o ) > ( word_N3645301735248828278l_num1 > $o ) > $o ) > ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > $o ).
thf(func_def_238,type,
bNF_re5013357767504289739m1_o_o: ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > ( $o > $o > $o ) > ( word_N3645301735248828278l_num1 > $o ) > ( word_N3645301735248828278l_num1 > $o ) > $o ).
thf(func_def_239,type,
binomial: nat > nat > nat ).
thf(func_def_240,type,
bit_bi6516823479961619367ts_int: ( nat > $o ) > int ).
thf(func_def_241,type,
bit_wf_set_bits_int: ( nat > $o ) > $o ).
thf(func_def_242,type,
bit_concat_bit: nat > int > int > int ).
thf(func_def_243,type,
bit_ri7632146776885996613nteger: code_integer > code_integer ).
thf(func_def_244,type,
bit_ri7919022796975470100ot_int: int > int ).
thf(func_def_245,type,
bit_ri631733984087533419it_int: nat > int > int ).
thf(func_def_246,type,
bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
thf(func_def_247,type,
bit_se725231765392027082nd_int: int > int > int ).
thf(func_def_248,type,
bit_se727722235901077358nd_nat: nat > nat > nat ).
thf(func_def_249,type,
bit_se3928097537394005634nteger: nat > code_integer > code_integer ).
thf(func_def_250,type,
bit_se8568078237143864401it_int: nat > int > int ).
thf(func_def_251,type,
bit_se8570568707652914677it_nat: nat > nat > nat ).
thf(func_def_252,type,
bit_se3964402333458159761uint32: nat > uint32 > uint32 ).
thf(func_def_253,type,
bit_se5176125413884933531l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 ).
thf(func_def_254,type,
bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
thf(func_def_255,type,
bit_se2159334234014336723it_int: nat > int > int ).
thf(func_def_256,type,
bit_se2161824704523386999it_nat: nat > nat > nat ).
thf(func_def_257,type,
bit_se2119862282449309892nteger: nat > code_integer ).
thf(func_def_258,type,
bit_se2000444600071755411sk_int: nat > int ).
thf(func_def_259,type,
bit_se2002935070580805687sk_nat: nat > nat ).
thf(func_def_260,type,
bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).
thf(func_def_261,type,
bit_se1409905431419307370or_int: int > int > int ).
thf(func_def_262,type,
bit_se1412395901928357646or_nat: nat > nat > nat ).
thf(func_def_263,type,
bit_se2966626333419230250uint32: uint32 > uint32 > uint32 ).
thf(func_def_264,type,
bit_se7788150548672797655nteger: nat > code_integer > code_integer ).
thf(func_def_265,type,
bit_se545348938243370406it_int: nat > int > int ).
thf(func_def_266,type,
bit_se547839408752420682it_nat: nat > nat > nat ).
thf(func_def_267,type,
bit_se5742574853984576102uint32: nat > uint32 > uint32 ).
thf(func_def_268,type,
bit_se837345729053750000l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 ).
thf(func_def_269,type,
bit_se2793503036327961859nteger: nat > code_integer > code_integer ).
thf(func_def_270,type,
bit_se7879613467334960850it_int: nat > int > int ).
thf(func_def_271,type,
bit_se7882103937844011126it_nat: nat > nat > nat ).
thf(func_def_272,type,
bit_se1745604003318907178nteger: nat > code_integer > code_integer ).
thf(func_def_273,type,
bit_se2923211474154528505it_int: nat > int > int ).
thf(func_def_274,type,
bit_se2925701944663578781it_nat: nat > nat > nat ).
thf(func_def_275,type,
bit_se8260200283734997820nteger: nat > code_integer > code_integer ).
thf(func_def_276,type,
bit_se4203085406695923979it_int: nat > int > int ).
thf(func_def_277,type,
bit_se4205575877204974255it_nat: nat > nat > nat ).
thf(func_def_278,type,
bit_se3222712562003087583nteger: code_integer > code_integer > code_integer ).
thf(func_def_279,type,
bit_se6526347334894502574or_int: int > int > int ).
thf(func_def_280,type,
bit_se6528837805403552850or_nat: nat > nat > nat ).
thf(func_def_281,type,
bit_se9216721137139052372nteger: code_integer > nat > $o ).
thf(func_def_282,type,
bit_se1146084159140164899it_int: int > nat > $o ).
thf(func_def_283,type,
bit_se1148574629649215175it_nat: nat > nat > $o ).
thf(func_def_284,type,
bit_se5367290876889521763uint32: uint32 > nat > $o ).
thf(func_def_285,type,
bit_se6859397288646540909l_num1: word_N3645301735248828278l_num1 > nat > $o ).
thf(func_def_286,type,
bit_Sh3965577149348748681tl_nat: nat > nat > nat ).
thf(func_def_287,type,
bit_Sh2154871086232339855tr_nat: nat > nat > nat ).
thf(func_def_288,type,
bits_integer_set_bit: code_integer > code_integer > $o > code_integer ).
thf(func_def_289,type,
bits_integer_shiftl: code_integer > code_integer > code_integer ).
thf(func_def_290,type,
bits_integer_shiftr: code_integer > code_integer > code_integer ).
thf(func_def_291,type,
code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
thf(func_def_292,type,
code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_293,type,
code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_294,type,
code_int_of_integer: code_integer > int ).
thf(func_def_295,type,
code_integer_of_int: int > code_integer ).
thf(func_def_296,type,
code_integer_of_nat: nat > code_integer ).
thf(func_def_297,type,
code_integer_of_num: num > code_integer ).
thf(func_def_298,type,
code_nat_of_integer: code_integer > nat ).
thf(func_def_299,type,
code_negative: num > code_integer ).
thf(func_def_300,type,
code_num_of_integer: code_integer > num ).
thf(func_def_301,type,
code_positive: num > code_integer ).
thf(func_def_302,type,
complete_Inf_Inf_nat: set_nat > nat ).
thf(func_def_303,type,
comple7806235888213564991et_nat: set_set_nat > set_nat ).
thf(func_def_304,type,
complete_Sup_Sup_int: set_int > int ).
thf(func_def_305,type,
complete_Sup_Sup_nat: set_nat > nat ).
thf(func_def_306,type,
comple1385675409528146559p_real: set_real > real ).
thf(func_def_307,type,
complex2: real > real > complex ).
thf(func_def_308,type,
has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
thf(func_def_309,type,
adjust_div: product_prod_int_int > int ).
thf(func_def_310,type,
adjust_mod: int > int > int ).
thf(func_def_311,type,
divmod_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_312,type,
eucl_rel_int: int > int > product_prod_int_int > $o ).
thf(func_def_313,type,
unique6319869463603278526ux_int: product_prod_int_int > $o ).
thf(func_def_314,type,
unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
thf(func_def_315,type,
unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
thf(func_def_316,type,
unique5052692396658037445od_int: num > num > product_prod_int_int ).
thf(func_def_317,type,
unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
thf(func_def_318,type,
unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_319,type,
unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
thf(func_def_320,type,
unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_321,type,
semiri1408675320244567234ct_nat: nat > nat ).
thf(func_def_322,type,
semiri2265585572941072030t_real: nat > real ).
thf(func_def_323,type,
inverse_inverse_real: real > real ).
thf(func_def_324,type,
at_bot_real: filter_real ).
thf(func_def_325,type,
at_top_nat: filter_nat ).
thf(func_def_326,type,
at_top_real: filter_real ).
thf(func_def_327,type,
eventually_nat: ( nat > $o ) > filter_nat > $o ).
thf(func_def_328,type,
eventually_real: ( real > $o ) > filter_real > $o ).
thf(func_def_329,type,
filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
thf(func_def_330,type,
filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
thf(func_def_331,type,
filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
thf(func_def_332,type,
finite_Fpow_o: set_o > set_set_o ).
thf(func_def_333,type,
finite1532502677820914807nteger: set_Code_integer > set_set_Code_integer ).
thf(func_def_334,type,
finite_Fpow_complex: set_complex > set_set_complex ).
thf(func_def_335,type,
finite_Fpow_int: set_int > set_set_int ).
thf(func_def_336,type,
finite_Fpow_nat: set_nat > set_set_nat ).
thf(func_def_337,type,
finite_Fpow_set_nat: set_set_nat > set_set_set_nat ).
thf(func_def_338,type,
finite_card_o: set_o > nat ).
thf(func_def_339,type,
finite4902975817058060853nteger: set_Code_integer > nat ).
thf(func_def_340,type,
finite_card_complex: set_complex > nat ).
thf(func_def_341,type,
finite_card_int: set_int > nat ).
thf(func_def_342,type,
finite_card_list_o: set_list_o > nat ).
thf(func_def_343,type,
finite5823187341872139973nteger: set_li6976499617229504675nteger > nat ).
thf(func_def_344,type,
finite5120063068150530198omplex: set_list_complex > nat ).
thf(func_def_345,type,
finite_card_list_int: set_list_int > nat ).
thf(func_def_346,type,
finite7325466520557071688st_nat: set_list_list_nat > nat ).
thf(func_def_347,type,
finite_card_list_nat: set_list_nat > nat ).
thf(func_def_348,type,
finite4141703471298347796t_real: set_list_real > nat ).
thf(func_def_349,type,
finite5631907774883551598et_nat: set_list_set_nat > nat ).
thf(func_def_350,type,
finite7554361855635516162iteral: set_list_literal > nat ).
thf(func_def_351,type,
finite5915292604075114978T_VEBT: set_list_VEBT_VEBT > nat ).
thf(func_def_352,type,
finite_card_nat: set_nat > nat ).
thf(func_def_353,type,
finite_card_num: set_num > nat ).
thf(func_def_354,type,
finite6454714172617411596l_num0: set_Numeral_num0 > nat ).
thf(func_def_355,type,
finite410649719033368117t_unit: set_Product_unit > nat ).
thf(func_def_356,type,
finite_card_rat: set_rat > nat ).
thf(func_def_357,type,
finite_card_real: set_real > nat ).
thf(func_def_358,type,
finite_card_set_nat: set_set_nat > nat ).
thf(func_def_359,type,
finite_card_literal: set_literal > nat ).
thf(func_def_360,type,
finite7802652506058667612T_VEBT: set_VEBT_VEBT > nat ).
thf(func_def_361,type,
finite_finite_o: set_o > $o ).
thf(func_def_362,type,
finite6017078050557962740nteger: set_Code_integer > $o ).
thf(func_def_363,type,
finite3207457112153483333omplex: set_complex > $o ).
thf(func_def_364,type,
finite_finite_int: set_int > $o ).
thf(func_def_365,type,
finite_finite_list_o: set_list_o > $o ).
thf(func_def_366,type,
finite1283093830868386564nteger: set_li6976499617229504675nteger > $o ).
thf(func_def_367,type,
finite8712137658972009173omplex: set_list_complex > $o ).
thf(func_def_368,type,
finite3922522038869484883st_int: set_list_int > $o ).
thf(func_def_369,type,
finite8100373058378681591st_nat: set_list_nat > $o ).
thf(func_def_370,type,
finite306553202115118035t_real: set_list_real > $o ).
thf(func_def_371,type,
finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
thf(func_def_372,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_373,type,
finite_finite_num: set_num > $o ).
thf(func_def_374,type,
finite_finite_rat: set_rat > $o ).
thf(func_def_375,type,
finite_finite_real: set_real > $o ).
thf(func_def_376,type,
finite_finite_set_o: set_set_o > $o ).
thf(func_def_377,type,
finite6931041176100689706nteger: set_set_Code_integer > $o ).
thf(func_def_378,type,
finite6551019134538273531omplex: set_set_complex > $o ).
thf(func_def_379,type,
finite6197958912794628473et_int: set_set_int > $o ).
thf(func_def_380,type,
finite1152437895449049373et_nat: set_set_nat > $o ).
thf(func_def_381,type,
finite9007344921179782393t_real: set_set_real > $o ).
thf(func_def_382,type,
finite9070685783930458813T_VEBT: set_set_VEBT_VEBT > $o ).
thf(func_def_383,type,
finite5847741373460823677iteral: set_literal > $o ).
thf(func_def_384,type,
finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
thf(func_def_385,type,
comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_386,type,
comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_387,type,
comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
thf(func_def_388,type,
comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
thf(func_def_389,type,
comp_nat_o_nat: ( nat > $o ) > ( nat > nat ) > nat > $o ).
thf(func_def_390,type,
comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(func_def_391,type,
comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).
thf(func_def_392,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_393,type,
inj_on_real_real: ( real > real ) > set_real > $o ).
thf(func_def_394,type,
inj_on_set_nat_nat: ( set_nat > nat ) > set_set_nat > $o ).
thf(func_def_395,type,
strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_396,type,
the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
thf(func_def_397,type,
gcd_Gcd_int: set_int > int ).
thf(func_def_398,type,
gcd_Gcd_nat: set_nat > nat ).
thf(func_def_399,type,
bezw: nat > nat > product_prod_int_int ).
thf(func_def_400,type,
bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_401,type,
gcd_gcd_int: int > int > int ).
thf(func_def_402,type,
gcd_gcd_nat: nat > nat > nat ).
thf(func_def_403,type,
gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_404,type,
semiri4256215615220890538in_int: set_int > int ).
thf(func_def_405,type,
semiri4258706085729940814in_nat: set_nat > nat ).
thf(func_def_406,type,
generi2397576812484419408nteger: code_integer > nat > $o > code_integer ).
thf(func_def_407,type,
generi1993664874377053279uint32: uint32 > nat > $o > uint32 ).
thf(func_def_408,type,
generi5268133209446125161l_num1: word_N3645301735248828278l_num1 > nat > $o > word_N3645301735248828278l_num1 ).
thf(func_def_409,type,
abs_abs_Code_integer: code_integer > code_integer ).
thf(func_def_410,type,
abs_abs_int: int > int ).
thf(func_def_411,type,
abs_abs_rat: rat > rat ).
thf(func_def_412,type,
abs_abs_real: real > real ).
thf(func_def_413,type,
minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).
thf(func_def_414,type,
minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
thf(func_def_415,type,
minus_1139252259498527702_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
thf(func_def_416,type,
minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_417,type,
minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).
thf(func_def_418,type,
minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
thf(func_def_419,type,
minus_2794559001203777698VEBT_o: ( vEBT_VEBT > $o ) > ( vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
thf(func_def_420,type,
minus_minus_assn: assn > assn > assn ).
thf(func_def_421,type,
minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
thf(func_def_422,type,
minus_minus_complex: complex > complex > complex ).
thf(func_def_423,type,
minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
thf(func_def_424,type,
minus_minus_int: int > int > int ).
thf(func_def_425,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_426,type,
minus_minus_rat: rat > rat > rat ).
thf(func_def_427,type,
minus_minus_real: real > real > real ).
thf(func_def_428,type,
minus_minus_set_o: set_o > set_o > set_o ).
thf(func_def_429,type,
minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
thf(func_def_430,type,
minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
thf(func_def_431,type,
minus_minus_set_int: set_int > set_int > set_int ).
thf(func_def_432,type,
minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).
thf(func_def_433,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_434,type,
minus_minus_set_num: set_num > set_num > set_num ).
thf(func_def_435,type,
minus_minus_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_436,type,
minus_minus_set_real: set_real > set_real > set_real ).
thf(func_def_437,type,
minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
thf(func_def_438,type,
minus_7832829386415567259iteral: set_literal > set_literal > set_literal ).
thf(func_def_439,type,
minus_3697805406911847364_VEBTi: set_VEBT_VEBTi > set_VEBT_VEBTi > set_VEBT_VEBTi ).
thf(func_def_440,type,
minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_441,type,
minus_minus_uint32: uint32 > uint32 > uint32 ).
thf(func_def_442,type,
one_one_assn: assn ).
thf(func_def_443,type,
one_one_Code_integer: code_integer ).
thf(func_def_444,type,
one_one_complex: complex ).
thf(func_def_445,type,
one_one_int: int ).
thf(func_def_446,type,
one_one_nat: nat ).
thf(func_def_447,type,
one_one_rat: rat ).
thf(func_def_448,type,
one_one_real: real ).
thf(func_def_449,type,
one_one_uint32: uint32 ).
thf(func_def_450,type,
plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
thf(func_def_451,type,
plus_plus_complex: complex > complex > complex ).
thf(func_def_452,type,
plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
thf(func_def_453,type,
plus_plus_int: int > int > int ).
thf(func_def_454,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_455,type,
plus_plus_num: num > num > num ).
thf(func_def_456,type,
plus_plus_rat: rat > rat > rat ).
thf(func_def_457,type,
plus_plus_real: real > real > real ).
thf(func_def_458,type,
plus_plus_uint32: uint32 > uint32 > uint32 ).
thf(func_def_459,type,
sgn_sgn_Code_integer: code_integer > code_integer ).
thf(func_def_460,type,
sgn_sgn_int: int > int ).
thf(func_def_461,type,
sgn_sgn_rat: rat > rat ).
thf(func_def_462,type,
sgn_sgn_real: real > real ).
thf(func_def_463,type,
times_times_assn: assn > assn > assn ).
thf(func_def_464,type,
times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
thf(func_def_465,type,
times_times_complex: complex > complex > complex ).
thf(func_def_466,type,
times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
thf(func_def_467,type,
times_times_int: int > int > int ).
thf(func_def_468,type,
times_times_nat: nat > nat > nat ).
thf(func_def_469,type,
times_times_rat: rat > rat > rat ).
thf(func_def_470,type,
times_times_real: real > real > real ).
thf(func_def_471,type,
times_times_uint32: uint32 > uint32 > uint32 ).
thf(func_def_472,type,
uminus1680532995456772888plex_o: ( complex > $o ) > complex > $o ).
thf(func_def_473,type,
uminus_uminus_int_o: ( int > $o ) > int > $o ).
thf(func_def_474,type,
uminus5770388063884162150_nat_o: ( list_nat > $o ) > list_nat > $o ).
thf(func_def_475,type,
uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).
thf(func_def_476,type,
uminus_uminus_real_o: ( real > $o ) > real > $o ).
thf(func_def_477,type,
uminus6401447641752708672_nat_o: ( set_nat > $o ) > set_nat > $o ).
thf(func_def_478,type,
uminus2746543603091002386VEBT_o: ( vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
thf(func_def_479,type,
uminus_uminus_assn: assn > assn ).
thf(func_def_480,type,
uminus1351360451143612070nteger: code_integer > code_integer ).
thf(func_def_481,type,
uminus1482373934393186551omplex: complex > complex ).
thf(func_def_482,type,
uminus_uminus_int: int > int ).
thf(func_def_483,type,
uminus_uminus_rat: rat > rat ).
thf(func_def_484,type,
uminus_uminus_real: real > real ).
thf(func_def_485,type,
uminus_uminus_set_o: set_o > set_o ).
thf(func_def_486,type,
uminus8566677241136511917omplex: set_complex > set_complex ).
thf(func_def_487,type,
uminus1532241313380277803et_int: set_int > set_int ).
thf(func_def_488,type,
uminus3195874150345416415st_nat: set_list_nat > set_list_nat ).
thf(func_def_489,type,
uminus5710092332889474511et_nat: set_nat > set_nat ).
thf(func_def_490,type,
uminus612125837232591019t_real: set_real > set_real ).
thf(func_def_491,type,
uminus613421341184616069et_nat: set_set_nat > set_set_nat ).
thf(func_def_492,type,
uminus8041839845116263051T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_493,type,
uminus_uminus_uint32: uint32 > uint32 ).
thf(func_def_494,type,
zero_z3403309356797280102nteger: code_integer ).
thf(func_def_495,type,
zero_zero_complex: complex ).
thf(func_def_496,type,
zero_z5237406670263579293d_enat: extended_enat ).
thf(func_def_497,type,
zero_zero_int: int ).
thf(func_def_498,type,
zero_zero_nat: nat ).
thf(func_def_499,type,
zero_zero_rat: rat ).
thf(func_def_500,type,
zero_zero_real: real ).
thf(func_def_501,type,
zero_zero_uint32: uint32 ).
thf(func_def_502,type,
groups8507830703676809646_o_nat: ( $o > nat ) > set_o > nat ).
thf(func_def_503,type,
groups7872700643590313910_o_rat: ( $o > rat ) > set_o > rat ).
thf(func_def_504,type,
groups8691415230153176458o_real: ( $o > real ) > set_o > real ).
thf(func_def_505,type,
groups7241207224191747786uint32: ( $o > uint32 ) > set_o > uint32 ).
thf(func_def_506,type,
groups8024822376189712711omplex: ( code_integer > complex ) > set_Code_integer > complex ).
thf(func_def_507,type,
groups7234854612051535045er_int: ( code_integer > int ) > set_Code_integer > int ).
thf(func_def_508,type,
groups7237345082560585321er_nat: ( code_integer > nat ) > set_Code_integer > nat ).
thf(func_def_509,type,
groups6602215022474089585er_rat: ( code_integer > rat ) > set_Code_integer > rat ).
thf(func_def_510,type,
groups1270011288395367621r_real: ( code_integer > real ) > set_Code_integer > real ).
thf(func_def_511,type,
groups8847630953604152069uint32: ( code_integer > uint32 ) > set_Code_integer > uint32 ).
thf(func_def_512,type,
groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).
thf(func_def_513,type,
groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
thf(func_def_514,type,
groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).
thf(func_def_515,type,
groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).
thf(func_def_516,type,
groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).
thf(func_def_517,type,
groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).
thf(func_def_518,type,
groups8736914816313324502uint32: ( complex > uint32 ) > set_complex > uint32 ).
thf(func_def_519,type,
groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).
thf(func_def_520,type,
groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).
thf(func_def_521,type,
groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
thf(func_def_522,type,
groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).
thf(func_def_523,type,
groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).
thf(func_def_524,type,
groups8778361861064173332t_real: ( int > real ) > set_int > real ).
thf(func_def_525,type,
groups5712668689793887828uint32: ( int > uint32 ) > set_int > uint32 ).
thf(func_def_526,type,
groups4396056296759096172at_nat: ( list_nat > nat ) > set_list_nat > nat ).
thf(func_def_527,type,
groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).
thf(func_def_528,type,
groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).
thf(func_def_529,type,
groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_530,type,
groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).
thf(func_def_531,type,
groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).
thf(func_def_532,type,
groups833757482993574392uint32: ( nat > uint32 ) > set_nat > uint32 ).
thf(func_def_533,type,
groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).
thf(func_def_534,type,
groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).
thf(func_def_535,type,
groups1932886352136224148al_int: ( real > int ) > set_real > int ).
thf(func_def_536,type,
groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).
thf(func_def_537,type,
groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).
thf(func_def_538,type,
groups8097168146408367636l_real: ( real > real ) > set_real > real ).
thf(func_def_539,type,
groups5944083974425963860uint32: ( real > uint32 ) > set_real > uint32 ).
thf(func_def_540,type,
groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).
thf(func_def_541,type,
groups8556826181031883383nteger: ( literal > code_integer ) > set_literal > code_integer ).
thf(func_def_542,type,
groups8649609317433967686al_int: ( literal > int ) > set_literal > int ).
thf(func_def_543,type,
groups8652099787943017962al_nat: ( literal > nat ) > set_literal > nat ).
thf(func_def_544,type,
groups2795228986978005958l_real: ( literal > real ) > set_literal > real ).
thf(func_def_545,type,
groups4542640294765070598uint32: ( literal > uint32 ) > set_literal > uint32 ).
thf(func_def_546,type,
groups5748017345553531991nteger: ( vEBT_VEBT > code_integer ) > set_VEBT_VEBT > code_integer ).
thf(func_def_547,type,
groups1794756597179926696omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > complex ).
thf(func_def_548,type,
groups769130701875090982BT_int: ( vEBT_VEBT > int ) > set_VEBT_VEBT > int ).
thf(func_def_549,type,
groups771621172384141258BT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > nat ).
thf(func_def_550,type,
groups136491112297645522BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > rat ).
thf(func_def_551,type,
groups2240296850493347238T_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > real ).
thf(func_def_552,type,
groups8325533452322294502uint32: ( vEBT_VEBT > uint32 ) > set_VEBT_VEBT > uint32 ).
thf(func_def_553,type,
groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_554,type,
groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
thf(func_def_555,type,
groups4561878855575611511st_nat: list_nat > nat ).
thf(func_def_556,type,
the_int: ( int > $o ) > int ).
thf(func_def_557,type,
the_real: ( real > $o ) > real ).
thf(func_def_558,type,
undefi7330133036835070352uint32: ( nat > uint32 > uint32 ) > code_integer > uint32 > uint32 ).
thf(func_def_559,type,
undefi8952517107220742160uint32: ( nat > uint32 > uint32 ) > uint32 > code_integer > uint32 ).
thf(func_def_560,type,
undefi8537048349889504752uint32: ( uint32 > nat > $o > uint32 ) > uint32 > code_integer > $o > uint32 ).
thf(func_def_561,type,
undefi6981832269580975664eger_o: ( uint32 > nat > $o ) > uint32 > code_integer > $o ).
thf(func_def_562,type,
undefi1878487536576149250nteger: code_integer > code_integer > $o > code_integer ).
thf(func_def_563,type,
undefi8133104259855420269nteger: code_integer > code_integer > code_integer ).
thf(func_def_564,type,
size_a6397454172108246045_VEBTi: ( vEBT_VEBTi > nat ) > array_VEBT_VEBTi > nat ).
thf(func_def_565,type,
heap_Time_return_nat: nat > heap_Time_Heap_nat ).
thf(func_def_566,type,
heap_T3487192422709364219on_nat: option_nat > heap_T2636463487746394924on_nat ).
thf(func_def_567,type,
hoare_hoare_triple_o: assn > heap_Time_Heap_o > ( $o > assn ) > $o ).
thf(func_def_568,type,
hoare_3067605981109127869le_nat: assn > heap_Time_Heap_nat > ( nat > assn ) > $o ).
thf(func_def_569,type,
hoare_7629718768684598413on_nat: assn > heap_T2636463487746394924on_nat > ( option_nat > assn ) > $o ).
thf(func_def_570,type,
hoare_1429296392585015714_VEBTi: assn > heap_T8145700208782473153_VEBTi > ( vEBT_VEBTi > assn ) > $o ).
thf(func_def_571,type,
if_assn: $o > assn > assn > assn ).
thf(func_def_572,type,
if_Code_integer: $o > code_integer > code_integer > code_integer ).
thf(func_def_573,type,
if_complex: $o > complex > complex > complex ).
thf(func_def_574,type,
if_int: $o > int > int > int ).
thf(func_def_575,type,
if_list_int: $o > list_int > list_int > list_int ).
thf(func_def_576,type,
if_list_nat: $o > list_nat > list_nat > list_nat ).
thf(func_def_577,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_578,type,
if_num: $o > num > num > num ).
thf(func_def_579,type,
if_option_nat: $o > option_nat > option_nat > option_nat ).
thf(func_def_580,type,
if_option_set_o: $o > option_set_o > option_set_o > option_set_o ).
thf(func_def_581,type,
if_option_set_int: $o > option_set_int > option_set_int > option_set_int ).
thf(func_def_582,type,
if_option_set_nat: $o > option_set_nat > option_set_nat > option_set_nat ).
thf(func_def_583,type,
if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).
thf(func_def_584,type,
if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_585,type,
if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
thf(func_def_586,type,
if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_587,type,
if_Pro1135515155860407935uint32: $o > produc827990862158126777uint32 > produc827990862158126777uint32 > produc827990862158126777uint32 ).
thf(func_def_588,type,
if_rat: $o > rat > rat > rat ).
thf(func_def_589,type,
if_real: $o > real > real > real ).
thf(func_def_590,type,
if_set_int: $o > set_int > set_int > set_int ).
thf(func_def_591,type,
if_uint32: $o > uint32 > uint32 > uint32 ).
thf(func_def_592,type,
if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_593,type,
infini8530281810654367211te_nat: set_nat > nat > nat ).
thf(func_def_594,type,
int_ge_less_than: int > set_Pr958786334691620121nt_int ).
thf(func_def_595,type,
int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
thf(func_def_596,type,
nat2: int > nat ).
thf(func_def_597,type,
ring_1_Ints_int: set_int ).
thf(func_def_598,type,
ring_1_Ints_rat: set_rat ).
thf(func_def_599,type,
ring_1_Ints_real: set_real ).
thf(func_def_600,type,
ring_1_Ints_uint32: set_uint32 ).
thf(func_def_601,type,
ring_18347121197199848620nteger: int > code_integer ).
thf(func_def_602,type,
ring_1_of_int_rat: int > rat ).
thf(func_def_603,type,
ring_1_of_int_real: int > real ).
thf(func_def_604,type,
inf_inf_assn: assn > assn > assn ).
thf(func_def_605,type,
inf_inf_nat: nat > nat > nat ).
thf(func_def_606,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_607,type,
semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_608,type,
sup_sup_assn: assn > assn > assn ).
thf(func_def_609,type,
sup_sup_nat: nat > nat > nat ).
thf(func_def_610,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_611,type,
lattic1921953407002678535_Max_o: set_o > $o ).
thf(func_def_612,type,
lattic4901227151466704046nteger: set_Code_integer > code_integer ).
thf(func_def_613,type,
lattic8263393255366662781ax_int: set_int > int ).
thf(func_def_614,type,
lattic8265883725875713057ax_nat: set_nat > nat ).
thf(func_def_615,type,
lattic4823215512031491691ax_num: set_num > num ).
thf(func_def_616,type,
lattic7630753665789217321ax_rat: set_rat > rat ).
thf(func_def_617,type,
lattic4275903605611617917x_real: set_real > real ).
thf(func_def_618,type,
lattic1973801136483472281_Min_o: set_o > $o ).
thf(func_def_619,type,
lattic1063845414844153500nteger: set_Code_integer > code_integer ).
thf(func_def_620,type,
lattic8718645017227715691in_int: set_int > int ).
thf(func_def_621,type,
lattic8721135487736765967in_nat: set_nat > nat ).
thf(func_def_622,type,
lattic5278467273892544601in_num: set_num > num ).
thf(func_def_623,type,
lattic8086005427650270231in_rat: set_rat > rat ).
thf(func_def_624,type,
lattic3629708407755379051n_real: set_real > real ).
thf(func_def_625,type,
lattic2140725968369957399_o_rat: ( $o > rat ) > set_o > $o ).
thf(func_def_626,type,
lattic8697145971487455083o_real: ( $o > real ) > set_o > $o ).
thf(func_def_627,type,
lattic5439806495466278992er_rat: ( code_integer > rat ) > set_Code_integer > code_integer ).
thf(func_def_628,type,
lattic2659822949269061924r_real: ( code_integer > real ) > set_Code_integer > code_integer ).
thf(func_def_629,type,
lattic1922116423962787043ex_num: ( complex > num ) > set_complex > complex ).
thf(func_def_630,type,
lattic4729654577720512673ex_rat: ( complex > rat ) > set_complex > complex ).
thf(func_def_631,type,
lattic8794016678065449205x_real: ( complex > real ) > set_complex > complex ).
thf(func_def_632,type,
lattic7811156612396918303nt_rat: ( int > rat ) > set_int > int ).
thf(func_def_633,type,
lattic2675449441010098035t_real: ( int > real ) > set_int > int ).
thf(func_def_634,type,
lattic6811802900495863747at_rat: ( nat > rat ) > set_nat > nat ).
thf(func_def_635,type,
lattic488527866317076247t_real: ( nat > real ) > set_nat > nat ).
thf(func_def_636,type,
lattic1613168225601753569al_num: ( real > num ) > set_real > real ).
thf(func_def_637,type,
lattic4420706379359479199al_rat: ( real > rat ) > set_real > real ).
thf(func_def_638,type,
lattic3331990488459210229BT_num: ( vEBT_VEBT > num ) > set_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_639,type,
lattic6139528642216935859BT_rat: ( vEBT_VEBT > rat ) > set_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_640,type,
bfun_nat_real: ( nat > real ) > filter_nat > $o ).
thf(func_def_641,type,
at_infinity_real: filter_real ).
thf(func_def_642,type,
append_o: list_o > list_o > list_o ).
thf(func_def_643,type,
append_int: list_int > list_int > list_int ).
thf(func_def_644,type,
append_nat: list_nat > list_nat > list_nat ).
thf(func_def_645,type,
butlast_o: list_o > list_o ).
thf(func_def_646,type,
butlast_int: list_int > list_int ).
thf(func_def_647,type,
butlast_nat: list_nat > list_nat ).
thf(func_def_648,type,
butlast_real: list_real > list_real ).
thf(func_def_649,type,
butlast_VEBT_VEBTi: list_VEBT_VEBTi > list_VEBT_VEBTi ).
thf(func_def_650,type,
butlast_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_651,type,
concat_o: list_list_o > list_o ).
thf(func_def_652,type,
concat_nat: list_list_nat > list_nat ).
thf(func_def_653,type,
concat_real: list_list_real > list_real ).
thf(func_def_654,type,
concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_655,type,
count_list_o: list_o > $o > nat ).
thf(func_def_656,type,
count_3970941599679287265nteger: list_Code_integer > code_integer > nat ).
thf(func_def_657,type,
count_list_complex: list_complex > complex > nat ).
thf(func_def_658,type,
count_list_int: list_int > int > nat ).
thf(func_def_659,type,
count_list_nat: list_nat > nat > nat ).
thf(func_def_660,type,
count_list_real: list_real > real > nat ).
thf(func_def_661,type,
count_list_set_nat: list_set_nat > set_nat > nat ).
thf(func_def_662,type,
count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_663,type,
distinct_o: list_o > $o ).
thf(func_def_664,type,
distin1543349897113766820nteger: list_Code_integer > $o ).
thf(func_def_665,type,
distinct_complex: list_complex > $o ).
thf(func_def_666,type,
distinct_int: list_int > $o ).
thf(func_def_667,type,
distinct_nat: list_nat > $o ).
thf(func_def_668,type,
distinct_num: list_num > $o ).
thf(func_def_669,type,
distinct_rat: list_rat > $o ).
thf(func_def_670,type,
distinct_real: list_real > $o ).
thf(func_def_671,type,
distinct_set_nat: list_set_nat > $o ).
thf(func_def_672,type,
distinct_VEBT_VEBTi: list_VEBT_VEBTi > $o ).
thf(func_def_673,type,
distinct_VEBT_VEBT: list_VEBT_VEBT > $o ).
thf(func_def_674,type,
enumerate_o: nat > list_o > list_P7333126701944960589_nat_o ).
thf(func_def_675,type,
enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
thf(func_def_676,type,
enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
thf(func_def_677,type,
enumerate_real: nat > list_real > list_P3644420460460130531t_real ).
thf(func_def_678,type,
enumerate_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_P2320588648998582380_VEBTi ).
thf(func_def_679,type,
enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(func_def_680,type,
filter_nat2: ( nat > $o ) > list_nat > list_nat ).
thf(func_def_681,type,
foldl_assn_assn: ( assn > assn > assn ) > assn > list_assn > assn ).
thf(func_def_682,type,
foldl_int_int: ( int > int > int ) > int > list_int > int ).
thf(func_def_683,type,
foldl_nat_o: ( nat > $o > nat ) > nat > list_o > nat ).
thf(func_def_684,type,
foldl_nat_nat: ( nat > nat > nat ) > nat > list_nat > nat ).
thf(func_def_685,type,
foldl_nat_real: ( nat > real > nat ) > nat > list_real > nat ).
thf(func_def_686,type,
foldl_nat_VEBT_VEBT: ( nat > vEBT_VEBT > nat ) > nat > list_VEBT_VEBT > nat ).
thf(func_def_687,type,
foldl_rat_rat: ( rat > rat > rat ) > rat > list_rat > rat ).
thf(func_def_688,type,
foldl_real_real: ( real > real > real ) > real > list_real > real ).
thf(func_def_689,type,
foldl_uint32_uint32: ( uint32 > uint32 > uint32 ) > uint32 > list_uint32 > uint32 ).
thf(func_def_690,type,
foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).
thf(func_def_691,type,
foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
thf(func_def_692,type,
foldr_real_nat: ( real > nat > nat ) > list_real > nat > nat ).
thf(func_def_693,type,
foldr_real_real: ( real > real > real ) > list_real > real > real ).
thf(func_def_694,type,
foldr_VEBT_VEBT_nat: ( vEBT_VEBT > nat > nat ) > list_VEBT_VEBT > nat > nat ).
thf(func_def_695,type,
last_o: list_o > $o ).
thf(func_def_696,type,
last_int: list_int > int ).
thf(func_def_697,type,
last_nat: list_nat > nat ).
thf(func_def_698,type,
last_real: list_real > real ).
thf(func_def_699,type,
last_VEBT_VEBTi: list_VEBT_VEBTi > vEBT_VEBTi ).
thf(func_def_700,type,
last_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_701,type,
lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
thf(func_def_702,type,
lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
thf(func_def_703,type,
lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
thf(func_def_704,type,
lenlex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real ).
thf(func_def_705,type,
lenlex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32 ).
thf(func_def_706,type,
lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
thf(func_def_707,type,
lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
thf(func_def_708,type,
lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
thf(func_def_709,type,
lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
thf(func_def_710,type,
lex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real ).
thf(func_def_711,type,
lex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32 ).
thf(func_def_712,type,
lex_VEBT_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr4797120415438012619_VEBTi ).
thf(func_def_713,type,
lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
thf(func_def_714,type,
linord3142498349692569832_set_o: set_o > list_o ).
thf(func_def_715,type,
linord2324613341767563021nteger: set_Code_integer > list_Code_integer ).
thf(func_def_716,type,
linord2612477271533052124et_int: set_int > list_int ).
thf(func_def_717,type,
linord2614967742042102400et_nat: set_nat > list_nat ).
thf(func_def_718,type,
linord8395671565052656842et_num: set_num > list_num ).
thf(func_def_719,type,
linord1979837681955606664et_rat: set_rat > list_rat ).
thf(func_def_720,type,
linord4252657396651189596t_real: set_real > list_real ).
thf(func_def_721,type,
linord2913955441264437540iteral: set_literal > list_literal ).
thf(func_def_722,type,
cons_o: $o > list_o > list_o ).
thf(func_def_723,type,
cons_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
thf(func_def_724,type,
cons_int: int > list_int > list_int ).
thf(func_def_725,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_726,type,
cons_num: num > list_num > list_num ).
thf(func_def_727,type,
cons_P8766293264717362397od_o_o: product_prod_o_o > list_P4002435161011370285od_o_o > list_P4002435161011370285od_o_o ).
thf(func_def_728,type,
cons_P1455986808126089405_o_int: product_prod_o_int > list_P3795440434834930179_o_int > list_P3795440434834930179_o_int ).
thf(func_def_729,type,
cons_P5633837827635286113_o_nat: product_prod_o_nat > list_P6285523579766656935_o_nat > list_P6285523579766656935_o_nat ).
thf(func_def_730,type,
cons_P7321330006258091179_int_o: product_prod_int_o > list_P5087981734274514673_int_o > list_P5087981734274514673_int_o ).
thf(func_def_731,type,
cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(func_def_732,type,
cons_P7512249878480867347nt_nat: product_prod_int_nat > list_P8198026277950538467nt_nat > list_P8198026277950538467nt_nat ).
thf(func_def_733,type,
cons_P9142372351690779143_nat_o: product_prod_nat_o > list_P7333126701944960589_nat_o > list_P7333126701944960589_nat_o ).
thf(func_def_734,type,
cons_P2335045147070616083at_int: product_prod_nat_int > list_P3521021558325789923at_int > list_P3521021558325789923at_int ).
thf(func_def_735,type,
cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
thf(func_def_736,type,
cons_P3149448846263281007uint32: produc827990862158126777uint32 > list_P3069071885182933823uint32 > list_P3069071885182933823uint32 ).
thf(func_def_737,type,
cons_rat: rat > list_rat > list_rat ).
thf(func_def_738,type,
cons_real: real > list_real > list_real ).
thf(func_def_739,type,
cons_set_nat: set_nat > list_set_nat > list_set_nat ).
thf(func_def_740,type,
cons_uint32: uint32 > list_uint32 > list_uint32 ).
thf(func_def_741,type,
cons_VEBT_VEBTi: vEBT_VEBTi > list_VEBT_VEBTi > list_VEBT_VEBTi ).
thf(func_def_742,type,
cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_743,type,
nil_o: list_o ).
thf(func_def_744,type,
nil_int: list_int ).
thf(func_def_745,type,
nil_nat: list_nat ).
thf(func_def_746,type,
hd_nat: list_nat > nat ).
thf(func_def_747,type,
map_nat_o: ( nat > $o ) > list_nat > list_o ).
thf(func_def_748,type,
map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
thf(func_def_749,type,
map_Pr7541730621154948341_o_o_o: ( product_prod_o_o > $o ) > list_P4002435161011370285od_o_o > list_o ).
thf(func_def_750,type,
map_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > list_nat ).
thf(func_def_751,type,
map_VEBT_VEBT_real: ( vEBT_VEBT > real ) > list_VEBT_VEBT > list_real ).
thf(func_def_752,type,
set_Pr400311997697478754_nat_o: list_P7985473006766602707_nat_o > set_Pr4532377907799695533_nat_o ).
thf(func_def_753,type,
set_o2: list_o > set_o ).
thf(func_def_754,type,
set_Code_integer2: list_Code_integer > set_Code_integer ).
thf(func_def_755,type,
set_complex2: list_complex > set_complex ).
thf(func_def_756,type,
set_int2: list_int > set_int ).
thf(func_def_757,type,
set_list_o2: list_list_o > set_list_o ).
thf(func_def_758,type,
set_list_int2: list_list_int > set_list_int ).
thf(func_def_759,type,
set_list_nat2: list_list_nat > set_list_nat ).
thf(func_def_760,type,
set_list_real2: list_list_real > set_list_real ).
thf(func_def_761,type,
set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
thf(func_def_762,type,
set_nat2: list_nat > set_nat ).
thf(func_def_763,type,
set_num2: list_num > set_num ).
thf(func_def_764,type,
set_Pr7458301993993767461et_nat: list_P362550909693114634et_nat > set_Pr8536935166611901872et_nat ).
thf(func_def_765,type,
set_Pr364071364088684201et_nat: list_P2321686559999237006et_nat > set_Pr3286484037609594932et_nat ).
thf(func_def_766,type,
set_Product_prod_o_o2: list_P4002435161011370285od_o_o > set_Product_prod_o_o ).
thf(func_def_767,type,
set_Pr3864771053587467565et_nat: list_P9062070895058802706et_nat > set_Pr3948176798113811640et_nat ).
thf(func_def_768,type,
set_Pr8694291782656941196_int_o: list_P5087981734274514673_int_o > set_Pr903927857289325719_int_o ).
thf(func_def_769,type,
set_Pr2470121279949933262nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_770,type,
set_Pr6647972299459129970nt_nat: list_P8198026277950538467nt_nat > set_Pr3448869479623346877nt_nat ).
thf(func_def_771,type,
set_Pr112895574167722958t_real: list_P6863124054624500543t_real > set_Pr3538720872664544793t_real ).
thf(func_def_772,type,
set_Pr8714266321650254504T_VEBT: list_P7524865323317820941T_VEBT > set_Pr8044002425091019955T_VEBT ).
thf(func_def_773,type,
set_Pr1470767568048878706at_int: list_P3521021558325789923at_int > set_Pr7995236796853374141at_int ).
thf(func_def_774,type,
set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_775,type,
set_Pr8219819362198175822al_int: list_P4344331454722006975al_int > set_Pr1019928272762051225al_int ).
thf(func_def_776,type,
set_Pr5999470521830281550l_real: list_P8689742595348180415l_real > set_Pr6218003697084177305l_real ).
thf(func_def_777,type,
set_Pr8897343066327330088T_VEBT: list_P877281246627933069T_VEBT > set_Pr6019664923565264691T_VEBT ).
thf(func_def_778,type,
set_Pr9040384385603167362et_nat: list_P6254988961118846195et_nat > set_Pr5488025237498180813et_nat ).
thf(func_def_779,type,
set_Pr2418681094996576974uint32: list_P3069071885182933823uint32 > set_Pr1773385645901665561uint32 ).
thf(func_def_780,type,
set_Pr7708085864119495200VEBT_o: list_P3126845725202233233VEBT_o > set_Pr3175402225741728619VEBT_o ).
thf(func_def_781,type,
set_Pr2853735649769556538BT_int: list_P4547456442757143711BT_int > set_Pr5066593544530342725BT_int ).
thf(func_def_782,type,
set_Pr7031586669278753246BT_nat: list_P7037539587688870467BT_nat > set_Pr7556676689462069481BT_nat ).
thf(func_def_783,type,
set_Pr1087130671499945274T_real: list_P2623026923184700063T_real > set_Pr7765410600122031685T_real ).
thf(func_def_784,type,
set_Pr9182192707038809660T_VEBT: list_P7413028617227757229T_VEBT > set_Pr6192946355708809607T_VEBT ).
thf(func_def_785,type,
set_rat2: list_rat > set_rat ).
thf(func_def_786,type,
set_real2: list_real > set_real ).
thf(func_def_787,type,
set_set_nat2: list_set_nat > set_set_nat ).
thf(func_def_788,type,
set_literal2: list_literal > set_literal ).
thf(func_def_789,type,
set_uint322: list_uint32 > set_uint32 ).
thf(func_def_790,type,
set_VEBT_VEBTi2: list_VEBT_VEBTi > set_VEBT_VEBTi ).
thf(func_def_791,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_792,type,
size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
thf(func_def_793,type,
list_u6943956310655620667_nat_o: list_P7985473006766602707_nat_o > nat > ( produc3658429121746597890et_nat > $o ) > list_P7985473006766602707_nat_o ).
thf(func_def_794,type,
list_update_o: list_o > nat > $o > list_o ).
thf(func_def_795,type,
list_update_int: list_int > nat > int > list_int ).
thf(func_def_796,type,
list_update_nat: list_nat > nat > nat > list_nat ).
thf(func_def_797,type,
list_u1913845194572276492et_nat: list_P362550909693114634et_nat > nat > produc2732055786443039994et_nat > list_P362550909693114634et_nat ).
thf(func_def_798,type,
list_u1866171116859985808et_nat: list_P2321686559999237006et_nat > nat > produc3925858234332021118et_nat > list_P2321686559999237006et_nat ).
thf(func_def_799,type,
list_u1537252308907898773od_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o > list_P4002435161011370285od_o_o ).
thf(func_def_800,type,
list_u9060326803697358356et_nat: list_P9062070895058802706et_nat > nat > produc3658429121746597890et_nat > list_P9062070895058802706et_nat ).
thf(func_def_801,type,
list_u3002344382305578791nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int > list_P5707943133018811711nt_int ).
thf(func_def_802,type,
list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
thf(func_def_803,type,
list_u2546161786664092711uint32: list_P3069071885182933823uint32 > nat > produc827990862158126777uint32 > list_P3069071885182933823uint32 ).
thf(func_def_804,type,
list_u30558089781959097_VEBTi: list_P785718909624839377_VEBTi > nat > produc3777764054643897931_VEBTi > list_P785718909624839377_VEBTi ).
thf(func_def_805,type,
list_u9044509791230035014T_VEBT: list_P5988454224134618948T_VEBT > nat > produc2810682830582626868T_VEBT > list_P5988454224134618948T_VEBT ).
thf(func_def_806,type,
list_u636002643828906794_VEBTi: list_P735349106241217576_VEBTi > nat > produc3625547720036274456_VEBTi > list_P735349106241217576_VEBTi ).
thf(func_def_807,type,
list_u6961636818849549845T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT > list_P7413028617227757229T_VEBT ).
thf(func_def_808,type,
list_update_real: list_real > nat > real > list_real ).
thf(func_def_809,type,
list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
thf(func_def_810,type,
list_update_uint32: list_uint32 > nat > uint32 > list_uint32 ).
thf(func_def_811,type,
list_u6098035379799741383_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi > list_VEBT_VEBTi ).
thf(func_def_812,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_813,type,
listrel1_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
thf(func_def_814,type,
listrel1_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
thf(func_def_815,type,
listrel1_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
thf(func_def_816,type,
listrel1_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real ).
thf(func_def_817,type,
listrel1_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32 ).
thf(func_def_818,type,
listrel1_VEBT_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr4797120415438012619_VEBTi ).
thf(func_def_819,type,
listrel1_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
thf(func_def_820,type,
nth_o: list_o > nat > $o ).
thf(func_def_821,type,
nth_int: list_int > nat > int ).
thf(func_def_822,type,
nth_nat: list_nat > nat > nat ).
thf(func_def_823,type,
nth_num: list_num > nat > num ).
thf(func_def_824,type,
nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int ).
thf(func_def_825,type,
nth_Pr731366597535767232t_real: list_P6863124054624500543t_real > nat > produc679980390762269497t_real ).
thf(func_def_826,type,
nth_Pr5092243222550848201_VEBTi: list_P4447955379000644808_VEBTi > nat > produc2062302194595185346_VEBTi ).
thf(func_def_827,type,
nth_Pr3474266648193625910T_VEBT: list_P7524865323317820941T_VEBT > nat > produc1531783533982839933T_VEBT ).
thf(func_def_828,type,
nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
thf(func_def_829,type,
nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
thf(func_def_830,type,
nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
thf(func_def_831,type,
nth_Pr7767817059697521252t_real: list_P3644420460460130531t_real > nat > produc7716430852924023517t_real ).
thf(func_def_832,type,
nth_Pr3244165891152107629_VEBTi: list_P2320588648998582380_VEBTi > nat > produc214224863196444774_VEBTi ).
thf(func_def_833,type,
nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
thf(func_def_834,type,
nth_Pr6139322253122866368uint32: list_P3069071885182933823uint32 > nat > produc827990862158126777uint32 ).
thf(func_def_835,type,
nth_Pr3306050735993963089EBTi_o: list_P8833571063612306856EBTi_o > nat > produc5014006835512566296EBTi_o ).
thf(func_def_836,type,
nth_Pr2733638074192486473Ti_int: list_P7392757774524453448Ti_int > nat > produc8927069083091599426Ti_int ).
thf(func_def_837,type,
nth_Pr3433448822664029129i_real: list_P8536626330812492744i_real > nat > produc6680258955013199682i_real ).
thf(func_def_838,type,
nth_Pr6329974346453275474_VEBTi: list_P785718909624839377_VEBTi > nat > produc3777764054643897931_VEBTi ).
thf(func_def_839,type,
nth_Pr8725177398587324397T_VEBT: list_P5988454224134618948T_VEBT > nat > produc2810682830582626868T_VEBT ).
thf(func_def_840,type,
nth_rat: list_rat > nat > rat ).
thf(func_def_841,type,
nth_real: list_real > nat > real ).
thf(func_def_842,type,
nth_set_nat: list_set_nat > nat > set_nat ).
thf(func_def_843,type,
nth_uint32: list_uint32 > nat > uint32 ).
thf(func_def_844,type,
nth_VEBT_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi ).
thf(func_def_845,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_846,type,
remove1_o: $o > list_o > list_o ).
thf(func_def_847,type,
remove1_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
thf(func_def_848,type,
remove1_int: int > list_int > list_int ).
thf(func_def_849,type,
remove1_nat: nat > list_nat > list_nat ).
thf(func_def_850,type,
remove1_num: num > list_num > list_num ).
thf(func_def_851,type,
remove1_rat: rat > list_rat > list_rat ).
thf(func_def_852,type,
remove1_real: real > list_real > list_real ).
thf(func_def_853,type,
remove1_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_854,type,
removeAll_o: $o > list_o > list_o ).
thf(func_def_855,type,
removeAll_int: int > list_int > list_int ).
thf(func_def_856,type,
removeAll_nat: nat > list_nat > list_nat ).
thf(func_def_857,type,
removeAll_real: real > list_real > list_real ).
thf(func_def_858,type,
removeAll_set_nat: set_nat > list_set_nat > list_set_nat ).
thf(func_def_859,type,
removeAll_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_860,type,
replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_861,type,
rotate1_o: list_o > list_o ).
thf(func_def_862,type,
rotate1_nat: list_nat > list_nat ).
thf(func_def_863,type,
rotate1_real: list_real > list_real ).
thf(func_def_864,type,
rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_865,type,
sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).
thf(func_def_866,type,
sorted710888440204495920nteger: ( code_integer > code_integer > $o ) > list_Code_integer > $o ).
thf(func_def_867,type,
sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
thf(func_def_868,type,
sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
thf(func_def_869,type,
sorted_wrt_num: ( num > num > $o ) > list_num > $o ).
thf(func_def_870,type,
sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).
thf(func_def_871,type,
sorted_wrt_real: ( real > real > $o ) > list_real > $o ).
thf(func_def_872,type,
sorted_wrt_literal: ( literal > literal > $o ) > list_literal > $o ).
thf(func_def_873,type,
sorted9206477368072086664_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi > $o ) > list_VEBT_VEBTi > $o ).
thf(func_def_874,type,
sorted_wrt_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > list_VEBT_VEBT > $o ).
thf(func_def_875,type,
subseqs_o: list_o > list_list_o ).
thf(func_def_876,type,
subseqs_int: list_int > list_list_int ).
thf(func_def_877,type,
subseqs_nat: list_nat > list_list_nat ).
thf(func_def_878,type,
subseqs_real: list_real > list_list_real ).
thf(func_def_879,type,
subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
thf(func_def_880,type,
take_o: nat > list_o > list_o ).
thf(func_def_881,type,
take_int: nat > list_int > list_int ).
thf(func_def_882,type,
take_nat: nat > list_nat > list_nat ).
thf(func_def_883,type,
take_num: nat > list_num > list_num ).
thf(func_def_884,type,
take_rat: nat > list_rat > list_rat ).
thf(func_def_885,type,
take_real: nat > list_real > list_real ).
thf(func_def_886,type,
take_set_nat: nat > list_set_nat > list_set_nat ).
thf(func_def_887,type,
take_uint32: nat > list_uint32 > list_uint32 ).
thf(func_def_888,type,
take_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_VEBT_VEBTi ).
thf(func_def_889,type,
take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_890,type,
upt: nat > nat > list_nat ).
thf(func_def_891,type,
upto: int > int > list_int ).
thf(func_def_892,type,
upto_aux: int > int > list_int > list_int ).
thf(func_def_893,type,
upto_rel: product_prod_int_int > product_prod_int_int > $o ).
thf(func_def_894,type,
zip_Pr8136144321567152340et_nat: list_P7985473006766602707_nat_o > list_P2321686559999237006et_nat > list_P362550909693114634et_nat ).
thf(func_def_895,type,
zip_Pr7134870689397686104et_nat: list_P7985473006766602707_nat_o > list_P9062070895058802706et_nat > list_P2321686559999237006et_nat ).
thf(func_def_896,type,
zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
thf(func_def_897,type,
zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
thf(func_def_898,type,
zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
thf(func_def_899,type,
zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
thf(func_def_900,type,
zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
thf(func_def_901,type,
zip_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
thf(func_def_902,type,
zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
thf(func_def_903,type,
zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
thf(func_def_904,type,
zip_int_real: list_int > list_real > list_P6863124054624500543t_real ).
thf(func_def_905,type,
zip_int_VEBT_VEBTi: list_int > list_VEBT_VEBTi > list_P4447955379000644808_VEBTi ).
thf(func_def_906,type,
zip_int_VEBT_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
thf(func_def_907,type,
zip_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
thf(func_def_908,type,
zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
thf(func_def_909,type,
zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
thf(func_def_910,type,
zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
thf(func_def_911,type,
zip_real_int: list_real > list_int > list_P4344331454722006975al_int ).
thf(func_def_912,type,
zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
thf(func_def_913,type,
zip_real_real: list_real > list_real > list_P8689742595348180415l_real ).
thf(func_def_914,type,
zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT ).
thf(func_def_915,type,
zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat ).
thf(func_def_916,type,
zip_uint32_uint32: list_uint32 > list_uint32 > list_P3069071885182933823uint32 ).
thf(func_def_917,type,
zip_VEBT_VEBTi_o: list_VEBT_VEBTi > list_o > list_P8833571063612306856EBTi_o ).
thf(func_def_918,type,
zip_VEBT_VEBTi_int: list_VEBT_VEBTi > list_int > list_P7392757774524453448Ti_int ).
thf(func_def_919,type,
zip_VEBT_VEBTi_real: list_VEBT_VEBTi > list_real > list_P8536626330812492744i_real ).
thf(func_def_920,type,
zip_VE793581609497812771_VEBTi: list_VEBT_VEBTi > list_VEBT_VEBTi > list_P785718909624839377_VEBTi ).
thf(func_def_921,type,
zip_VE7413257051550508102T_VEBT: list_VEBT_VEBTi > list_VEBT_VEBT > list_P5988454224134618948T_VEBT ).
thf(func_def_922,type,
zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
thf(func_def_923,type,
zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
thf(func_def_924,type,
zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
thf(func_def_925,type,
zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real ).
thf(func_def_926,type,
zip_VE6444338338598820466_VEBTi: list_VEBT_VEBT > list_VEBT_VEBTi > list_P735349106241217576_VEBTi ).
thf(func_def_927,type,
zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(func_def_928,type,
biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o ).
thf(func_def_929,type,
biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o ).
thf(func_def_930,type,
bijective_int_int: set_Pr958786334691620121nt_int > $o ).
thf(func_def_931,type,
bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_932,type,
biject2923219584331114343uint32: set_Pr1773385645901665561uint32 > $o ).
thf(func_def_933,type,
dflt_None_set_o: set_o > option_set_o ).
thf(func_def_934,type,
dflt_None_set_int: set_int > option_set_int ).
thf(func_def_935,type,
dflt_None_set_nat: set_nat > option_set_nat ).
thf(func_def_936,type,
mergesort_remdups_o: list_o > list_o ).
thf(func_def_937,type,
merges1654122896337280797ps_int: list_int > list_int ).
thf(func_def_938,type,
merges1656613366846331073ps_nat: list_nat > list_nat ).
thf(func_def_939,type,
merges7437317189856885515ps_num: list_num > list_num ).
thf(func_def_940,type,
merges1021483306759835337ps_rat: list_rat > list_rat ).
thf(func_def_941,type,
merges7559785487730971421s_real: list_real > list_real ).
thf(func_def_942,type,
slice_o: nat > nat > list_o > list_o ).
thf(func_def_943,type,
slice_int: nat > nat > list_int > list_int ).
thf(func_def_944,type,
slice_nat: nat > nat > list_nat > list_nat ).
thf(func_def_945,type,
slice_real: nat > nat > list_real > list_real ).
thf(func_def_946,type,
slice_VEBT_VEBTi: nat > nat > list_VEBT_VEBTi > list_VEBT_VEBTi ).
thf(func_def_947,type,
slice_VEBT_VEBT: nat > nat > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_948,type,
the_default_nat: nat > option_nat > nat ).
thf(func_def_949,type,
the_de3812365490807259288at_nat: product_prod_nat_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_950,type,
the_default_set_o: set_o > option_set_o > set_o ).
thf(func_def_951,type,
the_default_set_int: set_int > option_set_int > set_int ).
thf(func_def_952,type,
the_default_set_nat: set_nat > option_set_nat > set_nat ).
thf(func_def_953,type,
suc: nat > nat ).
thf(func_def_954,type,
compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
thf(func_def_955,type,
semiri4939895301339042750nteger: nat > code_integer ).
thf(func_def_956,type,
semiri1314217659103216013at_int: nat > int ).
thf(func_def_957,type,
semiri1316708129612266289at_nat: nat > nat ).
thf(func_def_958,type,
semiri681578069525770553at_rat: nat > rat ).
thf(func_def_959,type,
semiri5074537144036343181t_real: nat > real ).
thf(func_def_960,type,
semiri2565882477558803405uint32: nat > uint32 ).
thf(func_def_961,type,
size_size_list_o: list_o > nat ).
thf(func_def_962,type,
size_s3445333598471063425nteger: list_Code_integer > nat ).
thf(func_def_963,type,
size_s3451745648224563538omplex: list_complex > nat ).
thf(func_def_964,type,
size_size_list_int: list_int > nat ).
thf(func_def_965,type,
size_s2710708370519433104list_o: list_list_o > nat ).
thf(func_def_966,type,
size_s3023201423986296836st_nat: list_list_nat > nat ).
thf(func_def_967,type,
size_s6660260683639930848t_real: list_list_real > nat ).
thf(func_def_968,type,
size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
thf(func_def_969,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_970,type,
size_size_list_num: list_num > nat ).
thf(func_def_971,type,
size_s2624279037499656343o_real: list_P5232166724548748803o_real > nat ).
thf(func_def_972,type,
size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
thf(func_def_973,type,
size_s987546567493390085real_o: list_P3595434254542482545real_o > nat ).
thf(func_def_974,type,
size_s1877336372972134351al_nat: list_P6834414599653733731al_nat > nat ).
thf(func_def_975,type,
size_s3932428310213730859l_real: list_P8689742595348180415l_real > nat ).
thf(func_def_976,type,
size_s3289364478449617953T_VEBT: list_P877281246627933069T_VEBT > nat ).
thf(func_def_977,type,
size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
thf(func_def_978,type,
size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
thf(func_def_979,type,
size_s5035110155006384947T_real: list_P2623026923184700063T_real > nat ).
thf(func_def_980,type,
size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
thf(func_def_981,type,
size_size_list_rat: list_rat > nat ).
thf(func_def_982,type,
size_size_list_real: list_real > nat ).
thf(func_def_983,type,
size_s3254054031482475050et_nat: list_set_nat > nat ).
thf(func_def_984,type,
size_s2501651207091587910iteral: list_literal > nat ).
thf(func_def_985,type,
size_s4844771616002835472uint32: list_uint32 > nat ).
thf(func_def_986,type,
size_s7982070591426661849_VEBTi: list_VEBT_VEBTi > nat ).
thf(func_def_987,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(func_def_988,type,
size_size_num: num > nat ).
thf(func_def_989,type,
size_size_option_nat: option_nat > nat ).
thf(func_def_990,type,
size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
thf(func_def_991,type,
size_size_VEBT_VEBTi: vEBT_VEBTi > nat ).
thf(func_def_992,type,
size_size_VEBT_VEBT: vEBT_VEBT > nat ).
thf(func_def_993,type,
nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
thf(func_def_994,type,
nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_995,type,
nat_set_decode: nat > set_nat ).
thf(func_def_996,type,
nat_set_encode: set_nat > nat ).
thf(func_def_997,type,
nat_triangle: nat > nat ).
thf(func_def_998,type,
root: nat > real > real ).
thf(func_def_999,type,
sqrt: real > real ).
thf(func_def_1000,type,
bitM: num > num ).
thf(func_def_1001,type,
inc: num > num ).
thf(func_def_1002,type,
neg_nu3811975205180677377ec_int: int > int ).
thf(func_def_1003,type,
neg_nu3179335615603231917ec_rat: rat > rat ).
thf(func_def_1004,type,
neg_nu6075765906172075777c_real: real > real ).
thf(func_def_1005,type,
neg_nu965353292909893953uint32: uint32 > uint32 ).
thf(func_def_1006,type,
neg_nu5851722552734809277nc_int: int > int ).
thf(func_def_1007,type,
neg_nu5219082963157363817nc_rat: rat > rat ).
thf(func_def_1008,type,
neg_nu8295874005876285629c_real: real > real ).
thf(func_def_1009,type,
neg_nu4269007558841261821uint32: uint32 > uint32 ).
thf(func_def_1010,type,
bit0: num > num ).
thf(func_def_1011,type,
bit1: num > num ).
thf(func_def_1012,type,
one: num ).
thf(func_def_1013,type,
size_num: num > nat ).
thf(func_def_1014,type,
numera6620942414471956472nteger: num > code_integer ).
thf(func_def_1015,type,
numera1916890842035813515d_enat: num > extended_enat ).
thf(func_def_1016,type,
numeral_numeral_int: num > int ).
thf(func_def_1017,type,
numeral_numeral_nat: num > nat ).
thf(func_def_1018,type,
numeral_numeral_real: num > real ).
thf(func_def_1019,type,
numera9087168376688890119uint32: num > uint32 ).
thf(func_def_1020,type,
none_nat: option_nat ).
thf(func_def_1021,type,
none_P199884684680593241et_nat: option2860828798490689354et_nat ).
thf(func_def_1022,type,
none_P4972525538344268765et_nat: option5190343406534369742et_nat ).
thf(func_def_1023,type,
none_P2377608414092835994nt_int: option4624381673175914239nt_int ).
thf(func_def_1024,type,
none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
thf(func_def_1025,type,
none_P7441528354948028570uint32: option3972171592325465343uint32 ).
thf(func_def_1026,type,
none_set_o: option_set_o ).
thf(func_def_1027,type,
none_set_int: option_set_int ).
thf(func_def_1028,type,
none_set_nat: option_set_nat ).
thf(func_def_1029,type,
some_int: int > option_int ).
thf(func_def_1030,type,
some_nat: nat > option_nat ).
thf(func_def_1031,type,
some_num: num > option_num ).
thf(func_def_1032,type,
some_P1630309045189364437et_nat: produc2732055786443039994et_nat > option2860828798490689354et_nat ).
thf(func_def_1033,type,
some_P750831030444334937et_nat: produc3925858234332021118et_nat > option5190343406534369742et_nat ).
thf(func_def_1034,type,
some_P4184893108420464158nt_int: product_prod_int_int > option4624381673175914239nt_int ).
thf(func_def_1035,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(func_def_1036,type,
some_P6695178580830101022uint32: produc827990862158126777uint32 > option3972171592325465343uint32 ).
thf(func_def_1037,type,
some_rat: rat > option_rat ).
thf(func_def_1038,type,
some_real: real > option_real ).
thf(func_def_1039,type,
some_set_o: set_o > option_set_o ).
thf(func_def_1040,type,
some_set_int: set_int > option_set_int ).
thf(func_def_1041,type,
some_set_nat: set_nat > option_set_nat ).
thf(func_def_1042,type,
case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
thf(func_def_1043,type,
case_o1383228350324149268at_nat: option_nat > ( product_prod_nat_nat > option_nat ) > option4927543243414619207at_nat > option_nat ).
thf(func_def_1044,type,
case_o2442805151034396888at_nat: vEBT_VEBT > ( product_prod_nat_nat > vEBT_VEBT ) > option4927543243414619207at_nat > vEBT_VEBT ).
thf(func_def_1045,type,
size_option_nat: ( nat > nat ) > option_nat > nat ).
thf(func_def_1046,type,
size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).
thf(func_def_1047,type,
the_nat: option_nat > nat ).
thf(func_def_1048,type,
bot_bo3790638025767943357_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
thf(func_def_1049,type,
bot_bo5580076615179976505_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_1050,type,
bot_bot_o_o: $o > $o ).
thf(func_def_1051,type,
bot_bot_complex_o: complex > $o ).
thf(func_def_1052,type,
bot_bot_int_int_o: int > int > $o ).
thf(func_def_1053,type,
bot_bot_int_o: int > $o ).
thf(func_def_1054,type,
bot_bot_list_nat_o: list_nat > $o ).
thf(func_def_1055,type,
bot_bot_nat_nat_o: nat > nat > $o ).
thf(func_def_1056,type,
bot_bot_nat_o: nat > $o ).
thf(func_def_1057,type,
bot_bot_real_o: real > $o ).
thf(func_def_1058,type,
bot_bot_set_nat_o: set_nat > $o ).
thf(func_def_1059,type,
bot_bo8112279147790955290nt32_o: uint32 > uint32 > $o ).
thf(func_def_1060,type,
bot_bot_VEBT_VEBT_o: vEBT_VEBT > $o ).
thf(func_def_1062,type,
bot_bot_assn: assn ).
thf(func_def_1063,type,
bot_bot_nat: nat ).
thf(func_def_1064,type,
bot_bot_set_o: set_o ).
thf(func_def_1065,type,
bot_bo3990330152332043303nteger: set_Code_integer ).
thf(func_def_1066,type,
bot_bot_set_complex: set_complex ).
thf(func_def_1067,type,
bot_bot_set_int: set_int ).
thf(func_def_1068,type,
bot_bot_set_list_nat: set_list_nat ).
thf(func_def_1069,type,
bot_bot_set_nat: set_nat ).
thf(func_def_1070,type,
bot_bot_set_num: set_num ).
thf(func_def_1071,type,
bot_bo5635537948650799172et_nat: set_Pr8536935166611901872et_nat ).
thf(func_def_1072,type,
bot_bo1481135142794719944et_nat: set_Pr3286484037609594932et_nat ).
thf(func_def_1073,type,
bot_bo7073875226086086771od_o_o: set_Product_prod_o_o ).
thf(func_def_1074,type,
bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).
thf(func_def_1075,type,
bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1076,type,
bot_bo8438649754162204037uint32: set_Pr1773385645901665561uint32 ).
thf(func_def_1077,type,
bot_bo5088076668136028147T_VEBT: set_Pr6192946355708809607T_VEBT ).
thf(func_def_1078,type,
bot_bot_set_rat: set_rat ).
thf(func_def_1079,type,
bot_bot_set_real: set_real ).
thf(func_def_1080,type,
bot_bot_set_set_int: set_set_int ).
thf(func_def_1081,type,
bot_bot_set_set_nat: set_set_nat ).
thf(func_def_1082,type,
bot_bot_set_literal: set_literal ).
thf(func_def_1083,type,
bot_bot_set_uint32: set_uint32 ).
thf(func_def_1084,type,
bot_bo8982466882572371071_VEBTi: set_VEBT_VEBTi ).
thf(func_def_1085,type,
bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).
thf(func_def_1086,type,
ord_Least_nat: ( nat > $o ) > nat ).
thf(func_def_1087,type,
ord_Least_real: ( real > $o ) > real ).
thf(func_def_1088,type,
ord_less_int_o: ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_1089,type,
ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_1090,type,
ord_less_real_o: ( real > $o ) > ( real > $o ) > $o ).
thf(func_def_1091,type,
ord_less_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).
thf(func_def_1092,type,
ord_less_VEBT_VEBT_o: ( vEBT_VEBT > $o ) > ( vEBT_VEBT > $o ) > $o ).
thf(func_def_1093,type,
ord_less_o: $o > $o > $o ).
thf(func_def_1094,type,
ord_less_assn: assn > assn > $o ).
thf(func_def_1095,type,
ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
thf(func_def_1096,type,
ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
thf(func_def_1097,type,
ord_less_int: int > int > $o ).
thf(func_def_1098,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_1099,type,
ord_less_num: num > num > $o ).
thf(func_def_1100,type,
ord_less_option_int: option_int > option_int > $o ).
thf(func_def_1101,type,
ord_less_option_nat: option_nat > option_nat > $o ).
thf(func_def_1102,type,
ord_less_option_num: option_num > option_num > $o ).
thf(func_def_1103,type,
ord_less_option_rat: option_rat > option_rat > $o ).
thf(func_def_1104,type,
ord_less_option_real: option_real > option_real > $o ).
thf(func_def_1105,type,
ord_less_rat: rat > rat > $o ).
thf(func_def_1106,type,
ord_less_real: real > real > $o ).
thf(func_def_1107,type,
ord_less_set_o: set_o > set_o > $o ).
thf(func_def_1108,type,
ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).
thf(func_def_1109,type,
ord_less_set_complex: set_complex > set_complex > $o ).
thf(func_def_1110,type,
ord_less_set_int: set_int > set_int > $o ).
thf(func_def_1111,type,
ord_le1190675801316882794st_nat: set_list_nat > set_list_nat > $o ).
thf(func_def_1112,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(func_def_1113,type,
ord_less_set_num: set_num > set_num > $o ).
thf(func_def_1114,type,
ord_less_set_rat: set_rat > set_rat > $o ).
thf(func_def_1115,type,
ord_less_set_real: set_real > set_real > $o ).
thf(func_def_1116,type,
ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
thf(func_def_1117,type,
ord_less_set_literal: set_literal > set_literal > $o ).
thf(func_def_1118,type,
ord_le3480810397992357184T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(func_def_1119,type,
ord_less_char: char > char > $o ).
thf(func_def_1120,type,
ord_less_literal: literal > literal > $o ).
thf(func_def_1121,type,
ord_less_uint32: uint32 > uint32 > $o ).
thf(func_def_1122,type,
ord_le750835935415966154l_num1: word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ).
thf(func_def_1123,type,
ord_le6753239538765779593_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > $o ).
thf(func_def_1124,type,
ord_le8000401564054156549_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > $o ).
thf(func_def_1125,type,
ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).
thf(func_def_1126,type,
ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_1127,type,
ord_le2646555220125990790_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_1128,type,
ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_1129,type,
ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
thf(func_def_1130,type,
ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).
thf(func_def_1131,type,
ord_le5999336846926846542nt32_o: ( uint32 > uint32 > $o ) > ( uint32 > uint32 > $o ) > $o ).
thf(func_def_1132,type,
ord_le418104280809901481VEBT_o: ( vEBT_VEBT > $o ) > ( vEBT_VEBT > $o ) > $o ).
thf(func_def_1133,type,
ord_less_eq_o: $o > $o > $o ).
thf(func_def_1134,type,
ord_less_eq_assn: assn > assn > $o ).
thf(func_def_1135,type,
ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
thf(func_def_1136,type,
ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
thf(func_def_1137,type,
ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
thf(func_def_1138,type,
ord_le4104064031414453916r_real: filter_real > filter_real > $o ).
thf(func_def_1139,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_1140,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_1141,type,
ord_less_eq_num: num > num > $o ).
thf(func_def_1142,type,
ord_le1736525451366464988on_int: option_int > option_int > $o ).
thf(func_def_1143,type,
ord_le5914376470875661696on_nat: option_nat > option_nat > $o ).
thf(func_def_1144,type,
ord_le6622620407824499402on_num: option_num > option_num > $o ).
thf(func_def_1145,type,
ord_le2406147912482264968on_rat: option_rat > option_rat > $o ).
thf(func_def_1146,type,
ord_le353528952715127954et_int: option_set_int > option_set_int > $o ).
thf(func_def_1147,type,
ord_less_eq_rat: rat > rat > $o ).
thf(func_def_1148,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_1149,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(func_def_1150,type,
ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
thf(func_def_1151,type,
ord_le211207098394363844omplex: set_complex > set_complex > $o ).
thf(func_def_1152,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(func_def_1153,type,
ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).
thf(func_def_1154,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_1155,type,
ord_less_eq_set_num: set_num > set_num > $o ).
thf(func_def_1156,type,
ord_le4763372923235995152et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > $o ).
thf(func_def_1157,type,
ord_le5966269811547037844et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > $o ).
thf(func_def_1158,type,
ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1159,type,
ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1160,type,
ord_le6429528607962791097uint32: set_Pr1773385645901665561uint32 > set_Pr1773385645901665561uint32 > $o ).
thf(func_def_1161,type,
ord_less_eq_set_rat: set_rat > set_rat > $o ).
thf(func_def_1162,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(func_def_1163,type,
ord_le4403425263959731960et_int: set_set_int > set_set_int > $o ).
thf(func_def_1164,type,
ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
thf(func_def_1165,type,
ord_le9131159989063066194et_nat: set_set_set_nat > set_set_set_nat > $o ).
thf(func_def_1166,type,
ord_le7307670543136651348iteral: set_literal > set_literal > $o ).
thf(func_def_1167,type,
ord_le6592769550269828683_VEBTi: set_VEBT_VEBTi > set_VEBT_VEBTi > $o ).
thf(func_def_1168,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(func_def_1169,type,
ord_less_eq_char: char > char > $o ).
thf(func_def_1170,type,
ord_less_eq_uint32: uint32 > uint32 > $o ).
thf(func_def_1171,type,
ord_le3335648743751981014l_num1: word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ).
thf(func_def_1172,type,
ord_max_o: $o > $o > $o ).
thf(func_def_1173,type,
ord_max_assn: assn > assn > assn ).
thf(func_def_1174,type,
ord_max_Code_integer: code_integer > code_integer > code_integer ).
thf(func_def_1175,type,
ord_max_int: int > int > int ).
thf(func_def_1176,type,
ord_max_nat: nat > nat > nat ).
thf(func_def_1177,type,
ord_max_num: num > num > num ).
thf(func_def_1178,type,
ord_max_rat: rat > rat > rat ).
thf(func_def_1179,type,
ord_max_real: real > real > real ).
thf(func_def_1180,type,
ord_max_set_o: set_o > set_o > set_o ).
thf(func_def_1181,type,
ord_max_set_int: set_int > set_int > set_int ).
thf(func_def_1182,type,
ord_max_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1183,type,
ord_min_Code_integer: code_integer > code_integer > code_integer ).
thf(func_def_1184,type,
ord_min_int: int > int > int ).
thf(func_def_1185,type,
ord_min_nat: nat > nat > nat ).
thf(func_def_1186,type,
order_Greatest_nat: ( nat > $o ) > nat ).
thf(func_def_1187,type,
ordering_top_assn: ( assn > assn > $o ) > ( assn > assn > $o ) > assn > $o ).
thf(func_def_1188,type,
ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).
thf(func_def_1189,type,
ordering_top_set_o: ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > set_o > $o ).
thf(func_def_1190,type,
ordering_top_set_int: ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > set_int > $o ).
thf(func_def_1191,type,
ordering_top_set_nat: ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > set_nat > $o ).
thf(func_def_1192,type,
top_top_assn: assn ).
thf(func_def_1193,type,
top_top_set_o: set_o ).
thf(func_def_1194,type,
top_top_set_int: set_int ).
thf(func_def_1195,type,
top_top_set_nat: set_nat ).
thf(func_def_1196,type,
top_to3689904424835650196l_num0: set_Numeral_num0 ).
thf(func_def_1197,type,
top_to1996260823553986621t_unit: set_Product_unit ).
thf(func_def_1198,type,
top_top_set_real: set_real ).
thf(func_def_1199,type,
top_top_set_literal: set_literal ).
thf(func_def_1200,type,
power_power_assn: assn > nat > assn ).
thf(func_def_1201,type,
power_8256067586552552935nteger: code_integer > nat > code_integer ).
thf(func_def_1202,type,
power_power_complex: complex > nat > complex ).
thf(func_def_1203,type,
power_power_int: int > nat > int ).
thf(func_def_1204,type,
power_power_nat: nat > nat > nat ).
thf(func_def_1205,type,
power_power_rat: rat > nat > rat ).
thf(func_def_1206,type,
power_power_real: real > nat > real ).
thf(func_def_1207,type,
power_power_uint32: uint32 > nat > uint32 ).
thf(func_def_1208,type,
produc2245416461498447860et_nat: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).
thf(func_def_1209,type,
produc5001842942810119800et_nat: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat ).
thf(func_def_1210,type,
product_Pair_o_o: $o > $o > product_prod_o_o ).
thf(func_def_1211,type,
product_Pair_o_int: $o > int > product_prod_o_int ).
thf(func_def_1212,type,
product_Pair_o_nat: $o > nat > product_prod_o_nat ).
thf(func_def_1213,type,
produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
thf(func_def_1214,type,
produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_1215,type,
produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > set_nat > produc3658429121746597890et_nat ).
thf(func_def_1216,type,
product_Pair_int_o: int > $o > product_prod_int_o ).
thf(func_def_1217,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(func_def_1218,type,
product_Pair_int_nat: int > nat > product_prod_int_nat ).
thf(func_def_1219,type,
produc801115645435158769t_real: int > real > produc679980390762269497t_real ).
thf(func_def_1220,type,
produc4497823428076633978_VEBTi: int > vEBT_VEBTi > produc2062302194595185346_VEBTi ).
thf(func_def_1221,type,
produc3329399203697025711T_VEBT: int > vEBT_VEBT > produc1531783533982839933T_VEBT ).
thf(func_def_1222,type,
produc8435520187683070743list_o: list_o > list_o > produc7102631898165422375list_o ).
thf(func_def_1223,type,
produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int ).
thf(func_def_1224,type,
produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat ).
thf(func_def_1225,type,
produc1408950526243324945t_real: list_real > list_real > produc478978216448986841t_real ).
thf(func_def_1226,type,
produc7487160679990061969uint32: list_uint32 > list_uint32 > produc823665806539077721uint32 ).
thf(func_def_1227,type,
produc4384243565435462691_VEBTi: list_VEBT_VEBTi > list_VEBT_VEBTi > produc3089554586268799851_VEBTi ).
thf(func_def_1228,type,
produc3897820843166775703T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > produc9211091688327510695T_VEBT ).
thf(func_def_1229,type,
product_Pair_nat_o: nat > $o > product_prod_nat_o ).
thf(func_def_1230,type,
product_Pair_nat_int: nat > int > product_prod_nat_int ).
thf(func_def_1231,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_1232,type,
produc7837566107596912789t_real: nat > real > produc7716430852924023517t_real ).
thf(func_def_1233,type,
produc2649746096677893406_VEBTi: nat > vEBT_VEBTi > produc214224863196444774_VEBTi ).
thf(func_def_1234,type,
produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
thf(func_def_1235,type,
produc1940133919992309389et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat > produc5657529347773406293et_nat ).
thf(func_def_1236,type,
produc8599840265553166229et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat > produc6830853553727218525et_nat ).
thf(func_def_1237,type,
produc3646306378393792727nt_int: product_prod_int_int > product_prod_int_int > produc1219242969750017639nt_int ).
thf(func_def_1238,type,
produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
thf(func_def_1239,type,
produc6884863695460953815uint32: produc827990862158126777uint32 > produc827990862158126777uint32 > produc8822557026176459367uint32 ).
thf(func_def_1240,type,
produc3179012173361985393al_int: real > int > produc8786904178792722361al_int ).
thf(func_def_1241,type,
produc4511245868158468465l_real: real > real > produc2422161461964618553l_real ).
thf(func_def_1242,type,
produc6931449550656315951T_VEBT: real > vEBT_VEBT > produc3757001726724277373T_VEBT ).
thf(func_def_1243,type,
produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).
thf(func_def_1244,type,
produc1400373151660368625uint32: uint32 > uint32 > produc827990862158126777uint32 ).
thf(func_def_1245,type,
produc8194178580519725514EBTi_o: vEBT_VEBTi > $o > produc5014006835512566296EBTi_o ).
thf(func_def_1246,type,
produc7190175284220460154Ti_int: vEBT_VEBTi > int > produc8927069083091599426Ti_int ).
thf(func_def_1247,type,
produc8457151488442208762i_real: vEBT_VEBTi > real > produc6680258955013199682i_real ).
thf(func_def_1248,type,
produc436343169921013763_VEBTi: vEBT_VEBTi > vEBT_VEBTi > produc3777764054643897931_VEBTi ).
thf(func_def_1249,type,
produc7053807326796202854T_VEBT: vEBT_VEBTi > vEBT_VEBT > produc2810682830582626868T_VEBT ).
thf(func_def_1250,type,
produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
thf(func_def_1251,type,
produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
thf(func_def_1252,type,
produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
thf(func_def_1253,type,
produc8117437818029410057T_real: vEBT_VEBT > real > produc5170161368751668367T_real ).
thf(func_def_1254,type,
produc6084888613844515218_VEBTi: vEBT_VEBT > vEBT_VEBTi > produc3625547720036274456_VEBTi ).
thf(func_def_1255,type,
produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
thf(func_def_1256,type,
produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1257,type,
produc6197397395684419436_o_o_o: ( $o > $o > $o ) > product_prod_o_o > $o ).
thf(func_def_1258,type,
produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
thf(func_def_1259,type,
produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
thf(func_def_1260,type,
produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
thf(func_def_1261,type,
produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
thf(func_def_1262,type,
produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1263,type,
produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
thf(func_def_1264,type,
produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
thf(func_def_1265,type,
produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1266,type,
produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_1267,type,
produc2484365769952853102on_nat: ( nat > nat > option_nat ) > product_prod_nat_nat > option_nat ).
thf(func_def_1268,type,
produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1269,type,
produc3169358591047799142T_VEBT: ( nat > nat > vEBT_VEBT ) > product_prod_nat_nat > vEBT_VEBT ).
thf(func_def_1270,type,
produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).
thf(func_def_1271,type,
produc1824681642469235216et_nat: produc3658429121746597890et_nat > heap_e7401611519738050253t_unit ).
thf(func_def_1272,type,
product_fst_int_int: product_prod_int_int > int ).
thf(func_def_1273,type,
product_fst_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_1274,type,
produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
thf(func_def_1275,type,
produc8586169260539613262et_nat: produc3658429121746597890et_nat > set_nat ).
thf(func_def_1276,type,
product_snd_int_int: product_prod_int_int > int ).
thf(func_def_1277,type,
product_snd_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_1278,type,
normalize: product_prod_int_int > product_prod_int_int ).
thf(func_def_1279,type,
real_V1022390504157884413omplex: complex > real ).
thf(func_def_1280,type,
refine_Imp_refines_o: heap_Time_Heap_o > heap_Time_Heap_o > $o ).
thf(func_def_1281,type,
refine7594492741263601813on_nat: heap_T2636463487746394924on_nat > heap_T2636463487746394924on_nat > $o ).
thf(func_def_1282,type,
refine5565527176597971370_VEBTi: heap_T8145700208782473153_VEBTi > heap_T8145700208782473153_VEBTi > $o ).
thf(func_def_1283,type,
total_on_o: set_o > set_Product_prod_o_o > $o ).
thf(func_def_1284,type,
total_on_int: set_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1285,type,
total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1286,type,
total_on_real: set_real > set_Pr6218003697084177305l_real > $o ).
thf(func_def_1287,type,
total_on_set_nat: set_set_nat > set_Pr5488025237498180813et_nat > $o ).
thf(func_def_1288,type,
total_on_uint32: set_uint32 > set_Pr1773385645901665561uint32 > $o ).
thf(func_def_1289,type,
total_on_VEBT_VEBT: set_VEBT_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
thf(func_def_1290,type,
divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
thf(func_def_1291,type,
divide_divide_int: int > int > int ).
thf(func_def_1292,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_1293,type,
divide_divide_real: real > real > real ).
thf(func_def_1294,type,
dvd_dvd_Code_integer: code_integer > code_integer > $o ).
thf(func_def_1295,type,
dvd_dvd_int: int > int > $o ).
thf(func_def_1296,type,
dvd_dvd_nat: nat > nat > $o ).
thf(func_def_1297,type,
modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
thf(func_def_1298,type,
modulo_modulo_int: int > int > int ).
thf(func_def_1299,type,
modulo_modulo_nat: nat > nat > nat ).
thf(func_def_1300,type,
zero_n2684676970156552555ol_int: $o > int ).
thf(func_def_1301,type,
zero_n2687167440665602831ol_nat: $o > nat ).
thf(func_def_1302,type,
suminf_real: ( nat > real ) > real ).
thf(func_def_1303,type,
summable_real: ( nat > real ) > $o ).
thf(func_def_1304,type,
sums_real: ( nat > real ) > real > $o ).
thf(func_def_1305,type,
collect_o: ( $o > $o ) > set_o ).
thf(func_def_1306,type,
collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).
thf(func_def_1307,type,
collect_complex: ( complex > $o ) > set_complex ).
thf(func_def_1308,type,
collect_int: ( int > $o ) > set_int ).
thf(func_def_1309,type,
collect_list_o: ( list_o > $o ) > set_list_o ).
thf(func_def_1310,type,
collec3483841146883906114nteger: ( list_Code_integer > $o ) > set_li6976499617229504675nteger ).
thf(func_def_1311,type,
collect_list_complex: ( list_complex > $o ) > set_list_complex ).
thf(func_def_1312,type,
collect_list_int: ( list_int > $o ) > set_list_int ).
thf(func_def_1313,type,
collec5989764272469232197st_nat: ( list_list_nat > $o ) > set_list_list_nat ).
thf(func_def_1314,type,
collect_list_nat: ( list_nat > $o ) > set_list_nat ).
thf(func_def_1315,type,
collect_list_real: ( list_real > $o ) > set_list_real ).
thf(func_def_1316,type,
collect_list_set_nat: ( list_set_nat > $o ) > set_list_set_nat ).
thf(func_def_1317,type,
collect_list_literal: ( list_literal > $o ) > set_list_literal ).
thf(func_def_1318,type,
collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
thf(func_def_1319,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_1320,type,
collect_num: ( num > $o ) > set_num ).
thf(func_def_1321,type,
collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
thf(func_def_1322,type,
collect_rat: ( rat > $o ) > set_rat ).
thf(func_def_1323,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_1324,type,
collec574505750873337192nteger: ( set_Code_integer > $o ) > set_set_Code_integer ).
thf(func_def_1325,type,
collect_set_complex: ( set_complex > $o ) > set_set_complex ).
thf(func_def_1326,type,
collect_set_int: ( set_int > $o ) > set_set_int ).
thf(func_def_1327,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(func_def_1328,type,
collect_literal: ( literal > $o ) > set_literal ).
thf(func_def_1329,type,
collect_VEBT_VEBT: ( vEBT_VEBT > $o ) > set_VEBT_VEBT ).
thf(func_def_1330,type,
pow_nat: set_nat > set_set_nat ).
thf(func_def_1331,type,
image_o_o: ( $o > $o ) > set_o > set_o ).
thf(func_def_1332,type,
image_o_int: ( $o > int ) > set_o > set_int ).
thf(func_def_1333,type,
image_o_nat: ( $o > nat ) > set_o > set_nat ).
thf(func_def_1334,type,
image_o_VEBT_VEBT: ( $o > vEBT_VEBT ) > set_o > set_VEBT_VEBT ).
thf(func_def_1335,type,
image_4470545334726330049nteger: ( code_integer > code_integer ) > set_Code_integer > set_Code_integer ).
thf(func_def_1336,type,
image_3397630267976458002omplex: ( code_integer > complex ) > set_Code_integer > set_complex ).
thf(func_def_1337,type,
image_948535463418740880er_int: ( code_integer > int ) > set_Code_integer > set_int ).
thf(func_def_1338,type,
image_951025933927791156er_nat: ( code_integer > nat ) > set_Code_integer > set_nat ).
thf(func_def_1339,type,
image_315895873841295420er_rat: ( code_integer > rat ) > set_Code_integer > set_rat ).
thf(func_def_1340,type,
image_7738145705984076560r_real: ( code_integer > real ) > set_Code_integer > set_real ).
thf(func_def_1341,type,
image_1994230757181692690nteger: ( complex > code_integer ) > set_complex > set_Code_integer ).
thf(func_def_1342,type,
image_1468599708987790691omplex: ( complex > complex ) > set_complex > set_complex ).
thf(func_def_1343,type,
image_complex_int: ( complex > int ) > set_complex > set_int ).
thf(func_def_1344,type,
image_complex_nat: ( complex > nat ) > set_complex > set_nat ).
thf(func_def_1345,type,
image_complex_rat: ( complex > rat ) > set_complex > set_rat ).
thf(func_def_1346,type,
image_complex_real: ( complex > real ) > set_complex > set_real ).
thf(func_def_1347,type,
image_932796090930683071T_VEBT: ( complex > vEBT_VEBT ) > set_complex > set_VEBT_VEBT ).
thf(func_def_1348,type,
image_int_o: ( int > $o ) > set_int > set_o ).
thf(func_def_1349,type,
image_1587234942943678608nteger: ( int > code_integer ) > set_int > set_Code_integer ).
thf(func_def_1350,type,
image_int_complex: ( int > complex ) > set_int > set_complex ).
thf(func_def_1351,type,
image_int_int: ( int > int ) > set_int > set_int ).
thf(func_def_1352,type,
image_int_nat: ( int > nat ) > set_int > set_nat ).
thf(func_def_1353,type,
image_int_real: ( int > real ) > set_int > set_real ).
thf(func_def_1354,type,
image_int_literal: ( int > literal ) > set_int > set_literal ).
thf(func_def_1355,type,
image_int_VEBT_VEBT: ( int > vEBT_VEBT ) > set_int > set_VEBT_VEBT ).
thf(func_def_1356,type,
image_list_o_set_o: ( list_o > set_o ) > set_list_o > set_set_o ).
thf(func_def_1357,type,
image_3606813740839090725et_int: ( list_int > set_int ) > set_list_int > set_set_int ).
thf(func_def_1358,type,
image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
thf(func_def_1359,type,
image_1775855109352712557et_nat: ( list_nat > set_nat ) > set_list_nat > set_set_nat ).
thf(func_def_1360,type,
image_6239767680843085477t_real: ( list_real > set_real ) > set_list_real > set_set_real ).
thf(func_def_1361,type,
image_6463372868993444447T_VEBT: ( list_VEBT_VEBT > set_VEBT_VEBT ) > set_list_VEBT_VEBT > set_set_VEBT_VEBT ).
thf(func_def_1362,type,
image_nat_o: ( nat > $o ) > set_nat > set_o ).
thf(func_def_1363,type,
image_1215581382706833972nteger: ( nat > code_integer ) > set_nat > set_Code_integer ).
thf(func_def_1364,type,
image_nat_complex: ( nat > complex ) > set_nat > set_complex ).
thf(func_def_1365,type,
image_nat_int: ( nat > int ) > set_nat > set_int ).
thf(func_def_1366,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_1367,type,
image_nat_rat: ( nat > rat ) > set_nat > set_rat ).
thf(func_def_1368,type,
image_nat_real: ( nat > real ) > set_nat > set_real ).
thf(func_def_1369,type,
image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
thf(func_def_1370,type,
image_nat_literal: ( nat > literal ) > set_nat > set_literal ).
thf(func_def_1371,type,
image_nat_VEBT_VEBTi: ( nat > vEBT_VEBTi ) > set_nat > set_VEBT_VEBTi ).
thf(func_def_1372,type,
image_nat_VEBT_VEBT: ( nat > vEBT_VEBT ) > set_nat > set_VEBT_VEBT ).
thf(func_def_1373,type,
image_rat_rat: ( rat > rat ) > set_rat > set_rat ).
thf(func_def_1374,type,
image_4958697645175560720nteger: ( real > code_integer ) > set_real > set_Code_integer ).
thf(func_def_1375,type,
image_real_complex: ( real > complex ) > set_real > set_complex ).
thf(func_def_1376,type,
image_real_int: ( real > int ) > set_real > set_int ).
thf(func_def_1377,type,
image_real_nat: ( real > nat ) > set_real > set_nat ).
thf(func_def_1378,type,
image_real_real: ( real > real ) > set_real > set_real ).
thf(func_def_1379,type,
image_real_VEBT_VEBT: ( real > vEBT_VEBT ) > set_real > set_VEBT_VEBT ).
thf(func_def_1380,type,
image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).
thf(func_def_1381,type,
image_524474410958335435et_int: ( set_int > set_int ) > set_set_int > set_set_int ).
thf(func_def_1382,type,
image_4702325430467532143et_nat: ( set_int > set_nat ) > set_set_int > set_set_nat ).
thf(func_def_1383,type,
image_set_nat_int: ( set_nat > int ) > set_set_nat > set_int ).
thf(func_def_1384,type,
image_set_nat_nat: ( set_nat > nat ) > set_set_nat > set_nat ).
thf(func_def_1385,type,
image_3739036796817536367et_int: ( set_nat > set_int ) > set_set_nat > set_set_int ).
thf(func_def_1386,type,
image_7916887816326733075et_nat: ( set_nat > set_nat ) > set_set_nat > set_set_nat ).
thf(func_def_1387,type,
image_6725021117256019401et_nat: ( set_nat > set_set_nat ) > set_set_nat > set_set_set_nat ).
thf(func_def_1388,type,
image_2436557299294012491t_real: ( set_real > set_real ) > set_set_real > set_set_real ).
thf(func_def_1389,type,
image_7884819252390400639et_nat: ( set_set_nat > set_set_nat ) > set_set_set_nat > set_set_set_nat ).
thf(func_def_1390,type,
image_1661326939266726661T_VEBT: ( set_VEBT_VEBT > set_VEBT_VEBT ) > set_set_VEBT_VEBT > set_set_VEBT_VEBT ).
thf(func_def_1391,type,
image_4442872163159017964nteger: ( literal > code_integer ) > set_literal > set_Code_integer ).
thf(func_def_1392,type,
image_5274195009022015549omplex: ( literal > complex ) > set_literal > set_complex ).
thf(func_def_1393,type,
image_literal_nat: ( literal > nat ) > set_literal > set_nat ).
thf(func_def_1394,type,
image_8195128725298311301iteral: ( literal > literal ) > set_literal > set_literal ).
thf(func_def_1395,type,
image_uint32_uint32: ( uint32 > uint32 ) > set_uint32 > set_uint32 ).
thf(func_def_1396,type,
image_VEBT_VEBTi_int: ( vEBT_VEBTi > int ) > set_VEBT_VEBTi > set_int ).
thf(func_def_1397,type,
image_VEBT_VEBTi_nat: ( vEBT_VEBTi > nat ) > set_VEBT_VEBTi > set_nat ).
thf(func_def_1398,type,
image_6202559892754154600i_real: ( vEBT_VEBTi > real ) > set_VEBT_VEBTi > set_real ).
thf(func_def_1399,type,
image_7547481670047419768T_VEBT: ( vEBT_VEBTi > vEBT_VEBT ) > set_VEBT_VEBTi > set_VEBT_VEBT ).
thf(func_def_1400,type,
image_VEBT_VEBT_o: ( vEBT_VEBT > $o ) > set_VEBT_VEBT > set_o ).
thf(func_def_1401,type,
image_2092689629700589388nteger: ( vEBT_VEBT > code_integer ) > set_VEBT_VEBT > set_Code_integer ).
thf(func_def_1402,type,
image_3793382806556112285omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > set_complex ).
thf(func_def_1403,type,
image_VEBT_VEBT_int: ( vEBT_VEBT > int ) > set_VEBT_VEBT > set_int ).
thf(func_def_1404,type,
image_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > set_nat ).
thf(func_def_1405,type,
image_VEBT_VEBT_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > set_real ).
thf(func_def_1406,type,
image_3375948659692109573T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_1407,type,
insert_o: $o > set_o > set_o ).
thf(func_def_1408,type,
insert_Code_integer: code_integer > set_Code_integer > set_Code_integer ).
thf(func_def_1409,type,
insert_complex: complex > set_complex > set_complex ).
thf(func_def_1410,type,
insert_int: int > set_int > set_int ).
thf(func_def_1411,type,
insert_list_nat: list_nat > set_list_nat > set_list_nat ).
thf(func_def_1412,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_1413,type,
insert_num: num > set_num > set_num ).
thf(func_def_1414,type,
insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
thf(func_def_1415,type,
insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_1416,type,
insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1417,type,
insert4454361187789264009uint32: produc827990862158126777uint32 > set_Pr1773385645901665561uint32 > set_Pr1773385645901665561uint32 ).
thf(func_def_1418,type,
insert494605675473494903T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > set_Pr6192946355708809607T_VEBT ).
thf(func_def_1419,type,
insert_rat: rat > set_rat > set_rat ).
thf(func_def_1420,type,
insert_real: real > set_real > set_real ).
thf(func_def_1421,type,
insert_set_nat: set_nat > set_set_nat > set_set_nat ).
thf(func_def_1422,type,
insert_literal: literal > set_literal > set_literal ).
thf(func_def_1423,type,
insert_uint32: uint32 > set_uint32 > set_uint32 ).
thf(func_def_1424,type,
insert_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > set_VEBT_VEBTi ).
thf(func_def_1425,type,
insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_1426,type,
is_singleton_o: set_o > $o ).
thf(func_def_1427,type,
is_singleton_complex: set_complex > $o ).
thf(func_def_1428,type,
is_singleton_int: set_int > $o ).
thf(func_def_1429,type,
is_sin2641923865335537900st_nat: set_list_nat > $o ).
thf(func_def_1430,type,
is_singleton_nat: set_nat > $o ).
thf(func_def_1431,type,
is_singleton_real: set_real > $o ).
thf(func_def_1432,type,
is_singleton_set_nat: set_set_nat > $o ).
thf(func_def_1433,type,
is_singleton_literal: set_literal > $o ).
thf(func_def_1434,type,
is_sin24926331636114728T_VEBT: set_VEBT_VEBT > $o ).
thf(func_def_1435,type,
remove_o: $o > set_o > set_o ).
thf(func_def_1436,type,
remove_int: int > set_int > set_int ).
thf(func_def_1437,type,
remove_nat: nat > set_nat > set_nat ).
thf(func_def_1438,type,
remove_real: real > set_real > set_real ).
thf(func_def_1439,type,
remove_set_nat: set_nat > set_set_nat > set_set_nat ).
thf(func_def_1440,type,
remove_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_1441,type,
the_elem_o: set_o > $o ).
thf(func_def_1442,type,
the_elem_int: set_int > int ).
thf(func_def_1443,type,
the_elem_nat: set_nat > nat ).
thf(func_def_1444,type,
the_elem_set_nat: set_set_nat > set_nat ).
thf(func_def_1445,type,
the_elem_VEBT_VEBT: set_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_1446,type,
set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
thf(func_def_1447,type,
set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_1448,type,
set_or1266510415728281911st_int: int > int > set_int ).
thf(func_def_1449,type,
set_or1269000886237332187st_nat: nat > nat > set_nat ).
thf(func_def_1450,type,
set_or1222579329274155063t_real: real > real > set_real ).
thf(func_def_1451,type,
set_or7139685690850216873Than_o: $o > $o > set_o ).
thf(func_def_1452,type,
set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_1453,type,
set_or4662586982721622107an_int: int > int > set_int ).
thf(func_def_1454,type,
set_or4665077453230672383an_nat: nat > nat > set_nat ).
thf(func_def_1455,type,
set_or1222409239386451017an_num: num > num > set_num ).
thf(func_def_1456,type,
set_or4029947393144176647an_rat: rat > rat > set_rat ).
thf(func_def_1457,type,
set_or66887138388493659n_real: real > real > set_real ).
thf(func_def_1458,type,
set_or8585797421378605585et_int: set_int > set_int > set_set_int ).
thf(func_def_1459,type,
set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat ).
thf(func_def_1460,type,
set_ord_atMost_int: int > set_int ).
thf(func_def_1461,type,
set_ord_atMost_nat: nat > set_nat ).
thf(func_def_1462,type,
set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_1463,type,
set_or6659071591806873216st_nat: nat > nat > set_nat ).
thf(func_def_1464,type,
set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer ).
thf(func_def_1465,type,
set_or5834768355832116004an_nat: nat > nat > set_nat ).
thf(func_def_1466,type,
set_or1633881224788618240n_real: real > real > set_real ).
thf(func_def_1467,type,
set_ord_lessThan_o: $o > set_o ).
thf(func_def_1468,type,
set_ord_lessThan_int: int > set_int ).
thf(func_def_1469,type,
set_ord_lessThan_nat: nat > set_nat ).
thf(func_def_1470,type,
set_ord_lessThan_num: num > set_num ).
thf(func_def_1471,type,
set_ord_lessThan_rat: rat > set_rat ).
thf(func_def_1472,type,
set_or5984915006950818249n_real: real > set_real ).
thf(func_def_1473,type,
set_or890127255671739683et_nat: set_nat > set_set_nat ).
thf(func_def_1474,type,
signed6292675348222524329lo_int: int > int > int ).
thf(func_def_1475,type,
char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
thf(func_def_1476,type,
time_TBOUND_o: heap_Time_Heap_o > nat > $o ).
thf(func_def_1477,type,
time_TBOUND_nat: heap_Time_Heap_nat > nat > $o ).
thf(func_def_1478,type,
time_T8353473612707095248on_nat: heap_T2636463487746394924on_nat > nat > $o ).
thf(func_def_1479,type,
time_T5737551269749752165_VEBTi: heap_T8145700208782473153_VEBTi > nat > $o ).
thf(func_def_1480,type,
time_htt_o: assn > heap_Time_Heap_o > ( $o > assn ) > nat > $o ).
thf(func_def_1481,type,
time_htt_nat: assn > heap_Time_Heap_nat > ( nat > assn ) > nat > $o ).
thf(func_def_1482,type,
time_htt_option_nat: assn > heap_T2636463487746394924on_nat > ( option_nat > assn ) > nat > $o ).
thf(func_def_1483,type,
time_htt_VEBT_VEBTi: assn > heap_T8145700208782473153_VEBTi > ( vEBT_VEBTi > assn ) > nat > $o ).
thf(func_def_1484,type,
time_time_VEBT_VEBTi: heap_T8145700208782473153_VEBTi > heap_e7401611519738050253t_unit > nat ).
thf(func_def_1485,type,
topolo6980174941875973593q_real: ( nat > real ) > $o ).
thf(func_def_1486,type,
topolo2177554685111907308n_real: real > set_real > filter_real ).
thf(func_def_1487,type,
topolo2815343760600316023s_real: real > filter_real ).
thf(func_def_1488,type,
topolo4055970368930404560y_real: ( nat > real ) > $o ).
thf(func_def_1489,type,
arccos: real > real ).
thf(func_def_1490,type,
arcosh_real: real > real ).
thf(func_def_1491,type,
arcsin: real > real ).
thf(func_def_1492,type,
arctan: real > real ).
thf(func_def_1493,type,
artanh_real: real > real ).
thf(func_def_1494,type,
cos_real: real > real ).
thf(func_def_1495,type,
cos_coeff: nat > real ).
thf(func_def_1496,type,
cosh_real: real > real ).
thf(func_def_1497,type,
cot_real: real > real ).
thf(func_def_1498,type,
exp_real: real > real ).
thf(func_def_1499,type,
ln_ln_real: real > real ).
thf(func_def_1500,type,
log: real > real > real ).
thf(func_def_1501,type,
pi: real ).
thf(func_def_1502,type,
powr_real: real > real > real ).
thf(func_def_1503,type,
sin_real: real > real ).
thf(func_def_1504,type,
sin_coeff: nat > real ).
thf(func_def_1505,type,
sinh_real: real > real ).
thf(func_def_1506,type,
tan_real: real > real ).
thf(func_def_1507,type,
tanh_real: real > real ).
thf(func_def_1508,type,
transitive_trancl_o: set_Product_prod_o_o > set_Product_prod_o_o ).
thf(func_def_1509,type,
transi6261509568448316235cl_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_1510,type,
transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1511,type,
transi5221092739591632921et_nat: set_Pr3444600963470892981et_nat > set_Pr3444600963470892981et_nat ).
thf(func_def_1512,type,
transi3145040225084697757et_nat: set_Pr7928877670098842301et_nat > set_Pr7928877670098842301et_nat ).
thf(func_def_1513,type,
transi6288783178788033498nt_int: set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int ).
thf(func_def_1514,type,
transi243908449541399842at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_1515,type,
transi5456044692924788698uint32: set_Pr3773659940955823943uint32 > set_Pr3773659940955823943uint32 ).
thf(func_def_1516,type,
transi1789104906590519371l_real: set_Pr6218003697084177305l_real > set_Pr6218003697084177305l_real ).
thf(func_def_1517,type,
transi3114468042090999947uint32: set_Pr1773385645901665561uint32 > set_Pr1773385645901665561uint32 ).
thf(func_def_1518,type,
transi2803566869205510612_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr2227491710730465451_VEBTi ).
thf(func_def_1519,type,
transi8906537157094044885T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr6192946355708809607T_VEBT ).
thf(func_def_1520,type,
type_l4264026598287037464l_num0: itself_Numeral_num0 > nat ).
thf(func_def_1521,type,
type_d8366093980585677751er_int: ( code_integer > int ) > ( int > code_integer ) > set_int > $o ).
thf(func_def_1522,type,
div0_uint32: uint32 > uint32 ).
thf(func_def_1523,type,
mod0_uint32: uint32 > uint32 ).
thf(func_def_1524,type,
set_bits_aux_uint32: ( nat > $o ) > nat > uint32 > uint32 ).
thf(func_def_1525,type,
signed489701013188660438uint32: nat > uint32 > uint32 ).
thf(func_def_1526,type,
rep_uint32: uint32 > word_N3645301735248828278l_num1 ).
thf(func_def_1527,type,
uint32_divmod: uint32 > uint32 > produc827990862158126777uint32 ).
thf(func_def_1528,type,
uint32_sdiv: uint32 > uint32 > uint32 ).
thf(func_def_1529,type,
uint32_set_bit: uint32 > code_integer > $o > uint32 ).
thf(func_def_1530,type,
uint32_shiftl: uint32 > code_integer > uint32 ).
thf(func_def_1531,type,
uint32_shiftr: uint32 > code_integer > uint32 ).
thf(func_def_1532,type,
uint32_sshiftr: uint32 > code_integer > uint32 ).
thf(func_def_1533,type,
uint32_test_bit: uint32 > code_integer > $o ).
thf(func_def_1534,type,
vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
thf(func_def_1535,type,
vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
thf(func_def_1536,type,
vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1537,type,
vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1538,type,
vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
thf(func_def_1539,type,
vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1540,type,
vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
thf(func_def_1541,type,
vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
thf(func_def_1542,type,
vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1543,type,
vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1544,type,
vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
thf(func_def_1545,type,
vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1546,type,
vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
thf(func_def_1547,type,
vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1548,type,
vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
thf(func_def_1549,type,
vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
thf(func_def_1550,type,
vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1551,type,
vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1552,type,
vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
thf(func_def_1553,type,
vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
thf(func_def_1554,type,
vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1555,type,
vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1556,type,
vEBT_V441764108873111860ildupi: nat > nat ).
thf(func_def_1557,type,
vEBT_V9176841429113362141ildupi: nat > int ).
thf(func_def_1558,type,
vEBT_V3352910403632780892pi_rel: nat > nat > $o ).
thf(func_def_1559,type,
vEBT_V2957053500504383685pi_rel: nat > nat > $o ).
thf(func_def_1560,type,
vEBT_VEBT_Tb: nat > int ).
thf(func_def_1561,type,
vEBT_VEBT_Tb2: nat > nat ).
thf(func_def_1562,type,
vEBT_VEBT_Tb_rel: nat > nat > $o ).
thf(func_def_1563,type,
vEBT_VEBT_Tb_rel2: nat > nat > $o ).
thf(func_def_1564,type,
vEBT_VEBT_highi: nat > nat > heap_Time_Heap_nat ).
thf(func_def_1565,type,
vEBT_VEBT_lowi: nat > nat > heap_Time_Heap_nat ).
thf(func_def_1566,type,
vEBT_VEBT_minNulli: vEBT_VEBTi > heap_Time_Heap_o ).
thf(func_def_1567,type,
vEBT_V739175172307565963ildupi: nat > heap_T8145700208782473153_VEBTi ).
thf(func_def_1568,type,
vEBT_V3964819847710782039nserti: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
thf(func_def_1569,type,
vEBT_V854960066525838166emberi: vEBT_VEBT > vEBT_VEBTi > nat > heap_Time_Heap_o ).
thf(func_def_1570,type,
vEBT_Leafi: $o > $o > vEBT_VEBTi ).
thf(func_def_1571,type,
vEBT_Nodei: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > vEBT_VEBTi ).
thf(func_def_1572,type,
vEBT_size_VEBTi: vEBT_VEBTi > nat ).
thf(func_def_1573,type,
vEBT_vebt_assn_raw: vEBT_VEBT > vEBT_VEBTi > assn ).
thf(func_def_1574,type,
vEBT_v8524038756793281170aw_rel: produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ).
thf(func_def_1575,type,
vEBT_vebt_buildupi: nat > heap_T8145700208782473153_VEBTi ).
thf(func_def_1576,type,
vEBT_vebt_inserti: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
thf(func_def_1577,type,
vEBT_vebt_maxti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
thf(func_def_1578,type,
vEBT_vebt_maxti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
thf(func_def_1579,type,
vEBT_vebt_memberi: vEBT_VEBTi > nat > heap_Time_Heap_o ).
thf(func_def_1580,type,
vEBT_vebt_minti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
thf(func_def_1581,type,
vEBT_vebt_minti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
thf(func_def_1582,type,
vEBT_Leaf: $o > $o > vEBT_VEBT ).
thf(func_def_1583,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1584,type,
vEBT_size_VEBT: vEBT_VEBT > nat ).
thf(func_def_1585,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(func_def_1586,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(func_def_1587,type,
vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
thf(func_def_1588,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(func_def_1589,type,
vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
thf(func_def_1590,type,
vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1591,type,
vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
thf(func_def_1592,type,
vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1593,type,
vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
thf(func_def_1594,type,
vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1595,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(func_def_1596,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(func_def_1597,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
thf(func_def_1598,type,
vEBT_v4011308405150292612up_rel: nat > nat > $o ).
thf(func_def_1599,type,
vEBT_V1365221501068881998eletei: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
thf(func_def_1600,type,
vEBT_vebt_deletei: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
thf(func_def_1601,type,
vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
thf(func_def_1602,type,
vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1603,type,
vEBT_V1232361888498592333_e_t_e: vEBT_VEBT > nat > nat ).
thf(func_def_1604,type,
vEBT_V6368547301243506412_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1605,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1606,type,
vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1607,type,
vEBT_VEBT_height: vEBT_VEBT > nat ).
thf(func_def_1608,type,
vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1609,type,
vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1610,type,
vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1611,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1612,type,
vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1613,type,
vEBT_Intf_vebt_assn: nat > set_nat > vEBT_VEBTi > assn ).
thf(func_def_1614,type,
vEBT_L6286945158656146733_VEBTi: set_nat > ( $o > vEBT_VEBTi > assn ) > list_o > list_VEBT_VEBTi > assn ).
thf(func_def_1615,type,
vEBT_L1319876754960170684T_VEBT: set_nat > ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
thf(func_def_1616,type,
vEBT_L3563379889750563018_int_o: set_nat > ( int > $o > assn ) > list_int > list_o > assn ).
thf(func_def_1617,type,
vEBT_L8888932350013902202nt_int: set_nat > ( int > int > assn ) > list_int > list_int > assn ).
thf(func_def_1618,type,
vEBT_L8891422820522952478nt_nat: set_nat > ( int > nat > assn ) > list_int > list_nat > assn ).
thf(func_def_1619,type,
vEBT_L7077748017936769786t_real: set_nat > ( int > real > assn ) > list_int > list_real > assn ).
thf(func_def_1620,type,
vEBT_L114188773329725699_VEBTi: set_nat > ( int > vEBT_VEBTi > assn ) > list_int > list_VEBT_VEBTi > assn ).
thf(func_def_1621,type,
vEBT_L2018189785592951398T_VEBT: set_nat > ( int > vEBT_VEBT > assn ) > list_int > list_VEBT_VEBT > assn ).
thf(func_def_1622,type,
vEBT_L7489483478785760935_VEBTi: set_nat > ( nat > vEBT_VEBTi > assn ) > list_nat > list_VEBT_VEBTi > assn ).
thf(func_def_1623,type,
vEBT_L8511957252848910786T_VEBT: set_nat > ( nat > vEBT_VEBT > assn ) > list_nat > list_VEBT_VEBT > assn ).
thf(func_def_1624,type,
vEBT_L7851252805511451907_VEBTi: set_nat > ( real > vEBT_VEBTi > assn ) > list_real > list_VEBT_VEBTi > assn ).
thf(func_def_1625,type,
vEBT_L3095048238742455910T_VEBT: set_nat > ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
thf(func_def_1626,type,
vEBT_L3328983362619735041EBTi_o: set_nat > ( vEBT_VEBTi > $o > assn ) > list_VEBT_VEBTi > list_o > assn ).
thf(func_def_1627,type,
vEBT_L2806540629473551875Ti_int: set_nat > ( vEBT_VEBTi > int > assn ) > list_VEBT_VEBTi > list_int > assn ).
thf(func_def_1628,type,
vEBT_L2809031099982602151Ti_nat: set_nat > ( vEBT_VEBTi > nat > assn ) > list_VEBT_VEBTi > list_nat > assn ).
thf(func_def_1629,type,
vEBT_L7728200936804140803i_real: set_nat > ( vEBT_VEBTi > real > assn ) > list_VEBT_VEBTi > list_real > assn ).
thf(func_def_1630,type,
vEBT_L886525131989349516_VEBTi: set_nat > ( vEBT_VEBTi > vEBT_VEBTi > assn ) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn ).
thf(func_def_1631,type,
vEBT_L2497118539674116125T_VEBT: set_nat > ( vEBT_VEBTi > vEBT_VEBT > assn ) > list_VEBT_VEBTi > list_VEBT_VEBT > assn ).
thf(func_def_1632,type,
vEBT_L8650695023172932196BT_nat: set_nat > ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
thf(func_def_1633,type,
vEBT_L1528199826722428489_VEBTi: set_nat > ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
thf(func_def_1634,type,
vEBT_L3204528365124325536T_VEBT: set_nat > ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
thf(func_def_1635,type,
vEBT_L4725278957065240257o_real: ( $o > real > assn ) > list_o > list_real > assn ).
thf(func_def_1636,type,
vEBT_L1750719106661372127T_VEBT: ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
thf(func_def_1637,type,
vEBT_L74593716426352029nt_int: ( int > int > assn ) > list_int > list_int > assn ).
thf(func_def_1638,type,
vEBT_L77084186935402305nt_nat: ( int > nat > assn ) > list_int > list_nat > assn ).
thf(func_def_1639,type,
vEBT_L6235239671944049190_VEBTi: ( int > vEBT_VEBTi > assn ) > list_int > list_VEBT_VEBTi > assn ).
thf(func_def_1640,type,
vEBT_L1664421287176695555T_VEBT: ( int > vEBT_VEBT > assn ) > list_int > list_VEBT_VEBT > assn ).
thf(func_def_1641,type,
vEBT_L6102073776069194049t_real: ( nat > real > assn ) > list_nat > list_real > assn ).
thf(func_def_1642,type,
vEBT_L8158188754432654943T_VEBT: ( nat > vEBT_VEBT > assn ) > list_nat > list_VEBT_VEBT > assn ).
thf(func_def_1643,type,
vEBT_L6234343332106409831real_o: ( real > $o > assn ) > list_real > list_o > assn ).
thf(func_def_1644,type,
vEBT_L1930518968523514909l_real: ( real > real > assn ) > list_real > list_real > assn ).
thf(func_def_1645,type,
vEBT_L4595930785310033027T_VEBT: ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
thf(func_def_1646,type,
vEBT_L8927591528087875366Ti_int: ( vEBT_VEBTi > int > assn ) > list_VEBT_VEBTi > list_int > assn ).
thf(func_def_1647,type,
vEBT_L8930081998596925642Ti_nat: ( vEBT_VEBTi > nat > assn ) > list_VEBT_VEBTi > list_nat > assn ).
thf(func_def_1648,type,
vEBT_L1891944875198410415_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi > assn ) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn ).
thf(func_def_1649,type,
vEBT_L7265847600308530106T_VEBT: ( vEBT_VEBTi > vEBT_VEBT > assn ) > list_VEBT_VEBTi > list_VEBT_VEBT > assn ).
thf(func_def_1650,type,
vEBT_L7489408758114837031VEBT_o: ( vEBT_VEBT > $o > assn ) > list_VEBT_VEBT > list_o > assn ).
thf(func_def_1651,type,
vEBT_L8296926524756676353BT_nat: ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
thf(func_def_1652,type,
vEBT_L5781919052683127133T_real: ( vEBT_VEBT > real > assn ) > list_VEBT_VEBT > list_real > assn ).
thf(func_def_1653,type,
vEBT_L6296928887356842470_VEBTi: ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
thf(func_def_1654,type,
vEBT_L1279224858307276611T_VEBT: ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
thf(func_def_1655,type,
vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
thf(func_def_1656,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(func_def_1657,type,
vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1658,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(func_def_1659,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(func_def_1660,type,
vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1661,type,
vEBT_VEBT_add: option_nat > option_nat > option_nat ).
thf(func_def_1662,type,
vEBT_VEBT_greater: option_nat > option_nat > $o ).
thf(func_def_1663,type,
vEBT_VEBT_less: option_nat > option_nat > $o ).
thf(func_def_1664,type,
vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
thf(func_def_1665,type,
vEBT_VEBT_max_in_set: set_nat > nat > $o ).
thf(func_def_1666,type,
vEBT_VEBT_min_in_set: set_nat > nat > $o ).
thf(func_def_1667,type,
vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
thf(func_def_1668,type,
vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
thf(func_def_1669,type,
vEBT_VEBT_power: option_nat > option_nat > option_nat ).
thf(func_def_1670,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(func_def_1671,type,
vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1672,type,
vEBT_vebt_mint: vEBT_VEBT > option_nat ).
thf(func_def_1673,type,
vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1674,type,
vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
thf(func_def_1675,type,
vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
thf(func_def_1676,type,
vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1677,type,
vEBT_V8646137997579335489_i_l_d: nat > nat ).
thf(func_def_1678,type,
vEBT_V8346862874174094_d_u_p: nat > nat ).
thf(func_def_1679,type,
vEBT_V1247956027447740395_p_rel: nat > nat > $o ).
thf(func_def_1680,type,
vEBT_V5144397997797733112_d_rel: nat > nat > $o ).
thf(func_def_1681,type,
vEBT_VEBT_cnt: vEBT_VEBT > real ).
thf(func_def_1682,type,
vEBT_VEBT_cnt2: vEBT_VEBT > nat ).
thf(func_def_1683,type,
vEBT_VEBT_cnt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1684,type,
vEBT_VEBT_cnt_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1685,type,
vEBT_VEBT_space: vEBT_VEBT > nat ).
thf(func_def_1686,type,
vEBT_VEBT_space2: vEBT_VEBT > nat ).
thf(func_def_1687,type,
vEBT_VEBT_space_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1688,type,
vEBT_VEBT_space_rel2: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1689,type,
vEBT_VEBT_vebt_predi: vEBT_VEBT > vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
thf(func_def_1690,type,
vEBT_VEBT_vebt_succi: vEBT_VEBT > vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
thf(func_def_1691,type,
vEBT_vebt_predi: vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
thf(func_def_1692,type,
vEBT_vebt_succi: vEBT_VEBTi > nat > heap_T2636463487746394924on_nat ).
thf(func_def_1693,type,
vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
thf(func_def_1694,type,
vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
thf(func_def_1695,type,
vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1696,type,
vEBT_V6289311342943941716sTrans: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1697,type,
accp_nat: ( nat > nat > $o ) > nat > $o ).
thf(func_def_1698,type,
accp_P1862375125659990705et_nat: ( produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ) > produc2732055786443039994et_nat > $o ).
thf(func_def_1699,type,
accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
thf(func_def_1700,type,
accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_1701,type,
accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
thf(func_def_1702,type,
accp_P7675410724331315407_VEBTi: ( produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ) > produc3625547720036274456_VEBTi > $o ).
thf(func_def_1703,type,
accp_VEBT_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi > $o ) > vEBT_VEBTi > $o ).
thf(func_def_1704,type,
accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
thf(func_def_1705,type,
signed5000768011106662067l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 ).
thf(func_def_1706,type,
member6576561426505652726_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o > $o ).
thf(func_def_1707,type,
member_o: $o > set_o > $o ).
thf(func_def_1708,type,
member_Code_integer: code_integer > set_Code_integer > $o ).
thf(func_def_1709,type,
member_complex: complex > set_complex > $o ).
thf(func_def_1710,type,
member_int: int > set_int > $o ).
thf(func_def_1711,type,
member_list_o: list_o > set_list_o > $o ).
thf(func_def_1712,type,
member_list_nat: list_nat > set_list_nat > $o ).
thf(func_def_1713,type,
member_list_real: list_real > set_list_real > $o ).
thf(func_def_1714,type,
member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
thf(func_def_1715,type,
member_nat: nat > set_nat > $o ).
thf(func_def_1716,type,
member_num: num > set_num > $o ).
thf(func_def_1717,type,
member6124377750444531601et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > $o ).
thf(func_def_1718,type,
member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o ).
thf(func_def_1719,type,
member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o ).
thf(func_def_1720,type,
member6260224972018164377et_nat: produc3658429121746597890et_nat > set_Pr3948176798113811640et_nat > $o ).
thf(func_def_1721,type,
member4489920277610959864_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > $o ).
thf(func_def_1722,type,
member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1723,type,
member216504246829706758nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > $o ).
thf(func_def_1724,type,
member2744130022092475746t_real: produc679980390762269497t_real > set_Pr3538720872664544793t_real > $o ).
thf(func_def_1725,type,
member2056185340421749780T_VEBT: produc1531783533982839933T_VEBT > set_Pr8044002425091019955T_VEBT > $o ).
thf(func_def_1726,type,
member4159035015898711888list_o: produc7102631898165422375list_o > set_Pr6227168374412355847list_o > $o ).
thf(func_def_1727,type,
member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o ).
thf(func_def_1728,type,
member7340969449405702474st_nat: produc1828647624359046049st_nat > set_Pr3451248702717554689st_nat > $o ).
thf(func_def_1729,type,
member6584958104391596930t_real: produc478978216448986841t_real > set_Pr611352295856513593t_real > $o ).
thf(func_def_1730,type,
member2333554998283850498uint32: produc823665806539077721uint32 > set_Pr2258164808687509945uint32 > $o ).
thf(func_def_1731,type,
member4173000155140927252_VEBTi: produc3089554586268799851_VEBTi > set_Pr4797120415438012619_VEBTi > $o ).
thf(func_def_1732,type,
member4439316823752958928T_VEBT: produc9211091688327510695T_VEBT > set_Pr1916528119006554503T_VEBT > $o ).
thf(func_def_1733,type,
member4262671552274231302at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > $o ).
thf(func_def_1734,type,
member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1735,type,
member6341495586645257982et_nat: produc5657529347773406293et_nat > set_Pr3444600963470892981et_nat > $o ).
thf(func_def_1736,type,
member4763271486408492550et_nat: produc6830853553727218525et_nat > set_Pr7928877670098842301et_nat > $o ).
thf(func_def_1737,type,
member8566619992076573584nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > $o ).
thf(func_def_1738,type,
member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1739,type,
member4724532482705224080uint32: produc8822557026176459367uint32 > set_Pr3773659940955823943uint32 > $o ).
thf(func_def_1740,type,
member1627681773268152802al_int: produc8786904178792722361al_int > set_Pr1019928272762051225al_int > $o ).
thf(func_def_1741,type,
member7849222048561428706l_real: produc2422161461964618553l_real > set_Pr6218003697084177305l_real > $o ).
thf(func_def_1742,type,
member7262085504369356948T_VEBT: produc3757001726724277373T_VEBT > set_Pr6019664923565264691T_VEBT > $o ).
thf(func_def_1743,type,
member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
thf(func_def_1744,type,
member8027108493173000802uint32: produc827990862158126777uint32 > set_Pr1773385645901665561uint32 > $o ).
thf(func_def_1745,type,
member660371905731732212_VEBTi: produc3777764054643897931_VEBTi > set_Pr2227491710730465451_VEBTi > $o ).
thf(func_def_1746,type,
member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o ).
thf(func_def_1747,type,
member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o ).
thf(func_def_1748,type,
member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
thf(func_def_1749,type,
member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o ).
thf(func_def_1750,type,
member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
thf(func_def_1751,type,
member_rat: rat > set_rat > $o ).
thf(func_def_1752,type,
member_real: real > set_real > $o ).
thf(func_def_1753,type,
member_set_o: set_o > set_set_o > $o ).
thf(func_def_1754,type,
member_set_int: set_int > set_set_int > $o ).
thf(func_def_1755,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_1756,type,
member_set_real: set_real > set_set_real > $o ).
thf(func_def_1757,type,
member_set_set_nat: set_set_nat > set_set_set_nat > $o ).
thf(func_def_1758,type,
member_set_VEBT_VEBT: set_VEBT_VEBT > set_set_VEBT_VEBT > $o ).
thf(func_def_1759,type,
member_literal: literal > set_literal > $o ).
thf(func_def_1760,type,
member_uint32: uint32 > set_uint32 > $o ).
thf(func_def_1761,type,
member_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > $o ).
thf(func_def_1762,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(func_def_1763,type,
a: heap_e7401611519738050253t_unit ).
thf(func_def_1764,type,
b: set_nat ).
thf(func_def_1765,type,
n: nat ).
thf(func_def_1766,type,
r: vEBT_VEBTi ).
thf(func_def_1767,type,
s: set_nat ).
thf(func_def_1768,type,
t: vEBT_VEBT ).
thf(func_def_1769,type,
x: nat ).
thf(func_def_1770,type,
xa: nat ).
thf(func_def_1789,type,
sP0: option_nat > vEBT_VEBT > $o ).
thf(func_def_1790,type,
sP1: nat > nat > nat > nat > list_VEBT_VEBT > $o ).
thf(func_def_1791,type,
sP2: vEBT_VEBT > $o > $o ).
thf(func_def_1792,type,
sP3: vEBT_VEBT > $o > $o ).
thf(func_def_1793,type,
sP4: vEBT_VEBT > nat > $o ).
thf(func_def_1794,type,
sP5: nat > vEBT_VEBT > $o ).
thf(func_def_1795,type,
sP6: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_1796,type,
sP7: nat > nat > list_VEBT_VEBT > nat > nat > $o ).
thf(func_def_1797,type,
sP8: nat > list_VEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1798,type,
sP9: list_VEBT_VEBT > nat > nat > nat > nat > $o ).
thf(func_def_1799,type,
sP10: vEBT_VEBT > list_VEBT_VEBT > nat > $o ).
thf(func_def_1800,type,
sP11: nat > vEBT_VEBT > $o ).
thf(func_def_1801,type,
sP12: nat > vEBT_VEBT > $o ).
thf(func_def_1802,type,
sP13: vEBT_VEBT > nat > $o ).
thf(func_def_1803,type,
sP14: nat > vEBT_VEBT > $o ).
thf(func_def_1804,type,
sP15: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_1805,type,
sP16: nat > nat > nat > $o ).
thf(func_def_1806,type,
sP17: nat > nat > nat > $o ).
thf(func_def_1807,type,
sP18: nat > nat > nat > $o ).
thf(func_def_1808,type,
sP19: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_1809,type,
sP20: $o > $o > nat > $o ).
thf(func_def_1810,type,
sP21: $o > $o > $o > nat > $o ).
thf(func_def_1811,type,
sP22: nat > nat > list_VEBT_VEBT > nat > nat > $o ).
thf(func_def_1812,type,
sP23: $o > nat > nat > list_VEBT_VEBT > nat > nat > $o ).
thf(func_def_1813,type,
sP24: $o > vEBT_VEBT > $o ).
thf(func_def_1814,type,
sP25: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1815,type,
sP26: nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1816,type,
sP27: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1817,type,
sP28: set_nat > ( set_nat > $o ) > $o ).
thf(func_def_1818,type,
sP29: nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1819,type,
sP30: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_1820,type,
sP31: nat > nat > set_nat > set_nat > $o ).
thf(func_def_1821,type,
sP32: nat > nat > set_nat > set_nat > $o ).
thf(func_def_1822,type,
sP33: nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1823,type,
sP34: vEBT_VEBT > list_VEBT_VEBT > nat > $o ).
thf(func_def_1824,type,
sP35: vEBT_VEBT > option_nat > $o ).
thf(func_def_1825,type,
sP36: $o > $o > nat > $o ).
thf(func_def_1826,type,
sK37: nat > nat > nat ).
thf(func_def_1827,type,
sK38: ( nat > $o ) > nat > nat ).
thf(func_def_1828,type,
sK39: ( nat > $o ) > nat > nat ).
thf(func_def_1829,type,
sK40: set_nat > set_nat > nat ).
thf(func_def_1830,type,
sK41: set_nat > set_nat > nat ).
thf(func_def_1831,type,
sK42: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_1832,type,
sK43: produc3925858234332021118et_nat > produc3658429121746597890et_nat ).
thf(func_def_1833,type,
sK44: vEBT_VEBT > nat ).
thf(func_def_1834,type,
sK45: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1835,type,
sK46: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1836,type,
sK47: ( nat > $o ) > nat ).
thf(func_def_1837,type,
sK48: ( nat > $o ) > nat > nat ).
thf(func_def_1838,type,
sK49: ( nat > $o ) > nat > nat ).
thf(func_def_1839,type,
sK50: nat > nat > nat ).
thf(func_def_1840,type,
sK51: nat > nat ).
thf(func_def_1841,type,
sK52: ( produc2732055786443039994et_nat > $o ) > set_nat ).
thf(func_def_1842,type,
sK53: ( produc2732055786443039994et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_1843,type,
sK54: ( produc2732055786443039994et_nat > $o ) > heap_e7401611519738050253t_unit ).
thf(func_def_1844,type,
sK55: ( produc2732055786443039994et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_1845,type,
sK56: ( nat > $o ) > nat > nat ).
thf(func_def_1846,type,
sK57: ( nat > $o ) > nat > nat ).
thf(func_def_1847,type,
sK58: vEBT_VEBT > $o ).
thf(func_def_1848,type,
sK59: vEBT_VEBT > $o ).
thf(func_def_1849,type,
sK60: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1850,type,
sK61: vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_1851,type,
sK62: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1852,type,
sK63: vEBT_VEBT > nat ).
thf(func_def_1853,type,
sK64: ( nat > $o ) > nat ).
thf(func_def_1854,type,
sK65: nat > nat ).
thf(func_def_1855,type,
sK66: ( nat > $o ) > set_nat > nat ).
thf(func_def_1856,type,
sK67: ( nat > $o ) > nat ).
thf(func_def_1857,type,
sK68: ( set_nat > $o ) > nat ).
thf(func_def_1858,type,
sK69: ( set_nat > $o ) > set_nat ).
thf(func_def_1859,type,
sK70: ( set_nat > $o ) > set_nat ).
thf(func_def_1860,type,
sK71: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_1861,type,
sK72: ( nat > $o ) > nat > nat > nat ).
thf(func_def_1862,type,
sK73: nat > nat ).
thf(func_def_1863,type,
sK74: set_nat > set_nat ).
thf(func_def_1864,type,
sK75: set_nat > nat ).
thf(func_def_1865,type,
sK76: nat > set_nat > nat ).
thf(func_def_1866,type,
sK77: set_nat > nat > nat ).
thf(func_def_1867,type,
sK78: nat > nat ).
thf(func_def_1868,type,
sK79: ( nat > $o ) > nat ).
thf(func_def_1869,type,
sK80: ( nat > nat ) > nat ).
thf(func_def_1870,type,
sK81: produc3658429121746597890et_nat > set_nat ).
thf(func_def_1871,type,
sK82: produc3658429121746597890et_nat > heap_e7401611519738050253t_unit ).
thf(func_def_1872,type,
sK83: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_1873,type,
sK84: list_VEBT_VEBT > nat ).
thf(func_def_1874,type,
sK85: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1875,type,
sK86: vEBT_VEBT > nat ).
thf(func_def_1876,type,
sK87: ( nat > $o ) > nat ).
thf(func_def_1877,type,
sK88: set_nat > nat ).
thf(func_def_1878,type,
sK89: ( nat > nat > $o ) > nat ).
thf(func_def_1879,type,
sK90: ( nat > nat > $o ) > nat ).
thf(func_def_1880,type,
sK91: ( nat > nat > $o ) > nat ).
thf(func_def_1881,type,
sK92: ( nat > nat > $o ) > nat ).
thf(func_def_1882,type,
sK93: ( nat > nat > $o ) > nat ).
thf(func_def_1883,type,
sK94: ( nat > $o ) > nat ).
thf(func_def_1884,type,
sK95: option_nat > vEBT_VEBT > $o ).
thf(func_def_1885,type,
sK96: option_nat > vEBT_VEBT > $o ).
thf(func_def_1886,type,
sK97: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1887,type,
sK98: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1888,type,
sK99: vEBT_VEBT > nat ).
thf(func_def_1889,type,
sK100: vEBT_VEBT > option_nat > nat ).
thf(func_def_1890,type,
sK101: vEBT_VEBT > option_nat > nat ).
thf(func_def_1891,type,
sK102: vEBT_VEBT > option_nat > nat ).
thf(func_def_1892,type,
sK103: vEBT_VEBT > option_nat > vEBT_VEBT ).
thf(func_def_1893,type,
sK104: vEBT_VEBT > option_nat > list_VEBT_VEBT ).
thf(func_def_1894,type,
sK105: vEBT_VEBT > nat ).
thf(func_def_1895,type,
sK106: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1896,type,
sK107: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1897,type,
sK108: vEBT_VEBT > $o ).
thf(func_def_1898,type,
sK109: vEBT_VEBT > $o ).
thf(func_def_1899,type,
sK110: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1900,type,
sK111: vEBT_VEBT > nat ).
thf(func_def_1901,type,
sK112: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_1902,type,
sK113: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1903,type,
sK114: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_1904,type,
sK115: vEBT_VEBT > nat > $o ).
thf(func_def_1905,type,
sK116: vEBT_VEBT > nat > $o ).
thf(func_def_1906,type,
sK117: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1907,type,
sK118: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1908,type,
sK119: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_1909,type,
sK120: nat > vEBT_VEBT > nat ).
thf(func_def_1910,type,
sK121: nat > vEBT_VEBT > nat ).
thf(func_def_1911,type,
sK122: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1912,type,
sK123: nat > vEBT_VEBT > nat ).
thf(func_def_1913,type,
sK124: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1914,type,
sK125: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_1915,type,
sK126: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1916,type,
sK127: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1917,type,
sK128: vEBT_VEBT > nat ).
thf(func_def_1918,type,
sK129: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1919,type,
sK130: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1920,type,
sK131: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_1921,type,
sK132: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_1922,type,
sK133: produc2732055786443039994et_nat > produc3658429121746597890et_nat ).
thf(func_def_1923,type,
sK134: nat > nat ).
thf(func_def_1924,type,
sK135: nat > vEBT_VEBT > nat ).
thf(func_def_1925,type,
sK136: nat > vEBT_VEBT > nat ).
thf(func_def_1926,type,
sK137: nat > vEBT_VEBT > nat ).
thf(func_def_1927,type,
sK138: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1928,type,
sK139: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1929,type,
sK140: vEBT_VEBT > nat > $o ).
thf(func_def_1930,type,
sK141: vEBT_VEBT > nat > $o ).
thf(func_def_1931,type,
sK142: set_nat > nat ).
thf(func_def_1932,type,
sK143: nat > set_nat > nat ).
thf(func_def_1933,type,
sK144: option4927543243414619207at_nat > nat ).
thf(func_def_1934,type,
sK145: option4927543243414619207at_nat > nat ).
thf(func_def_1935,type,
sK146: set_nat > nat > nat ).
thf(func_def_1936,type,
sK147: nat > ( nat > $o ) > nat ).
thf(func_def_1937,type,
sK148: nat > ( nat > $o ) > nat ).
thf(func_def_1938,type,
sK149: ( nat > nat ) > nat ).
thf(func_def_1939,type,
sK150: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_1940,type,
sK151: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_1941,type,
sK152: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_1942,type,
sK153: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_1943,type,
sK154: list_VEBT_VEBT > nat ).
thf(func_def_1944,type,
sK155: vEBT_VEBT > nat ).
thf(func_def_1945,type,
sK156: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_1946,type,
sK157: assn > produc3658429121746597890et_nat ).
thf(func_def_1947,type,
sK158: assn > produc3658429121746597890et_nat ).
thf(func_def_1948,type,
sK159: ( nat > rat ) > ( set_nat > $o ) > set_nat ).
thf(func_def_1949,type,
sK160: ( nat > rat ) > ( set_nat > $o ) > nat ).
thf(func_def_1950,type,
sK161: ( nat > $o ) > nat > nat > nat ).
thf(func_def_1951,type,
sK162: assn > assn > produc3658429121746597890et_nat ).
thf(func_def_1952,type,
sK163: assn > assn > produc3658429121746597890et_nat ).
thf(func_def_1953,type,
sK164: ( nat > nat > $o ) > nat ).
thf(func_def_1954,type,
sK165: ( nat > nat > $o ) > nat ).
thf(func_def_1955,type,
sK166: ( nat > nat > $o ) > nat ).
thf(func_def_1956,type,
sK167: ( nat > nat > $o ) > nat ).
thf(func_def_1957,type,
sK168: ( nat > $o ) > nat > nat ).
thf(func_def_1958,type,
sK169: nat > set_nat > nat ).
thf(func_def_1959,type,
sK170: nat > nat ).
thf(func_def_1960,type,
sK171: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1961,type,
sK172: vEBT_VEBT > nat > option4927543243414619207at_nat ).
thf(func_def_1962,type,
sK173: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_1963,type,
sK174: ( nat > nat > $o ) > nat ).
thf(func_def_1964,type,
sK175: ( nat > nat > $o ) > nat ).
thf(func_def_1965,type,
sK176: ( nat > nat > $o ) > nat ).
thf(func_def_1966,type,
sK177: ( nat > nat > $o ) > nat ).
thf(func_def_1967,type,
sK178: ( nat > nat ) > nat ).
thf(func_def_1968,type,
sK179: ( nat > $o ) > nat ).
thf(func_def_1969,type,
sK180: ( nat > $o ) > nat ).
thf(func_def_1970,type,
sK181: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1971,type,
sK182: nat > vEBT_VEBT > nat ).
thf(func_def_1972,type,
sK183: nat > vEBT_VEBT > nat ).
thf(func_def_1973,type,
sK184: nat > vEBT_VEBT > nat ).
thf(func_def_1974,type,
sK185: nat > vEBT_VEBT > nat ).
thf(func_def_1975,type,
sK186: nat > vEBT_VEBT > nat ).
thf(func_def_1976,type,
sK187: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1977,type,
sK188: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_1978,type,
sK189: vEBT_VEBT > nat > nat ).
thf(func_def_1979,type,
sK190: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1980,type,
sK191: vEBT_VEBT > nat > nat ).
thf(func_def_1981,type,
sK192: vEBT_VEBT > nat > nat ).
thf(func_def_1982,type,
sK193: nat > vEBT_VEBT > nat ).
thf(func_def_1983,type,
sK194: nat > vEBT_VEBT > nat ).
thf(func_def_1984,type,
sK195: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1985,type,
sK196: nat > vEBT_VEBT > nat ).
thf(func_def_1986,type,
sK197: nat > vEBT_VEBT > nat ).
thf(func_def_1987,type,
sK198: nat > vEBT_VEBT > nat ).
thf(func_def_1988,type,
sK199: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1989,type,
sK200: nat > vEBT_VEBT > nat ).
thf(func_def_1990,type,
sK201: nat > vEBT_VEBT > nat ).
thf(func_def_1991,type,
sK202: nat > vEBT_VEBT > nat ).
thf(func_def_1992,type,
sK203: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1993,type,
sK204: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1994,type,
sK205: nat > list_VEBT_VEBT > nat ).
thf(func_def_1995,type,
sK206: nat > list_VEBT_VEBT > nat ).
thf(func_def_1996,type,
sK207: vEBT_VEBT > $o ).
thf(func_def_1997,type,
sK208: vEBT_VEBT > $o ).
thf(func_def_1998,type,
sK209: ( nat > $o ) > nat ).
thf(func_def_1999,type,
sK210: ( nat > nat ) > nat ).
thf(func_def_2000,type,
sK211: ( nat > nat ) > nat ).
thf(func_def_2001,type,
sK212: nat > set_nat > nat ).
thf(func_def_2002,type,
sK213: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2003,type,
sK214: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2004,type,
sK215: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2005,type,
sK216: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2006,type,
sK217: ( nat > $o ) > nat > nat > nat ).
thf(func_def_2007,type,
sK218: nat > ( nat > $o ) > nat > nat ).
thf(func_def_2008,type,
sK219: ( nat > $o ) > nat ).
thf(func_def_2009,type,
sK220: ( set_nat > $o ) > nat ).
thf(func_def_2010,type,
sK221: ( set_nat > $o ) > set_nat ).
thf(func_def_2011,type,
sK222: ( set_nat > $o ) > nat ).
thf(func_def_2012,type,
sK223: vEBT_VEBT > $o ).
thf(func_def_2013,type,
sK224: vEBT_VEBT > $o ).
thf(func_def_2014,type,
sK225: assn > $o > produc3658429121746597890et_nat ).
thf(func_def_2015,type,
sK226: set_nat > nat > nat ).
thf(func_def_2016,type,
sK227: nat > vEBT_VEBT > nat ).
thf(func_def_2017,type,
sK228: produc3925858234332021118et_nat > set_nat ).
thf(func_def_2018,type,
sK229: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2019,type,
sK230: produc3925858234332021118et_nat > heap_e7401611519738050253t_unit ).
thf(func_def_2020,type,
sK231: nat > nat ).
thf(func_def_2021,type,
sK232: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2022,type,
sK233: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2023,type,
sK234: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2024,type,
sK235: vEBT_VEBT > $o > nat > $o ).
thf(func_def_2025,type,
sK236: vEBT_VEBT > $o > nat > $o ).
thf(func_def_2026,type,
sK237: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_2027,type,
sK238: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2028,type,
sK239: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2029,type,
sK240: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_2030,type,
sK241: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2031,type,
sK242: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2032,type,
sK243: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2033,type,
sK244: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2034,type,
sK245: vEBT_VEBT > nat ).
thf(func_def_2035,type,
sK246: vEBT_VEBT > nat > $o > nat ).
thf(func_def_2036,type,
sK247: vEBT_VEBT > nat > $o > nat ).
thf(func_def_2037,type,
sK248: vEBT_VEBT > nat > $o > list_VEBT_VEBT ).
thf(func_def_2038,type,
sK249: vEBT_VEBT > nat > $o > nat ).
thf(func_def_2039,type,
sK250: vEBT_VEBT > nat > $o > vEBT_VEBT ).
thf(func_def_2040,type,
sK251: nat > nat > nat ).
thf(func_def_2041,type,
sK252: ( nat > $o ) > nat > nat ).
thf(func_def_2042,type,
sK253: set_nat > nat > nat ).
thf(func_def_2043,type,
sK254: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2044,type,
sK255: produc2732055786443039994et_nat > produc3925858234332021118et_nat ).
thf(func_def_2045,type,
sK256: ( nat > $o ) > nat ).
thf(func_def_2046,type,
sK257: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2047,type,
sK258: produc3925858234332021118et_nat > produc3658429121746597890et_nat ).
thf(func_def_2048,type,
sK259: ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_2049,type,
sK260: ( nat > nat > $o ) > set_nat > set_nat > nat ).
thf(func_def_2050,type,
sK261: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2051,type,
sK262: vEBT_VEBT > nat ).
thf(func_def_2052,type,
sK263: vEBT_VEBT > nat ).
thf(func_def_2053,type,
sK264: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2054,type,
sK265: vEBT_VEBT > nat ).
thf(func_def_2055,type,
sK266: vEBT_VEBT > $o ).
thf(func_def_2056,type,
sK267: vEBT_VEBT > $o ).
thf(func_def_2057,type,
sK268: vEBT_VEBT > nat ).
thf(func_def_2058,type,
sK269: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2059,type,
sK270: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2060,type,
sK271: nat > set_nat > nat ).
thf(func_def_2061,type,
sK272: assn > $o > produc3658429121746597890et_nat ).
thf(func_def_2062,type,
sK273: list_VEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_2063,type,
sK274: list_VEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_2064,type,
sK275: nat > list_VEBT_VEBT > nat > nat > nat > nat ).
thf(func_def_2065,type,
sK276: nat > list_VEBT_VEBT > nat > nat > nat > nat ).
thf(func_def_2066,type,
sK277: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2067,type,
sK278: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_2068,type,
sK279: list_VEBT_VEBT > nat ).
thf(func_def_2069,type,
sK280: ( nat > nat > $o ) > nat ).
thf(func_def_2070,type,
sK281: ( nat > nat > $o ) > nat ).
thf(func_def_2071,type,
sK282: ( nat > nat > $o ) > nat ).
thf(func_def_2072,type,
sK283: ( nat > nat > $o ) > nat ).
thf(func_def_2073,type,
sK284: ( nat > nat > $o ) > nat ).
thf(func_def_2074,type,
sK285: ( produc2732055786443039994et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_2075,type,
sK286: ( produc2732055786443039994et_nat > $o ) > produc3658429121746597890et_nat ).
thf(func_def_2076,type,
sK287: ( produc2732055786443039994et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_2077,type,
sK288: ( produc3925858234332021118et_nat > $o ) > heap_e7401611519738050253t_unit ).
thf(func_def_2078,type,
sK289: ( produc3925858234332021118et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_2079,type,
sK290: ( produc3925858234332021118et_nat > $o ) > set_nat ).
thf(func_def_2080,type,
sK291: ( nat > nat ) > nat ).
thf(func_def_2081,type,
sK292: nat > nat ).
thf(func_def_2082,type,
sK293: vEBT_VEBT > nat ).
thf(func_def_2083,type,
sK294: produc2732055786443039994et_nat > produc3925858234332021118et_nat ).
thf(func_def_2084,type,
sK295: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2085,type,
sK296: vEBT_VEBT > $o ).
thf(func_def_2086,type,
sK297: vEBT_VEBT > $o ).
thf(func_def_2087,type,
sK298: nat > nat ).
thf(func_def_2088,type,
sK299: ( nat > $o ) > nat ).
thf(func_def_2089,type,
sK300: ( set_nat > $o ) > set_nat ).
thf(func_def_2090,type,
sK301: ( nat > nat > $o ) > nat ).
thf(func_def_2091,type,
sK302: ( nat > nat > $o ) > nat ).
thf(func_def_2092,type,
sK303: ( nat > nat > $o ) > nat ).
thf(func_def_2093,type,
sK304: ( nat > nat > $o ) > nat ).
thf(func_def_2094,type,
sK305: set_nat > ( set_nat > $o ) > set_nat ).
thf(func_def_2095,type,
sK306: set_nat > ( set_nat > $o ) > set_nat ).
thf(func_def_2096,type,
sK307: set_nat > nat ).
thf(func_def_2097,type,
sK308: ( nat > $o ) > nat ).
thf(func_def_2098,type,
sK309: ( nat > nat ) > nat ).
thf(func_def_2099,type,
sK310: ( nat > nat ) > nat ).
thf(func_def_2100,type,
sK311: product_prod_nat_nat > nat ).
thf(func_def_2101,type,
sK312: product_prod_nat_nat > nat ).
thf(func_def_2102,type,
sK313: nat > nat > nat ).
thf(func_def_2103,type,
sK314: nat > ( nat > $o ) > nat ).
thf(func_def_2104,type,
sK315: nat > ( nat > $o ) > nat ).
thf(func_def_2105,type,
sK316: ( produc3925858234332021118et_nat > $o ) > produc3658429121746597890et_nat ).
thf(func_def_2106,type,
sK317: ( produc3925858234332021118et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_2107,type,
sK318: nat > nat ).
thf(func_def_2108,type,
sK319: nat > nat > nat ).
thf(func_def_2109,type,
sK320: produc2732055786443039994et_nat > heap_e7401611519738050253t_unit ).
thf(func_def_2110,type,
sK321: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2111,type,
sK322: produc2732055786443039994et_nat > set_nat ).
thf(func_def_2112,type,
sK323: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2113,type,
sK324: nat > nat ).
thf(func_def_2114,type,
sK325: vEBT_VEBT > nat ).
thf(func_def_2115,type,
sK326: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2116,type,
sK327: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2117,type,
sK328: vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_2118,type,
sK329: vEBT_VEBT > $o ).
thf(func_def_2119,type,
sK330: vEBT_VEBT > $o ).
thf(func_def_2120,type,
sK331: ( set_nat > $o ) > nat ).
thf(func_def_2121,type,
sK332: ( set_nat > $o ) > set_nat ).
thf(func_def_2122,type,
sK333: nat > set_nat > set_nat ).
thf(func_def_2123,type,
sK334: nat > set_nat > nat ).
thf(func_def_2124,type,
sK335: nat > vEBT_VEBT > nat ).
thf(func_def_2125,type,
sK336: ( nat > $o ) > ( nat > $o ) > set_nat > nat ).
thf(func_def_2126,type,
sK337: ( nat > $o ) > nat ).
thf(func_def_2127,type,
sK338: ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2128,type,
sK339: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2129,type,
sK340: nat > ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2130,type,
sK341: nat > nat > set_nat > set_nat > set_nat ).
thf(func_def_2131,type,
sK342: set_nat > nat > nat ).
thf(func_def_2132,type,
sK343: nat > nat ).
thf(func_def_2133,type,
sK344: nat > nat ).
thf(func_def_2134,type,
sK345: vEBT_VEBT > $o ).
thf(func_def_2135,type,
sK346: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2136,type,
sK347: vEBT_VEBT > nat ).
thf(func_def_2137,type,
sK348: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2138,type,
sK349: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_2139,type,
sK350: vEBT_VEBT > $o ).
thf(func_def_2140,type,
sK351: nat > nat ).
thf(func_def_2141,type,
sK352: set_int > ( nat > int > $o ) > set_nat > int ).
thf(func_def_2142,type,
sK353: set_int > ( nat > int > $o ) > set_nat > nat ).
thf(func_def_2143,type,
sK354: product_prod_nat_nat > nat ).
thf(func_def_2144,type,
sK355: product_prod_nat_nat > nat ).
thf(func_def_2145,type,
sK356: ( nat > $o ) > set_nat > nat ).
thf(func_def_2146,type,
sK357: ( nat > nat ) > nat ).
thf(func_def_2147,type,
sK358: nat > set_nat > nat ).
thf(func_def_2148,type,
sK359: nat > nat ).
thf(func_def_2149,type,
sK360: set_nat > nat ).
thf(func_def_2150,type,
sK361: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2151,type,
sK362: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_2152,type,
sK363: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2153,type,
sK364: vEBT_VEBT > nat ).
thf(func_def_2154,type,
sK365: vEBT_VEBT > $o ).
thf(func_def_2155,type,
sK366: vEBT_VEBT > $o ).
thf(func_def_2156,type,
sK367: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2157,type,
sK368: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2158,type,
sK369: vEBT_VEBT > nat ).
thf(func_def_2159,type,
sK370: ( produc2732055786443039994et_nat > $o ) > produc3925858234332021118et_nat ).
thf(func_def_2160,type,
sK371: ( produc2732055786443039994et_nat > $o ) > produc3658429121746597890et_nat > $o ).
thf(func_def_2161,type,
sK372: ( set_nat > $o ) > nat ).
thf(func_def_2162,type,
sK373: ( set_nat > $o ) > set_nat ).
thf(func_def_2163,type,
sK374: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_2164,type,
sK375: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_2165,type,
sK376: set_nat > nat > nat ).
thf(func_def_2166,type,
sK377: nat > nat ).
thf(func_def_2167,type,
sK378: nat > set_nat > set_nat ).
thf(func_def_2168,type,
sK379: vEBT_VEBT > list_VEBT_VEBT > nat > nat ).
thf(func_def_2169,type,
sK380: vEBT_VEBT > list_VEBT_VEBT > nat > nat ).
thf(func_def_2170,type,
sK381: nat > list_VEBT_VEBT > nat > nat > nat > nat ).
thf(func_def_2171,type,
sK382: nat > list_VEBT_VEBT > nat > nat > nat > nat ).
thf(func_def_2172,type,
sK383: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_2173,type,
sK384: list_VEBT_VEBT > nat ).
thf(func_def_2174,type,
sK385: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_2175,type,
sK386: ( nat > $o ) > nat > nat ).
thf(func_def_2176,type,
sK387: ( nat > $o ) > nat ).
thf(func_def_2177,type,
sK388: nat > ( nat > $o ) > nat ).
thf(func_def_2178,type,
sK389: assn > assn > produc3658429121746597890et_nat ).
thf(func_def_2179,type,
sK390: nat > ( nat > $o ) > nat ).
thf(func_def_2180,type,
sK391: nat > ( nat > $o ) > nat ).
thf(func_def_2181,type,
sK392: nat > nat ).
thf(func_def_2182,type,
sK393: set_nat > nat > nat ).
thf(func_def_2183,type,
sK394: nat > set_nat > nat ).
thf(func_def_2184,type,
sK395: nat > nat ).
thf(func_def_2185,type,
sK396: nat ).
thf(func_def_2186,type,
sK397: nat ).
thf(func_def_2187,type,
sK398: nat > nat ).
thf(func_def_2188,type,
sK399: vEBT_VEBT > $o ).
thf(func_def_2189,type,
sK400: vEBT_VEBT > $o ).
thf(func_def_2190,type,
sK401: ( nat > $o ) > nat > nat ).
thf(func_def_2191,type,
sK402: nat > set_nat > nat ).
thf(func_def_2192,type,
sK403: ( nat > $o ) > nat ).
thf(func_def_2193,type,
sK404: ( nat > $o ) > nat > nat ).
thf(func_def_2194,type,
sK405: set_nat > nat > nat ).
thf(func_def_2195,type,
sK406: vEBT_VEBT > option_nat > $o ).
thf(func_def_2196,type,
sK407: vEBT_VEBT > option_nat > $o ).
thf(func_def_2197,type,
sK408: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2198,type,
sK409: vEBT_VEBT > nat ).
thf(func_def_2199,type,
sK410: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2200,type,
sK411: vEBT_VEBT > option_nat > nat ).
thf(func_def_2201,type,
sK412: vEBT_VEBT > option_nat > nat ).
thf(func_def_2202,type,
sK413: vEBT_VEBT > option_nat > list_VEBT_VEBT ).
thf(func_def_2203,type,
sK414: vEBT_VEBT > option_nat > nat ).
thf(func_def_2204,type,
sK415: vEBT_VEBT > option_nat > vEBT_VEBT ).
thf(func_def_2205,type,
sK416: nat > nat ).
thf(func_def_2206,type,
sK417: set_nat > nat > nat ).
thf(func_def_2207,type,
sK418: ( set_nat > $o ) > nat ).
thf(func_def_2208,type,
sK419: ( set_nat > $o ) > set_nat ).
thf(func_def_2209,type,
sK420: ( nat > $o ) > nat ).
thf(func_def_2210,type,
sK421: ( set_nat > $o ) > nat ).
thf(func_def_2211,type,
sK422: ( set_nat > $o ) > set_nat ).
thf(func_def_2212,type,
sK423: nat > ( nat > $o ) > nat ).
thf(func_def_2213,type,
sK424: nat > ( nat > $o ) > nat ).
thf(func_def_2214,type,
sK425: nat > vEBT_VEBT > nat ).
thf(func_def_2215,type,
sK426: nat > ( nat > $o ) > nat ).
thf(func_def_2216,type,
sK427: nat > ( nat > $o ) > nat ).
thf(func_def_2217,type,
sK428: ( nat > $o ) > nat ).
thf(func_def_2218,type,
sK429: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2219,type,
sK430: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o ).
thf(func_def_2220,type,
sK431: produc2732055786443039994et_nat > heap_e7401611519738050253t_unit ).
thf(func_def_2221,type,
sK432: produc2732055786443039994et_nat > set_nat ).
thf(func_def_2222,type,
sK433: nat > nat > nat ).
thf(func_def_2224,type,
ph435:
!>[X0: $tType] : X0 ).
thf(f28893,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28804,f28892]) ).
thf(f28892,plain,
spl434_3,
inference(avatar_split_clause,[status(thm)],[f28891,f28696]) ).
thf(f28696,definition,
( spl434_3
<=> ! [X0: nat] :
( ( vEBT_invar_vebt @ t @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl434_3])],[avatar_definition]) ).
thf(f28891,plain,
! [X0: nat] :
( ( vEBT_invar_vebt @ t @ X0 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f28890,f25951]) ).
thf(f25951,plain,
x != xa,
inference(cnf_transformation,[status(thm)],[f24225]) ).
thf(f24225,plain,
x != xa,
inference(flattening,[status(thm)],[f9151]) ).
thf(f9151,negated_conjecture,
x != xa,
inference(negated_conjecture,[status(cth)],[f9150]) ).
thf(f9150,conjecture,
x = xa,
file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_5) ).
thf(f28890,plain,
! [X0: nat] :
( ( x = xa )
| ( ( vEBT_invar_vebt @ t @ X0 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f28888,f28677]) ).
thf(f28677,plain,
( ( vEBT_V8194947554948674370ptions @ t @ xa )
= $true ),
inference(superposition,[status(thm)],[f26940,f28664]) ).
thf(f28664,plain,
( ( member_nat @ xa @ ( collect_nat @ ( vEBT_V8194947554948674370ptions @ t ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27502]) ).
thf(f27502,plain,
( ( member_nat @ xa
@ ( ^ [Y0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Y0 ) )
@ t ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f26533,f27027]) ).
thf(f27027,plain,
( vEBT_set_vebt
= ( ^ [Y0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23040]) ).
thf(f23040,plain,
( vEBT_set_vebt
= ( ^ [Y0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f23039]) ).
thf(f23039,plain,
( ( ^ [X0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ X0 ) ) )
= vEBT_set_vebt ),
inference(rectify,[status(thm)],[f6534]) ).
thf(f6534,axiom,
( ( ^ [X117: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ X117 ) ) )
= vEBT_set_vebt ),
file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',fact_6533_set__vebt__def) ).
thf(f26533,plain,
( ( member_nat @ xa @ ( vEBT_set_vebt @ t ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f19631]) ).
thf(f19631,plain,
( ( member_nat @ xa @ ( vEBT_set_vebt @ t ) )
= $true ),
inference(fool_elimination,[status(thm)],[f19630]) ).
thf(f19630,plain,
member_nat @ xa @ ( vEBT_set_vebt @ t ),
inference(rectify,[status(thm)],[f9148]) ).
thf(f9148,axiom,
member_nat @ xa @ ( vEBT_set_vebt @ t ),
file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_3) ).
thf(f26940,plain,
! [X0: nat,X1: nat > $o] :
( ( X1 @ X0 )
= ( member_nat @ X0 @ ( collect_nat @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f24248]) ).
thf(f24248,plain,
! [X0: nat,X1: nat > $o] :
( ( X1 @ X0 )
= ( member_nat @ X0 @ ( collect_nat @ X1 ) ) ),
inference(rectify,[status(thm)],[f61]) ).
thf(f61,axiom,
! [X12: nat,X21: nat > $o] :
( ( member_nat @ X12 @ ( collect_nat @ X21 ) )
= ( X21 @ X12 ) ),
file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',fact_60_mem__Collect__eq) ).
thf(f28888,plain,
! [X0: nat] :
( ( ( vEBT_V8194947554948674370ptions @ t @ xa )
!= $true )
| ( x = xa )
| ( ( vEBT_invar_vebt @ t @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f28887]) ).
thf(f28887,plain,
! [X0: nat] :
( ( ( vEBT_V8194947554948674370ptions @ t @ xa )
!= $true )
| ( x = xa )
| ( ( vEBT_invar_vebt @ t @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f28742,f26941]) ).
thf(f26941,plain,
! [X2: nat,X3: nat,X0: vEBT_VEBT,X1: nat] :
( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 )
= $true )
| ( ( vEBT_invar_vebt @ X0 @ X3 )
!= $true )
| ( X1 = X2 )
| ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f25758]) ).
thf(f25758,plain,
! [X0: vEBT_VEBT,X1: nat,X2: nat,X3: nat] :
( ( ( vEBT_invar_vebt @ X0 @ X3 )
!= $true )
| ( ( ( ( X1 != X2 )
& ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
= $true ) )
| ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 )
!= $true ) )
& ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 )
= $true )
| ( X1 = X2 )
| ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f25757]) ).
thf(f25757,plain,
! [X0: vEBT_VEBT,X1: nat,X2: nat,X3: nat] :
( ( ( vEBT_invar_vebt @ X0 @ X3 )
!= $true )
| ( ( ( ( X1 != X2 )
& ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
= $true ) )
| ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 )
!= $true ) )
& ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 )
= $true )
| ( X1 = X2 )
| ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f24878]) ).
thf(f24878,plain,
! [X0: vEBT_VEBT,X1: nat,X2: nat,X3: nat] :
( ( ( vEBT_invar_vebt @ X0 @ X3 )
!= $true )
| ( ( ( X1 != X2 )
& ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
= $true ) )
<=> ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f22872]) ).
thf(f22872,plain,
! [X0: vEBT_VEBT,X1: nat,X2: nat,X3: nat] :
( ( ( vEBT_invar_vebt @ X0 @ X3 )
= $true )
=> ( ( ( X1 != X2 )
& ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
= $true ) )
<=> ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f22871]) ).
thf(f22871,plain,
! [X0: vEBT_VEBT,X1: nat,X2: nat,X3: nat] :
( ( vEBT_invar_vebt @ X0 @ X3 )
=> ( ( X1 != X2 )
& ( ( vEBT_V8194947554948674370ptions @ X0 @ X1 )
= ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,axiom,
! [X0: vEBT_VEBT,X7: nat,X2: nat,X1: nat] :
( ( vEBT_invar_vebt @ X0 @ X1 )
=> ( ( X2 != X7 )
& ( ( vEBT_V8194947554948674370ptions @ X0 @ X7 )
= ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X0 @ X2 ) @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',fact_23_dele__bmo__cont__corr) ).
thf(f28742,plain,
( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ t @ x ) @ xa )
!= $true ),
inference(superposition,[status(thm)],[f28663,f26940]) ).
thf(f28663,plain,
( ( member_nat @ xa @ ( collect_nat @ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ t @ x ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f27399]) ).
thf(f27399,plain,
( ( member_nat @ xa
@ ( ^ [Y0: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ Y0 ) )
@ ( vEBT_vebt_delete @ t @ x ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f26344,f27027]) ).
thf(f26344,plain,
( ( member_nat @ xa @ ( vEBT_set_vebt @ ( vEBT_vebt_delete @ t @ x ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f24226]) ).
thf(f24226,plain,
( ( member_nat @ xa @ ( vEBT_set_vebt @ ( vEBT_vebt_delete @ t @ x ) ) )
!= $true ),
inference(flattening,[status(thm)],[f14171]) ).
thf(f14171,plain,
( ( member_nat @ xa @ ( vEBT_set_vebt @ ( vEBT_vebt_delete @ t @ x ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f14170]) ).
thf(f14170,plain,
~ ( member_nat @ xa @ ( vEBT_set_vebt @ ( vEBT_vebt_delete @ t @ x ) ) ),
inference(rectify,[status(thm)],[f9149]) ).
thf(f9149,axiom,
~ ( member_nat @ xa @ ( vEBT_set_vebt @ ( vEBT_vebt_delete @ t @ x ) ) ),
file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_4) ).
thf(f28804,plain,
~ spl434_3,
inference(avatar_contradiction_clause,[status(thm)],[f28803]) ).
thf(f28803,plain,
( $false
| ~ spl434_3 ),
inference(trivial_inequality_removal,[status(thm)],[f28772]) ).
thf(f28772,plain,
( ( $true != $true )
| ~ spl434_3 ),
inference(superposition,[status(thm)],[f28697,f26119]) ).
thf(f26119,plain,
( ( vEBT_invar_vebt @ t @ n )
= $true ),
inference(cnf_transformation,[status(thm)],[f20679]) ).
thf(f20679,plain,
( ( vEBT_invar_vebt @ t @ n )
= $true ),
inference(fool_elimination,[status(thm)],[f20678]) ).
thf(f20678,plain,
vEBT_invar_vebt @ t @ n,
inference(rectify,[status(thm)],[f9146]) ).
thf(f9146,axiom,
vEBT_invar_vebt @ t @ n,
file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_1) ).
thf(f28697,plain,
( ! [X0: nat] :
( ( vEBT_invar_vebt @ t @ X0 )
!= $true )
| ~ spl434_3 ),
inference(avatar_component_clause,[status(thm)],[f28696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP292^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n001.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 18:59:20 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.51 ---- Original DTF file ---
% 0.29/0.51 thf(spec,logic,$$dhol).
% 0.29/0.51 %------------------------------------------------------------------------------
% 0.29/0.51 % File : ITP292^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.29/0.51 % Domain : Interactive Theorem Proving
% 0.29/0.51 % Problem : Sledgehammer problem VEBT_Intf_Imperative 00161_004904
% 0.29/0.51 % Version : [Des22] axioms.
% 0.29/0.51 % English :
% 0.29/0.51
% 0.29/0.51 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.51 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.29/0.51 % Source : [Des22]
% 0.29/0.51 % Names : 0096_VEBT_Intf_Imperative_00161_004904 [Des22]
% 0.29/0.51
% 0.29/0.51 % Status : Theorem
% 0.29/0.51 % Rating : ? v9.2.1
% 0.29/0.51 % Syntax : Number of formulae : 10921 (3598 unt;1771 typ; 0 def)
% 0.29/0.51 % Number of atoms : 31412 (11678 equ; 2 cnn)
% 0.29/0.51 % Maximal formula atoms : 71 ( 3 avg)
% 0.29/0.51 % Number of connectives : 126270 (3401 ~; 433 |;2629 &;105382 @)
% 0.29/0.51 % ( 0 <=>;14425 =>; 0 <=; 0 <~>)
% 0.29/0.51 % Maximal formula depth : 39 ( 7 avg)
% 0.29/0.51 % Number of types : 211 ( 210 usr)
% 0.29/0.51 % Number of type conns : 6094 (6094 >; 0 *; 0 +; 0 <<)
% 0.29/0.51 % Number of symbols : 1566 (1561 usr; 83 con; 0-8 aty)
% 0.29/0.51 % Number of variables : 27945 (2245 ^;24428 !;1272 ?;27945 :)
% 0.29/0.51 % SPC : TH0_THM_EQU_NAR
% 0.29/0.51
% 0.29/0.51 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.51 % from the van Emde Boas Trees session in the Archive of Formal
% 0.29/0.51 % proofs -
% 0.29/0.51 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.29/0.51 % 2022-02-18 23:43:13.532
% 0.29/0.51 % Bugfixes : Added ()s around negated sides of equations.
% 0.29/0.51 %------------------------------------------------------------------------------
% 0.29/0.51 % Could-be-implicit typings (210)
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% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.51 bNF_re3376528473927230327_nat_o: ( int > int > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( int > nat > $o ) > ( int > nat > $o ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 0.29/0.51 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.51 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.51 bNF_re3715656647883201625at_nat: ( int > int > $o ) > ( nat > nat > $o ) > ( int > nat ) > ( int > nat ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.51 bNF_re4785983289428654063nt_int: ( nat > nat > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( nat > int > int ) > ( nat > int > int ) > $o ).
% 0.29/0.51
% 0.29/0.51 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,
% 0.29/0.51 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 0.29/0.51
% 0.29/0.51 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,
% 0.29/0.51 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 0.29/0.51 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.51 bNF_re6650684261131312217nt_int: ( nat > nat > $o ) > ( int > int > $o ) > ( nat > int ) > ( nat > int ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.51 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 0.29/0.51 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.51 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J_001t__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J_001_062_It__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J_M_Eo_J_001_062_It__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J_M_Eo_J,type,
% 0.29/0.51 bNF_re7364608769721783435num1_o: ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > ( ( word_N3645301735248828278l_num1 > $o ) > ( word_N3645301735248828278l_num1 > $o ) > $o ) > ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_BNF__Def_Orel__fun_001t__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J_001t__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J_001_Eo_001_Eo,type,
% 0.29/0.51 bNF_re5013357767504289739m1_o_o: ( word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o ) > ( $o > $o > $o ) > ( word_N3645301735248828278l_num1 > $o ) > ( word_N3645301735248828278l_num1 > $o ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_Binomial_Obinomial,type,
% 0.29/0.51 binomial: nat > nat > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Comprehension_Obit__comprehension__class_Oset__bits_001t__Int__Oint,type,
% 0.29/0.51 bit_bi6516823479961619367ts_int: ( nat > $o ) > int ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Comprehension_Owf__set__bits__int,type,
% 0.29/0.51 bit_wf_set_bits_int: ( nat > $o ) > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 0.29/0.51 bit_concat_bit: nat > int > int > int ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 0.29/0.51 bit_ri7919022796975470100ot_int: int > int ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 0.29/0.51 bit_se727722235901077358nd_nat: nat > nat > nat ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Uint32__Ouint32,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J,type,
% 0.29/0.51 bit_se5176125413884933531l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 0.29/0.51 bit_se2161824704523386999it_nat: nat > nat > nat ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
% 0.29/0.51 bit_se2000444600071755411sk_int: nat > int ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 0.29/0.51 bit_se2002935070580805687sk_nat: nat > nat ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Code____Numeral__Ointeger,type,
% 0.29/0.51 bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
% 0.29/0.51 bit_se1412395901928357646or_nat: nat > nat > nat ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Uint32__Ouint32,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Int__Oint,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Nat__Onat,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Uint32__Ouint32,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Opush__bit_001t__Word__Oword_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Obit0_It__Numeral____Type__Onum1_J_J_J_J_J_J,type,
% 0.29/0.51 bit_se837345729053750000l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 ).
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Int__Oint,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oset__bit_001t__Nat__Onat,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Int__Oint,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Otake__bit_001t__Nat__Onat,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Int__Oint,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Ounset__bit_001t__Nat__Onat,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Int__Oint,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oxor_001t__Nat__Onat,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Nat__Onat,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Uint32__Ouint32,type,
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% 0.29/0.51 thf(sy_c_Bit__Shifts__Infix__Syntax_Osemiring__bit__operations__class_Oshiftl_001t__Nat__Onat,type,
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% 0.29/0.51 thf(sy_c_Bits__Integer_Ointeger__shiftl,type,
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% 0.29/0.51 thf(sy_c_Code__Numeral_Obit__cut__integer,type,
% 0.29/0.51 code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_Code__Numeral_Odivmod__abs,type,
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% 0.29/0.51 thf(sy_c_Code__Numeral_Odivmod__integer,type,
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% 0.29/0.51 thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
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% 0.29/0.51 thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
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% 0.29/0.51 thf(sy_c_Code__Numeral_Ointeger__of__nat,type,
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% 0.29/0.51 thf(sy_c_Code__Numeral_Ointeger__of__num,type,
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% 0.29/0.51 thf(sy_c_Code__Numeral_Onat__of__integer,type,
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% 0.29/0.51 enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
% 0.29/0.51 enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Oenumerate_001t__Real__Oreal,type,
% 0.29/0.51 enumerate_real: nat > list_real > list_P3644420460460130531t_real ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Oenumerate_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.51 enumerate_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_P2320588648998582380_VEBTi ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Oenumerate_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.51 enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 0.29/0.51 filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 0.29/0.51 foldl_assn_assn: ( assn > assn > assn ) > assn > list_assn > assn ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.51 foldl_int_int: ( int > int > int ) > int > list_int > int ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001_Eo,type,
% 0.29/0.51 foldl_nat_o: ( nat > $o > nat ) > nat > list_o > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.51 foldl_nat_nat: ( nat > nat > nat ) > nat > list_nat > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.29/0.51 foldl_nat_real: ( nat > real > nat ) > nat > list_real > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.51 foldl_nat_VEBT_VEBT: ( nat > vEBT_VEBT > nat ) > nat > list_VEBT_VEBT > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Rat__Orat_001t__Rat__Orat,type,
% 0.29/0.51 foldl_rat_rat: ( rat > rat > rat ) > rat > list_rat > rat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.29/0.51 foldl_real_real: ( real > real > real ) > real > list_real > real ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldl_001t__Uint32__Ouint32_001t__Uint32__Ouint32,type,
% 0.29/0.51 foldl_uint32_uint32: ( uint32 > uint32 > uint32 ) > uint32 > list_uint32 > uint32 ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldr_001_Eo_001t__Nat__Onat,type,
% 0.29/0.51 foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.51 foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Nat__Onat,type,
% 0.29/0.51 foldr_real_nat: ( real > nat > nat ) > list_real > nat > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.29/0.51 foldr_real_real: ( real > real > real ) > list_real > real > real ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Ofoldr_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.29/0.51 foldr_VEBT_VEBT_nat: ( vEBT_VEBT > nat > nat ) > list_VEBT_VEBT > nat > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olast_001_Eo,type,
% 0.29/0.51 last_o: list_o > $o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olast_001t__Int__Oint,type,
% 0.29/0.51 last_int: list_int > int ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 0.29/0.51 last_nat: list_nat > nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olast_001t__Real__Oreal,type,
% 0.29/0.51 last_real: list_real > real ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olast_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.51 last_VEBT_VEBTi: list_VEBT_VEBTi > vEBT_VEBTi ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olast_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.51 last_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olenlex_001_Eo,type,
% 0.29/0.51 lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olenlex_001t__Int__Oint,type,
% 0.29/0.51 lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olenlex_001t__Nat__Onat,type,
% 0.29/0.51 lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olenlex_001t__Real__Oreal,type,
% 0.29/0.51 lenlex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olenlex_001t__Uint32__Ouint32,type,
% 0.29/0.51 lenlex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32 ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olenlex_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.51 lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olex_001_Eo,type,
% 0.29/0.51 lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olex_001t__Int__Oint,type,
% 0.29/0.51 lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 0.29/0.51 lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olex_001t__Real__Oreal,type,
% 0.29/0.51 lex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olex_001t__Uint32__Ouint32,type,
% 0.29/0.51 lex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32 ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olex_001t__VEBT____BuildupMemImp__OVEBTi,type,
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% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olex_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.51 lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001_Eo,type,
% 0.29/0.51 linord3142498349692569832_set_o: set_o > list_o ).
% 0.29/0.51
% 0.29/0.51 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Int__Oint,type,
% 0.29/0.52 linord2612477271533052124et_int: set_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 0.29/0.52 linord2614967742042102400et_nat: set_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Num__Onum,type,
% 0.29/0.52 linord8395671565052656842et_num: set_num > list_num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Rat__Orat,type,
% 0.29/0.52 linord1979837681955606664et_rat: set_rat > list_rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Real__Oreal,type,
% 0.29/0.52 linord4252657396651189596t_real: set_real > list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__String__Oliteral,type,
% 0.29/0.52 linord2913955441264437540iteral: set_literal > list_literal ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 0.29/0.52 cons_o: $o > list_o > list_o ).
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Code____Numeral__Ointeger,type,
% 0.29/0.52 cons_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 0.29/0.52 cons_int: int > list_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.29/0.52 cons_nat: nat > list_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 0.29/0.52 cons_num: num > list_num > list_num ).
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 0.29/0.52 cons_P8766293264717362397od_o_o: product_prod_o_o > list_P4002435161011370285od_o_o > list_P4002435161011370285od_o_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 0.29/0.52 cons_P1455986808126089405_o_int: product_prod_o_int > list_P3795440434834930179_o_int > list_P3795440434834930179_o_int ).
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Rat__Orat,type,
% 0.29/0.52 cons_rat: rat > list_rat > list_rat ).
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Real__Oreal,type,
% 0.29/0.52 cons_real: real > list_real > list_real ).
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.52 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
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% 0.29/0.52 cons_uint32: uint32 > list_uint32 > list_uint32 ).
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% 0.29/0.52 thf(sy_c_List_Olist_OCons_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
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% 0.29/0.52 thf(sy_c_List_Olist_ONil_001_Eo,type,
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% 0.29/0.52 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
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% 0.29/0.52 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
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% 0.29/0.52 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001_Eo,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.52 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
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% 0.29/0.52
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% 0.29/0.52 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
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% 0.29/0.52 nth_Pr3306050735993963089EBTi_o: list_P8833571063612306856EBTi_o > nat > produc5014006835512566296EBTi_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__Int__Oint_J,type,
% 0.29/0.52 nth_Pr2733638074192486473Ti_int: list_P7392757774524453448Ti_int > nat > produc8927069083091599426Ti_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__Real__Oreal_J,type,
% 0.29/0.52 nth_Pr3433448822664029129i_real: list_P8536626330812492744i_real > nat > produc6680258955013199682i_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__VEBT____BuildupMemImp__OVEBTi_J,type,
% 0.29/0.52 nth_Pr6329974346453275474_VEBTi: list_P785718909624839377_VEBTi > nat > produc3777764054643897931_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.29/0.52 nth_Pr8725177398587324397T_VEBT: list_P5988454224134618948T_VEBT > nat > produc2810682830582626868T_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Rat__Orat,type,
% 0.29/0.52 nth_rat: list_rat > nat > rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 0.29/0.52 nth_real: list_real > nat > real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.52 nth_set_nat: list_set_nat > nat > set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__Uint32__Ouint32,type,
% 0.29/0.52 nth_uint32: list_uint32 > nat > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 nth_VEBT_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001_Eo,type,
% 0.29/0.52 remove1_o: $o > list_o > list_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001t__Code____Numeral__Ointeger,type,
% 0.29/0.52 remove1_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001t__Int__Oint,type,
% 0.29/0.52 remove1_int: int > list_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001t__Nat__Onat,type,
% 0.29/0.52 remove1_nat: nat > list_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001t__Num__Onum,type,
% 0.29/0.52 remove1_num: num > list_num > list_num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001t__Rat__Orat,type,
% 0.29/0.52 remove1_rat: rat > list_rat > list_rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001t__Real__Oreal,type,
% 0.29/0.52 remove1_real: real > list_real > list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oremove1_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 remove1_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_OremoveAll_001_Eo,type,
% 0.29/0.52 removeAll_o: $o > list_o > list_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_OremoveAll_001t__Int__Oint,type,
% 0.29/0.52 removeAll_int: int > list_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_OremoveAll_001t__Nat__Onat,type,
% 0.29/0.52 removeAll_nat: nat > list_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_OremoveAll_001t__Real__Oreal,type,
% 0.29/0.52 removeAll_real: real > list_real > list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_OremoveAll_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.52 removeAll_set_nat: set_nat > list_set_nat > list_set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_OremoveAll_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 removeAll_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Orotate1_001_Eo,type,
% 0.29/0.52 rotate1_o: list_o > list_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 0.29/0.52 rotate1_nat: list_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Orotate1_001t__Real__Oreal,type,
% 0.29/0.52 rotate1_real: list_real > list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001_Eo,type,
% 0.29/0.52 sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__Code____Numeral__Ointeger,type,
% 0.29/0.52 sorted710888440204495920nteger: ( code_integer > code_integer > $o ) > list_Code_integer > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 0.29/0.52 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 0.29/0.52 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__Num__Onum,type,
% 0.29/0.52 sorted_wrt_num: ( num > num > $o ) > list_num > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__Rat__Orat,type,
% 0.29/0.52 sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__Real__Oreal,type,
% 0.29/0.52 sorted_wrt_real: ( real > real > $o ) > list_real > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__String__Oliteral,type,
% 0.29/0.52 sorted_wrt_literal: ( literal > literal > $o ) > list_literal > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__VEBT____BuildupMemImp__OVEBTi,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osorted__wrt_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 sorted_wrt_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > list_VEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osubseqs_001_Eo,type,
% 0.29/0.52 subseqs_o: list_o > list_list_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 0.29/0.52 subseqs_int: list_int > list_list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 0.29/0.52 subseqs_nat: list_nat > list_list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osubseqs_001t__Real__Oreal,type,
% 0.29/0.52 subseqs_real: list_real > list_list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Osubseqs_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001_Eo,type,
% 0.29/0.52 take_o: nat > list_o > list_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__Int__Oint,type,
% 0.29/0.52 take_int: nat > list_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 0.29/0.52 take_nat: nat > list_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__Num__Onum,type,
% 0.29/0.52 take_num: nat > list_num > list_num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__Rat__Orat,type,
% 0.29/0.52 take_rat: nat > list_rat > list_rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__Real__Oreal,type,
% 0.29/0.52 take_real: nat > list_real > list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.52 take_set_nat: nat > list_set_nat > list_set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__Uint32__Ouint32,type,
% 0.29/0.52 take_uint32: nat > list_uint32 > list_uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Otake_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 take_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_VEBT_VEBTi ).
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% 0.29/0.52 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oupt,type,
% 0.29/0.52 upt: nat > nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oupto,type,
% 0.29/0.52 upto: int > int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oupto__aux,type,
% 0.29/0.52 upto_aux: int > int > list_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Oupto__rel,type,
% 0.29/0.52 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001_Eo_001_Eo,type,
% 0.29/0.52 zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 0.29/0.52 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001_Eo_001t__Nat__Onat,type,
% 0.29/0.52 zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001_Eo_001t__Real__Oreal,type,
% 0.29/0.52 zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Int__Oint_001_Eo,type,
% 0.29/0.52 zip_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.52 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Nat__Onat,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Real__Oreal,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__Int__Oint_001t__VEBT____BuildupMemImp__OVEBTi,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__Nat__Onat_001_Eo,type,
% 0.29/0.52 zip_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Int__Oint,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Real__Oreal_001_Eo,type,
% 0.29/0.52 zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Int__Oint,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Nat__Onat,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Real__Oreal,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__Uint32__Ouint32_001t__Uint32__Ouint32,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001_Eo,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001t__Real__Oreal,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001_Eo,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
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% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
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% 0.29/0.52 zip_VE6444338338598820466_VEBTi: list_VEBT_VEBT > list_VEBT_VEBTi > list_P735349106241217576_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Obijective_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 0.29/0.52 biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Obijective_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 0.29/0.52 biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Obijective_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.52 bijective_int_int: set_Pr958786334691620121nt_int > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Obijective_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.52 bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Obijective_001t__Uint32__Ouint32_001t__Uint32__Ouint32,type,
% 0.29/0.52 biject2923219584331114343uint32: set_Pr1773385645901665561uint32 > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Odflt__None__set_001_Eo,type,
% 0.29/0.52 dflt_None_set_o: set_o > option_set_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Odflt__None__set_001t__Int__Oint,type,
% 0.29/0.52 dflt_None_set_int: set_int > option_set_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Odflt__None__set_001t__Nat__Onat,type,
% 0.29/0.52 dflt_None_set_nat: set_nat > option_set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Omergesort__remdups_001_Eo,type,
% 0.29/0.52 mergesort_remdups_o: list_o > list_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Omergesort__remdups_001t__Int__Oint,type,
% 0.29/0.52 merges1654122896337280797ps_int: list_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Omergesort__remdups_001t__Nat__Onat,type,
% 0.29/0.52 merges1656613366846331073ps_nat: list_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Omergesort__remdups_001t__Num__Onum,type,
% 0.29/0.52 merges7437317189856885515ps_num: list_num > list_num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Omergesort__remdups_001t__Rat__Orat,type,
% 0.29/0.52 merges1021483306759835337ps_rat: list_rat > list_rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Omergesort__remdups_001t__Real__Oreal,type,
% 0.29/0.52 merges7559785487730971421s_real: list_real > list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Oslice_001_Eo,type,
% 0.29/0.52 slice_o: nat > nat > list_o > list_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 0.29/0.52 slice_int: nat > nat > list_int > list_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
% 0.29/0.52 slice_nat: nat > nat > list_nat > list_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Oslice_001t__Real__Oreal,type,
% 0.29/0.52 slice_real: nat > nat > list_real > list_real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Oslice_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 slice_VEBT_VEBTi: nat > nat > list_VEBT_VEBTi > list_VEBT_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Oslice_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 slice_VEBT_VEBT: nat > nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Othe__default_001t__Nat__Onat,type,
% 0.29/0.52 the_default_nat: nat > option_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Othe__default_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.52 the_de3812365490807259288at_nat: product_prod_nat_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Othe__default_001t__Set__Oset_I_Eo_J,type,
% 0.29/0.52 the_default_set_o: set_o > option_set_o > set_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Othe__default_001t__Set__Oset_It__Int__Oint_J,type,
% 0.29/0.52 the_default_set_int: set_int > option_set_int > set_int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Misc_Othe__default_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.52 the_default_set_nat: set_nat > option_set_nat > set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_OSuc,type,
% 0.29/0.52 suc: nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.29/0.52 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 0.29/0.52 semiri4939895301339042750nteger: nat > code_integer ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.29/0.52 semiri1314217659103216013at_int: nat > int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.29/0.52 semiri1316708129612266289at_nat: nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 0.29/0.52 semiri681578069525770553at_rat: nat > rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 0.29/0.52 semiri5074537144036343181t_real: nat > real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Uint32__Ouint32,type,
% 0.29/0.52 semiri2565882477558803405uint32: nat > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 0.29/0.52 size_size_list_o: list_o > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 0.29/0.52 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 0.29/0.52 size_s3451745648224563538omplex: list_complex > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 0.29/0.52 size_size_list_int: list_int > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 0.29/0.52 size_s2710708370519433104list_o: list_list_o > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.29/0.52 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Real__Oreal_J_J,type,
% 0.29/0.52 size_s6660260683639930848t_real: list_list_real > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 0.29/0.52 size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.29/0.52 size_size_list_nat: list_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 0.29/0.52 size_size_list_num: list_num > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Real__Oreal_J_J,type,
% 0.29/0.52 size_s2624279037499656343o_real: list_P5232166724548748803o_real > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.29/0.52 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_M_Eo_J_J,type,
% 0.29/0.52 size_s987546567493390085real_o: list_P3595434254542482545real_o > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
% 0.29/0.52 size_s1877336372972134351al_nat: list_P6834414599653733731al_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 0.29/0.52 size_s3932428310213730859l_real: list_P8689742595348180415l_real > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.29/0.52 size_s3289364478449617953T_VEBT: list_P877281246627933069T_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 0.29/0.52 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 0.29/0.52 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J_J,type,
% 0.29/0.52 size_s5035110155006384947T_real: list_P2623026923184700063T_real > nat ).
% 0.29/0.52
% 0.29/0.52 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,
% 0.29/0.52 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Rat__Orat_J,type,
% 0.29/0.52 size_size_list_rat: list_rat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 0.29/0.52 size_size_list_real: list_real > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.29/0.52 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__String__Oliteral_J,type,
% 0.29/0.52 size_s2501651207091587910iteral: list_literal > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Uint32__Ouint32_J,type,
% 0.29/0.52 size_s4844771616002835472uint32: list_uint32 > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____BuildupMemImp__OVEBTi_J,type,
% 0.29/0.52 size_s7982070591426661849_VEBTi: list_VEBT_VEBTi > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 0.29/0.52 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 0.29/0.52 size_size_num: num > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.29/0.52 size_size_option_nat: option_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.52 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 size_size_VEBT_VEBTi: vEBT_VEBTi > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 0.29/0.52 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 0.29/0.52 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 0.29/0.52 nat_set_decode: nat > set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 0.29/0.52 nat_set_encode: set_nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.29/0.52 nat_triangle: nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_NthRoot_Oroot,type,
% 0.29/0.52 root: nat > real > real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_NthRoot_Osqrt,type,
% 0.29/0.52 sqrt: real > real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_OBitM,type,
% 0.29/0.52 bitM: num > num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oinc,type,
% 0.29/0.52 inc: num > num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 0.29/0.52 neg_nu3811975205180677377ec_int: int > int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 0.29/0.52 neg_nu3179335615603231917ec_rat: rat > rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 0.29/0.52 neg_nu6075765906172075777c_real: real > real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Uint32__Ouint32,type,
% 0.29/0.52 neg_nu965353292909893953uint32: uint32 > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 0.29/0.52 neg_nu5851722552734809277nc_int: int > int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 0.29/0.52 neg_nu5219082963157363817nc_rat: rat > rat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 0.29/0.52 neg_nu8295874005876285629c_real: real > real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Uint32__Ouint32,type,
% 0.29/0.52 neg_nu4269007558841261821uint32: uint32 > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onum_OBit0,type,
% 0.29/0.52 bit0: num > num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onum_OBit1,type,
% 0.29/0.52 bit1: num > num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onum_OOne,type,
% 0.29/0.52 one: num ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onum_Osize__num,type,
% 0.29/0.52 size_num: num > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 0.29/0.52 numera6620942414471956472nteger: num > code_integer ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 0.29/0.52 numera1916890842035813515d_enat: num > extended_enat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 0.29/0.52 numeral_numeral_int: num > int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 0.29/0.52 numeral_numeral_nat: num > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 0.29/0.52 numeral_numeral_real: num > real ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Uint32__Ouint32,type,
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% 0.29/0.52 thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
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% 0.29/0.52 thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
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% 0.29/0.52 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_I_Eo_J,type,
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% 0.29/0.52 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Int__Oint_J,type,
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% 0.29/0.52 thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
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% 0.29/0.52 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
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% 0.29/0.52 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
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% 0.29/0.52 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Int__Oint,type,
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% 0.29/0.52 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
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% 0.29/0.52 transi2803566869205510612_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr2227491710730465451_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Transitive__Closure_Otrancl_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 transi8906537157094044885T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr6192946355708809607T_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Numeral____Type__Onum0,type,
% 0.29/0.52 type_l4264026598287037464l_num0: itself_Numeral_num0 > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 0.29/0.52 type_d8366093980585677751er_int: ( code_integer > int ) > ( int > code_integer ) > set_int > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Odiv0__uint32,type,
% 0.29/0.52 div0_uint32: uint32 > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Omod0__uint32,type,
% 0.29/0.52 mod0_uint32: uint32 > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Oset__bits__aux__uint32,type,
% 0.29/0.52 set_bits_aux_uint32: ( nat > $o ) > nat > uint32 > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Osigned__drop__bit__uint32,type,
% 0.29/0.52 signed489701013188660438uint32: nat > uint32 > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32_ORep__uint32,type,
% 0.29/0.52 rep_uint32: uint32 > word_N3645301735248828278l_num1 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32__divmod,type,
% 0.29/0.52 uint32_divmod: uint32 > uint32 > produc827990862158126777uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32__sdiv,type,
% 0.29/0.52 uint32_sdiv: uint32 > uint32 > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32__set__bit,type,
% 0.29/0.52 uint32_set_bit: uint32 > code_integer > $o > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32__shiftl,type,
% 0.29/0.52 uint32_shiftl: uint32 > code_integer > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32__shiftr,type,
% 0.29/0.52 uint32_shiftr: uint32 > code_integer > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32__sshiftr,type,
% 0.29/0.52 uint32_sshiftr: uint32 > code_integer > uint32 ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_Uint32_Ouint32__test__bit,type,
% 0.29/0.52 uint32_test_bit: uint32 > code_integer > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 0.29/0.52 vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 0.29/0.52 vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 0.29/0.52 vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 0.29/0.52 vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 0.29/0.52 vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 0.29/0.52 vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 0.29/0.52 vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 0.29/0.52 vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 0.29/0.52 vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 0.29/0.52 vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 0.29/0.52 vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l__rel,type,
% 0.29/0.52 vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 0.29/0.52 vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 0.29/0.52 vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d,type,
% 0.29/0.52 vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H,type,
% 0.29/0.52 vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H__rel,type,
% 0.29/0.52 vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 0.29/0.52 vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 0.29/0.52 vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 0.29/0.52 vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 0.29/0.52 vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 0.29/0.52 vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi,type,
% 0.29/0.52 vEBT_V441764108873111860ildupi: nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi_H,type,
% 0.29/0.52 vEBT_V9176841429113362141ildupi: nat > int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi_H__rel,type,
% 0.29/0.52 vEBT_V3352910403632780892pi_rel: nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi__rel,type,
% 0.29/0.52 vEBT_V2957053500504383685pi_rel: nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb,type,
% 0.29/0.52 vEBT_VEBT_Tb: nat > int ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb_H,type,
% 0.29/0.52 vEBT_VEBT_Tb2: nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb_H__rel,type,
% 0.29/0.52 vEBT_VEBT_Tb_rel: nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb__rel,type,
% 0.29/0.52 vEBT_VEBT_Tb_rel2: nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ohighi,type,
% 0.29/0.52 vEBT_VEBT_highi: nat > nat > heap_Time_Heap_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Olowi,type,
% 0.29/0.52 vEBT_VEBT_lowi: nat > nat > heap_Time_Heap_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OminNulli,type,
% 0.29/0.52 vEBT_VEBT_minNulli: vEBT_VEBTi > heap_Time_Heap_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__buildupi_H,type,
% 0.29/0.52 vEBT_V739175172307565963ildupi: nat > heap_T8145700208782473153_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__inserti_H,type,
% 0.29/0.52 vEBT_V3964819847710782039nserti: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__memberi_H,type,
% 0.29/0.52 vEBT_V854960066525838166emberi: vEBT_VEBT > vEBT_VEBTi > nat > heap_Time_Heap_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_OLeafi,type,
% 0.29/0.52 vEBT_Leafi: $o > $o > vEBT_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_ONodei,type,
% 0.29/0.52 vEBT_Nodei: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > vEBT_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Osize__VEBTi,type,
% 0.29/0.52 vEBT_size_VEBTi: vEBT_VEBTi > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw,type,
% 0.29/0.52 vEBT_vebt_assn_raw: vEBT_VEBT > vEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw__rel,type,
% 0.29/0.52 vEBT_v8524038756793281170aw_rel: produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__buildupi,type,
% 0.29/0.52 vEBT_vebt_buildupi: nat > heap_T8145700208782473153_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__inserti,type,
% 0.29/0.52 vEBT_vebt_inserti: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__maxti,type,
% 0.29/0.52 vEBT_vebt_maxti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__maxti__rel,type,
% 0.29/0.52 vEBT_vebt_maxti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__memberi,type,
% 0.29/0.52 vEBT_vebt_memberi: vEBT_VEBTi > nat > heap_Time_Heap_o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__minti,type,
% 0.29/0.52 vEBT_vebt_minti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__BuildupMemImp_Ovebt__minti__rel,type,
% 0.29/0.52 vEBT_vebt_minti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 0.29/0.52 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 0.29/0.52 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 0.29/0.52 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 0.29/0.52 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 0.29/0.52 vEBT_VEBT_high: nat > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 0.29/0.52 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 0.29/0.52 vEBT_VEBT_low: nat > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 0.29/0.52 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 0.29/0.52 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 0.29/0.52 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 0.29/0.52 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 0.29/0.52 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 0.29/0.52 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 0.29/0.52 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 0.29/0.52 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 0.29/0.52 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 0.29/0.52 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__DelImperative_OVEBT__internal_Ovebt__deletei_H,type,
% 0.29/0.52 vEBT_V1365221501068881998eletei: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__DelImperative_Ovebt__deletei,type,
% 0.29/0.52 vEBT_vebt_deletei: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e,type,
% 0.29/0.52 vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e__rel,type,
% 0.29/0.52 vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__DeleteBounds_OVEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H,type,
% 0.29/0.52 vEBT_V1232361888498592333_e_t_e: vEBT_VEBT > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__DeleteBounds_OVEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H__rel,type,
% 0.29/0.52 vEBT_V6368547301243506412_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 0.29/0.52 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 0.29/0.52 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 0.29/0.52 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 0.29/0.52 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H,type,
% 0.29/0.52 vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H__rel,type,
% 0.29/0.52 vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 0.29/0.52 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 0.29/0.52 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Intf__Imperative_Ovebt__assn,type,
% 0.29/0.52 vEBT_Intf_vebt_assn: nat > set_nat > vEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001_Eo_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L6286945158656146733_VEBTi: set_nat > ( $o > vEBT_VEBTi > assn ) > list_o > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L1319876754960170684T_VEBT: set_nat > ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001_Eo,type,
% 0.29/0.52 vEBT_L3563379889750563018_int_o: set_nat > ( int > $o > assn ) > list_int > list_o > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.52 vEBT_L8888932350013902202nt_int: set_nat > ( int > int > assn ) > list_int > list_int > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.52 vEBT_L8891422820522952478nt_nat: set_nat > ( int > nat > assn ) > list_int > list_nat > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Real__Oreal,type,
% 0.29/0.52 vEBT_L7077748017936769786t_real: set_nat > ( int > real > assn ) > list_int > list_real > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L114188773329725699_VEBTi: set_nat > ( int > vEBT_VEBTi > assn ) > list_int > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L2018189785592951398T_VEBT: set_nat > ( int > vEBT_VEBT > assn ) > list_int > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L7489483478785760935_VEBTi: set_nat > ( nat > vEBT_VEBTi > assn ) > list_nat > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L8511957252848910786T_VEBT: set_nat > ( nat > vEBT_VEBT > assn ) > list_nat > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L7851252805511451907_VEBTi: set_nat > ( real > vEBT_VEBTi > assn ) > list_real > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L3095048238742455910T_VEBT: set_nat > ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001_Eo,type,
% 0.29/0.52 vEBT_L3328983362619735041EBTi_o: set_nat > ( vEBT_VEBTi > $o > assn ) > list_VEBT_VEBTi > list_o > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
% 0.29/0.52 vEBT_L2806540629473551875Ti_int: set_nat > ( vEBT_VEBTi > int > assn ) > list_VEBT_VEBTi > list_int > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 0.29/0.52 vEBT_L2809031099982602151Ti_nat: set_nat > ( vEBT_VEBTi > nat > assn ) > list_VEBT_VEBTi > list_nat > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Real__Oreal,type,
% 0.29/0.52 vEBT_L7728200936804140803i_real: set_nat > ( vEBT_VEBTi > real > assn ) > list_VEBT_VEBTi > list_real > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L886525131989349516_VEBTi: set_nat > ( vEBT_VEBTi > vEBT_VEBTi > assn ) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L2497118539674116125T_VEBT: set_nat > ( vEBT_VEBTi > vEBT_VEBT > assn ) > list_VEBT_VEBTi > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.29/0.52 vEBT_L8650695023172932196BT_nat: set_nat > ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L1528199826722428489_VEBTi: set_nat > ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L3204528365124325536T_VEBT: set_nat > ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__Real__Oreal,type,
% 0.29/0.52 vEBT_L4725278957065240257o_real: ( $o > real > assn ) > list_o > list_real > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L1750719106661372127T_VEBT: ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.52 vEBT_L74593716426352029nt_int: ( int > int > assn ) > list_int > list_int > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Nat__Onat,type,
% 0.29/0.52 vEBT_L77084186935402305nt_nat: ( int > nat > assn ) > list_int > list_nat > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L6235239671944049190_VEBTi: ( int > vEBT_VEBTi > assn ) > list_int > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L1664421287176695555T_VEBT: ( int > vEBT_VEBT > assn ) > list_int > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001t__Real__Oreal,type,
% 0.29/0.52 vEBT_L6102073776069194049t_real: ( nat > real > assn ) > list_nat > list_real > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L8158188754432654943T_VEBT: ( nat > vEBT_VEBT > assn ) > list_nat > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001_Eo,type,
% 0.29/0.52 vEBT_L6234343332106409831real_o: ( real > $o > assn ) > list_real > list_o > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.29/0.52 vEBT_L1930518968523514909l_real: ( real > real > assn ) > list_real > list_real > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L4595930785310033027T_VEBT: ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
% 0.29/0.52 vEBT_L8927591528087875366Ti_int: ( vEBT_VEBTi > int > assn ) > list_VEBT_VEBTi > list_int > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 0.29/0.52 vEBT_L8930081998596925642Ti_nat: ( vEBT_VEBTi > nat > assn ) > list_VEBT_VEBTi > list_nat > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L1891944875198410415_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi > assn ) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L7265847600308530106T_VEBT: ( vEBT_VEBTi > vEBT_VEBT > assn ) > list_VEBT_VEBTi > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.29/0.52 vEBT_L7489408758114837031VEBT_o: ( vEBT_VEBT > $o > assn ) > list_VEBT_VEBT > list_o > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.29/0.52 vEBT_L8296926524756676353BT_nat: ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 0.29/0.52 vEBT_L5781919052683127133T_real: ( vEBT_VEBT > real > assn ) > list_VEBT_VEBT > list_real > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 vEBT_L6296928887356842470_VEBTi: ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 vEBT_L1279224858307276611T_VEBT: ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 0.29/0.52 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 0.29/0.52 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 0.29/0.52 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 0.29/0.52 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 0.29/0.52 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 0.29/0.52 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 0.29/0.52 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 0.29/0.52 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 0.29/0.52 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 0.29/0.52 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 0.29/0.52 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 0.29/0.52 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 0.29/0.52 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 0.29/0.52 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 0.29/0.52 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 0.29/0.52 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 0.29/0.52 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 0.29/0.52 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 0.29/0.52 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 0.29/0.52 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 0.29/0.52 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 0.29/0.52 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d,type,
% 0.29/0.52 vEBT_V8646137997579335489_i_l_d: nat > nat ).
% 0.29/0.52
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% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 0.29/0.52 member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__Uint32__Ouint32_Mt__Uint32__Ouint32_J,type,
% 0.29/0.52 member8027108493173000802uint32: produc827990862158126777uint32 > set_Pr1773385645901665561uint32 > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__VEBT____BuildupMemImp__OVEBTi_J,type,
% 0.29/0.52 member660371905731732212_VEBTi: produc3777764054643897931_VEBTi > set_Pr2227491710730465451_VEBTi > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 0.29/0.52 member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 0.29/0.52 member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.29/0.52 member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J,type,
% 0.29/0.52 member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.29/0.52 member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Rat__Orat,type,
% 0.29/0.52 member_rat: rat > set_rat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Real__Oreal,type,
% 0.29/0.52 member_real: real > set_real > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Set__Oset_I_Eo_J,type,
% 0.29/0.52 member_set_o: set_o > set_set_o > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 0.29/0.52 member_set_int: set_int > set_set_int > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.52 member_set_nat: set_nat > set_set_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.29/0.52 member_set_real: set_real > set_set_real > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.29/0.52 member_set_set_nat: set_set_nat > set_set_set_nat > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 0.29/0.52 member_set_VEBT_VEBT: set_VEBT_VEBT > set_set_VEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__String__Oliteral,type,
% 0.29/0.52 member_literal: literal > set_literal > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__Uint32__Ouint32,type,
% 0.29/0.52 member_uint32: uint32 > set_uint32 > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 0.29/0.52 member_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 0.29/0.52 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_a,type,
% 0.29/0.52 a: heap_e7401611519738050253t_unit ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_b,type,
% 0.29/0.52 b: set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_n,type,
% 0.29/0.52 n: nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_r,type,
% 0.29/0.52 r: vEBT_VEBTi ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_s,type,
% 0.29/0.52 s: set_nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_t,type,
% 0.29/0.52 t: vEBT_VEBT ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_x,type,
% 0.29/0.52 x: nat ).
% 0.29/0.52
% 0.29/0.52 thf(sy_v_xa,type,
% 0.29/0.52 xa: nat ).
% 0.29/0.52
% 0.29/0.52 % Relevant facts (9099)
% 0.29/0.52 thf(fact_0_invar__vebt__delete,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 0.29/0.52
% 0.29/0.52 % invar_vebt_delete
% 0.29/0.52 thf(fact_1_set__vebt__equal,axiom,
% 0.29/0.52 ! [T_1: vEBT_VEBT,N: nat,T_2: vEBT_VEBT] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T_1 @ N )
% 0.29/0.52 => ( ( vEBT_invar_vebt @ T_2 @ N )
% 0.29/0.52 => ( ( T_1 = T_2 )
% 0.29/0.52 = ( ( vEBT_set_vebt @ T_1 )
% 0.29/0.52 = ( vEBT_set_vebt @ T_2 ) ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % set_vebt_equal
% 0.29/0.52 thf(fact_2_unique__tree,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,S: vEBT_VEBT] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_invar_vebt @ S @ N )
% 0.29/0.52 => ( ( ( vEBT_set_vebt @ T )
% 0.29/0.52 = ( vEBT_set_vebt @ S ) )
% 0.29/0.52 => ( S = T ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % unique_tree
% 0.29/0.52 thf(fact_3_insert_H__pres__valid,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( vEBT_invar_vebt @ ( vEBT_VEBT_insert @ T @ X ) @ N ) ) ).
% 0.29/0.52
% 0.29/0.52 % insert'_pres_valid
% 0.29/0.52 thf(fact_4_perIT__concat,axiom,
% 0.29/0.52 ! [S: vEBT_VEBT,T: vEBT_VEBT,U: vEBT_VEBT] :
% 0.29/0.52 ( ( vEBT_V6289311342943941716sTrans @ S @ T )
% 0.29/0.52 => ( ( vEBT_V6289311342943941716sTrans @ T @ U )
% 0.29/0.52 => ( vEBT_V6289311342943941716sTrans @ S @ U ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % perIT_concat
% 0.29/0.52 thf(fact_5_set__vebt__set__vebt_H__valid,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_set_vebt @ T )
% 0.29/0.52 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % set_vebt_set_vebt'_valid
% 0.29/0.52 thf(fact_6_uniquetree,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,S: vEBT_VEBT] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_invar_vebt @ S @ N )
% 0.29/0.52 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 0.29/0.52 = ( vEBT_VEBT_set_vebt @ S ) )
% 0.29/0.52 => ( S = T ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % uniquetree
% 0.29/0.52 thf(fact_7_Rep__assn__inject,axiom,
% 0.29/0.52 ! [X: assn,Y: assn] :
% 0.29/0.52 ( ( ( rep_assn @ X )
% 0.29/0.52 = ( rep_assn @ Y ) )
% 0.29/0.52 = ( X = Y ) ) ).
% 0.29/0.52
% 0.29/0.52 % Rep_assn_inject
% 0.29/0.52 thf(fact_8_prod_Oinject,axiom,
% 0.29/0.52 ! [X1: uint32,X2: uint32,Y1: uint32,Y2: uint32] :
% 0.29/0.52 ( ( ( produc1400373151660368625uint32 @ X1 @ X2 )
% 0.29/0.52 = ( produc1400373151660368625uint32 @ Y1 @ Y2 ) )
% 0.29/0.52 = ( ( X1 = Y1 )
% 0.29/0.52 & ( X2 = Y2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod.inject
% 0.29/0.52 thf(fact_9_prod_Oinject,axiom,
% 0.29/0.52 ! [X1: nat,X2: nat,Y1: nat,Y2: nat] :
% 0.29/0.52 ( ( ( product_Pair_nat_nat @ X1 @ X2 )
% 0.29/0.52 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 0.29/0.52 = ( ( X1 = Y1 )
% 0.29/0.52 & ( X2 = Y2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod.inject
% 0.29/0.52 thf(fact_10_prod_Oinject,axiom,
% 0.29/0.52 ! [X1: int,X2: int,Y1: int,Y2: int] :
% 0.29/0.52 ( ( ( product_Pair_int_int @ X1 @ X2 )
% 0.29/0.52 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 0.29/0.52 = ( ( X1 = Y1 )
% 0.29/0.52 & ( X2 = Y2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod.inject
% 0.29/0.52 thf(fact_11_prod_Oinject,axiom,
% 0.29/0.52 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( ( produc5001842942810119800et_nat @ X1 @ X2 )
% 0.29/0.52 = ( produc5001842942810119800et_nat @ Y1 @ Y2 ) )
% 0.29/0.52 = ( ( X1 = Y1 )
% 0.29/0.52 & ( X2 = Y2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod.inject
% 0.29/0.52 thf(fact_12_prod_Oinject,axiom,
% 0.29/0.52 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( ( produc2245416461498447860et_nat @ X1 @ X2 )
% 0.29/0.52 = ( produc2245416461498447860et_nat @ Y1 @ Y2 ) )
% 0.29/0.52 = ( ( X1 = Y1 )
% 0.29/0.52 & ( X2 = Y2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % prod.inject
% 0.29/0.52 thf(fact_13_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: uint32,B: uint32,A2: uint32,B2: uint32] :
% 0.29/0.52 ( ( ( produc1400373151660368625uint32 @ A @ B )
% 0.29/0.52 = ( produc1400373151660368625uint32 @ A2 @ B2 ) )
% 0.29/0.52 = ( ( A = A2 )
% 0.29/0.52 & ( B = B2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_14_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.29/0.52 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.29/0.52 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.29/0.52 = ( ( A = A2 )
% 0.29/0.52 & ( B = B2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_15_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: int,B: int,A2: int,B2: int] :
% 0.29/0.52 ( ( ( product_Pair_int_int @ A @ B )
% 0.29/0.52 = ( product_Pair_int_int @ A2 @ B2 ) )
% 0.29/0.52 = ( ( A = A2 )
% 0.29/0.52 & ( B = B2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_16_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.29/0.52 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 0.29/0.52 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 0.29/0.52 = ( ( A = A2 )
% 0.29/0.52 & ( B = B2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_17_old_Oprod_Oinject,axiom,
% 0.29/0.52 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 0.29/0.52 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 0.29/0.52 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 0.29/0.52 = ( ( A = A2 )
% 0.29/0.52 & ( B = B2 ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % old.prod.inject
% 0.29/0.52 thf(fact_18_valid__eq,axiom,
% 0.29/0.52 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 0.29/0.52
% 0.29/0.52 % valid_eq
% 0.29/0.52 thf(fact_19_valid__eq1,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,D: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ D )
% 0.29/0.52 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 0.29/0.52
% 0.29/0.52 % valid_eq1
% 0.29/0.52 thf(fact_20_valid__eq2,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,D: nat] :
% 0.29/0.52 ( ( vEBT_VEBT_valid @ T @ D )
% 0.29/0.52 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 0.29/0.52
% 0.29/0.52 % valid_eq2
% 0.29/0.52 thf(fact_21_set__vebt__member,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_vebt_member @ T @ X )
% 0.29/0.52 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % set_vebt_member
% 0.29/0.52 thf(fact_22_dele__member__cont__corr,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 0.29/0.52 = ( ( X != Y )
% 0.29/0.52 & ( vEBT_vebt_member @ T @ Y ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % dele_member_cont_corr
% 0.29/0.52 thf(fact_23_dele__bmo__cont__corr,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 0.29/0.52 = ( ( X != Y )
% 0.29/0.52 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % dele_bmo_cont_corr
% 0.29/0.52 thf(fact_24_valid__member__both__member__options,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.29/0.52 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.29/0.52
% 0.29/0.52 % valid_member_both_member_options
% 0.29/0.52 thf(fact_25_both__member__options__equiv__member,axiom,
% 0.29/0.52 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.52 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.29/0.53 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % both_member_options_equiv_member
% 0.29/0.53 thf(fact_26_times__assn__raw_Ocases,axiom,
% 0.29/0.53 ! [X: produc2732055786443039994et_nat] :
% 0.29/0.53 ~ ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.29/0.53 ( X
% 0.29/0.53 != ( produc2245416461498447860et_nat @ P @ ( produc5001842942810119800et_nat @ Q @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % times_assn_raw.cases
% 0.29/0.53 thf(fact_27_prod__induct4,axiom,
% 0.29/0.53 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.53 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D2: set_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D2 ) ) ) )
% 0.29/0.53 => ( P2 @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_induct4
% 0.29/0.53 thf(fact_28_prod__induct3,axiom,
% 0.29/0.53 ! [P2: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 0.29/0.53 ( ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) )
% 0.29/0.53 => ( P2 @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_induct3
% 0.29/0.53 thf(fact_29_prod__induct3,axiom,
% 0.29/0.53 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.53 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) )
% 0.29/0.53 => ( P2 @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_induct3
% 0.29/0.53 thf(fact_30_prod__cases4,axiom,
% 0.29/0.53 ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.53 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D2: set_nat] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases4
% 0.29/0.53 thf(fact_31_prod__cases3,axiom,
% 0.29/0.53 ! [Y: produc3925858234332021118et_nat] :
% 0.29/0.53 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases3
% 0.29/0.53 thf(fact_32_prod__cases3,axiom,
% 0.29/0.53 ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.53 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases3
% 0.29/0.53 thf(fact_33_Pair__inject,axiom,
% 0.29/0.53 ! [A: uint32,B: uint32,A2: uint32,B2: uint32] :
% 0.29/0.53 ( ( ( produc1400373151660368625uint32 @ A @ B )
% 0.29/0.53 = ( produc1400373151660368625uint32 @ A2 @ B2 ) )
% 0.29/0.53 => ~ ( ( A = A2 )
% 0.29/0.53 => ( B != B2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Pair_inject
% 0.29/0.53 thf(fact_34_Pair__inject,axiom,
% 0.29/0.53 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.29/0.53 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.29/0.53 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.29/0.53 => ~ ( ( A = A2 )
% 0.29/0.53 => ( B != B2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Pair_inject
% 0.29/0.53 thf(fact_35_Pair__inject,axiom,
% 0.29/0.53 ! [A: int,B: int,A2: int,B2: int] :
% 0.29/0.53 ( ( ( product_Pair_int_int @ A @ B )
% 0.29/0.53 = ( product_Pair_int_int @ A2 @ B2 ) )
% 0.29/0.53 => ~ ( ( A = A2 )
% 0.29/0.53 => ( B != B2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Pair_inject
% 0.29/0.53 thf(fact_36_Pair__inject,axiom,
% 0.29/0.53 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 0.29/0.53 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 0.29/0.53 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 0.29/0.53 => ~ ( ( A = A2 )
% 0.29/0.53 => ( B != B2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Pair_inject
% 0.29/0.53 thf(fact_37_Pair__inject,axiom,
% 0.29/0.53 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 0.29/0.53 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 0.29/0.53 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 0.29/0.53 => ~ ( ( A = A2 )
% 0.29/0.53 => ( B != B2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Pair_inject
% 0.29/0.53 thf(fact_38_prod__cases,axiom,
% 0.29/0.53 ! [P2: produc827990862158126777uint32 > $o,P3: produc827990862158126777uint32] :
% 0.29/0.53 ( ! [A3: uint32,B3: uint32] : ( P2 @ ( produc1400373151660368625uint32 @ A3 @ B3 ) )
% 0.29/0.53 => ( P2 @ P3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases
% 0.29/0.53 thf(fact_39_prod__cases,axiom,
% 0.29/0.53 ! [P2: product_prod_nat_nat > $o,P3: product_prod_nat_nat] :
% 0.29/0.53 ( ! [A3: nat,B3: nat] : ( P2 @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.29/0.53 => ( P2 @ P3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases
% 0.29/0.53 thf(fact_40_prod__cases,axiom,
% 0.29/0.53 ! [P2: product_prod_int_int > $o,P3: product_prod_int_int] :
% 0.29/0.53 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 0.29/0.53 => ( P2 @ P3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases
% 0.29/0.53 thf(fact_41_prod__cases,axiom,
% 0.29/0.53 ! [P2: produc3925858234332021118et_nat > $o,P3: produc3925858234332021118et_nat] :
% 0.29/0.53 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ B3 ) )
% 0.29/0.53 => ( P2 @ P3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases
% 0.29/0.53 thf(fact_42_prod__cases,axiom,
% 0.29/0.53 ! [P2: produc2732055786443039994et_nat > $o,P3: produc2732055786443039994et_nat] :
% 0.29/0.53 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ B3 ) )
% 0.29/0.53 => ( P2 @ P3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % prod_cases
% 0.29/0.53 thf(fact_43_surj__pair,axiom,
% 0.29/0.53 ! [P3: produc827990862158126777uint32] :
% 0.29/0.53 ? [X3: uint32,Y3: uint32] :
% 0.29/0.53 ( P3
% 0.29/0.53 = ( produc1400373151660368625uint32 @ X3 @ Y3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % surj_pair
% 0.29/0.53 thf(fact_44_surj__pair,axiom,
% 0.29/0.53 ! [P3: product_prod_nat_nat] :
% 0.29/0.53 ? [X3: nat,Y3: nat] :
% 0.29/0.53 ( P3
% 0.29/0.53 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % surj_pair
% 0.29/0.53 thf(fact_45_surj__pair,axiom,
% 0.29/0.53 ! [P3: product_prod_int_int] :
% 0.29/0.53 ? [X3: int,Y3: int] :
% 0.29/0.53 ( P3
% 0.29/0.53 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % surj_pair
% 0.29/0.53 thf(fact_46_surj__pair,axiom,
% 0.29/0.53 ! [P3: produc3925858234332021118et_nat] :
% 0.29/0.53 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 0.29/0.53 ( P3
% 0.29/0.53 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % surj_pair
% 0.29/0.53 thf(fact_47_surj__pair,axiom,
% 0.29/0.53 ! [P3: produc2732055786443039994et_nat] :
% 0.29/0.53 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 0.29/0.53 ( P3
% 0.29/0.53 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % surj_pair
% 0.29/0.53 thf(fact_48_old_Oprod_Oexhaust,axiom,
% 0.29/0.53 ! [Y: produc827990862158126777uint32] :
% 0.29/0.53 ~ ! [A3: uint32,B3: uint32] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( produc1400373151660368625uint32 @ A3 @ B3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.prod.exhaust
% 0.29/0.53 thf(fact_49_old_Oprod_Oexhaust,axiom,
% 0.29/0.53 ! [Y: product_prod_nat_nat] :
% 0.29/0.53 ~ ! [A3: nat,B3: nat] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.prod.exhaust
% 0.29/0.53 thf(fact_50_old_Oprod_Oexhaust,axiom,
% 0.29/0.53 ! [Y: product_prod_int_int] :
% 0.29/0.53 ~ ! [A3: int,B3: int] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.prod.exhaust
% 0.29/0.53 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 0.29/0.53 ! [Y: produc3925858234332021118et_nat] :
% 0.29/0.53 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( produc5001842942810119800et_nat @ A3 @ B3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.prod.exhaust
% 0.29/0.53 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 0.29/0.53 ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.53 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( produc2245416461498447860et_nat @ A3 @ B3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.prod.exhaust
% 0.29/0.53 thf(fact_53_one__assn__raw_Ocases,axiom,
% 0.29/0.53 ! [X: produc3658429121746597890et_nat] :
% 0.29/0.53 ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.29/0.53 ( X
% 0.29/0.53 != ( produc7507926704131184380et_nat @ H @ As ) ) ).
% 0.29/0.53
% 0.29/0.53 % one_assn_raw.cases
% 0.29/0.53 thf(fact_54_set__vebt__finite,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.53 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_vebt_finite
% 0.29/0.53 thf(fact_55_mem__Collect__eq,axiom,
% 0.29/0.53 ! [A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.29/0.53 ( ( member_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P2 ) )
% 0.29/0.53 = ( P2 @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % mem_Collect_eq
% 0.29/0.53 thf(fact_56_mem__Collect__eq,axiom,
% 0.29/0.53 ! [A: real,P2: real > $o] :
% 0.29/0.53 ( ( member_real @ A @ ( collect_real @ P2 ) )
% 0.29/0.53 = ( P2 @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % mem_Collect_eq
% 0.29/0.53 thf(fact_57_mem__Collect__eq,axiom,
% 0.29/0.53 ! [A: complex,P2: complex > $o] :
% 0.29/0.53 ( ( member_complex @ A @ ( collect_complex @ P2 ) )
% 0.29/0.53 = ( P2 @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % mem_Collect_eq
% 0.29/0.53 thf(fact_58_mem__Collect__eq,axiom,
% 0.29/0.53 ! [A: list_nat,P2: list_nat > $o] :
% 0.29/0.53 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 0.29/0.53 = ( P2 @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % mem_Collect_eq
% 0.29/0.53 thf(fact_59_mem__Collect__eq,axiom,
% 0.29/0.53 ! [A: set_nat,P2: set_nat > $o] :
% 0.29/0.53 ( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 0.29/0.53 = ( P2 @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % mem_Collect_eq
% 0.29/0.53 thf(fact_60_mem__Collect__eq,axiom,
% 0.29/0.53 ! [A: nat,P2: nat > $o] :
% 0.29/0.53 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 0.29/0.53 = ( P2 @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % mem_Collect_eq
% 0.29/0.53 thf(fact_61_mem__Collect__eq,axiom,
% 0.29/0.53 ! [A: int,P2: int > $o] :
% 0.29/0.53 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 0.29/0.53 = ( P2 @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % mem_Collect_eq
% 0.29/0.53 thf(fact_62_Collect__mem__eq,axiom,
% 0.29/0.53 ! [A4: set_VEBT_VEBT] :
% 0.29/0.53 ( ( collect_VEBT_VEBT
% 0.29/0.53 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A4 ) )
% 0.29/0.53 = A4 ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_mem_eq
% 0.29/0.53 thf(fact_63_Collect__mem__eq,axiom,
% 0.29/0.53 ! [A4: set_real] :
% 0.29/0.53 ( ( collect_real
% 0.29/0.53 @ ^ [X4: real] : ( member_real @ X4 @ A4 ) )
% 0.29/0.53 = A4 ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_mem_eq
% 0.29/0.53 thf(fact_64_Collect__mem__eq,axiom,
% 0.29/0.53 ! [A4: set_complex] :
% 0.29/0.53 ( ( collect_complex
% 0.29/0.53 @ ^ [X4: complex] : ( member_complex @ X4 @ A4 ) )
% 0.29/0.53 = A4 ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_mem_eq
% 0.29/0.53 thf(fact_65_Collect__mem__eq,axiom,
% 0.29/0.53 ! [A4: set_list_nat] :
% 0.29/0.53 ( ( collect_list_nat
% 0.29/0.53 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A4 ) )
% 0.29/0.53 = A4 ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_mem_eq
% 0.29/0.53 thf(fact_66_Collect__mem__eq,axiom,
% 0.29/0.53 ! [A4: set_set_nat] :
% 0.29/0.53 ( ( collect_set_nat
% 0.29/0.53 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 0.29/0.53 = A4 ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_mem_eq
% 0.29/0.53 thf(fact_67_Collect__mem__eq,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ( collect_nat
% 0.29/0.53 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 0.29/0.53 = A4 ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_mem_eq
% 0.29/0.53 thf(fact_68_Collect__mem__eq,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ( collect_int
% 0.29/0.53 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 0.29/0.53 = A4 ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_mem_eq
% 0.29/0.53 thf(fact_69_Collect__cong,axiom,
% 0.29/0.53 ! [P2: complex > $o,Q2: complex > $o] :
% 0.29/0.53 ( ! [X3: complex] :
% 0.29/0.53 ( ( P2 @ X3 )
% 0.29/0.53 = ( Q2 @ X3 ) )
% 0.29/0.53 => ( ( collect_complex @ P2 )
% 0.29/0.53 = ( collect_complex @ Q2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_cong
% 0.29/0.53 thf(fact_70_Collect__cong,axiom,
% 0.29/0.53 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 0.29/0.53 ( ! [X3: list_nat] :
% 0.29/0.53 ( ( P2 @ X3 )
% 0.29/0.53 = ( Q2 @ X3 ) )
% 0.29/0.53 => ( ( collect_list_nat @ P2 )
% 0.29/0.53 = ( collect_list_nat @ Q2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_cong
% 0.29/0.53 thf(fact_71_Collect__cong,axiom,
% 0.29/0.53 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 0.29/0.53 ( ! [X3: set_nat] :
% 0.29/0.53 ( ( P2 @ X3 )
% 0.29/0.53 = ( Q2 @ X3 ) )
% 0.29/0.53 => ( ( collect_set_nat @ P2 )
% 0.29/0.53 = ( collect_set_nat @ Q2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_cong
% 0.29/0.53 thf(fact_72_Collect__cong,axiom,
% 0.29/0.53 ! [P2: nat > $o,Q2: nat > $o] :
% 0.29/0.53 ( ! [X3: nat] :
% 0.29/0.53 ( ( P2 @ X3 )
% 0.29/0.53 = ( Q2 @ X3 ) )
% 0.29/0.53 => ( ( collect_nat @ P2 )
% 0.29/0.53 = ( collect_nat @ Q2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_cong
% 0.29/0.53 thf(fact_73_Collect__cong,axiom,
% 0.29/0.53 ! [P2: int > $o,Q2: int > $o] :
% 0.29/0.53 ( ! [X3: int] :
% 0.29/0.53 ( ( P2 @ X3 )
% 0.29/0.53 = ( Q2 @ X3 ) )
% 0.29/0.53 => ( ( collect_int @ P2 )
% 0.29/0.53 = ( collect_int @ Q2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_cong
% 0.29/0.53 thf(fact_74_VEBT__internal_OperInsTrans_Ointros_I1_J,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT] : ( vEBT_V6289311342943941716sTrans @ T @ T ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.perInsTrans.intros(1)
% 0.29/0.53 thf(fact_75_valid__tree__deg__neq__0,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT] :
% 0.29/0.53 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % valid_tree_deg_neq_0
% 0.29/0.53 thf(fact_76_valid__0__not,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT] :
% 0.29/0.53 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % valid_0_not
% 0.29/0.53 thf(fact_77_min__Null__member,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT,X: nat] :
% 0.29/0.53 ( ( vEBT_VEBT_minNull @ T )
% 0.29/0.53 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % min_Null_member
% 0.29/0.53 thf(fact_78_not__min__Null__member,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT] :
% 0.29/0.53 ( ~ ( vEBT_VEBT_minNull @ T )
% 0.29/0.53 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 0.29/0.53
% 0.29/0.53 % not_min_Null_member
% 0.29/0.53 thf(fact_79_deg__deg__n,axiom,
% 0.29/0.53 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.29/0.53 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.53 => ( Deg = N ) ) ).
% 0.29/0.53
% 0.29/0.53 % deg_deg_n
% 0.29/0.53 thf(fact_80_ssubst__Pair__rhs,axiom,
% 0.29/0.53 ! [R: uint32,S: uint32,R2: set_Pr1773385645901665561uint32,S2: uint32] :
% 0.29/0.53 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ R @ S ) @ R2 )
% 0.29/0.53 => ( ( S2 = S )
% 0.29/0.53 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ssubst_Pair_rhs
% 0.29/0.53 thf(fact_81_ssubst__Pair__rhs,axiom,
% 0.29/0.53 ! [R: nat,S: nat,R2: set_Pr1261947904930325089at_nat,S2: nat] :
% 0.29/0.53 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S ) @ R2 )
% 0.29/0.53 => ( ( S2 = S )
% 0.29/0.53 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ssubst_Pair_rhs
% 0.29/0.53 thf(fact_82_ssubst__Pair__rhs,axiom,
% 0.29/0.53 ! [R: int,S: int,R2: set_Pr958786334691620121nt_int,S2: int] :
% 0.29/0.53 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S ) @ R2 )
% 0.29/0.53 => ( ( S2 = S )
% 0.29/0.53 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ssubst_Pair_rhs
% 0.29/0.53 thf(fact_83_ssubst__Pair__rhs,axiom,
% 0.29/0.53 ! [R: produc3658429121746597890et_nat > $o,S: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,S2: produc3658429121746597890et_nat] :
% 0.29/0.53 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R @ S ) @ R2 )
% 0.29/0.53 => ( ( S2 = S )
% 0.29/0.53 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ssubst_Pair_rhs
% 0.29/0.53 thf(fact_84_ssubst__Pair__rhs,axiom,
% 0.29/0.53 ! [R: produc3658429121746597890et_nat > $o,S: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,S2: produc3925858234332021118et_nat] :
% 0.29/0.53 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R @ S ) @ R2 )
% 0.29/0.53 => ( ( S2 = S )
% 0.29/0.53 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R @ S2 ) @ R2 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ssubst_Pair_rhs
% 0.29/0.53 thf(fact_85_bex2I,axiom,
% 0.29/0.53 ! [A: uint32,B: uint32,S3: set_Pr1773385645901665561uint32,P2: uint32 > uint32 > $o] :
% 0.29/0.53 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ S3 )
% 0.29/0.53 => ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ S3 )
% 0.29/0.53 => ( P2 @ A @ B ) )
% 0.29/0.53 => ? [A3: uint32,B3: uint32] :
% 0.29/0.53 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A3 @ B3 ) @ S3 )
% 0.29/0.53 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % bex2I
% 0.29/0.53 thf(fact_86_bex2I,axiom,
% 0.29/0.53 ! [A: nat,B: nat,S3: set_Pr1261947904930325089at_nat,P2: nat > nat > $o] :
% 0.29/0.53 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S3 )
% 0.29/0.53 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S3 )
% 0.29/0.53 => ( P2 @ A @ B ) )
% 0.29/0.53 => ? [A3: nat,B3: nat] :
% 0.29/0.53 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ S3 )
% 0.29/0.53 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % bex2I
% 0.29/0.53 thf(fact_87_bex2I,axiom,
% 0.29/0.53 ! [A: int,B: int,S3: set_Pr958786334691620121nt_int,P2: int > int > $o] :
% 0.29/0.53 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S3 )
% 0.29/0.53 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S3 )
% 0.29/0.53 => ( P2 @ A @ B ) )
% 0.29/0.53 => ? [A3: int,B3: int] :
% 0.29/0.53 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ S3 )
% 0.29/0.53 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % bex2I
% 0.29/0.53 thf(fact_88_bex2I,axiom,
% 0.29/0.53 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S3: set_Pr3286484037609594932et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 0.29/0.53 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S3 )
% 0.29/0.53 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S3 )
% 0.29/0.53 => ( P2 @ A @ B ) )
% 0.29/0.53 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 0.29/0.53 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A3 @ B3 ) @ S3 )
% 0.29/0.53 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % bex2I
% 0.29/0.53 thf(fact_89_bex2I,axiom,
% 0.29/0.53 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S3: set_Pr8536935166611901872et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 0.29/0.53 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S3 )
% 0.29/0.53 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S3 )
% 0.29/0.53 => ( P2 @ A @ B ) )
% 0.29/0.53 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 0.29/0.53 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A3 @ B3 ) @ S3 )
% 0.29/0.53 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % bex2I
% 0.29/0.53 thf(fact_90_set__vebt__minNull,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.53 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53 => ( ( vEBT_VEBT_minNull @ T )
% 0.29/0.53 = ( ( vEBT_set_vebt @ T )
% 0.29/0.53 = bot_bot_set_nat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_vebt_minNull
% 0.29/0.53 thf(fact_91_VEBT_Oinject_I1_J,axiom,
% 0.29/0.53 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 0.29/0.53 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.29/0.53 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 0.29/0.53 = ( ( X11 = Y11 )
% 0.29/0.53 & ( X12 = Y12 )
% 0.29/0.53 & ( X13 = Y13 )
% 0.29/0.53 & ( X14 = Y14 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT.inject(1)
% 0.29/0.53 thf(fact_92_deg__not__0,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.53 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.53 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % deg_not_0
% 0.29/0.53 thf(fact_93_deg__SUcn__Node,axiom,
% 0.29/0.53 ! [Tree: vEBT_VEBT,N: nat] :
% 0.29/0.53 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 0.29/0.53 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.29/0.53 ( Tree
% 0.29/0.53 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % deg_SUcn_Node
% 0.29/0.53 thf(fact_94_Leaf__0__not,axiom,
% 0.29/0.53 ! [A: $o,B: $o] :
% 0.29/0.53 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % Leaf_0_not
% 0.29/0.53 thf(fact_95_divides__aux__eq,axiom,
% 0.29/0.53 ! [Q3: nat,R: nat] :
% 0.29/0.53 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R ) )
% 0.29/0.53 = ( R = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % divides_aux_eq
% 0.29/0.53 thf(fact_96_divides__aux__eq,axiom,
% 0.29/0.53 ! [Q3: int,R: int] :
% 0.29/0.53 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.29/0.53 = ( R = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % divides_aux_eq
% 0.29/0.53 thf(fact_97_zero__natural_Orsp,axiom,
% 0.29/0.53 zero_zero_nat = zero_zero_nat ).
% 0.29/0.53
% 0.29/0.53 % zero_natural.rsp
% 0.29/0.53 thf(fact_98_VEBT_Oinject_I2_J,axiom,
% 0.29/0.53 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 0.29/0.53 ( ( ( vEBT_Leaf @ X21 @ X22 )
% 0.29/0.53 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 0.29/0.53 = ( ( X21 = Y21 )
% 0.29/0.53 & ( X22 = Y22 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT.inject(2)
% 0.29/0.53 thf(fact_99_not__gr__zero,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.29/0.53 = ( N = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % not_gr_zero
% 0.29/0.53 thf(fact_100_succ__none__empty,axiom,
% 0.29/0.53 ! [Xs: set_nat,A: nat] :
% 0.29/0.53 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A @ X_1 )
% 0.29/0.53 => ( ( finite_finite_nat @ Xs )
% 0.29/0.53 => ~ ? [X5: nat] :
% 0.29/0.53 ( ( member_nat @ X5 @ Xs )
% 0.29/0.53 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % succ_none_empty
% 0.29/0.53 thf(fact_101_pred__none__empty,axiom,
% 0.29/0.53 ! [Xs: set_nat,A: nat] :
% 0.29/0.53 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A @ X_1 )
% 0.29/0.53 => ( ( finite_finite_nat @ Xs )
% 0.29/0.53 => ~ ? [X5: nat] :
% 0.29/0.53 ( ( member_nat @ X5 @ Xs )
% 0.29/0.53 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_none_empty
% 0.29/0.53 thf(fact_102_memb__imp__not__empty,axiom,
% 0.29/0.53 ! [X: vEBT_VEBT,S3: set_VEBT_VEBT] :
% 0.29/0.53 ( ( member_VEBT_VEBT @ X @ S3 )
% 0.29/0.53 => ( S3 != bot_bo8194388402131092736T_VEBT ) ) ).
% 0.29/0.53
% 0.29/0.53 % memb_imp_not_empty
% 0.29/0.53 thf(fact_103_memb__imp__not__empty,axiom,
% 0.29/0.53 ! [X: real,S3: set_real] :
% 0.29/0.53 ( ( member_real @ X @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_real ) ) ).
% 0.29/0.53
% 0.29/0.53 % memb_imp_not_empty
% 0.29/0.53 thf(fact_104_memb__imp__not__empty,axiom,
% 0.29/0.53 ! [X: set_nat,S3: set_set_nat] :
% 0.29/0.53 ( ( member_set_nat @ X @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % memb_imp_not_empty
% 0.29/0.53 thf(fact_105_memb__imp__not__empty,axiom,
% 0.29/0.53 ! [X: nat,S3: set_nat] :
% 0.29/0.53 ( ( member_nat @ X @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % memb_imp_not_empty
% 0.29/0.53 thf(fact_106_memb__imp__not__empty,axiom,
% 0.29/0.53 ! [X: int,S3: set_int] :
% 0.29/0.53 ( ( member_int @ X @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % memb_imp_not_empty
% 0.29/0.53 thf(fact_107_memb__imp__not__empty,axiom,
% 0.29/0.53 ! [X: $o,S3: set_o] :
% 0.29/0.53 ( ( member_o @ X @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % memb_imp_not_empty
% 0.29/0.53 thf(fact_108_set__notEmptyE,axiom,
% 0.29/0.53 ! [S3: set_VEBT_VEBT] :
% 0.29/0.53 ( ( S3 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.53 => ~ ! [X3: vEBT_VEBT] :
% 0.29/0.53 ~ ( member_VEBT_VEBT @ X3 @ S3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_notEmptyE
% 0.29/0.53 thf(fact_109_set__notEmptyE,axiom,
% 0.29/0.53 ! [S3: set_real] :
% 0.29/0.53 ( ( S3 != bot_bot_set_real )
% 0.29/0.53 => ~ ! [X3: real] :
% 0.29/0.53 ~ ( member_real @ X3 @ S3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_notEmptyE
% 0.29/0.53 thf(fact_110_set__notEmptyE,axiom,
% 0.29/0.53 ! [S3: set_set_nat] :
% 0.29/0.53 ( ( S3 != bot_bot_set_set_nat )
% 0.29/0.53 => ~ ! [X3: set_nat] :
% 0.29/0.53 ~ ( member_set_nat @ X3 @ S3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_notEmptyE
% 0.29/0.53 thf(fact_111_set__notEmptyE,axiom,
% 0.29/0.53 ! [S3: set_nat] :
% 0.29/0.53 ( ( S3 != bot_bot_set_nat )
% 0.29/0.53 => ~ ! [X3: nat] :
% 0.29/0.53 ~ ( member_nat @ X3 @ S3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_notEmptyE
% 0.29/0.53 thf(fact_112_set__notEmptyE,axiom,
% 0.29/0.53 ! [S3: set_int] :
% 0.29/0.53 ( ( S3 != bot_bot_set_int )
% 0.29/0.53 => ~ ! [X3: int] :
% 0.29/0.53 ~ ( member_int @ X3 @ S3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_notEmptyE
% 0.29/0.53 thf(fact_113_set__notEmptyE,axiom,
% 0.29/0.53 ! [S3: set_o] :
% 0.29/0.53 ( ( S3 != bot_bot_set_o )
% 0.29/0.53 => ~ ! [X3: $o] :
% 0.29/0.53 ~ ( member_o @ X3 @ S3 ) ) ).
% 0.29/0.53
% 0.29/0.53 % set_notEmptyE
% 0.29/0.53 thf(fact_114_gr__zeroI,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( N != zero_zero_nat )
% 0.29/0.53 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr_zeroI
% 0.29/0.53 thf(fact_115_not__less__zero,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % not_less_zero
% 0.29/0.53 thf(fact_116_gr__implies__not__zero,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( N != zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr_implies_not_zero
% 0.29/0.53 thf(fact_117_zero__less__iff__neq__zero,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.53 = ( N != zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_less_iff_neq_zero
% 0.29/0.53 thf(fact_118_VEBT_Odistinct_I1_J,axiom,
% 0.29/0.53 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 0.29/0.53 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.29/0.53 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT.distinct(1)
% 0.29/0.53 thf(fact_119_VEBT_Oexhaust,axiom,
% 0.29/0.53 ! [Y: vEBT_VEBT] :
% 0.29/0.53 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 0.29/0.53 => ~ ! [X212: $o,X222: $o] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT.exhaust
% 0.29/0.53 thf(fact_120_finite_OemptyI,axiom,
% 0.29/0.53 finite3207457112153483333omplex @ bot_bot_set_complex ).
% 0.29/0.53
% 0.29/0.53 % finite.emptyI
% 0.29/0.53 thf(fact_121_finite_OemptyI,axiom,
% 0.29/0.53 finite6017078050557962740nteger @ bot_bo3990330152332043303nteger ).
% 0.29/0.53
% 0.29/0.53 % finite.emptyI
% 0.29/0.53 thf(fact_122_finite_OemptyI,axiom,
% 0.29/0.53 finite_finite_nat @ bot_bot_set_nat ).
% 0.29/0.53
% 0.29/0.53 % finite.emptyI
% 0.29/0.53 thf(fact_123_finite_OemptyI,axiom,
% 0.29/0.53 finite_finite_int @ bot_bot_set_int ).
% 0.29/0.53
% 0.29/0.53 % finite.emptyI
% 0.29/0.53 thf(fact_124_finite_OemptyI,axiom,
% 0.29/0.53 finite_finite_o @ bot_bot_set_o ).
% 0.29/0.53
% 0.29/0.53 % finite.emptyI
% 0.29/0.53 thf(fact_125_infinite__imp__nonempty,axiom,
% 0.29/0.53 ! [S3: set_complex] :
% 0.29/0.53 ( ~ ( finite3207457112153483333omplex @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_complex ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_imp_nonempty
% 0.29/0.53 thf(fact_126_infinite__imp__nonempty,axiom,
% 0.29/0.53 ! [S3: set_Code_integer] :
% 0.29/0.53 ( ~ ( finite6017078050557962740nteger @ S3 )
% 0.29/0.53 => ( S3 != bot_bo3990330152332043303nteger ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_imp_nonempty
% 0.29/0.53 thf(fact_127_infinite__imp__nonempty,axiom,
% 0.29/0.53 ! [S3: set_nat] :
% 0.29/0.53 ( ~ ( finite_finite_nat @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_imp_nonempty
% 0.29/0.53 thf(fact_128_infinite__imp__nonempty,axiom,
% 0.29/0.53 ! [S3: set_int] :
% 0.29/0.53 ( ~ ( finite_finite_int @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_imp_nonempty
% 0.29/0.53 thf(fact_129_infinite__imp__nonempty,axiom,
% 0.29/0.53 ! [S3: set_o] :
% 0.29/0.53 ( ~ ( finite_finite_o @ S3 )
% 0.29/0.53 => ( S3 != bot_bot_set_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_imp_nonempty
% 0.29/0.53 thf(fact_130_VEBT__internal_Onaive__member_Ocases,axiom,
% 0.29/0.53 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.53 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.29/0.53 ( X
% 0.29/0.53 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.29/0.53 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 0.29/0.53 ( X
% 0.29/0.53 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) )
% 0.29/0.53 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT,X3: nat] :
% 0.29/0.53 ( X
% 0.29/0.53 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ X3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.naive_member.cases
% 0.29/0.53 thf(fact_131_invar__vebt_Ointros_I1_J,axiom,
% 0.29/0.53 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % invar_vebt.intros(1)
% 0.29/0.53 thf(fact_132_mod__h__bot__indep,axiom,
% 0.29/0.53 ! [P2: assn,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 0.29/0.53 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.29/0.53 = ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % mod_h_bot_indep
% 0.29/0.53 thf(fact_133_zero__reorient,axiom,
% 0.29/0.53 ! [X: uint32] :
% 0.29/0.53 ( ( zero_zero_uint32 = X )
% 0.29/0.53 = ( X = zero_zero_uint32 ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_reorient
% 0.29/0.53 thf(fact_134_zero__reorient,axiom,
% 0.29/0.53 ! [X: real] :
% 0.29/0.53 ( ( zero_zero_real = X )
% 0.29/0.53 = ( X = zero_zero_real ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_reorient
% 0.29/0.53 thf(fact_135_zero__reorient,axiom,
% 0.29/0.53 ! [X: rat] :
% 0.29/0.53 ( ( zero_zero_rat = X )
% 0.29/0.53 = ( X = zero_zero_rat ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_reorient
% 0.29/0.53 thf(fact_136_zero__reorient,axiom,
% 0.29/0.53 ! [X: nat] :
% 0.29/0.53 ( ( zero_zero_nat = X )
% 0.29/0.53 = ( X = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_reorient
% 0.29/0.53 thf(fact_137_zero__reorient,axiom,
% 0.29/0.53 ! [X: int] :
% 0.29/0.53 ( ( zero_zero_int = X )
% 0.29/0.53 = ( X = zero_zero_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_reorient
% 0.29/0.53 thf(fact_138_zero__less__Suc,axiom,
% 0.29/0.53 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_less_Suc
% 0.29/0.53 thf(fact_139_less__Suc0,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.29/0.53 = ( N = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_Suc0
% 0.29/0.53 thf(fact_140_bot__nat__0_Onot__eq__extremum,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ( ( A != zero_zero_nat )
% 0.29/0.53 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_nat_0.not_eq_extremum
% 0.29/0.53 thf(fact_141_neq0__conv,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( N != zero_zero_nat )
% 0.29/0.53 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % neq0_conv
% 0.29/0.53 thf(fact_142_less__nat__zero__code,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % less_nat_zero_code
% 0.29/0.53 thf(fact_143_lessI,axiom,
% 0.29/0.53 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % lessI
% 0.29/0.53 thf(fact_144_Suc__mono,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_mono
% 0.29/0.53 thf(fact_145_Suc__less__eq,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.53 = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_less_eq
% 0.29/0.53 thf(fact_146_vebt__delete_Osimps_I2_J,axiom,
% 0.29/0.53 ! [A: $o,B: $o] :
% 0.29/0.53 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.53 = ( vEBT_Leaf @ A @ $false ) ) ).
% 0.29/0.53
% 0.29/0.53 % vebt_delete.simps(2)
% 0.29/0.53 thf(fact_147_invar__vebt__buildup,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N )
% 0.29/0.53 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % invar_vebt_buildup
% 0.29/0.53 thf(fact_148_buildup__gives__valid,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.53 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % buildup_gives_valid
% 0.29/0.53 thf(fact_149_T__vebt__buildupi__gq__0,axiom,
% 0.29/0.53 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % T_vebt_buildupi_gq_0
% 0.29/0.53 thf(fact_150_set__vebt__buildup,axiom,
% 0.29/0.53 ! [I: nat] :
% 0.29/0.53 ( ( vEBT_set_vebt @ ( vEBT_vebt_buildup @ I ) )
% 0.29/0.53 = bot_bot_set_nat ) ).
% 0.29/0.53
% 0.29/0.53 % set_vebt_buildup
% 0.29/0.53 thf(fact_151_buildup__gives__empty,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 0.29/0.53 = bot_bot_set_nat ) ).
% 0.29/0.53
% 0.29/0.53 % buildup_gives_empty
% 0.29/0.53 thf(fact_152_old_Onat_Oinject,axiom,
% 0.29/0.53 ! [Nat: nat,Nat2: nat] :
% 0.29/0.53 ( ( ( suc @ Nat )
% 0.29/0.53 = ( suc @ Nat2 ) )
% 0.29/0.53 = ( Nat = Nat2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.nat.inject
% 0.29/0.53 thf(fact_153_nat_Oinject,axiom,
% 0.29/0.53 ! [X2: nat,Y2: nat] :
% 0.29/0.53 ( ( ( suc @ X2 )
% 0.29/0.53 = ( suc @ Y2 ) )
% 0.29/0.53 = ( X2 = Y2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat.inject
% 0.29/0.53 thf(fact_154_obtain__set__pred,axiom,
% 0.29/0.53 ! [Z: nat,X: nat,A4: set_nat] :
% 0.29/0.53 ( ( ord_less_nat @ Z @ X )
% 0.29/0.53 => ( ( vEBT_VEBT_min_in_set @ A4 @ Z )
% 0.29/0.53 => ( ( finite_finite_nat @ A4 )
% 0.29/0.53 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A4 @ X @ X_1 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % obtain_set_pred
% 0.29/0.53 thf(fact_155_obtain__set__succ,axiom,
% 0.29/0.53 ! [X: nat,Z: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.53 ( ( ord_less_nat @ X @ Z )
% 0.29/0.53 => ( ( vEBT_VEBT_max_in_set @ A4 @ Z )
% 0.29/0.53 => ( ( finite_finite_nat @ B4 )
% 0.29/0.53 => ( ( A4 = B4 )
% 0.29/0.53 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A4 @ X @ X_1 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % obtain_set_succ
% 0.29/0.53 thf(fact_156_finite__psubset__induct,axiom,
% 0.29/0.53 ! [A4: set_nat,P2: set_nat > $o] :
% 0.29/0.53 ( ( finite_finite_nat @ A4 )
% 0.29/0.53 => ( ! [A5: set_nat] :
% 0.29/0.53 ( ( finite_finite_nat @ A5 )
% 0.29/0.53 => ( ! [B5: set_nat] :
% 0.29/0.53 ( ( ord_less_set_nat @ B5 @ A5 )
% 0.29/0.53 => ( P2 @ B5 ) )
% 0.29/0.53 => ( P2 @ A5 ) ) )
% 0.29/0.53 => ( P2 @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_psubset_induct
% 0.29/0.53 thf(fact_157_finite__psubset__induct,axiom,
% 0.29/0.53 ! [A4: set_int,P2: set_int > $o] :
% 0.29/0.53 ( ( finite_finite_int @ A4 )
% 0.29/0.53 => ( ! [A5: set_int] :
% 0.29/0.53 ( ( finite_finite_int @ A5 )
% 0.29/0.53 => ( ! [B5: set_int] :
% 0.29/0.53 ( ( ord_less_set_int @ B5 @ A5 )
% 0.29/0.53 => ( P2 @ B5 ) )
% 0.29/0.53 => ( P2 @ A5 ) ) )
% 0.29/0.53 => ( P2 @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_psubset_induct
% 0.29/0.53 thf(fact_158_finite__psubset__induct,axiom,
% 0.29/0.53 ! [A4: set_complex,P2: set_complex > $o] :
% 0.29/0.53 ( ( finite3207457112153483333omplex @ A4 )
% 0.29/0.53 => ( ! [A5: set_complex] :
% 0.29/0.53 ( ( finite3207457112153483333omplex @ A5 )
% 0.29/0.53 => ( ! [B5: set_complex] :
% 0.29/0.53 ( ( ord_less_set_complex @ B5 @ A5 )
% 0.29/0.53 => ( P2 @ B5 ) )
% 0.29/0.53 => ( P2 @ A5 ) ) )
% 0.29/0.53 => ( P2 @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_psubset_induct
% 0.29/0.53 thf(fact_159_finite__psubset__induct,axiom,
% 0.29/0.53 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.53 => ( ! [A5: set_Code_integer] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ A5 )
% 0.29/0.53 => ( ! [B5: set_Code_integer] :
% 0.29/0.53 ( ( ord_le1307284697595431911nteger @ B5 @ A5 )
% 0.29/0.53 => ( P2 @ B5 ) )
% 0.29/0.53 => ( P2 @ A5 ) ) )
% 0.29/0.53 => ( P2 @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_psubset_induct
% 0.29/0.53 thf(fact_160_vebt__buildup_Osimps_I1_J,axiom,
% 0.29/0.53 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 0.29/0.53 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.29/0.53
% 0.29/0.53 % vebt_buildup.simps(1)
% 0.29/0.53 thf(fact_161_n__not__Suc__n,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( N
% 0.29/0.53 != ( suc @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % n_not_Suc_n
% 0.29/0.53 thf(fact_162_Suc__inject,axiom,
% 0.29/0.53 ! [X: nat,Y: nat] :
% 0.29/0.53 ( ( ( suc @ X )
% 0.29/0.53 = ( suc @ Y ) )
% 0.29/0.53 => ( X = Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_inject
% 0.29/0.53 thf(fact_163_linorder__neqE__nat,axiom,
% 0.29/0.53 ! [X: nat,Y: nat] :
% 0.29/0.53 ( ( X != Y )
% 0.29/0.53 => ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.53 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_neqE_nat
% 0.29/0.53 thf(fact_164_infinite__descent,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ! [N2: nat] :
% 0.29/0.53 ( ~ ( P2 @ N2 )
% 0.29/0.53 => ? [M2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.53 & ~ ( P2 @ M2 ) ) )
% 0.29/0.53 => ( P2 @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_descent
% 0.29/0.53 thf(fact_165_nat__less__induct,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ! [N2: nat] :
% 0.29/0.53 ( ! [M2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.53 => ( P2 @ M2 ) )
% 0.29/0.53 => ( P2 @ N2 ) )
% 0.29/0.53 => ( P2 @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_less_induct
% 0.29/0.53 thf(fact_166_less__irrefl__nat,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.53
% 0.29/0.53 % less_irrefl_nat
% 0.29/0.53 thf(fact_167_less__not__refl3,axiom,
% 0.29/0.53 ! [S: nat,T: nat] :
% 0.29/0.53 ( ( ord_less_nat @ S @ T )
% 0.29/0.53 => ( S != T ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_not_refl3
% 0.29/0.53 thf(fact_168_less__not__refl2,axiom,
% 0.29/0.53 ! [N: nat,M: nat] :
% 0.29/0.53 ( ( ord_less_nat @ N @ M )
% 0.29/0.53 => ( M != N ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_not_refl2
% 0.29/0.53 thf(fact_169_less__not__refl,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ N @ N ) ).
% 0.29/0.53
% 0.29/0.53 % less_not_refl
% 0.29/0.53 thf(fact_170_nat__neq__iff,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( M != N )
% 0.29/0.53 = ( ( ord_less_nat @ M @ N )
% 0.29/0.53 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_neq_iff
% 0.29/0.53 thf(fact_171_vebt__buildup_Osimps_I2_J,axiom,
% 0.29/0.53 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 0.29/0.53 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.29/0.53
% 0.29/0.53 % vebt_buildup.simps(2)
% 0.29/0.53 thf(fact_172_not0__implies__Suc,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( N != zero_zero_nat )
% 0.29/0.53 => ? [M3: nat] :
% 0.29/0.53 ( N
% 0.29/0.53 = ( suc @ M3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % not0_implies_Suc
% 0.29/0.53 thf(fact_173_Zero__not__Suc,axiom,
% 0.29/0.53 ! [M: nat] :
% 0.29/0.53 ( zero_zero_nat
% 0.29/0.53 != ( suc @ M ) ) ).
% 0.29/0.53
% 0.29/0.53 % Zero_not_Suc
% 0.29/0.53 thf(fact_174_Zero__neq__Suc,axiom,
% 0.29/0.53 ! [M: nat] :
% 0.29/0.53 ( zero_zero_nat
% 0.29/0.53 != ( suc @ M ) ) ).
% 0.29/0.53
% 0.29/0.53 % Zero_neq_Suc
% 0.29/0.53 thf(fact_175_Suc__neq__Zero,axiom,
% 0.29/0.53 ! [M: nat] :
% 0.29/0.53 ( ( suc @ M )
% 0.29/0.53 != zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_neq_Zero
% 0.29/0.53 thf(fact_176_zero__induct,axiom,
% 0.29/0.53 ! [P2: nat > $o,K: nat] :
% 0.29/0.53 ( ( P2 @ K )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ( P2 @ ( suc @ N2 ) )
% 0.29/0.53 => ( P2 @ N2 ) )
% 0.29/0.53 => ( P2 @ zero_zero_nat ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % zero_induct
% 0.29/0.53 thf(fact_177_diff__induct,axiom,
% 0.29/0.53 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 0.29/0.53 ( ! [X3: nat] : ( P2 @ X3 @ zero_zero_nat )
% 0.29/0.53 => ( ! [Y3: nat] : ( P2 @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.29/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.53 ( ( P2 @ X3 @ Y3 )
% 0.29/0.53 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.29/0.53 => ( P2 @ M @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % diff_induct
% 0.29/0.53 thf(fact_178_nat__induct,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ( P2 @ zero_zero_nat )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ( P2 @ N2 )
% 0.29/0.53 => ( P2 @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( P2 @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_induct
% 0.29/0.53 thf(fact_179_old_Onat_Oexhaust,axiom,
% 0.29/0.53 ! [Y: nat] :
% 0.29/0.53 ( ( Y != zero_zero_nat )
% 0.29/0.53 => ~ ! [Nat3: nat] :
% 0.29/0.53 ( Y
% 0.29/0.53 != ( suc @ Nat3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.nat.exhaust
% 0.29/0.53 thf(fact_180_nat_OdiscI,axiom,
% 0.29/0.53 ! [Nat: nat,X2: nat] :
% 0.29/0.53 ( ( Nat
% 0.29/0.53 = ( suc @ X2 ) )
% 0.29/0.53 => ( Nat != zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat.discI
% 0.29/0.53 thf(fact_181_old_Onat_Odistinct_I1_J,axiom,
% 0.29/0.53 ! [Nat2: nat] :
% 0.29/0.53 ( zero_zero_nat
% 0.29/0.53 != ( suc @ Nat2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % old.nat.distinct(1)
% 0.29/0.53 thf(fact_182_old_Onat_Odistinct_I2_J,axiom,
% 0.29/0.53 ! [Nat2: nat] :
% 0.29/0.53 ( ( suc @ Nat2 )
% 0.29/0.53 != zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % old.nat.distinct(2)
% 0.29/0.53 thf(fact_183_nat_Odistinct_I1_J,axiom,
% 0.29/0.53 ! [X2: nat] :
% 0.29/0.53 ( zero_zero_nat
% 0.29/0.53 != ( suc @ X2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat.distinct(1)
% 0.29/0.53 thf(fact_184_not__less__less__Suc__eq,axiom,
% 0.29/0.53 ! [N: nat,M: nat] :
% 0.29/0.53 ( ~ ( ord_less_nat @ N @ M )
% 0.29/0.53 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.53 = ( N = M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % not_less_less_Suc_eq
% 0.29/0.53 thf(fact_185_strict__inc__induct,axiom,
% 0.29/0.53 ! [I: nat,J: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ord_less_nat @ I @ J )
% 0.29/0.53 => ( ! [I2: nat] :
% 0.29/0.53 ( ( J
% 0.29/0.53 = ( suc @ I2 ) )
% 0.29/0.53 => ( P2 @ I2 ) )
% 0.29/0.53 => ( ! [I2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I2 @ J )
% 0.29/0.53 => ( ( P2 @ ( suc @ I2 ) )
% 0.29/0.53 => ( P2 @ I2 ) ) )
% 0.29/0.53 => ( P2 @ I ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % strict_inc_induct
% 0.29/0.53 thf(fact_186_less__Suc__induct,axiom,
% 0.29/0.53 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 0.29/0.53 ( ( ord_less_nat @ I @ J )
% 0.29/0.53 => ( ! [I2: nat] : ( P2 @ I2 @ ( suc @ I2 ) )
% 0.29/0.53 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I2 @ J2 )
% 0.29/0.53 => ( ( ord_less_nat @ J2 @ K2 )
% 0.29/0.53 => ( ( P2 @ I2 @ J2 )
% 0.29/0.53 => ( ( P2 @ J2 @ K2 )
% 0.29/0.53 => ( P2 @ I2 @ K2 ) ) ) ) )
% 0.29/0.53 => ( P2 @ I @ J ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_Suc_induct
% 0.29/0.53 thf(fact_187_less__trans__Suc,axiom,
% 0.29/0.53 ! [I: nat,J: nat,K: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I @ J )
% 0.29/0.53 => ( ( ord_less_nat @ J @ K )
% 0.29/0.53 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_trans_Suc
% 0.29/0.53 thf(fact_188_Suc__less__SucD,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.53 => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_less_SucD
% 0.29/0.53 thf(fact_189_less__antisym,axiom,
% 0.29/0.53 ! [N: nat,M: nat] :
% 0.29/0.53 ( ~ ( ord_less_nat @ N @ M )
% 0.29/0.53 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.53 => ( M = N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_antisym
% 0.29/0.53 thf(fact_190_Suc__less__eq2,axiom,
% 0.29/0.53 ! [N: nat,M: nat] :
% 0.29/0.53 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.29/0.53 = ( ? [M4: nat] :
% 0.29/0.53 ( ( M
% 0.29/0.53 = ( suc @ M4 ) )
% 0.29/0.53 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_less_eq2
% 0.29/0.53 thf(fact_191_Nat_OAll__less__Suc,axiom,
% 0.29/0.53 ! [N: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.53 => ( P2 @ I3 ) ) )
% 0.29/0.53 = ( ( P2 @ N )
% 0.29/0.53 & ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ N )
% 0.29/0.53 => ( P2 @ I3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Nat.All_less_Suc
% 0.29/0.53 thf(fact_192_not__less__eq,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.29/0.53 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % not_less_eq
% 0.29/0.53 thf(fact_193_less__Suc__eq,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.53 = ( ( ord_less_nat @ M @ N )
% 0.29/0.53 | ( M = N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_Suc_eq
% 0.29/0.53 thf(fact_194_Ex__less__Suc,axiom,
% 0.29/0.53 ! [N: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ? [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.53 & ( P2 @ I3 ) ) )
% 0.29/0.53 = ( ( P2 @ N )
% 0.29/0.53 | ? [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ N )
% 0.29/0.53 & ( P2 @ I3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ex_less_Suc
% 0.29/0.53 thf(fact_195_less__SucI,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_SucI
% 0.29/0.53 thf(fact_196_less__SucE,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.53 => ( ~ ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( M = N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_SucE
% 0.29/0.53 thf(fact_197_Suc__lessI,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( ( ( suc @ M )
% 0.29/0.53 != N )
% 0.29/0.53 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_lessI
% 0.29/0.53 thf(fact_198_Suc__lessE,axiom,
% 0.29/0.53 ! [I: nat,K: nat] :
% 0.29/0.53 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.29/0.53 => ~ ! [J2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I @ J2 )
% 0.29/0.53 => ( K
% 0.29/0.53 != ( suc @ J2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_lessE
% 0.29/0.53 thf(fact_199_Suc__lessD,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.29/0.53 => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_lessD
% 0.29/0.53 thf(fact_200_Nat_OlessE,axiom,
% 0.29/0.53 ! [I: nat,K: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I @ K )
% 0.29/0.53 => ( ( K
% 0.29/0.53 != ( suc @ I ) )
% 0.29/0.53 => ~ ! [J2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I @ J2 )
% 0.29/0.53 => ( K
% 0.29/0.53 != ( suc @ J2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Nat.lessE
% 0.29/0.53 thf(fact_201_infinite__descent0,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ( P2 @ zero_zero_nat )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.53 => ( ~ ( P2 @ N2 )
% 0.29/0.53 => ? [M2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.53 & ~ ( P2 @ M2 ) ) ) )
% 0.29/0.53 => ( P2 @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_descent0
% 0.29/0.53 thf(fact_202_gr__implies__not0,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( N != zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr_implies_not0
% 0.29/0.53 thf(fact_203_less__zeroE,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % less_zeroE
% 0.29/0.53 thf(fact_204_not__less0,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % not_less0
% 0.29/0.53 thf(fact_205_not__gr0,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.29/0.53 = ( N = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % not_gr0
% 0.29/0.53 thf(fact_206_gr0I,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( N != zero_zero_nat )
% 0.29/0.53 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr0I
% 0.29/0.53 thf(fact_207_bot__nat__0_Oextremum__strict,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.29/0.53
% 0.29/0.53 % bot_nat_0.extremum_strict
% 0.29/0.53 thf(fact_208_lift__Suc__mono__less__iff,axiom,
% 0.29/0.53 ! [F: nat > real,N: nat,M: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.53 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less_iff
% 0.29/0.53 thf(fact_209_lift__Suc__mono__less__iff,axiom,
% 0.29/0.53 ! [F: nat > rat,N: nat,M: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.53 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less_iff
% 0.29/0.53 thf(fact_210_lift__Suc__mono__less__iff,axiom,
% 0.29/0.53 ! [F: nat > num,N: nat,M: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.53 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less_iff
% 0.29/0.53 thf(fact_211_lift__Suc__mono__less__iff,axiom,
% 0.29/0.53 ! [F: nat > nat,N: nat,M: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.53 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less_iff
% 0.29/0.53 thf(fact_212_lift__Suc__mono__less__iff,axiom,
% 0.29/0.53 ! [F: nat > int,N: nat,M: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.53 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less_iff
% 0.29/0.53 thf(fact_213_lift__Suc__mono__less,axiom,
% 0.29/0.53 ! [F: nat > real,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less
% 0.29/0.53 thf(fact_214_lift__Suc__mono__less,axiom,
% 0.29/0.53 ! [F: nat > rat,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less
% 0.29/0.53 thf(fact_215_lift__Suc__mono__less,axiom,
% 0.29/0.53 ! [F: nat > num,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less
% 0.29/0.53 thf(fact_216_lift__Suc__mono__less,axiom,
% 0.29/0.53 ! [F: nat > nat,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less
% 0.29/0.53 thf(fact_217_lift__Suc__mono__less,axiom,
% 0.29/0.53 ! [F: nat > int,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_less
% 0.29/0.53 thf(fact_218_Ex__less__Suc2,axiom,
% 0.29/0.53 ! [N: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ? [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.53 & ( P2 @ I3 ) ) )
% 0.29/0.53 = ( ( P2 @ zero_zero_nat )
% 0.29/0.53 | ? [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ N )
% 0.29/0.53 & ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Ex_less_Suc2
% 0.29/0.53 thf(fact_219_gr0__conv__Suc,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.53 = ( ? [M5: nat] :
% 0.29/0.53 ( N
% 0.29/0.53 = ( suc @ M5 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr0_conv_Suc
% 0.29/0.53 thf(fact_220_All__less__Suc2,axiom,
% 0.29/0.53 ! [N: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.29/0.53 => ( P2 @ I3 ) ) )
% 0.29/0.53 = ( ( P2 @ zero_zero_nat )
% 0.29/0.53 & ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ N )
% 0.29/0.53 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % All_less_Suc2
% 0.29/0.53 thf(fact_221_gr0__implies__Suc,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.53 => ? [M3: nat] :
% 0.29/0.53 ( N
% 0.29/0.53 = ( suc @ M3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % gr0_implies_Suc
% 0.29/0.53 thf(fact_222_less__Suc__eq__0__disj,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.53 = ( ( M = zero_zero_nat )
% 0.29/0.53 | ? [J3: nat] :
% 0.29/0.53 ( ( M
% 0.29/0.53 = ( suc @ J3 ) )
% 0.29/0.53 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_Suc_eq_0_disj
% 0.29/0.53 thf(fact_223_vebt__delete_Osimps_I3_J,axiom,
% 0.29/0.53 ! [A: $o,B: $o,N: nat] :
% 0.29/0.53 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.29/0.53 = ( vEBT_Leaf @ A @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % vebt_delete.simps(3)
% 0.29/0.53 thf(fact_224_vebt__delete_Osimps_I1_J,axiom,
% 0.29/0.53 ! [A: $o,B: $o] :
% 0.29/0.53 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.29/0.53 = ( vEBT_Leaf @ $false @ B ) ) ).
% 0.29/0.53
% 0.29/0.53 % vebt_delete.simps(1)
% 0.29/0.53 thf(fact_225_succ__member,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 0.29/0.53 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 0.29/0.53 = ( ( vEBT_vebt_member @ T @ Y )
% 0.29/0.53 & ( ord_less_nat @ X @ Y )
% 0.29/0.53 & ! [Z2: nat] :
% 0.29/0.53 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 0.29/0.53 & ( ord_less_nat @ X @ Z2 ) )
% 0.29/0.53 => ( ord_less_eq_nat @ Y @ Z2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % succ_member
% 0.29/0.53 thf(fact_226_pred__member,axiom,
% 0.29/0.53 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 0.29/0.53 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 0.29/0.53 = ( ( vEBT_vebt_member @ T @ Y )
% 0.29/0.53 & ( ord_less_nat @ Y @ X )
% 0.29/0.53 & ! [Z2: nat] :
% 0.29/0.53 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 0.29/0.53 & ( ord_less_nat @ Z2 @ X ) )
% 0.29/0.53 => ( ord_less_eq_nat @ Z2 @ Y ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % pred_member
% 0.29/0.53 thf(fact_227_buildup__nothing__in__leaf,axiom,
% 0.29/0.53 ! [N: nat,X: nat] :
% 0.29/0.53 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.29/0.53
% 0.29/0.53 % buildup_nothing_in_leaf
% 0.29/0.53 thf(fact_228_VEBT__internal_OT__vebt__buildupi_Osimps_I2_J,axiom,
% 0.29/0.53 ( ( vEBT_V441764108873111860ildupi @ ( suc @ zero_zero_nat ) )
% 0.29/0.53 = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.T_vebt_buildupi.simps(2)
% 0.29/0.53 thf(fact_229_VEBT__internal_OT__vebt__buildupi_Osimps_I1_J,axiom,
% 0.29/0.53 ( ( vEBT_V441764108873111860ildupi @ zero_zero_nat )
% 0.29/0.53 = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.T_vebt_buildupi.simps(1)
% 0.29/0.53 thf(fact_230_VEBT__internal_Oinsert_H_Ocases,axiom,
% 0.29/0.53 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.53 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.29/0.53 ( X
% 0.29/0.53 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.29/0.53 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.53 ( X
% 0.29/0.53 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ X3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.insert'.cases
% 0.29/0.53 thf(fact_231_forall__finite_I3_J,axiom,
% 0.29/0.53 ! [X: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ ( suc @ X ) ) )
% 0.29/0.53 => ( P2 @ I3 ) ) )
% 0.29/0.53 = ( ( P2 @ zero_zero_nat )
% 0.29/0.53 & ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ X ) )
% 0.29/0.53 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % forall_finite(3)
% 0.29/0.53 thf(fact_232_forall__finite_I2_J,axiom,
% 0.29/0.53 ! [P2: nat > $o] :
% 0.29/0.53 ( ( ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ zero_zero_nat ) )
% 0.29/0.53 => ( P2 @ I3 ) ) )
% 0.29/0.53 = ( P2 @ zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % forall_finite(2)
% 0.29/0.53 thf(fact_233_Comparator__Generator_OAll__less__Suc,axiom,
% 0.29/0.53 ! [X: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ ( suc @ X ) )
% 0.29/0.53 => ( P2 @ I3 ) ) )
% 0.29/0.53 = ( ( P2 @ zero_zero_nat )
% 0.29/0.53 & ! [I3: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I3 @ X )
% 0.29/0.53 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Comparator_Generator.All_less_Suc
% 0.29/0.53 thf(fact_234_infinite__growing,axiom,
% 0.29/0.53 ! [X6: set_Code_integer] :
% 0.29/0.53 ( ( X6 != bot_bo3990330152332043303nteger )
% 0.29/0.53 => ( ! [X3: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X3 @ X6 )
% 0.29/0.53 => ? [Xa: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ Xa @ X6 )
% 0.29/0.53 & ( ord_le6747313008572928689nteger @ X3 @ Xa ) ) )
% 0.29/0.53 => ~ ( finite6017078050557962740nteger @ X6 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_growing
% 0.29/0.53 thf(fact_235_infinite__growing,axiom,
% 0.29/0.53 ! [X6: set_o] :
% 0.29/0.53 ( ( X6 != bot_bot_set_o )
% 0.29/0.53 => ( ! [X3: $o] :
% 0.29/0.53 ( ( member_o @ X3 @ X6 )
% 0.29/0.53 => ? [Xa: $o] :
% 0.29/0.53 ( ( member_o @ Xa @ X6 )
% 0.29/0.53 & ( ord_less_o @ X3 @ Xa ) ) )
% 0.29/0.53 => ~ ( finite_finite_o @ X6 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_growing
% 0.29/0.53 thf(fact_236_infinite__growing,axiom,
% 0.29/0.53 ! [X6: set_real] :
% 0.29/0.53 ( ( X6 != bot_bot_set_real )
% 0.29/0.53 => ( ! [X3: real] :
% 0.29/0.53 ( ( member_real @ X3 @ X6 )
% 0.29/0.53 => ? [Xa: real] :
% 0.29/0.53 ( ( member_real @ Xa @ X6 )
% 0.29/0.53 & ( ord_less_real @ X3 @ Xa ) ) )
% 0.29/0.53 => ~ ( finite_finite_real @ X6 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_growing
% 0.29/0.53 thf(fact_237_infinite__growing,axiom,
% 0.29/0.53 ! [X6: set_rat] :
% 0.29/0.53 ( ( X6 != bot_bot_set_rat )
% 0.29/0.53 => ( ! [X3: rat] :
% 0.29/0.53 ( ( member_rat @ X3 @ X6 )
% 0.29/0.53 => ? [Xa: rat] :
% 0.29/0.53 ( ( member_rat @ Xa @ X6 )
% 0.29/0.53 & ( ord_less_rat @ X3 @ Xa ) ) )
% 0.29/0.53 => ~ ( finite_finite_rat @ X6 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_growing
% 0.29/0.53 thf(fact_238_infinite__growing,axiom,
% 0.29/0.53 ! [X6: set_num] :
% 0.29/0.53 ( ( X6 != bot_bot_set_num )
% 0.29/0.53 => ( ! [X3: num] :
% 0.29/0.53 ( ( member_num @ X3 @ X6 )
% 0.29/0.53 => ? [Xa: num] :
% 0.29/0.53 ( ( member_num @ Xa @ X6 )
% 0.29/0.53 & ( ord_less_num @ X3 @ Xa ) ) )
% 0.29/0.53 => ~ ( finite_finite_num @ X6 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_growing
% 0.29/0.53 thf(fact_239_infinite__growing,axiom,
% 0.29/0.53 ! [X6: set_nat] :
% 0.29/0.53 ( ( X6 != bot_bot_set_nat )
% 0.29/0.53 => ( ! [X3: nat] :
% 0.29/0.53 ( ( member_nat @ X3 @ X6 )
% 0.29/0.53 => ? [Xa: nat] :
% 0.29/0.53 ( ( member_nat @ Xa @ X6 )
% 0.29/0.53 & ( ord_less_nat @ X3 @ Xa ) ) )
% 0.29/0.53 => ~ ( finite_finite_nat @ X6 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_growing
% 0.29/0.53 thf(fact_240_infinite__growing,axiom,
% 0.29/0.53 ! [X6: set_int] :
% 0.29/0.53 ( ( X6 != bot_bot_set_int )
% 0.29/0.53 => ( ! [X3: int] :
% 0.29/0.53 ( ( member_int @ X3 @ X6 )
% 0.29/0.53 => ? [Xa: int] :
% 0.29/0.53 ( ( member_int @ Xa @ X6 )
% 0.29/0.53 & ( ord_less_int @ X3 @ Xa ) ) )
% 0.29/0.53 => ~ ( finite_finite_int @ X6 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_growing
% 0.29/0.53 thf(fact_241_ex__min__if__finite,axiom,
% 0.29/0.53 ! [S3: set_Code_integer] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ S3 )
% 0.29/0.53 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.29/0.53 => ? [X3: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X3 @ S3 )
% 0.29/0.53 & ~ ? [Xa: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ Xa @ S3 )
% 0.29/0.53 & ( ord_le6747313008572928689nteger @ Xa @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_min_if_finite
% 0.29/0.53 thf(fact_242_ex__min__if__finite,axiom,
% 0.29/0.53 ! [S3: set_o] :
% 0.29/0.53 ( ( finite_finite_o @ S3 )
% 0.29/0.53 => ( ( S3 != bot_bot_set_o )
% 0.29/0.53 => ? [X3: $o] :
% 0.29/0.53 ( ( member_o @ X3 @ S3 )
% 0.29/0.53 & ~ ? [Xa: $o] :
% 0.29/0.53 ( ( member_o @ Xa @ S3 )
% 0.29/0.53 & ( ord_less_o @ Xa @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_min_if_finite
% 0.29/0.53 thf(fact_243_ex__min__if__finite,axiom,
% 0.29/0.53 ! [S3: set_real] :
% 0.29/0.53 ( ( finite_finite_real @ S3 )
% 0.29/0.53 => ( ( S3 != bot_bot_set_real )
% 0.29/0.53 => ? [X3: real] :
% 0.29/0.53 ( ( member_real @ X3 @ S3 )
% 0.29/0.53 & ~ ? [Xa: real] :
% 0.29/0.53 ( ( member_real @ Xa @ S3 )
% 0.29/0.53 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_min_if_finite
% 0.29/0.53 thf(fact_244_ex__min__if__finite,axiom,
% 0.29/0.53 ! [S3: set_rat] :
% 0.29/0.53 ( ( finite_finite_rat @ S3 )
% 0.29/0.53 => ( ( S3 != bot_bot_set_rat )
% 0.29/0.53 => ? [X3: rat] :
% 0.29/0.53 ( ( member_rat @ X3 @ S3 )
% 0.29/0.53 & ~ ? [Xa: rat] :
% 0.29/0.53 ( ( member_rat @ Xa @ S3 )
% 0.29/0.53 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_min_if_finite
% 0.29/0.53 thf(fact_245_ex__min__if__finite,axiom,
% 0.29/0.53 ! [S3: set_num] :
% 0.29/0.53 ( ( finite_finite_num @ S3 )
% 0.29/0.53 => ( ( S3 != bot_bot_set_num )
% 0.29/0.53 => ? [X3: num] :
% 0.29/0.53 ( ( member_num @ X3 @ S3 )
% 0.29/0.53 & ~ ? [Xa: num] :
% 0.29/0.53 ( ( member_num @ Xa @ S3 )
% 0.29/0.53 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_min_if_finite
% 0.29/0.53 thf(fact_246_ex__min__if__finite,axiom,
% 0.29/0.53 ! [S3: set_nat] :
% 0.29/0.53 ( ( finite_finite_nat @ S3 )
% 0.29/0.53 => ( ( S3 != bot_bot_set_nat )
% 0.29/0.53 => ? [X3: nat] :
% 0.29/0.53 ( ( member_nat @ X3 @ S3 )
% 0.29/0.53 & ~ ? [Xa: nat] :
% 0.29/0.53 ( ( member_nat @ Xa @ S3 )
% 0.29/0.53 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_min_if_finite
% 0.29/0.53 thf(fact_247_ex__min__if__finite,axiom,
% 0.29/0.53 ! [S3: set_int] :
% 0.29/0.53 ( ( finite_finite_int @ S3 )
% 0.29/0.53 => ( ( S3 != bot_bot_set_int )
% 0.29/0.53 => ? [X3: int] :
% 0.29/0.53 ( ( member_int @ X3 @ S3 )
% 0.29/0.53 & ~ ? [Xa: int] :
% 0.29/0.53 ( ( member_int @ Xa @ S3 )
% 0.29/0.53 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_min_if_finite
% 0.29/0.53 thf(fact_248_empty__Collect__eq,axiom,
% 0.29/0.53 ! [P2: complex > $o] :
% 0.29/0.53 ( ( bot_bot_set_complex
% 0.29/0.53 = ( collect_complex @ P2 ) )
% 0.29/0.53 = ( ! [X4: complex] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % empty_Collect_eq
% 0.29/0.53 thf(fact_249_empty__Collect__eq,axiom,
% 0.29/0.53 ! [P2: list_nat > $o] :
% 0.29/0.53 ( ( bot_bot_set_list_nat
% 0.29/0.53 = ( collect_list_nat @ P2 ) )
% 0.29/0.53 = ( ! [X4: list_nat] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % empty_Collect_eq
% 0.29/0.53 thf(fact_250_empty__Collect__eq,axiom,
% 0.29/0.53 ! [P2: set_nat > $o] :
% 0.29/0.53 ( ( bot_bot_set_set_nat
% 0.29/0.53 = ( collect_set_nat @ P2 ) )
% 0.29/0.53 = ( ! [X4: set_nat] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % empty_Collect_eq
% 0.29/0.53 thf(fact_251_empty__Collect__eq,axiom,
% 0.29/0.53 ! [P2: nat > $o] :
% 0.29/0.53 ( ( bot_bot_set_nat
% 0.29/0.53 = ( collect_nat @ P2 ) )
% 0.29/0.53 = ( ! [X4: nat] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % empty_Collect_eq
% 0.29/0.53 thf(fact_252_empty__Collect__eq,axiom,
% 0.29/0.53 ! [P2: int > $o] :
% 0.29/0.53 ( ( bot_bot_set_int
% 0.29/0.53 = ( collect_int @ P2 ) )
% 0.29/0.53 = ( ! [X4: int] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % empty_Collect_eq
% 0.29/0.53 thf(fact_253_empty__Collect__eq,axiom,
% 0.29/0.53 ! [P2: $o > $o] :
% 0.29/0.53 ( ( bot_bot_set_o
% 0.29/0.53 = ( collect_o @ P2 ) )
% 0.29/0.53 = ( ! [X4: $o] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % empty_Collect_eq
% 0.29/0.53 thf(fact_254_max__in__set__def,axiom,
% 0.29/0.53 ( vEBT_VEBT_max_in_set
% 0.29/0.53 = ( ^ [Xs2: set_nat,X4: nat] :
% 0.29/0.53 ( ( member_nat @ X4 @ Xs2 )
% 0.29/0.53 & ! [Y4: nat] :
% 0.29/0.53 ( ( member_nat @ Y4 @ Xs2 )
% 0.29/0.53 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % max_in_set_def
% 0.29/0.53 thf(fact_255_min__in__set__def,axiom,
% 0.29/0.53 ( vEBT_VEBT_min_in_set
% 0.29/0.53 = ( ^ [Xs2: set_nat,X4: nat] :
% 0.29/0.53 ( ( member_nat @ X4 @ Xs2 )
% 0.29/0.53 & ! [Y4: nat] :
% 0.29/0.53 ( ( member_nat @ Y4 @ Xs2 )
% 0.29/0.53 => ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % min_in_set_def
% 0.29/0.53 thf(fact_256_empty__iff,axiom,
% 0.29/0.53 ! [C2: vEBT_VEBT] :
% 0.29/0.53 ~ ( member_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ).
% 0.29/0.53
% 0.29/0.53 % empty_iff
% 0.29/0.53 thf(fact_257_empty__iff,axiom,
% 0.29/0.53 ! [C2: real] :
% 0.29/0.53 ~ ( member_real @ C2 @ bot_bot_set_real ) ).
% 0.29/0.53
% 0.29/0.53 % empty_iff
% 0.29/0.53 thf(fact_258_empty__iff,axiom,
% 0.29/0.53 ! [C2: set_nat] :
% 0.29/0.53 ~ ( member_set_nat @ C2 @ bot_bot_set_set_nat ) ).
% 0.29/0.53
% 0.29/0.53 % empty_iff
% 0.29/0.53 thf(fact_259_empty__iff,axiom,
% 0.29/0.53 ! [C2: nat] :
% 0.29/0.53 ~ ( member_nat @ C2 @ bot_bot_set_nat ) ).
% 0.29/0.53
% 0.29/0.53 % empty_iff
% 0.29/0.53 thf(fact_260_empty__iff,axiom,
% 0.29/0.53 ! [C2: int] :
% 0.29/0.53 ~ ( member_int @ C2 @ bot_bot_set_int ) ).
% 0.29/0.53
% 0.29/0.53 % empty_iff
% 0.29/0.53 thf(fact_261_empty__iff,axiom,
% 0.29/0.53 ! [C2: $o] :
% 0.29/0.53 ~ ( member_o @ C2 @ bot_bot_set_o ) ).
% 0.29/0.53
% 0.29/0.53 % empty_iff
% 0.29/0.53 thf(fact_262_all__not__in__conv,axiom,
% 0.29/0.53 ! [A4: set_VEBT_VEBT] :
% 0.29/0.53 ( ( ! [X4: vEBT_VEBT] :
% 0.29/0.53 ~ ( member_VEBT_VEBT @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 = bot_bo8194388402131092736T_VEBT ) ) ).
% 0.29/0.53
% 0.29/0.53 % all_not_in_conv
% 0.29/0.53 thf(fact_263_all__not__in__conv,axiom,
% 0.29/0.53 ! [A4: set_real] :
% 0.29/0.53 ( ( ! [X4: real] :
% 0.29/0.53 ~ ( member_real @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 = bot_bot_set_real ) ) ).
% 0.29/0.53
% 0.29/0.53 % all_not_in_conv
% 0.29/0.53 thf(fact_264_all__not__in__conv,axiom,
% 0.29/0.53 ! [A4: set_set_nat] :
% 0.29/0.53 ( ( ! [X4: set_nat] :
% 0.29/0.53 ~ ( member_set_nat @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 = bot_bot_set_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % all_not_in_conv
% 0.29/0.53 thf(fact_265_all__not__in__conv,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ( ! [X4: nat] :
% 0.29/0.53 ~ ( member_nat @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 = bot_bot_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % all_not_in_conv
% 0.29/0.53 thf(fact_266_all__not__in__conv,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ( ! [X4: int] :
% 0.29/0.53 ~ ( member_int @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 = bot_bot_set_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % all_not_in_conv
% 0.29/0.53 thf(fact_267_all__not__in__conv,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ( ( ! [X4: $o] :
% 0.29/0.53 ~ ( member_o @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 = bot_bot_set_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % all_not_in_conv
% 0.29/0.53 thf(fact_268_Collect__empty__eq,axiom,
% 0.29/0.53 ! [P2: complex > $o] :
% 0.29/0.53 ( ( ( collect_complex @ P2 )
% 0.29/0.53 = bot_bot_set_complex )
% 0.29/0.53 = ( ! [X4: complex] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_empty_eq
% 0.29/0.53 thf(fact_269_Collect__empty__eq,axiom,
% 0.29/0.53 ! [P2: list_nat > $o] :
% 0.29/0.53 ( ( ( collect_list_nat @ P2 )
% 0.29/0.53 = bot_bot_set_list_nat )
% 0.29/0.53 = ( ! [X4: list_nat] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_empty_eq
% 0.29/0.53 thf(fact_270_Collect__empty__eq,axiom,
% 0.29/0.53 ! [P2: set_nat > $o] :
% 0.29/0.53 ( ( ( collect_set_nat @ P2 )
% 0.29/0.53 = bot_bot_set_set_nat )
% 0.29/0.53 = ( ! [X4: set_nat] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_empty_eq
% 0.29/0.53 thf(fact_271_Collect__empty__eq,axiom,
% 0.29/0.53 ! [P2: nat > $o] :
% 0.29/0.53 ( ( ( collect_nat @ P2 )
% 0.29/0.53 = bot_bot_set_nat )
% 0.29/0.53 = ( ! [X4: nat] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_empty_eq
% 0.29/0.53 thf(fact_272_Collect__empty__eq,axiom,
% 0.29/0.53 ! [P2: int > $o] :
% 0.29/0.53 ( ( ( collect_int @ P2 )
% 0.29/0.53 = bot_bot_set_int )
% 0.29/0.53 = ( ! [X4: int] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_empty_eq
% 0.29/0.53 thf(fact_273_Collect__empty__eq,axiom,
% 0.29/0.53 ! [P2: $o > $o] :
% 0.29/0.53 ( ( ( collect_o @ P2 )
% 0.29/0.53 = bot_bot_set_o )
% 0.29/0.53 = ( ! [X4: $o] :
% 0.29/0.53 ~ ( P2 @ X4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Collect_empty_eq
% 0.29/0.53 thf(fact_274_le__zero__eq,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.53 = ( N = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_zero_eq
% 0.29/0.53 thf(fact_275_Suc__le__mono,axiom,
% 0.29/0.53 ! [N: nat,M: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.29/0.53 = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_le_mono
% 0.29/0.53 thf(fact_276_bot__nat__0_Oextremum,axiom,
% 0.29/0.53 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.29/0.53
% 0.29/0.53 % bot_nat_0.extremum
% 0.29/0.53 thf(fact_277_le0,axiom,
% 0.29/0.53 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.53
% 0.29/0.53 % le0
% 0.29/0.53 thf(fact_278_psubsetD,axiom,
% 0.29/0.53 ! [A4: set_nat,B4: set_nat,C2: nat] :
% 0.29/0.53 ( ( ord_less_set_nat @ A4 @ B4 )
% 0.29/0.53 => ( ( member_nat @ C2 @ A4 )
% 0.29/0.53 => ( member_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubsetD
% 0.29/0.53 thf(fact_279_psubsetD,axiom,
% 0.29/0.53 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,C2: vEBT_VEBT] :
% 0.29/0.53 ( ( ord_le3480810397992357184T_VEBT @ A4 @ B4 )
% 0.29/0.53 => ( ( member_VEBT_VEBT @ C2 @ A4 )
% 0.29/0.53 => ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubsetD
% 0.29/0.53 thf(fact_280_psubsetD,axiom,
% 0.29/0.53 ! [A4: set_real,B4: set_real,C2: real] :
% 0.29/0.53 ( ( ord_less_set_real @ A4 @ B4 )
% 0.29/0.53 => ( ( member_real @ C2 @ A4 )
% 0.29/0.53 => ( member_real @ C2 @ B4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubsetD
% 0.29/0.53 thf(fact_281_psubsetD,axiom,
% 0.29/0.53 ! [A4: set_int,B4: set_int,C2: int] :
% 0.29/0.53 ( ( ord_less_set_int @ A4 @ B4 )
% 0.29/0.53 => ( ( member_int @ C2 @ A4 )
% 0.29/0.53 => ( member_int @ C2 @ B4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubsetD
% 0.29/0.53 thf(fact_282_psubsetD,axiom,
% 0.29/0.53 ! [A4: set_set_nat,B4: set_set_nat,C2: set_nat] :
% 0.29/0.53 ( ( ord_less_set_set_nat @ A4 @ B4 )
% 0.29/0.53 => ( ( member_set_nat @ C2 @ A4 )
% 0.29/0.53 => ( member_set_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubsetD
% 0.29/0.53 thf(fact_283_Nat_Oex__has__greatest__nat,axiom,
% 0.29/0.53 ! [P2: nat > $o,K: nat,B: nat] :
% 0.29/0.53 ( ( P2 @ K )
% 0.29/0.53 => ( ! [Y3: nat] :
% 0.29/0.53 ( ( P2 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.29/0.53 => ? [X3: nat] :
% 0.29/0.53 ( ( P2 @ X3 )
% 0.29/0.53 & ! [Y5: nat] :
% 0.29/0.53 ( ( P2 @ Y5 )
% 0.29/0.53 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Nat.ex_has_greatest_nat
% 0.29/0.53 thf(fact_284_nat__le__linear,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_le_linear
% 0.29/0.53 thf(fact_285_le__antisym,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.53 => ( M = N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_antisym
% 0.29/0.53 thf(fact_286_eq__imp__le,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( M = N )
% 0.29/0.53 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % eq_imp_le
% 0.29/0.53 thf(fact_287_le__trans,axiom,
% 0.29/0.53 ! [I: nat,J: nat,K: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.53 => ( ( ord_less_eq_nat @ J @ K )
% 0.29/0.53 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_trans
% 0.29/0.53 thf(fact_288_le__refl,axiom,
% 0.29/0.53 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.29/0.53
% 0.29/0.53 % le_refl
% 0.29/0.53 thf(fact_289_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: set_int,B: set_int,C2: set_int,D: set_int] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ B @ C2 )
% 0.29/0.53 => ( ( C2 = D )
% 0.29/0.53 => ( ord_less_eq_set_int @ A @ D ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_290_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.53 => ( ( C2 = D )
% 0.29/0.53 => ( ord_less_eq_rat @ A @ D ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_291_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: num,B: num,C2: num,D: num] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.53 => ( ( C2 = D )
% 0.29/0.53 => ( ord_less_eq_num @ A @ D ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_292_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.53 => ( ( C2 = D )
% 0.29/0.53 => ( ord_less_eq_nat @ A @ D ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_293_ord__eq__le__eq__trans,axiom,
% 0.29/0.53 ! [A: int,B: int,C2: int,D: int] :
% 0.29/0.53 ( ( A = B )
% 0.29/0.53 => ( ( ord_less_eq_int @ B @ C2 )
% 0.29/0.53 => ( ( C2 = D )
% 0.29/0.53 => ( ord_less_eq_int @ A @ D ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_eq_trans
% 0.29/0.53 thf(fact_294_lift__Suc__antimono__le,axiom,
% 0.29/0.53 ! [F: nat > set_int,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_antimono_le
% 0.29/0.53 thf(fact_295_lift__Suc__antimono__le,axiom,
% 0.29/0.53 ! [F: nat > rat,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_antimono_le
% 0.29/0.53 thf(fact_296_lift__Suc__antimono__le,axiom,
% 0.29/0.53 ! [F: nat > num,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_antimono_le
% 0.29/0.53 thf(fact_297_lift__Suc__antimono__le,axiom,
% 0.29/0.53 ! [F: nat > nat,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_antimono_le
% 0.29/0.53 thf(fact_298_lift__Suc__antimono__le,axiom,
% 0.29/0.53 ! [F: nat > int,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_antimono_le
% 0.29/0.53 thf(fact_299_lift__Suc__mono__le,axiom,
% 0.29/0.53 ! [F: nat > set_int,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_le
% 0.29/0.53 thf(fact_300_lift__Suc__mono__le,axiom,
% 0.29/0.53 ! [F: nat > rat,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_le
% 0.29/0.53 thf(fact_301_lift__Suc__mono__le,axiom,
% 0.29/0.53 ! [F: nat > num,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_le
% 0.29/0.53 thf(fact_302_lift__Suc__mono__le,axiom,
% 0.29/0.53 ! [F: nat > nat,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_le
% 0.29/0.53 thf(fact_303_lift__Suc__mono__le,axiom,
% 0.29/0.53 ! [F: nat > int,N: nat,N3: nat] :
% 0.29/0.53 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ N @ N3 )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % lift_Suc_mono_le
% 0.29/0.53 thf(fact_304_zero__le,axiom,
% 0.29/0.53 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.29/0.53
% 0.29/0.53 % zero_le
% 0.29/0.53 thf(fact_305_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_real,A: real] :
% 0.29/0.53 ( ( finite_finite_real @ A4 )
% 0.29/0.53 => ( ( member_real @ A @ A4 )
% 0.29/0.53 => ? [X3: real] :
% 0.29/0.53 ( ( member_real @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_real @ A @ X3 )
% 0.29/0.53 & ! [Xa: real] :
% 0.29/0.53 ( ( member_real @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_real @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_306_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_set_nat,A: set_nat] :
% 0.29/0.53 ( ( finite1152437895449049373et_nat @ A4 )
% 0.29/0.53 => ( ( member_set_nat @ A @ A4 )
% 0.29/0.53 => ? [X3: set_nat] :
% 0.29/0.53 ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_set_nat @ A @ X3 )
% 0.29/0.53 & ! [Xa: set_nat] :
% 0.29/0.53 ( ( member_set_nat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_307_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_Code_integer,A: code_integer] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.53 => ( ( member_Code_integer @ A @ A4 )
% 0.29/0.53 => ? [X3: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X3 @ A4 )
% 0.29/0.53 & ( ord_le3102999989581377725nteger @ A @ X3 )
% 0.29/0.53 & ! [Xa: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_308_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_set_int,A: set_int] :
% 0.29/0.53 ( ( finite6197958912794628473et_int @ A4 )
% 0.29/0.53 => ( ( member_set_int @ A @ A4 )
% 0.29/0.53 => ? [X3: set_int] :
% 0.29/0.53 ( ( member_set_int @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_set_int @ A @ X3 )
% 0.29/0.53 & ! [Xa: set_int] :
% 0.29/0.53 ( ( member_set_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_309_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_rat,A: rat] :
% 0.29/0.53 ( ( finite_finite_rat @ A4 )
% 0.29/0.53 => ( ( member_rat @ A @ A4 )
% 0.29/0.53 => ? [X3: rat] :
% 0.29/0.53 ( ( member_rat @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_rat @ A @ X3 )
% 0.29/0.53 & ! [Xa: rat] :
% 0.29/0.53 ( ( member_rat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_310_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_num,A: num] :
% 0.29/0.53 ( ( finite_finite_num @ A4 )
% 0.29/0.53 => ( ( member_num @ A @ A4 )
% 0.29/0.53 => ? [X3: num] :
% 0.29/0.53 ( ( member_num @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_num @ A @ X3 )
% 0.29/0.53 & ! [Xa: num] :
% 0.29/0.53 ( ( member_num @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_num @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_311_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_nat,A: nat] :
% 0.29/0.53 ( ( finite_finite_nat @ A4 )
% 0.29/0.53 => ( ( member_nat @ A @ A4 )
% 0.29/0.53 => ? [X3: nat] :
% 0.29/0.53 ( ( member_nat @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_nat @ A @ X3 )
% 0.29/0.53 & ! [Xa: nat] :
% 0.29/0.53 ( ( member_nat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_312_finite__has__maximal2,axiom,
% 0.29/0.53 ! [A4: set_int,A: int] :
% 0.29/0.53 ( ( finite_finite_int @ A4 )
% 0.29/0.53 => ( ( member_int @ A @ A4 )
% 0.29/0.53 => ? [X3: int] :
% 0.29/0.53 ( ( member_int @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_int @ A @ X3 )
% 0.29/0.53 & ! [Xa: int] :
% 0.29/0.53 ( ( member_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_int @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal2
% 0.29/0.53 thf(fact_313_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_real,A: real] :
% 0.29/0.53 ( ( finite_finite_real @ A4 )
% 0.29/0.53 => ( ( member_real @ A @ A4 )
% 0.29/0.53 => ? [X3: real] :
% 0.29/0.53 ( ( member_real @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_real @ X3 @ A )
% 0.29/0.53 & ! [Xa: real] :
% 0.29/0.53 ( ( member_real @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_real @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_314_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_set_nat,A: set_nat] :
% 0.29/0.53 ( ( finite1152437895449049373et_nat @ A4 )
% 0.29/0.53 => ( ( member_set_nat @ A @ A4 )
% 0.29/0.53 => ? [X3: set_nat] :
% 0.29/0.53 ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_set_nat @ X3 @ A )
% 0.29/0.53 & ! [Xa: set_nat] :
% 0.29/0.53 ( ( member_set_nat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_315_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_Code_integer,A: code_integer] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.53 => ( ( member_Code_integer @ A @ A4 )
% 0.29/0.53 => ? [X3: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X3 @ A4 )
% 0.29/0.53 & ( ord_le3102999989581377725nteger @ X3 @ A )
% 0.29/0.53 & ! [Xa: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_le3102999989581377725nteger @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_316_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_set_int,A: set_int] :
% 0.29/0.53 ( ( finite6197958912794628473et_int @ A4 )
% 0.29/0.53 => ( ( member_set_int @ A @ A4 )
% 0.29/0.53 => ? [X3: set_int] :
% 0.29/0.53 ( ( member_set_int @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_set_int @ X3 @ A )
% 0.29/0.53 & ! [Xa: set_int] :
% 0.29/0.53 ( ( member_set_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_317_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_rat,A: rat] :
% 0.29/0.53 ( ( finite_finite_rat @ A4 )
% 0.29/0.53 => ( ( member_rat @ A @ A4 )
% 0.29/0.53 => ? [X3: rat] :
% 0.29/0.53 ( ( member_rat @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_rat @ X3 @ A )
% 0.29/0.53 & ! [Xa: rat] :
% 0.29/0.53 ( ( member_rat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_318_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_num,A: num] :
% 0.29/0.53 ( ( finite_finite_num @ A4 )
% 0.29/0.53 => ( ( member_num @ A @ A4 )
% 0.29/0.53 => ? [X3: num] :
% 0.29/0.53 ( ( member_num @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_num @ X3 @ A )
% 0.29/0.53 & ! [Xa: num] :
% 0.29/0.53 ( ( member_num @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_num @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_319_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_nat,A: nat] :
% 0.29/0.53 ( ( finite_finite_nat @ A4 )
% 0.29/0.53 => ( ( member_nat @ A @ A4 )
% 0.29/0.53 => ? [X3: nat] :
% 0.29/0.53 ( ( member_nat @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_nat @ X3 @ A )
% 0.29/0.53 & ! [Xa: nat] :
% 0.29/0.53 ( ( member_nat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_320_finite__has__minimal2,axiom,
% 0.29/0.53 ! [A4: set_int,A: int] :
% 0.29/0.53 ( ( finite_finite_int @ A4 )
% 0.29/0.53 => ( ( member_int @ A @ A4 )
% 0.29/0.53 => ? [X3: int] :
% 0.29/0.53 ( ( member_int @ X3 @ A4 )
% 0.29/0.53 & ( ord_less_eq_int @ X3 @ A )
% 0.29/0.53 & ! [Xa: int] :
% 0.29/0.53 ( ( member_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_int @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal2
% 0.29/0.53 thf(fact_321_Suc__leD,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.53 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_leD
% 0.29/0.53 thf(fact_322_le__SucE,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.29/0.53 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( M
% 0.29/0.53 = ( suc @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_SucE
% 0.29/0.53 thf(fact_323_le__SucI,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_SucI
% 0.29/0.53 thf(fact_324_Suc__le__D,axiom,
% 0.29/0.53 ! [N: nat,M6: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 0.29/0.53 => ? [M3: nat] :
% 0.29/0.53 ( M6
% 0.29/0.53 = ( suc @ M3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_le_D
% 0.29/0.53 thf(fact_325_le__Suc__eq,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.29/0.53 = ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 | ( M
% 0.29/0.53 = ( suc @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_Suc_eq
% 0.29/0.53 thf(fact_326_Suc__n__not__le__n,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_n_not_le_n
% 0.29/0.53 thf(fact_327_not__less__eq__eq,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.29/0.53 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.29/0.53
% 0.29/0.53 % not_less_eq_eq
% 0.29/0.53 thf(fact_328_full__nat__induct,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ! [N2: nat] :
% 0.29/0.53 ( ! [M2: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 0.29/0.53 => ( P2 @ M2 ) )
% 0.29/0.53 => ( P2 @ N2 ) )
% 0.29/0.53 => ( P2 @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % full_nat_induct
% 0.29/0.53 thf(fact_329_nat__induct__at__least,axiom,
% 0.29/0.53 ! [M: nat,N: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( ( P2 @ M )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N2 )
% 0.29/0.53 => ( ( P2 @ N2 )
% 0.29/0.53 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.29/0.53 => ( P2 @ N ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_induct_at_least
% 0.29/0.53 thf(fact_330_transitive__stepwise__le,axiom,
% 0.29/0.53 ! [M: nat,N: nat,R2: nat > nat > $o] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 0.29/0.53 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 0.29/0.53 ( ( R2 @ X3 @ Y3 )
% 0.29/0.53 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.53 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.53 => ( ! [N2: nat] : ( R2 @ N2 @ ( suc @ N2 ) )
% 0.29/0.53 => ( R2 @ M @ N ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % transitive_stepwise_le
% 0.29/0.53 thf(fact_331_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/0.53 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_nat.simps(1)
% 0.29/0.53 thf(fact_332_bot__nat__0_Oextremum__unique,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.53 = ( A = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_nat_0.extremum_unique
% 0.29/0.53 thf(fact_333_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.29/0.53 => ( A = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_nat_0.extremum_uniqueI
% 0.29/0.53 thf(fact_334_le__0__eq,axiom,
% 0.29/0.53 ! [N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.53 = ( N = zero_zero_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_0_eq
% 0.29/0.53 thf(fact_335_exists__leI,axiom,
% 0.29/0.53 ! [N: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ! [N4: nat] :
% 0.29/0.53 ( ( ord_less_nat @ N4 @ N )
% 0.29/0.53 => ~ ( P2 @ N4 ) )
% 0.29/0.53 => ( P2 @ N ) )
% 0.29/0.53 => ? [N5: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ N5 @ N )
% 0.29/0.53 & ( P2 @ N5 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % exists_leI
% 0.29/0.53 thf(fact_336_nat__less__le,axiom,
% 0.29/0.53 ( ord_less_nat
% 0.29/0.53 = ( ^ [M5: nat,N6: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M5 @ N6 )
% 0.29/0.53 & ( M5 != N6 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_less_le
% 0.29/0.53 thf(fact_337_less__imp__le__nat,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_imp_le_nat
% 0.29/0.53 thf(fact_338_le__eq__less__or__eq,axiom,
% 0.29/0.53 ( ord_less_eq_nat
% 0.29/0.53 = ( ^ [M5: nat,N6: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M5 @ N6 )
% 0.29/0.53 | ( M5 = N6 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_eq_less_or_eq
% 0.29/0.53 thf(fact_339_less__or__eq__imp__le,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ( ord_less_nat @ M @ N )
% 0.29/0.53 | ( M = N ) )
% 0.29/0.53 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_or_eq_imp_le
% 0.29/0.53 thf(fact_340_le__neq__implies__less,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( ( M != N )
% 0.29/0.53 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_neq_implies_less
% 0.29/0.53 thf(fact_341_less__mono__imp__le__mono,axiom,
% 0.29/0.53 ! [F: nat > nat,I: nat,J: nat] :
% 0.29/0.53 ( ! [I2: nat,J2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I2 @ J2 )
% 0.29/0.53 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_mono_imp_le_mono
% 0.29/0.53 thf(fact_342_finite__has__minimal,axiom,
% 0.29/0.53 ! [A4: set_Code_integer] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.53 => ? [X3: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_le3102999989581377725nteger @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal
% 0.29/0.53 thf(fact_343_finite__has__minimal,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ( ( finite_finite_o @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_o )
% 0.29/0.53 => ? [X3: $o] :
% 0.29/0.53 ( ( member_o @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: $o] :
% 0.29/0.53 ( ( member_o @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_o @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal
% 0.29/0.53 thf(fact_344_finite__has__minimal,axiom,
% 0.29/0.53 ! [A4: set_set_int] :
% 0.29/0.53 ( ( finite6197958912794628473et_int @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_set_int )
% 0.29/0.53 => ? [X3: set_int] :
% 0.29/0.53 ( ( member_set_int @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: set_int] :
% 0.29/0.53 ( ( member_set_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal
% 0.29/0.53 thf(fact_345_finite__has__minimal,axiom,
% 0.29/0.53 ! [A4: set_rat] :
% 0.29/0.53 ( ( finite_finite_rat @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.53 => ? [X3: rat] :
% 0.29/0.53 ( ( member_rat @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: rat] :
% 0.29/0.53 ( ( member_rat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal
% 0.29/0.53 thf(fact_346_finite__has__minimal,axiom,
% 0.29/0.53 ! [A4: set_num] :
% 0.29/0.53 ( ( finite_finite_num @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_num )
% 0.29/0.53 => ? [X3: num] :
% 0.29/0.53 ( ( member_num @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: num] :
% 0.29/0.53 ( ( member_num @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_num @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal
% 0.29/0.53 thf(fact_347_finite__has__minimal,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ( finite_finite_nat @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.53 => ? [X3: nat] :
% 0.29/0.53 ( ( member_nat @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: nat] :
% 0.29/0.53 ( ( member_nat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal
% 0.29/0.53 thf(fact_348_finite__has__minimal,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ( finite_finite_int @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_int )
% 0.29/0.53 => ? [X3: int] :
% 0.29/0.53 ( ( member_int @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: int] :
% 0.29/0.53 ( ( member_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_int @ Xa @ X3 )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_minimal
% 0.29/0.53 thf(fact_349_finite__has__maximal,axiom,
% 0.29/0.53 ! [A4: set_Code_integer] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.53 => ? [X3: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: code_integer] :
% 0.29/0.53 ( ( member_Code_integer @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal
% 0.29/0.53 thf(fact_350_finite__has__maximal,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ( ( finite_finite_o @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_o )
% 0.29/0.53 => ? [X3: $o] :
% 0.29/0.53 ( ( member_o @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: $o] :
% 0.29/0.53 ( ( member_o @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_o @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal
% 0.29/0.53 thf(fact_351_finite__has__maximal,axiom,
% 0.29/0.53 ! [A4: set_set_int] :
% 0.29/0.53 ( ( finite6197958912794628473et_int @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_set_int )
% 0.29/0.53 => ? [X3: set_int] :
% 0.29/0.53 ( ( member_set_int @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: set_int] :
% 0.29/0.53 ( ( member_set_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal
% 0.29/0.53 thf(fact_352_finite__has__maximal,axiom,
% 0.29/0.53 ! [A4: set_rat] :
% 0.29/0.53 ( ( finite_finite_rat @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.53 => ? [X3: rat] :
% 0.29/0.53 ( ( member_rat @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: rat] :
% 0.29/0.53 ( ( member_rat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal
% 0.29/0.53 thf(fact_353_finite__has__maximal,axiom,
% 0.29/0.53 ! [A4: set_num] :
% 0.29/0.53 ( ( finite_finite_num @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_num )
% 0.29/0.53 => ? [X3: num] :
% 0.29/0.53 ( ( member_num @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: num] :
% 0.29/0.53 ( ( member_num @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_num @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal
% 0.29/0.53 thf(fact_354_finite__has__maximal,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ( finite_finite_nat @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.53 => ? [X3: nat] :
% 0.29/0.53 ( ( member_nat @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: nat] :
% 0.29/0.53 ( ( member_nat @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal
% 0.29/0.53 thf(fact_355_finite__has__maximal,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ( finite_finite_int @ A4 )
% 0.29/0.53 => ( ( A4 != bot_bot_set_int )
% 0.29/0.53 => ? [X3: int] :
% 0.29/0.53 ( ( member_int @ X3 @ A4 )
% 0.29/0.53 & ! [Xa: int] :
% 0.29/0.53 ( ( member_int @ Xa @ A4 )
% 0.29/0.53 => ( ( ord_less_eq_int @ X3 @ Xa )
% 0.29/0.53 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_has_maximal
% 0.29/0.53 thf(fact_356_nat__compl__induct,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ( P2 @ zero_zero_nat )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ! [Nn: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ Nn @ N2 )
% 0.29/0.53 => ( P2 @ Nn ) )
% 0.29/0.53 => ( P2 @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( P2 @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_compl_induct
% 0.29/0.53 thf(fact_357_nat__compl__induct_H,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ( P2 @ zero_zero_nat )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ! [Nn: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ Nn @ N2 )
% 0.29/0.53 => ( P2 @ Nn ) )
% 0.29/0.53 => ( P2 @ ( suc @ N2 ) ) )
% 0.29/0.53 => ( P2 @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_compl_induct'
% 0.29/0.53 thf(fact_358_nat__in__between__eq_I1_J,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ( ord_less_nat @ A @ B )
% 0.29/0.53 & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 0.29/0.53 = ( B
% 0.29/0.53 = ( suc @ A ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_in_between_eq(1)
% 0.29/0.53 thf(fact_359_nat__in__between__eq_I2_J,axiom,
% 0.29/0.53 ! [A: nat,B: nat] :
% 0.29/0.53 ( ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53 & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 0.29/0.53 = ( B = A ) ) ).
% 0.29/0.53
% 0.29/0.53 % nat_in_between_eq(2)
% 0.29/0.53 thf(fact_360_Suc__leI,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ N )
% 0.29/0.53 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_leI
% 0.29/0.53 thf(fact_361_Suc__le__eq,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.53 = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_le_eq
% 0.29/0.53 thf(fact_362_dec__induct,axiom,
% 0.29/0.53 ! [I: nat,J: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.53 => ( ( P2 @ I )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ I @ N2 )
% 0.29/0.53 => ( ( ord_less_nat @ N2 @ J )
% 0.29/0.53 => ( ( P2 @ N2 )
% 0.29/0.53 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 0.29/0.53 => ( P2 @ J ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % dec_induct
% 0.29/0.53 thf(fact_363_inc__induct,axiom,
% 0.29/0.53 ! [I: nat,J: nat,P2: nat > $o] :
% 0.29/0.53 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.53 => ( ( P2 @ J )
% 0.29/0.53 => ( ! [N2: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ I @ N2 )
% 0.29/0.53 => ( ( ord_less_nat @ N2 @ J )
% 0.29/0.53 => ( ( P2 @ ( suc @ N2 ) )
% 0.29/0.53 => ( P2 @ N2 ) ) ) )
% 0.29/0.53 => ( P2 @ I ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % inc_induct
% 0.29/0.53 thf(fact_364_Suc__le__lessD,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.29/0.53 => ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % Suc_le_lessD
% 0.29/0.53 thf(fact_365_le__less__Suc__eq,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.29/0.53 = ( N = M ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_less_Suc_eq
% 0.29/0.53 thf(fact_366_less__Suc__eq__le,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.29/0.53 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_Suc_eq_le
% 0.29/0.53 thf(fact_367_less__eq__Suc__le,axiom,
% 0.29/0.53 ( ord_less_nat
% 0.29/0.53 = ( ^ [N6: nat] : ( ord_less_eq_nat @ ( suc @ N6 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % less_eq_Suc_le
% 0.29/0.53 thf(fact_368_le__imp__less__Suc,axiom,
% 0.29/0.53 ! [M: nat,N: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.53 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % le_imp_less_Suc
% 0.29/0.53 thf(fact_369_ex__least__nat__le,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ( P2 @ N )
% 0.29/0.53 => ( ~ ( P2 @ zero_zero_nat )
% 0.29/0.53 => ? [K2: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ K2 @ N )
% 0.29/0.53 & ! [I4: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I4 @ K2 )
% 0.29/0.53 => ~ ( P2 @ I4 ) )
% 0.29/0.53 & ( P2 @ K2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_least_nat_le
% 0.29/0.53 thf(fact_370_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 0.29/0.53 ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 0.29/0.53 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.naive_member.simps(2)
% 0.29/0.53 thf(fact_371_ex__least__nat__less,axiom,
% 0.29/0.53 ! [P2: nat > $o,N: nat] :
% 0.29/0.53 ( ( P2 @ N )
% 0.29/0.53 => ( ~ ( P2 @ zero_zero_nat )
% 0.29/0.53 => ? [K2: nat] :
% 0.29/0.53 ( ( ord_less_nat @ K2 @ N )
% 0.29/0.53 & ! [I4: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ I4 @ K2 )
% 0.29/0.53 => ~ ( P2 @ I4 ) )
% 0.29/0.53 & ( P2 @ ( suc @ K2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_least_nat_less
% 0.29/0.53 thf(fact_372_emptyE,axiom,
% 0.29/0.53 ! [A: vEBT_VEBT] :
% 0.29/0.53 ~ ( member_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ).
% 0.29/0.53
% 0.29/0.53 % emptyE
% 0.29/0.53 thf(fact_373_emptyE,axiom,
% 0.29/0.53 ! [A: real] :
% 0.29/0.53 ~ ( member_real @ A @ bot_bot_set_real ) ).
% 0.29/0.53
% 0.29/0.53 % emptyE
% 0.29/0.53 thf(fact_374_emptyE,axiom,
% 0.29/0.53 ! [A: set_nat] :
% 0.29/0.53 ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 0.29/0.53
% 0.29/0.53 % emptyE
% 0.29/0.53 thf(fact_375_emptyE,axiom,
% 0.29/0.53 ! [A: nat] :
% 0.29/0.53 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 0.29/0.53
% 0.29/0.53 % emptyE
% 0.29/0.53 thf(fact_376_emptyE,axiom,
% 0.29/0.53 ! [A: int] :
% 0.29/0.53 ~ ( member_int @ A @ bot_bot_set_int ) ).
% 0.29/0.53
% 0.29/0.53 % emptyE
% 0.29/0.53 thf(fact_377_emptyE,axiom,
% 0.29/0.53 ! [A: $o] :
% 0.29/0.53 ~ ( member_o @ A @ bot_bot_set_o ) ).
% 0.29/0.53
% 0.29/0.53 % emptyE
% 0.29/0.53 thf(fact_378_equals0D,axiom,
% 0.29/0.53 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT] :
% 0.29/0.53 ( ( A4 = bot_bo8194388402131092736T_VEBT )
% 0.29/0.53 => ~ ( member_VEBT_VEBT @ A @ A4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0D
% 0.29/0.53 thf(fact_379_equals0D,axiom,
% 0.29/0.53 ! [A4: set_real,A: real] :
% 0.29/0.53 ( ( A4 = bot_bot_set_real )
% 0.29/0.53 => ~ ( member_real @ A @ A4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0D
% 0.29/0.53 thf(fact_380_equals0D,axiom,
% 0.29/0.53 ! [A4: set_set_nat,A: set_nat] :
% 0.29/0.53 ( ( A4 = bot_bot_set_set_nat )
% 0.29/0.53 => ~ ( member_set_nat @ A @ A4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0D
% 0.29/0.53 thf(fact_381_equals0D,axiom,
% 0.29/0.53 ! [A4: set_nat,A: nat] :
% 0.29/0.53 ( ( A4 = bot_bot_set_nat )
% 0.29/0.53 => ~ ( member_nat @ A @ A4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0D
% 0.29/0.53 thf(fact_382_equals0D,axiom,
% 0.29/0.53 ! [A4: set_int,A: int] :
% 0.29/0.53 ( ( A4 = bot_bot_set_int )
% 0.29/0.53 => ~ ( member_int @ A @ A4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0D
% 0.29/0.53 thf(fact_383_equals0D,axiom,
% 0.29/0.53 ! [A4: set_o,A: $o] :
% 0.29/0.53 ( ( A4 = bot_bot_set_o )
% 0.29/0.53 => ~ ( member_o @ A @ A4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0D
% 0.29/0.53 thf(fact_384_equals0I,axiom,
% 0.29/0.53 ! [A4: set_VEBT_VEBT] :
% 0.29/0.53 ( ! [Y3: vEBT_VEBT] :
% 0.29/0.53 ~ ( member_VEBT_VEBT @ Y3 @ A4 )
% 0.29/0.53 => ( A4 = bot_bo8194388402131092736T_VEBT ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0I
% 0.29/0.53 thf(fact_385_equals0I,axiom,
% 0.29/0.53 ! [A4: set_real] :
% 0.29/0.53 ( ! [Y3: real] :
% 0.29/0.53 ~ ( member_real @ Y3 @ A4 )
% 0.29/0.53 => ( A4 = bot_bot_set_real ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0I
% 0.29/0.53 thf(fact_386_equals0I,axiom,
% 0.29/0.53 ! [A4: set_set_nat] :
% 0.29/0.53 ( ! [Y3: set_nat] :
% 0.29/0.53 ~ ( member_set_nat @ Y3 @ A4 )
% 0.29/0.53 => ( A4 = bot_bot_set_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0I
% 0.29/0.53 thf(fact_387_equals0I,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ! [Y3: nat] :
% 0.29/0.53 ~ ( member_nat @ Y3 @ A4 )
% 0.29/0.53 => ( A4 = bot_bot_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0I
% 0.29/0.53 thf(fact_388_equals0I,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ! [Y3: int] :
% 0.29/0.53 ~ ( member_int @ Y3 @ A4 )
% 0.29/0.53 => ( A4 = bot_bot_set_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0I
% 0.29/0.53 thf(fact_389_equals0I,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ( ! [Y3: $o] :
% 0.29/0.53 ~ ( member_o @ Y3 @ A4 )
% 0.29/0.53 => ( A4 = bot_bot_set_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % equals0I
% 0.29/0.53 thf(fact_390_ex__in__conv,axiom,
% 0.29/0.53 ! [A4: set_VEBT_VEBT] :
% 0.29/0.53 ( ( ? [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 != bot_bo8194388402131092736T_VEBT ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_in_conv
% 0.29/0.53 thf(fact_391_ex__in__conv,axiom,
% 0.29/0.53 ! [A4: set_real] :
% 0.29/0.53 ( ( ? [X4: real] : ( member_real @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 != bot_bot_set_real ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_in_conv
% 0.29/0.53 thf(fact_392_ex__in__conv,axiom,
% 0.29/0.53 ! [A4: set_set_nat] :
% 0.29/0.53 ( ( ? [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 != bot_bot_set_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_in_conv
% 0.29/0.53 thf(fact_393_ex__in__conv,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ( ? [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 != bot_bot_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_in_conv
% 0.29/0.53 thf(fact_394_ex__in__conv,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ( ? [X4: int] : ( member_int @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 != bot_bot_set_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_in_conv
% 0.29/0.53 thf(fact_395_ex__in__conv,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ( ( ? [X4: $o] : ( member_o @ X4 @ A4 ) )
% 0.29/0.53 = ( A4 != bot_bot_set_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % ex_in_conv
% 0.29/0.53 thf(fact_396_not__psubset__empty,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ~ ( ord_less_set_nat @ A4 @ bot_bot_set_nat ) ).
% 0.29/0.53
% 0.29/0.53 % not_psubset_empty
% 0.29/0.53 thf(fact_397_not__psubset__empty,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ~ ( ord_less_set_int @ A4 @ bot_bot_set_int ) ).
% 0.29/0.53
% 0.29/0.53 % not_psubset_empty
% 0.29/0.53 thf(fact_398_not__psubset__empty,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ~ ( ord_less_set_o @ A4 @ bot_bot_set_o ) ).
% 0.29/0.53
% 0.29/0.53 % not_psubset_empty
% 0.29/0.53 thf(fact_399_forall__finite_I1_J,axiom,
% 0.29/0.53 ! [P2: nat > $o,I4: nat] :
% 0.29/0.53 ( ( ord_less_nat @ I4 @ zero_zero_nat )
% 0.29/0.53 => ( P2 @ I4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % forall_finite(1)
% 0.29/0.53 thf(fact_400_member__valid__both__member__options,axiom,
% 0.29/0.53 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.53 ( ( vEBT_invar_vebt @ Tree @ N )
% 0.29/0.53 => ( ( vEBT_vebt_member @ Tree @ X )
% 0.29/0.53 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 0.29/0.53 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % member_valid_both_member_options
% 0.29/0.53 thf(fact_401_both__member__options__def,axiom,
% 0.29/0.53 ( vEBT_V8194947554948674370ptions
% 0.29/0.53 = ( ^ [T2: vEBT_VEBT,X4: nat] :
% 0.29/0.53 ( ( vEBT_V5719532721284313246member @ T2 @ X4 )
% 0.29/0.53 | ( vEBT_VEBT_membermima @ T2 @ X4 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % both_member_options_def
% 0.29/0.53 thf(fact_402_is__succ__in__set__def,axiom,
% 0.29/0.53 ( vEBT_is_succ_in_set
% 0.29/0.53 = ( ^ [Xs2: set_nat,X4: nat,Y4: nat] :
% 0.29/0.53 ( ( member_nat @ Y4 @ Xs2 )
% 0.29/0.53 & ( ord_less_nat @ X4 @ Y4 )
% 0.29/0.53 & ! [Z2: nat] :
% 0.29/0.53 ( ( member_nat @ Z2 @ Xs2 )
% 0.29/0.53 => ( ( ord_less_nat @ X4 @ Z2 )
% 0.29/0.53 => ( ord_less_eq_nat @ Y4 @ Z2 ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % is_succ_in_set_def
% 0.29/0.53 thf(fact_403_is__pred__in__set__def,axiom,
% 0.29/0.53 ( vEBT_is_pred_in_set
% 0.29/0.53 = ( ^ [Xs2: set_nat,X4: nat,Y4: nat] :
% 0.29/0.53 ( ( member_nat @ Y4 @ Xs2 )
% 0.29/0.53 & ( ord_less_nat @ Y4 @ X4 )
% 0.29/0.53 & ! [Z2: nat] :
% 0.29/0.53 ( ( member_nat @ Z2 @ Xs2 )
% 0.29/0.53 => ( ( ord_less_nat @ Z2 @ X4 )
% 0.29/0.53 => ( ord_less_eq_nat @ Z2 @ Y4 ) ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % is_pred_in_set_def
% 0.29/0.53 thf(fact_404_order__refl,axiom,
% 0.29/0.53 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 0.29/0.53
% 0.29/0.53 % order_refl
% 0.29/0.53 thf(fact_405_order__refl,axiom,
% 0.29/0.53 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 0.29/0.53
% 0.29/0.53 % order_refl
% 0.29/0.53 thf(fact_406_order__refl,axiom,
% 0.29/0.53 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 0.29/0.53
% 0.29/0.53 % order_refl
% 0.29/0.53 thf(fact_407_order__refl,axiom,
% 0.29/0.53 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.29/0.53
% 0.29/0.53 % order_refl
% 0.29/0.53 thf(fact_408_order__refl,axiom,
% 0.29/0.53 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 0.29/0.53
% 0.29/0.53 % order_refl
% 0.29/0.53 thf(fact_409_dual__order_Orefl,axiom,
% 0.29/0.53 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.29/0.53
% 0.29/0.53 % dual_order.refl
% 0.29/0.53 thf(fact_410_dual__order_Orefl,axiom,
% 0.29/0.53 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.29/0.53
% 0.29/0.53 % dual_order.refl
% 0.29/0.53 thf(fact_411_dual__order_Orefl,axiom,
% 0.29/0.53 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.29/0.53
% 0.29/0.53 % dual_order.refl
% 0.29/0.53 thf(fact_412_dual__order_Orefl,axiom,
% 0.29/0.53 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.29/0.53
% 0.29/0.53 % dual_order.refl
% 0.29/0.53 thf(fact_413_dual__order_Orefl,axiom,
% 0.29/0.53 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.29/0.53
% 0.29/0.53 % dual_order.refl
% 0.29/0.53 thf(fact_414_buildup__nothing__in__min__max,axiom,
% 0.29/0.53 ! [N: nat,X: nat] :
% 0.29/0.53 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.29/0.53
% 0.29/0.53 % buildup_nothing_in_min_max
% 0.29/0.53 thf(fact_415_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 0.29/0.53 ! [Uu2: $o] :
% 0.29/0.53 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu2 @ $true ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.minNull.simps(3)
% 0.29/0.53 thf(fact_416_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 0.29/0.53 ! [Uv2: $o] :
% 0.29/0.53 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv2 ) ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.minNull.simps(2)
% 0.29/0.53 thf(fact_417_empty__subsetI,axiom,
% 0.29/0.53 ! [A4: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A4 ) ).
% 0.29/0.53
% 0.29/0.53 % empty_subsetI
% 0.29/0.53 thf(fact_418_empty__subsetI,axiom,
% 0.29/0.53 ! [A4: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A4 ) ).
% 0.29/0.53
% 0.29/0.53 % empty_subsetI
% 0.29/0.53 thf(fact_419_empty__subsetI,axiom,
% 0.29/0.53 ! [A4: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A4 ) ).
% 0.29/0.53
% 0.29/0.53 % empty_subsetI
% 0.29/0.53 thf(fact_420_subset__empty,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat )
% 0.29/0.53 = ( A4 = bot_bot_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_empty
% 0.29/0.53 thf(fact_421_subset__empty,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ( ( ord_less_eq_set_o @ A4 @ bot_bot_set_o )
% 0.29/0.53 = ( A4 = bot_bot_set_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_empty
% 0.29/0.53 thf(fact_422_subset__empty,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ A4 @ bot_bot_set_int )
% 0.29/0.53 = ( A4 = bot_bot_set_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_empty
% 0.29/0.53 thf(fact_423_psubsetI,axiom,
% 0.29/0.53 ! [A4: set_int,B4: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.53 => ( ( A4 != B4 )
% 0.29/0.53 => ( ord_less_set_int @ A4 @ B4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubsetI
% 0.29/0.53 thf(fact_424_bot__set__def,axiom,
% 0.29/0.53 ( bot_bot_set_complex
% 0.29/0.53 = ( collect_complex @ bot_bot_complex_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_set_def
% 0.29/0.53 thf(fact_425_bot__set__def,axiom,
% 0.29/0.53 ( bot_bot_set_list_nat
% 0.29/0.53 = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_set_def
% 0.29/0.53 thf(fact_426_bot__set__def,axiom,
% 0.29/0.53 ( bot_bot_set_set_nat
% 0.29/0.53 = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_set_def
% 0.29/0.53 thf(fact_427_bot__set__def,axiom,
% 0.29/0.53 ( bot_bot_set_nat
% 0.29/0.53 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_set_def
% 0.29/0.53 thf(fact_428_bot__set__def,axiom,
% 0.29/0.53 ( bot_bot_set_int
% 0.29/0.53 = ( collect_int @ bot_bot_int_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_set_def
% 0.29/0.53 thf(fact_429_bot__set__def,axiom,
% 0.29/0.53 ( bot_bot_set_o
% 0.29/0.53 = ( collect_o @ bot_bot_o_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % bot_set_def
% 0.29/0.53 thf(fact_430_bot__nat__def,axiom,
% 0.29/0.53 bot_bot_nat = zero_zero_nat ).
% 0.29/0.53
% 0.29/0.53 % bot_nat_def
% 0.29/0.53 thf(fact_431_subset__emptyI,axiom,
% 0.29/0.53 ! [A4: set_VEBT_VEBT] :
% 0.29/0.53 ( ! [X3: vEBT_VEBT] :
% 0.29/0.53 ~ ( member_VEBT_VEBT @ X3 @ A4 )
% 0.29/0.53 => ( ord_le4337996190870823476T_VEBT @ A4 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_emptyI
% 0.29/0.53 thf(fact_432_subset__emptyI,axiom,
% 0.29/0.53 ! [A4: set_real] :
% 0.29/0.53 ( ! [X3: real] :
% 0.29/0.53 ~ ( member_real @ X3 @ A4 )
% 0.29/0.53 => ( ord_less_eq_set_real @ A4 @ bot_bot_set_real ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_emptyI
% 0.29/0.53 thf(fact_433_subset__emptyI,axiom,
% 0.29/0.53 ! [A4: set_set_nat] :
% 0.29/0.53 ( ! [X3: set_nat] :
% 0.29/0.53 ~ ( member_set_nat @ X3 @ A4 )
% 0.29/0.53 => ( ord_le6893508408891458716et_nat @ A4 @ bot_bot_set_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_emptyI
% 0.29/0.53 thf(fact_434_subset__emptyI,axiom,
% 0.29/0.53 ! [A4: set_nat] :
% 0.29/0.53 ( ! [X3: nat] :
% 0.29/0.53 ~ ( member_nat @ X3 @ A4 )
% 0.29/0.53 => ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_emptyI
% 0.29/0.53 thf(fact_435_subset__emptyI,axiom,
% 0.29/0.53 ! [A4: set_o] :
% 0.29/0.53 ( ! [X3: $o] :
% 0.29/0.53 ~ ( member_o @ X3 @ A4 )
% 0.29/0.53 => ( ord_less_eq_set_o @ A4 @ bot_bot_set_o ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_emptyI
% 0.29/0.53 thf(fact_436_subset__emptyI,axiom,
% 0.29/0.53 ! [A4: set_int] :
% 0.29/0.53 ( ! [X3: int] :
% 0.29/0.53 ~ ( member_int @ X3 @ A4 )
% 0.29/0.53 => ( ord_less_eq_set_int @ A4 @ bot_bot_set_int ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_emptyI
% 0.29/0.53 thf(fact_437_rev__finite__subset,axiom,
% 0.29/0.53 ! [B4: set_nat,A4: set_nat] :
% 0.29/0.53 ( ( finite_finite_nat @ B4 )
% 0.29/0.53 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.53 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % rev_finite_subset
% 0.29/0.53 thf(fact_438_rev__finite__subset,axiom,
% 0.29/0.53 ! [B4: set_complex,A4: set_complex] :
% 0.29/0.53 ( ( finite3207457112153483333omplex @ B4 )
% 0.29/0.53 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.29/0.53 => ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % rev_finite_subset
% 0.29/0.53 thf(fact_439_rev__finite__subset,axiom,
% 0.29/0.53 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.29/0.53 ( ( finite6017078050557962740nteger @ B4 )
% 0.29/0.53 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.29/0.53 => ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % rev_finite_subset
% 0.29/0.53 thf(fact_440_rev__finite__subset,axiom,
% 0.29/0.53 ! [B4: set_int,A4: set_int] :
% 0.29/0.53 ( ( finite_finite_int @ B4 )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.53 => ( finite_finite_int @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % rev_finite_subset
% 0.29/0.53 thf(fact_441_infinite__super,axiom,
% 0.29/0.53 ! [S3: set_nat,T3: set_nat] :
% 0.29/0.53 ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 0.29/0.53 => ( ~ ( finite_finite_nat @ S3 )
% 0.29/0.53 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_super
% 0.29/0.53 thf(fact_442_infinite__super,axiom,
% 0.29/0.53 ! [S3: set_complex,T3: set_complex] :
% 0.29/0.53 ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.29/0.53 => ( ~ ( finite3207457112153483333omplex @ S3 )
% 0.29/0.53 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_super
% 0.29/0.53 thf(fact_443_infinite__super,axiom,
% 0.29/0.53 ! [S3: set_Code_integer,T3: set_Code_integer] :
% 0.29/0.53 ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.29/0.53 => ( ~ ( finite6017078050557962740nteger @ S3 )
% 0.29/0.53 => ~ ( finite6017078050557962740nteger @ T3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_super
% 0.29/0.53 thf(fact_444_infinite__super,axiom,
% 0.29/0.53 ! [S3: set_int,T3: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ S3 @ T3 )
% 0.29/0.53 => ( ~ ( finite_finite_int @ S3 )
% 0.29/0.53 => ~ ( finite_finite_int @ T3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % infinite_super
% 0.29/0.53 thf(fact_445_finite__subset,axiom,
% 0.29/0.53 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.53 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.53 => ( ( finite_finite_nat @ B4 )
% 0.29/0.53 => ( finite_finite_nat @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_subset
% 0.29/0.53 thf(fact_446_finite__subset,axiom,
% 0.29/0.53 ! [A4: set_complex,B4: set_complex] :
% 0.29/0.53 ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.29/0.53 => ( ( finite3207457112153483333omplex @ B4 )
% 0.29/0.53 => ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_subset
% 0.29/0.53 thf(fact_447_finite__subset,axiom,
% 0.29/0.53 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.29/0.53 ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.29/0.53 => ( ( finite6017078050557962740nteger @ B4 )
% 0.29/0.53 => ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_subset
% 0.29/0.53 thf(fact_448_finite__subset,axiom,
% 0.29/0.53 ! [A4: set_int,B4: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.53 => ( ( finite_finite_int @ B4 )
% 0.29/0.53 => ( finite_finite_int @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % finite_subset
% 0.29/0.53 thf(fact_449_mod__false,axiom,
% 0.29/0.53 ! [H2: produc3658429121746597890et_nat] :
% 0.29/0.53 ~ ( rep_assn @ bot_bot_assn @ H2 ) ).
% 0.29/0.53
% 0.29/0.53 % mod_false
% 0.29/0.53 thf(fact_450_subset__iff__psubset__eq,axiom,
% 0.29/0.53 ( ord_less_eq_set_int
% 0.29/0.53 = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.53 ( ( ord_less_set_int @ A6 @ B6 )
% 0.29/0.53 | ( A6 = B6 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_iff_psubset_eq
% 0.29/0.53 thf(fact_451_subset__psubset__trans,axiom,
% 0.29/0.53 ! [A4: set_int,B4: set_int,C3: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.53 => ( ( ord_less_set_int @ B4 @ C3 )
% 0.29/0.53 => ( ord_less_set_int @ A4 @ C3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_psubset_trans
% 0.29/0.53 thf(fact_452_subset__not__subset__eq,axiom,
% 0.29/0.53 ( ord_less_set_int
% 0.29/0.53 = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.29/0.53 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % subset_not_subset_eq
% 0.29/0.53 thf(fact_453_psubset__subset__trans,axiom,
% 0.29/0.53 ! [A4: set_int,B4: set_int,C3: set_int] :
% 0.29/0.53 ( ( ord_less_set_int @ A4 @ B4 )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ B4 @ C3 )
% 0.29/0.53 => ( ord_less_set_int @ A4 @ C3 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubset_subset_trans
% 0.29/0.53 thf(fact_454_psubset__imp__subset,axiom,
% 0.29/0.53 ! [A4: set_int,B4: set_int] :
% 0.29/0.53 ( ( ord_less_set_int @ A4 @ B4 )
% 0.29/0.53 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubset_imp_subset
% 0.29/0.53 thf(fact_455_psubset__eq,axiom,
% 0.29/0.53 ( ord_less_set_int
% 0.29/0.53 = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.29/0.53 & ( A6 != B6 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubset_eq
% 0.29/0.53 thf(fact_456_psubsetE,axiom,
% 0.29/0.53 ! [A4: set_int,B4: set_int] :
% 0.29/0.53 ( ( ord_less_set_int @ A4 @ B4 )
% 0.29/0.53 => ~ ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.53 => ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % psubsetE
% 0.29/0.53 thf(fact_457_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 0.29/0.53 ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 0.29/0.53 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) ).
% 0.29/0.53
% 0.29/0.53 % VEBT_internal.membermima.simps(1)
% 0.29/0.53 thf(fact_458_order__antisym__conv,axiom,
% 0.29/0.53 ! [Y: set_int,X: set_int] :
% 0.29/0.53 ( ( ord_less_eq_set_int @ Y @ X )
% 0.29/0.53 => ( ( ord_less_eq_set_int @ X @ Y )
% 0.29/0.53 = ( X = Y ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_antisym_conv
% 0.29/0.53 thf(fact_459_order__antisym__conv,axiom,
% 0.29/0.53 ! [Y: rat,X: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.53 => ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53 = ( X = Y ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_antisym_conv
% 0.29/0.53 thf(fact_460_order__antisym__conv,axiom,
% 0.29/0.53 ! [Y: num,X: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ Y @ X )
% 0.29/0.53 => ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.53 = ( X = Y ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_antisym_conv
% 0.29/0.53 thf(fact_461_order__antisym__conv,axiom,
% 0.29/0.53 ! [Y: nat,X: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.53 => ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53 = ( X = Y ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_antisym_conv
% 0.29/0.53 thf(fact_462_order__antisym__conv,axiom,
% 0.29/0.53 ! [Y: int,X: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.53 => ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.53 = ( X = Y ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_antisym_conv
% 0.29/0.53 thf(fact_463_linorder__le__cases,axiom,
% 0.29/0.53 ! [X: rat,Y: rat] :
% 0.29/0.53 ( ~ ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_le_cases
% 0.29/0.53 thf(fact_464_linorder__le__cases,axiom,
% 0.29/0.53 ! [X: num,Y: num] :
% 0.29/0.53 ( ~ ( ord_less_eq_num @ X @ Y )
% 0.29/0.53 => ( ord_less_eq_num @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_le_cases
% 0.29/0.53 thf(fact_465_linorder__le__cases,axiom,
% 0.29/0.53 ! [X: nat,Y: nat] :
% 0.29/0.53 ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_le_cases
% 0.29/0.53 thf(fact_466_linorder__le__cases,axiom,
% 0.29/0.53 ! [X: int,Y: int] :
% 0.29/0.53 ( ~ ( ord_less_eq_int @ X @ Y )
% 0.29/0.53 => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_le_cases
% 0.29/0.53 thf(fact_467_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_468_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_469_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_470_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 0.29/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_471_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: num,B: num,F: num > rat,C2: rat] :
% 0.29/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_472_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: num,B: num,F: num > num,C2: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_473_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: num,B: num,F: num > nat,C2: nat] :
% 0.29/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_474_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: num,B: num,F: num > int,C2: int] :
% 0.29/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_475_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_476_ord__le__eq__subst,axiom,
% 0.29/0.53 ! [A: nat,B: nat,F: nat > num,C2: num] :
% 0.29/0.53 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53 => ( ( ( F @ B )
% 0.29/0.53 = C2 )
% 0.29/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_le_eq_subst
% 0.29/0.53 thf(fact_477_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_478_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_479_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_480_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_481_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: rat,F: num > rat,B: num,C2: num] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_482_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: num,F: num > num,B: num,C2: num] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_483_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: nat,F: num > nat,B: num,C2: num] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_484_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: int,F: num > int,B: num,C2: num] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.53 => ( ! [X3: num,Y3: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_485_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_486_ord__eq__le__subst,axiom,
% 0.29/0.53 ! [A: num,F: nat > num,B: nat,C2: nat] :
% 0.29/0.53 ( ( A
% 0.29/0.53 = ( F @ B ) )
% 0.29/0.53 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.53 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.53 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.53
% 0.29/0.53 % ord_eq_le_subst
% 0.29/0.53 thf(fact_487_linorder__linear,axiom,
% 0.29/0.53 ! [X: rat,Y: rat] :
% 0.29/0.53 ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_linear
% 0.29/0.53 thf(fact_488_linorder__linear,axiom,
% 0.29/0.53 ! [X: num,Y: num] :
% 0.29/0.53 ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.53 | ( ord_less_eq_num @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_linear
% 0.29/0.53 thf(fact_489_linorder__linear,axiom,
% 0.29/0.53 ! [X: nat,Y: nat] :
% 0.29/0.53 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_linear
% 0.29/0.53 thf(fact_490_linorder__linear,axiom,
% 0.29/0.53 ! [X: int,Y: int] :
% 0.29/0.53 ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.53 | ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.53
% 0.29/0.53 % linorder_linear
% 0.29/0.53 thf(fact_491_order__eq__refl,axiom,
% 0.29/0.53 ! [X: set_int,Y: set_int] :
% 0.29/0.53 ( ( X = Y )
% 0.29/0.53 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_eq_refl
% 0.29/0.53 thf(fact_492_order__eq__refl,axiom,
% 0.29/0.53 ! [X: rat,Y: rat] :
% 0.29/0.53 ( ( X = Y )
% 0.29/0.53 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_eq_refl
% 0.29/0.53 thf(fact_493_order__eq__refl,axiom,
% 0.29/0.53 ! [X: num,Y: num] :
% 0.29/0.53 ( ( X = Y )
% 0.29/0.53 => ( ord_less_eq_num @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_eq_refl
% 0.29/0.53 thf(fact_494_order__eq__refl,axiom,
% 0.29/0.53 ! [X: nat,Y: nat] :
% 0.29/0.53 ( ( X = Y )
% 0.29/0.53 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_eq_refl
% 0.29/0.53 thf(fact_495_order__eq__refl,axiom,
% 0.29/0.53 ! [X: int,Y: int] :
% 0.29/0.53 ( ( X = Y )
% 0.29/0.53 => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.29/0.53
% 0.29/0.53 % order_eq_refl
% 0.29/0.53 thf(fact_496_order__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_497_order__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_498_order__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_499_order__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_500_order__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_501_order__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_502_order__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_503_order__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_504_order__subst2,axiom,
% 0.29/0.54 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_505_order__subst2,axiom,
% 0.29/0.54 ! [A: nat,B: nat,F: nat > num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst2
% 0.29/0.54 thf(fact_506_order__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_507_order__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: num > rat,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_508_order__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_509_order__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: int > rat,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_510_order__subst1,axiom,
% 0.29/0.54 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_511_order__subst1,axiom,
% 0.29/0.54 ! [A: num,F: num > num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_512_order__subst1,axiom,
% 0.29/0.54 ! [A: num,F: nat > num,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_513_order__subst1,axiom,
% 0.29/0.54 ! [A: num,F: int > num,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_514_order__subst1,axiom,
% 0.29/0.54 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_515_order__subst1,axiom,
% 0.29/0.54 ! [A: nat,F: num > nat,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_subst1
% 0.29/0.54 thf(fact_516_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: set_int,B7: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A7 @ B7 )
% 0.29/0.54 & ( ord_less_eq_set_int @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Orderings.order_eq_iff
% 0.29/0.54 thf(fact_517_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: rat,B7: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A7 @ B7 )
% 0.29/0.54 & ( ord_less_eq_rat @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Orderings.order_eq_iff
% 0.29/0.54 thf(fact_518_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: num,B7: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A7 @ B7 )
% 0.29/0.54 & ( ord_less_eq_num @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Orderings.order_eq_iff
% 0.29/0.54 thf(fact_519_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: nat,B7: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A7 @ B7 )
% 0.29/0.54 & ( ord_less_eq_nat @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Orderings.order_eq_iff
% 0.29/0.54 thf(fact_520_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: int,B7: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A7 @ B7 )
% 0.29/0.54 & ( ord_less_eq_int @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % Orderings.order_eq_iff
% 0.29/0.54 thf(fact_521_antisym,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym
% 0.29/0.54 thf(fact_522_antisym,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym
% 0.29/0.54 thf(fact_523_antisym,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ A )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym
% 0.29/0.54 thf(fact_524_antisym,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym
% 0.29/0.54 thf(fact_525_antisym,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym
% 0.29/0.54 thf(fact_526_dual__order_Otrans,axiom,
% 0.29/0.54 ! [B: set_int,A: set_int,C2: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ C2 @ B )
% 0.29/0.54 => ( ord_less_eq_set_int @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.trans
% 0.29/0.54 thf(fact_527_dual__order_Otrans,axiom,
% 0.29/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ C2 @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.trans
% 0.29/0.54 thf(fact_528_dual__order_Otrans,axiom,
% 0.29/0.54 ! [B: num,A: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_num @ C2 @ B )
% 0.29/0.54 => ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.trans
% 0.29/0.54 thf(fact_529_dual__order_Otrans,axiom,
% 0.29/0.54 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.29/0.54 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.trans
% 0.29/0.54 thf(fact_530_dual__order_Otrans,axiom,
% 0.29/0.54 ! [B: int,A: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ C2 @ B )
% 0.29/0.54 => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.trans
% 0.29/0.54 thf(fact_531_dual__order_Oantisym,axiom,
% 0.29/0.54 ! [B: set_int,A: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.antisym
% 0.29/0.54 thf(fact_532_dual__order_Oantisym,axiom,
% 0.29/0.54 ! [B: rat,A: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.antisym
% 0.29/0.54 thf(fact_533_dual__order_Oantisym,axiom,
% 0.29/0.54 ! [B: num,A: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.antisym
% 0.29/0.54 thf(fact_534_dual__order_Oantisym,axiom,
% 0.29/0.54 ! [B: nat,A: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.antisym
% 0.29/0.54 thf(fact_535_dual__order_Oantisym,axiom,
% 0.29/0.54 ! [B: int,A: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( A = B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.antisym
% 0.29/0.54 thf(fact_536_dual__order_Oeq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: set_int,B7: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ B7 @ A7 )
% 0.29/0.54 & ( ord_less_eq_set_int @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.eq_iff
% 0.29/0.54 thf(fact_537_dual__order_Oeq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: rat,B7: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B7 @ A7 )
% 0.29/0.54 & ( ord_less_eq_rat @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.eq_iff
% 0.29/0.54 thf(fact_538_dual__order_Oeq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: num,B7: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ B7 @ A7 )
% 0.29/0.54 & ( ord_less_eq_num @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.eq_iff
% 0.29/0.54 thf(fact_539_dual__order_Oeq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: nat,B7: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B7 @ A7 )
% 0.29/0.54 & ( ord_less_eq_nat @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.eq_iff
% 0.29/0.54 thf(fact_540_dual__order_Oeq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [A7: int,B7: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B7 @ A7 )
% 0.29/0.54 & ( ord_less_eq_int @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.eq_iff
% 0.29/0.54 thf(fact_541_linorder__wlog,axiom,
% 0.29/0.54 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 0.29/0.54 ( ! [A3: rat,B3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: rat,B3: rat] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_wlog
% 0.29/0.54 thf(fact_542_linorder__wlog,axiom,
% 0.29/0.54 ! [P2: num > num > $o,A: num,B: num] :
% 0.29/0.54 ( ! [A3: num,B3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: num,B3: num] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_wlog
% 0.29/0.54 thf(fact_543_linorder__wlog,axiom,
% 0.29/0.54 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.54 ( ! [A3: nat,B3: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: nat,B3: nat] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_wlog
% 0.29/0.54 thf(fact_544_linorder__wlog,axiom,
% 0.29/0.54 ! [P2: int > int > $o,A: int,B: int] :
% 0.29/0.54 ( ! [A3: int,B3: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: int,B3: int] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_wlog
% 0.29/0.54 thf(fact_545_order__trans,axiom,
% 0.29/0.54 ! [X: set_int,Y: set_int,Z: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ Y @ Z )
% 0.29/0.54 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_trans
% 0.29/0.54 thf(fact_546_order__trans,axiom,
% 0.29/0.54 ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.54 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_trans
% 0.29/0.54 thf(fact_547_order__trans,axiom,
% 0.29/0.54 ! [X: num,Y: num,Z: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_num @ Y @ Z )
% 0.29/0.54 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_trans
% 0.29/0.54 thf(fact_548_order__trans,axiom,
% 0.29/0.54 ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.54 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_trans
% 0.29/0.54 thf(fact_549_order__trans,axiom,
% 0.29/0.54 ! [X: int,Y: int,Z: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.54 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_trans
% 0.29/0.54 thf(fact_550_order_Otrans,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int,C2: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.trans
% 0.29/0.54 thf(fact_551_order_Otrans,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.trans
% 0.29/0.54 thf(fact_552_order_Otrans,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.trans
% 0.29/0.54 thf(fact_553_order_Otrans,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.trans
% 0.29/0.54 thf(fact_554_order_Otrans,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.trans
% 0.29/0.54 thf(fact_555_order__antisym,axiom,
% 0.29/0.54 ! [X: set_int,Y: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ Y @ X )
% 0.29/0.54 => ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_antisym
% 0.29/0.54 thf(fact_556_order__antisym,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.54 => ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_antisym
% 0.29/0.54 thf(fact_557_order__antisym,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_num @ Y @ X )
% 0.29/0.54 => ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_antisym
% 0.29/0.54 thf(fact_558_order__antisym,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.54 => ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_antisym
% 0.29/0.54 thf(fact_559_order__antisym,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.54 => ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_antisym
% 0.29/0.54 thf(fact_560_ord__le__eq__trans,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int,C2: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_le_eq_trans
% 0.29/0.54 thf(fact_561_ord__le__eq__trans,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_le_eq_trans
% 0.29/0.54 thf(fact_562_ord__le__eq__trans,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_le_eq_trans
% 0.29/0.54 thf(fact_563_ord__le__eq__trans,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_le_eq_trans
% 0.29/0.54 thf(fact_564_ord__le__eq__trans,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_le_eq_trans
% 0.29/0.54 thf(fact_565_ord__eq__le__trans,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int,C2: set_int] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_le_trans
% 0.29/0.54 thf(fact_566_ord__eq__le__trans,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_le_trans
% 0.29/0.54 thf(fact_567_ord__eq__le__trans,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_le_trans
% 0.29/0.54 thf(fact_568_ord__eq__le__trans,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_le_trans
% 0.29/0.54 thf(fact_569_ord__eq__le__trans,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_le_trans
% 0.29/0.54 thf(fact_570_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [X4: set_int,Y4: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 0.29/0.54 & ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_class.order_eq_iff
% 0.29/0.54 thf(fact_571_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [X4: rat,Y4: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.29/0.54 & ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_class.order_eq_iff
% 0.29/0.54 thf(fact_572_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [X4: num,Y4: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.29/0.54 & ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_class.order_eq_iff
% 0.29/0.54 thf(fact_573_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [X4: nat,Y4: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.29/0.54 & ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_class.order_eq_iff
% 0.29/0.54 thf(fact_574_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.54 = ( ^ [X4: int,Y4: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.29/0.54 & ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_class.order_eq_iff
% 0.29/0.54 thf(fact_575_le__cases3,axiom,
% 0.29/0.54 ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54 ( ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.54 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_rat @ X @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 0.29/0.54 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 0.29/0.54 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 0.29/0.54 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 0.29/0.54 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_cases3
% 0.29/0.54 thf(fact_576_le__cases3,axiom,
% 0.29/0.54 ! [X: num,Y: num,Z: num] :
% 0.29/0.54 ( ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_num @ Y @ X )
% 0.29/0.54 => ~ ( ord_less_eq_num @ X @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_num @ X @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 0.29/0.54 => ( ( ( ord_less_eq_num @ Z @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_num @ Y @ X ) )
% 0.29/0.54 => ( ( ( ord_less_eq_num @ Y @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_num @ Z @ X ) )
% 0.29/0.54 => ~ ( ( ord_less_eq_num @ Z @ X )
% 0.29/0.54 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_cases3
% 0.29/0.54 thf(fact_577_le__cases3,axiom,
% 0.29/0.54 ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.54 ( ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.54 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_nat @ X @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 0.29/0.54 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.29/0.54 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 0.29/0.54 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 0.29/0.54 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_cases3
% 0.29/0.54 thf(fact_578_le__cases3,axiom,
% 0.29/0.54 ! [X: int,Y: int,Z: int] :
% 0.29/0.54 ( ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.54 => ~ ( ord_less_eq_int @ X @ Z ) )
% 0.29/0.54 => ( ( ( ord_less_eq_int @ X @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 0.29/0.54 => ( ( ( ord_less_eq_int @ Z @ Y )
% 0.29/0.54 => ~ ( ord_less_eq_int @ Y @ X ) )
% 0.29/0.54 => ( ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.54 => ~ ( ord_less_eq_int @ Z @ X ) )
% 0.29/0.54 => ~ ( ( ord_less_eq_int @ Z @ X )
% 0.29/0.54 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % le_cases3
% 0.29/0.54 thf(fact_579_nle__le,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.54 = ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 & ( B != A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nle_le
% 0.29/0.54 thf(fact_580_nle__le,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 0.29/0.54 = ( ( ord_less_eq_num @ B @ A )
% 0.29/0.54 & ( B != A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nle_le
% 0.29/0.54 thf(fact_581_nle__le,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.29/0.54 = ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 & ( B != A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nle_le
% 0.29/0.54 thf(fact_582_nle__le,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.29/0.54 = ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 & ( B != A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % nle_le
% 0.29/0.54 thf(fact_583_order__less__imp__not__less,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_less
% 0.29/0.54 thf(fact_584_order__less__imp__not__less,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_less
% 0.29/0.54 thf(fact_585_order__less__imp__not__less,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_less
% 0.29/0.54 thf(fact_586_order__less__imp__not__less,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_less
% 0.29/0.54 thf(fact_587_order__less__imp__not__less,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_less
% 0.29/0.54 thf(fact_588_order__less__imp__not__eq2,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( Y != X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq2
% 0.29/0.54 thf(fact_589_order__less__imp__not__eq2,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( Y != X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq2
% 0.29/0.54 thf(fact_590_order__less__imp__not__eq2,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( Y != X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq2
% 0.29/0.54 thf(fact_591_order__less__imp__not__eq2,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( Y != X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq2
% 0.29/0.54 thf(fact_592_order__less__imp__not__eq2,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( Y != X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq2
% 0.29/0.54 thf(fact_593_order__less__imp__not__eq,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq
% 0.29/0.54 thf(fact_594_order__less__imp__not__eq,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq
% 0.29/0.54 thf(fact_595_order__less__imp__not__eq,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq
% 0.29/0.54 thf(fact_596_order__less__imp__not__eq,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq
% 0.29/0.54 thf(fact_597_order__less__imp__not__eq,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_not_eq
% 0.29/0.54 thf(fact_598_linorder__less__linear,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 | ( X = Y )
% 0.29/0.54 | ( ord_less_real @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_linear
% 0.29/0.54 thf(fact_599_linorder__less__linear,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 | ( X = Y )
% 0.29/0.54 | ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_linear
% 0.29/0.54 thf(fact_600_linorder__less__linear,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 | ( X = Y )
% 0.29/0.54 | ( ord_less_num @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_linear
% 0.29/0.54 thf(fact_601_linorder__less__linear,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 | ( X = Y )
% 0.29/0.54 | ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_linear
% 0.29/0.54 thf(fact_602_linorder__less__linear,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 | ( X = Y )
% 0.29/0.54 | ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_linear
% 0.29/0.54 thf(fact_603_order__less__imp__triv,axiom,
% 0.29/0.54 ! [X: real,Y: real,P2: $o] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( ( ord_less_real @ Y @ X )
% 0.29/0.54 => P2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_triv
% 0.29/0.54 thf(fact_604_order__less__imp__triv,axiom,
% 0.29/0.54 ! [X: rat,Y: rat,P2: $o] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_rat @ Y @ X )
% 0.29/0.54 => P2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_triv
% 0.29/0.54 thf(fact_605_order__less__imp__triv,axiom,
% 0.29/0.54 ! [X: num,Y: num,P2: $o] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( ( ord_less_num @ Y @ X )
% 0.29/0.54 => P2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_triv
% 0.29/0.54 thf(fact_606_order__less__imp__triv,axiom,
% 0.29/0.54 ! [X: nat,Y: nat,P2: $o] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_nat @ Y @ X )
% 0.29/0.54 => P2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_triv
% 0.29/0.54 thf(fact_607_order__less__imp__triv,axiom,
% 0.29/0.54 ! [X: int,Y: int,P2: $o] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_int @ Y @ X )
% 0.29/0.54 => P2 ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_triv
% 0.29/0.54 thf(fact_608_order__less__not__sym,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_not_sym
% 0.29/0.54 thf(fact_609_order__less__not__sym,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_not_sym
% 0.29/0.54 thf(fact_610_order__less__not__sym,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_not_sym
% 0.29/0.54 thf(fact_611_order__less__not__sym,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_not_sym
% 0.29/0.54 thf(fact_612_order__less__not__sym,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_not_sym
% 0.29/0.54 thf(fact_613_order__less__subst2,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_614_order__less__subst2,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_615_order__less__subst2,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > num,C2: num] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_616_order__less__subst2,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_617_order__less__subst2,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > int,C2: int] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_618_order__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_619_order__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_620_order__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_621_order__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_622_order__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst2
% 0.29/0.54 thf(fact_623_order__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: real > real,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_624_order__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_625_order__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: num > real,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_626_order__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: nat > real,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_627_order__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: int > real,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_int @ B @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_628_order__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: real > rat,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_629_order__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_630_order__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: num > rat,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_631_order__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_632_order__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: int > rat,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_int @ B @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_subst1
% 0.29/0.54 thf(fact_633_order__less__irrefl,axiom,
% 0.29/0.54 ! [X: real] :
% 0.29/0.54 ~ ( ord_less_real @ X @ X ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_irrefl
% 0.29/0.54 thf(fact_634_order__less__irrefl,axiom,
% 0.29/0.54 ! [X: rat] :
% 0.29/0.54 ~ ( ord_less_rat @ X @ X ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_irrefl
% 0.29/0.54 thf(fact_635_order__less__irrefl,axiom,
% 0.29/0.54 ! [X: num] :
% 0.29/0.54 ~ ( ord_less_num @ X @ X ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_irrefl
% 0.29/0.54 thf(fact_636_order__less__irrefl,axiom,
% 0.29/0.54 ! [X: nat] :
% 0.29/0.54 ~ ( ord_less_nat @ X @ X ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_irrefl
% 0.29/0.54 thf(fact_637_order__less__irrefl,axiom,
% 0.29/0.54 ! [X: int] :
% 0.29/0.54 ~ ( ord_less_int @ X @ X ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_irrefl
% 0.29/0.54 thf(fact_638_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_639_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_640_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > num,C2: num] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_641_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_642_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > int,C2: int] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_643_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_644_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_645_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_646_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_647_ord__less__eq__subst,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ( F @ B )
% 0.29/0.54 = C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_subst
% 0.29/0.54 thf(fact_648_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: real,F: real > real,B: real,C2: real] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_649_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: rat,F: real > rat,B: real,C2: real] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_650_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: num,F: real > num,B: real,C2: real] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_651_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: nat,F: real > nat,B: real,C2: real] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_652_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: int,F: real > int,B: real,C2: real] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_653_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_654_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_655_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_656_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_657_ord__eq__less__subst,axiom,
% 0.29/0.54 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 0.29/0.54 ( ( A
% 0.29/0.54 = ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_subst
% 0.29/0.54 thf(fact_658_order__less__trans,axiom,
% 0.29/0.54 ! [X: real,Y: real,Z: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( ( ord_less_real @ Y @ Z )
% 0.29/0.54 => ( ord_less_real @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_trans
% 0.29/0.54 thf(fact_659_order__less__trans,axiom,
% 0.29/0.54 ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_rat @ Y @ Z )
% 0.29/0.54 => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_trans
% 0.29/0.54 thf(fact_660_order__less__trans,axiom,
% 0.29/0.54 ! [X: num,Y: num,Z: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( ( ord_less_num @ Y @ Z )
% 0.29/0.54 => ( ord_less_num @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_trans
% 0.29/0.54 thf(fact_661_order__less__trans,axiom,
% 0.29/0.54 ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_nat @ Y @ Z )
% 0.29/0.54 => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_trans
% 0.29/0.54 thf(fact_662_order__less__trans,axiom,
% 0.29/0.54 ! [X: int,Y: int,Z: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_int @ Y @ Z )
% 0.29/0.54 => ( ord_less_int @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_trans
% 0.29/0.54 thf(fact_663_order__less__asym_H,axiom,
% 0.29/0.54 ! [A: real,B: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym'
% 0.29/0.54 thf(fact_664_order__less__asym_H,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym'
% 0.29/0.54 thf(fact_665_order__less__asym_H,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ~ ( ord_less_num @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym'
% 0.29/0.54 thf(fact_666_order__less__asym_H,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym'
% 0.29/0.54 thf(fact_667_order__less__asym_H,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym'
% 0.29/0.54 thf(fact_668_linorder__neq__iff,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 = ( ( ord_less_real @ X @ Y )
% 0.29/0.54 | ( ord_less_real @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neq_iff
% 0.29/0.54 thf(fact_669_linorder__neq__iff,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 = ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 | ( ord_less_rat @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neq_iff
% 0.29/0.54 thf(fact_670_linorder__neq__iff,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 = ( ( ord_less_num @ X @ Y )
% 0.29/0.54 | ( ord_less_num @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neq_iff
% 0.29/0.54 thf(fact_671_linorder__neq__iff,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 = ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neq_iff
% 0.29/0.54 thf(fact_672_linorder__neq__iff,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 = ( ( ord_less_int @ X @ Y )
% 0.29/0.54 | ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neq_iff
% 0.29/0.54 thf(fact_673_order__less__asym,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym
% 0.29/0.54 thf(fact_674_order__less__asym,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym
% 0.29/0.54 thf(fact_675_order__less__asym,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym
% 0.29/0.54 thf(fact_676_order__less__asym,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym
% 0.29/0.54 thf(fact_677_order__less__asym,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_asym
% 0.29/0.54 thf(fact_678_linorder__neqE,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 => ( ~ ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( ord_less_real @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neqE
% 0.29/0.54 thf(fact_679_linorder__neqE,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 => ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neqE
% 0.29/0.54 thf(fact_680_linorder__neqE,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 => ( ~ ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( ord_less_num @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neqE
% 0.29/0.54 thf(fact_681_linorder__neqE,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 => ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neqE
% 0.29/0.54 thf(fact_682_linorder__neqE,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( X != Y )
% 0.29/0.54 => ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_neqE
% 0.29/0.54 thf(fact_683_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [B: real,A: real] :
% 0.29/0.54 ( ( ord_less_real @ B @ A )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_not_eq
% 0.29/0.54 thf(fact_684_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [B: rat,A: rat] :
% 0.29/0.54 ( ( ord_less_rat @ B @ A )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_not_eq
% 0.29/0.54 thf(fact_685_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [B: num,A: num] :
% 0.29/0.54 ( ( ord_less_num @ B @ A )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_not_eq
% 0.29/0.54 thf(fact_686_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [B: nat,A: nat] :
% 0.29/0.54 ( ( ord_less_nat @ B @ A )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_not_eq
% 0.29/0.54 thf(fact_687_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [B: int,A: int] :
% 0.29/0.54 ( ( ord_less_int @ B @ A )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_not_eq
% 0.29/0.54 thf(fact_688_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [A: real,B: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_not_eq
% 0.29/0.54 thf(fact_689_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_not_eq
% 0.29/0.54 thf(fact_690_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_not_eq
% 0.29/0.54 thf(fact_691_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_not_eq
% 0.29/0.54 thf(fact_692_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( A != B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_not_eq
% 0.29/0.54 thf(fact_693_dual__order_Ostrict__trans,axiom,
% 0.29/0.54 ! [B: real,A: real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ B @ A )
% 0.29/0.54 => ( ( ord_less_real @ C2 @ B )
% 0.29/0.54 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans
% 0.29/0.54 thf(fact_694_dual__order_Ostrict__trans,axiom,
% 0.29/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ B @ A )
% 0.29/0.54 => ( ( ord_less_rat @ C2 @ B )
% 0.29/0.54 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans
% 0.29/0.54 thf(fact_695_dual__order_Ostrict__trans,axiom,
% 0.29/0.54 ! [B: num,A: num,C2: num] :
% 0.29/0.54 ( ( ord_less_num @ B @ A )
% 0.29/0.54 => ( ( ord_less_num @ C2 @ B )
% 0.29/0.54 => ( ord_less_num @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans
% 0.29/0.54 thf(fact_696_dual__order_Ostrict__trans,axiom,
% 0.29/0.54 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_nat @ B @ A )
% 0.29/0.54 => ( ( ord_less_nat @ C2 @ B )
% 0.29/0.54 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans
% 0.29/0.54 thf(fact_697_dual__order_Ostrict__trans,axiom,
% 0.29/0.54 ! [B: int,A: int,C2: int] :
% 0.29/0.54 ( ( ord_less_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_int @ C2 @ B )
% 0.29/0.54 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans
% 0.29/0.54 thf(fact_698_not__less__iff__gr__or__eq,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.29/0.54 = ( ( ord_less_real @ Y @ X )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_less_iff_gr_or_eq
% 0.29/0.54 thf(fact_699_not__less__iff__gr__or__eq,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.54 = ( ( ord_less_rat @ Y @ X )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_less_iff_gr_or_eq
% 0.29/0.54 thf(fact_700_not__less__iff__gr__or__eq,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.29/0.54 = ( ( ord_less_num @ Y @ X )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_less_iff_gr_or_eq
% 0.29/0.54 thf(fact_701_not__less__iff__gr__or__eq,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.54 = ( ( ord_less_nat @ Y @ X )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_less_iff_gr_or_eq
% 0.29/0.54 thf(fact_702_not__less__iff__gr__or__eq,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.54 = ( ( ord_less_int @ Y @ X )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_less_iff_gr_or_eq
% 0.29/0.54 thf(fact_703_order_Ostrict__trans,axiom,
% 0.29/0.54 ! [A: real,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans
% 0.29/0.54 thf(fact_704_order_Ostrict__trans,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans
% 0.29/0.54 thf(fact_705_order_Ostrict__trans,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_num @ B @ C2 )
% 0.29/0.54 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans
% 0.29/0.54 thf(fact_706_order_Ostrict__trans,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans
% 0.29/0.54 thf(fact_707_order_Ostrict__trans,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans
% 0.29/0.54 thf(fact_708_linorder__less__wlog,axiom,
% 0.29/0.54 ! [P2: real > real > $o,A: real,B: real] :
% 0.29/0.54 ( ! [A3: real,B3: real] :
% 0.29/0.54 ( ( ord_less_real @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: real] : ( P2 @ A3 @ A3 )
% 0.29/0.54 => ( ! [A3: real,B3: real] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_wlog
% 0.29/0.54 thf(fact_709_linorder__less__wlog,axiom,
% 0.29/0.54 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 0.29/0.54 ( ! [A3: rat,B3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: rat] : ( P2 @ A3 @ A3 )
% 0.29/0.54 => ( ! [A3: rat,B3: rat] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_wlog
% 0.29/0.54 thf(fact_710_linorder__less__wlog,axiom,
% 0.29/0.54 ! [P2: num > num > $o,A: num,B: num] :
% 0.29/0.54 ( ! [A3: num,B3: num] :
% 0.29/0.54 ( ( ord_less_num @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: num] : ( P2 @ A3 @ A3 )
% 0.29/0.54 => ( ! [A3: num,B3: num] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_wlog
% 0.29/0.54 thf(fact_711_linorder__less__wlog,axiom,
% 0.29/0.54 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.54 ( ! [A3: nat,B3: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: nat] : ( P2 @ A3 @ A3 )
% 0.29/0.54 => ( ! [A3: nat,B3: nat] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_wlog
% 0.29/0.54 thf(fact_712_linorder__less__wlog,axiom,
% 0.29/0.54 ! [P2: int > int > $o,A: int,B: int] :
% 0.29/0.54 ( ! [A3: int,B3: int] :
% 0.29/0.54 ( ( ord_less_int @ A3 @ B3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( ! [A3: int] : ( P2 @ A3 @ A3 )
% 0.29/0.54 => ( ! [A3: int,B3: int] :
% 0.29/0.54 ( ( P2 @ B3 @ A3 )
% 0.29/0.54 => ( P2 @ A3 @ B3 ) )
% 0.29/0.54 => ( P2 @ A @ B ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_less_wlog
% 0.29/0.54 thf(fact_713_exists__least__iff,axiom,
% 0.29/0.54 ( ( ^ [P4: nat > $o] :
% 0.29/0.54 ? [X7: nat] : ( P4 @ X7 ) )
% 0.29/0.54 = ( ^ [P5: nat > $o] :
% 0.29/0.54 ? [N6: nat] :
% 0.29/0.54 ( ( P5 @ N6 )
% 0.29/0.54 & ! [M5: nat] :
% 0.29/0.54 ( ( ord_less_nat @ M5 @ N6 )
% 0.29/0.54 => ~ ( P5 @ M5 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % exists_least_iff
% 0.29/0.54 thf(fact_714_dual__order_Oirrefl,axiom,
% 0.29/0.54 ! [A: real] :
% 0.29/0.54 ~ ( ord_less_real @ A @ A ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.irrefl
% 0.29/0.54 thf(fact_715_dual__order_Oirrefl,axiom,
% 0.29/0.54 ! [A: rat] :
% 0.29/0.54 ~ ( ord_less_rat @ A @ A ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.irrefl
% 0.29/0.54 thf(fact_716_dual__order_Oirrefl,axiom,
% 0.29/0.54 ! [A: num] :
% 0.29/0.54 ~ ( ord_less_num @ A @ A ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.irrefl
% 0.29/0.54 thf(fact_717_dual__order_Oirrefl,axiom,
% 0.29/0.54 ! [A: nat] :
% 0.29/0.54 ~ ( ord_less_nat @ A @ A ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.irrefl
% 0.29/0.54 thf(fact_718_dual__order_Oirrefl,axiom,
% 0.29/0.54 ! [A: int] :
% 0.29/0.54 ~ ( ord_less_int @ A @ A ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.irrefl
% 0.29/0.54 thf(fact_719_dual__order_Oasym,axiom,
% 0.29/0.54 ! [B: real,A: real] :
% 0.29/0.54 ( ( ord_less_real @ B @ A )
% 0.29/0.54 => ~ ( ord_less_real @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.asym
% 0.29/0.54 thf(fact_720_dual__order_Oasym,axiom,
% 0.29/0.54 ! [B: rat,A: rat] :
% 0.29/0.54 ( ( ord_less_rat @ B @ A )
% 0.29/0.54 => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.asym
% 0.29/0.54 thf(fact_721_dual__order_Oasym,axiom,
% 0.29/0.54 ! [B: num,A: num] :
% 0.29/0.54 ( ( ord_less_num @ B @ A )
% 0.29/0.54 => ~ ( ord_less_num @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.asym
% 0.29/0.54 thf(fact_722_dual__order_Oasym,axiom,
% 0.29/0.54 ! [B: nat,A: nat] :
% 0.29/0.54 ( ( ord_less_nat @ B @ A )
% 0.29/0.54 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.asym
% 0.29/0.54 thf(fact_723_dual__order_Oasym,axiom,
% 0.29/0.54 ! [B: int,A: int] :
% 0.29/0.54 ( ( ord_less_int @ B @ A )
% 0.29/0.54 => ~ ( ord_less_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.asym
% 0.29/0.54 thf(fact_724_linorder__cases,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ~ ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( ( X != Y )
% 0.29/0.54 => ( ord_less_real @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_cases
% 0.29/0.54 thf(fact_725_linorder__cases,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( ( X != Y )
% 0.29/0.54 => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_cases
% 0.29/0.54 thf(fact_726_linorder__cases,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ~ ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( ( X != Y )
% 0.29/0.54 => ( ord_less_num @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_cases
% 0.29/0.54 thf(fact_727_linorder__cases,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( ( X != Y )
% 0.29/0.54 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_cases
% 0.29/0.54 thf(fact_728_linorder__cases,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( ( X != Y )
% 0.29/0.54 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_cases
% 0.29/0.54 thf(fact_729_antisym__conv3,axiom,
% 0.29/0.54 ! [Y: real,X: real] :
% 0.29/0.54 ( ~ ( ord_less_real @ Y @ X )
% 0.29/0.54 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.29/0.54 = ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym_conv3
% 0.29/0.54 thf(fact_730_antisym__conv3,axiom,
% 0.29/0.54 ! [Y: rat,X: rat] :
% 0.29/0.54 ( ~ ( ord_less_rat @ Y @ X )
% 0.29/0.54 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.54 = ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym_conv3
% 0.29/0.54 thf(fact_731_antisym__conv3,axiom,
% 0.29/0.54 ! [Y: num,X: num] :
% 0.29/0.54 ( ~ ( ord_less_num @ Y @ X )
% 0.29/0.54 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.29/0.54 = ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym_conv3
% 0.29/0.54 thf(fact_732_antisym__conv3,axiom,
% 0.29/0.54 ! [Y: nat,X: nat] :
% 0.29/0.54 ( ~ ( ord_less_nat @ Y @ X )
% 0.29/0.54 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.54 = ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym_conv3
% 0.29/0.54 thf(fact_733_antisym__conv3,axiom,
% 0.29/0.54 ! [Y: int,X: int] :
% 0.29/0.54 ( ~ ( ord_less_int @ Y @ X )
% 0.29/0.54 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.54 = ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % antisym_conv3
% 0.29/0.54 thf(fact_734_less__induct,axiom,
% 0.29/0.54 ! [P2: nat > $o,A: nat] :
% 0.29/0.54 ( ! [X3: nat] :
% 0.29/0.54 ( ! [Y5: nat] :
% 0.29/0.54 ( ( ord_less_nat @ Y5 @ X3 )
% 0.29/0.54 => ( P2 @ Y5 ) )
% 0.29/0.54 => ( P2 @ X3 ) )
% 0.29/0.54 => ( P2 @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_induct
% 0.29/0.54 thf(fact_735_ord__less__eq__trans,axiom,
% 0.29/0.54 ! [A: real,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_trans
% 0.29/0.54 thf(fact_736_ord__less__eq__trans,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_trans
% 0.29/0.54 thf(fact_737_ord__less__eq__trans,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_trans
% 0.29/0.54 thf(fact_738_ord__less__eq__trans,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_trans
% 0.29/0.54 thf(fact_739_ord__less__eq__trans,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ( B = C2 )
% 0.29/0.54 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_less_eq_trans
% 0.29/0.54 thf(fact_740_ord__eq__less__trans,axiom,
% 0.29/0.54 ! [A: real,B: real,C2: real] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_trans
% 0.29/0.54 thf(fact_741_ord__eq__less__trans,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_trans
% 0.29/0.54 thf(fact_742_ord__eq__less__trans,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_num @ B @ C2 )
% 0.29/0.54 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_trans
% 0.29/0.54 thf(fact_743_ord__eq__less__trans,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_trans
% 0.29/0.54 thf(fact_744_ord__eq__less__trans,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( A = B )
% 0.29/0.54 => ( ( ord_less_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % ord_eq_less_trans
% 0.29/0.54 thf(fact_745_order_Oasym,axiom,
% 0.29/0.54 ! [A: real,B: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.asym
% 0.29/0.54 thf(fact_746_order_Oasym,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.asym
% 0.29/0.54 thf(fact_747_order_Oasym,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ~ ( ord_less_num @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.asym
% 0.29/0.54 thf(fact_748_order_Oasym,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.asym
% 0.29/0.54 thf(fact_749_order_Oasym,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.asym
% 0.29/0.54 thf(fact_750_less__imp__neq,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_imp_neq
% 0.29/0.54 thf(fact_751_less__imp__neq,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_imp_neq
% 0.29/0.54 thf(fact_752_less__imp__neq,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_imp_neq
% 0.29/0.54 thf(fact_753_less__imp__neq,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_imp_neq
% 0.29/0.54 thf(fact_754_less__imp__neq,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( X != Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_imp_neq
% 0.29/0.54 thf(fact_755_dense,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ? [Z3: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Z3 )
% 0.29/0.54 & ( ord_less_real @ Z3 @ Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense
% 0.29/0.54 thf(fact_756_dense,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ? [Z3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Z3 )
% 0.29/0.54 & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense
% 0.29/0.54 thf(fact_757_gt__ex,axiom,
% 0.29/0.54 ! [X: real] :
% 0.29/0.54 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 0.29/0.54
% 0.29/0.54 % gt_ex
% 0.29/0.54 thf(fact_758_gt__ex,axiom,
% 0.29/0.54 ! [X: rat] :
% 0.29/0.54 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 0.29/0.54
% 0.29/0.54 % gt_ex
% 0.29/0.54 thf(fact_759_gt__ex,axiom,
% 0.29/0.54 ! [X: nat] :
% 0.29/0.54 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.29/0.54
% 0.29/0.54 % gt_ex
% 0.29/0.54 thf(fact_760_gt__ex,axiom,
% 0.29/0.54 ! [X: int] :
% 0.29/0.54 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 0.29/0.54
% 0.29/0.54 % gt_ex
% 0.29/0.54 thf(fact_761_lt__ex,axiom,
% 0.29/0.54 ! [X: real] :
% 0.29/0.54 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 0.29/0.54
% 0.29/0.54 % lt_ex
% 0.29/0.54 thf(fact_762_lt__ex,axiom,
% 0.29/0.54 ! [X: rat] :
% 0.29/0.54 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 0.29/0.54
% 0.29/0.54 % lt_ex
% 0.29/0.54 thf(fact_763_lt__ex,axiom,
% 0.29/0.54 ! [X: int] :
% 0.29/0.54 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 0.29/0.54
% 0.29/0.54 % lt_ex
% 0.29/0.54 thf(fact_764_order__le__imp__less__or__eq,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ X @ Y )
% 0.29/0.54 => ( ( ord_less_real @ X @ Y )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_imp_less_or_eq
% 0.29/0.54 thf(fact_765_order__le__imp__less__or__eq,axiom,
% 0.29/0.54 ! [X: set_int,Y: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_set_int @ X @ Y )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_imp_less_or_eq
% 0.29/0.54 thf(fact_766_order__le__imp__less__or__eq,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_imp_less_or_eq
% 0.29/0.54 thf(fact_767_order__le__imp__less__or__eq,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.54 => ( ( ord_less_num @ X @ Y )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_imp_less_or_eq
% 0.29/0.54 thf(fact_768_order__le__imp__less__or__eq,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_imp_less_or_eq
% 0.29/0.54 thf(fact_769_order__le__imp__less__or__eq,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_int @ X @ Y )
% 0.29/0.54 | ( X = Y ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_imp_less_or_eq
% 0.29/0.54 thf(fact_770_linorder__le__less__linear,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ X @ Y )
% 0.29/0.54 | ( ord_less_real @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_le_less_linear
% 0.29/0.54 thf(fact_771_linorder__le__less__linear,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54 | ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_le_less_linear
% 0.29/0.54 thf(fact_772_linorder__le__less__linear,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.54 | ( ord_less_num @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_le_less_linear
% 0.29/0.54 thf(fact_773_linorder__le__less__linear,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54 | ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_le_less_linear
% 0.29/0.54 thf(fact_774_linorder__le__less__linear,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54 | ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_le_less_linear
% 0.29/0.54 thf(fact_775_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_776_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_777_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > real,C2: real] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_778_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: nat,B: nat,F: nat > real,C2: real] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_779_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: int,B: int,F: int > real,C2: real] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_780_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: real,B: real,F: real > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_781_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_782_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_783_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_784_order__less__le__subst2,axiom,
% 0.29/0.54 ! [A: int,B: int,F: int > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst2
% 0.29/0.54 thf(fact_785_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_786_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_787_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_num @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_788_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_789_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_790_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: real,F: num > real,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_791_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: num > rat,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_792_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: num,F: num > num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_793_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: nat,F: num > nat,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_794_order__less__le__subst1,axiom,
% 0.29/0.54 ! [A: int,F: num > int,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_subst1
% 0.29/0.54 thf(fact_795_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_796_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_797_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_798_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_799_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_800_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > real,C2: real] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_801_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_802_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_803_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_804_order__le__less__subst2,axiom,
% 0.29/0.54 ! [A: num,B: num,F: num > int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst2
% 0.29/0.54 thf(fact_805_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: real > real,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_806_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_807_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: num > real,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_808_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: nat > real,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_809_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: real,F: int > real,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_int @ B @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_810_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: real > rat,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ! [X3: real,Y3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_811_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: rat,Y3: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_812_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: num > rat,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_num @ B @ C2 )
% 0.29/0.54 => ( ! [X3: num,Y3: num] :
% 0.29/0.54 ( ( ord_less_num @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_813_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.54 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_814_order__le__less__subst1,axiom,
% 0.29/0.54 ! [A: rat,F: int > rat,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 0.29/0.54 => ( ( ord_less_int @ B @ C2 )
% 0.29/0.54 => ( ! [X3: int,Y3: int] :
% 0.29/0.54 ( ( ord_less_int @ X3 @ Y3 )
% 0.29/0.54 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.29/0.54 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_subst1
% 0.29/0.54 thf(fact_815_order__less__le__trans,axiom,
% 0.29/0.54 ! [X: real,Y: real,Z: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_real @ Y @ Z )
% 0.29/0.54 => ( ord_less_real @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_trans
% 0.29/0.54 thf(fact_816_order__less__le__trans,axiom,
% 0.29/0.54 ! [X: set_int,Y: set_int,Z: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ Y @ Z )
% 0.29/0.54 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_trans
% 0.29/0.54 thf(fact_817_order__less__le__trans,axiom,
% 0.29/0.54 ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.54 => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_trans
% 0.29/0.54 thf(fact_818_order__less__le__trans,axiom,
% 0.29/0.54 ! [X: num,Y: num,Z: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_num @ Y @ Z )
% 0.29/0.54 => ( ord_less_num @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_trans
% 0.29/0.54 thf(fact_819_order__less__le__trans,axiom,
% 0.29/0.54 ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.54 => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_trans
% 0.29/0.54 thf(fact_820_order__less__le__trans,axiom,
% 0.29/0.54 ! [X: int,Y: int,Z: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.54 => ( ord_less_int @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le_trans
% 0.29/0.54 thf(fact_821_order__le__less__trans,axiom,
% 0.29/0.54 ! [X: real,Y: real,Z: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ X @ Y )
% 0.29/0.54 => ( ( ord_less_real @ Y @ Z )
% 0.29/0.54 => ( ord_less_real @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_trans
% 0.29/0.54 thf(fact_822_order__le__less__trans,axiom,
% 0.29/0.54 ! [X: set_int,Y: set_int,Z: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_set_int @ Y @ Z )
% 0.29/0.54 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_trans
% 0.29/0.54 thf(fact_823_order__le__less__trans,axiom,
% 0.29/0.54 ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_rat @ Y @ Z )
% 0.29/0.54 => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_trans
% 0.29/0.54 thf(fact_824_order__le__less__trans,axiom,
% 0.29/0.54 ! [X: num,Y: num,Z: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.54 => ( ( ord_less_num @ Y @ Z )
% 0.29/0.54 => ( ord_less_num @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_trans
% 0.29/0.54 thf(fact_825_order__le__less__trans,axiom,
% 0.29/0.54 ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54 => ( ( ord_less_nat @ Y @ Z )
% 0.29/0.54 => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_trans
% 0.29/0.54 thf(fact_826_order__le__less__trans,axiom,
% 0.29/0.54 ! [X: int,Y: int,Z: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54 => ( ( ord_less_int @ Y @ Z )
% 0.29/0.54 => ( ord_less_int @ X @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less_trans
% 0.29/0.54 thf(fact_827_order__neq__le__trans,axiom,
% 0.29/0.54 ! [A: real,B: real] :
% 0.29/0.54 ( ( A != B )
% 0.29/0.54 => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54 => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_neq_le_trans
% 0.29/0.54 thf(fact_828_order__neq__le__trans,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int] :
% 0.29/0.54 ( ( A != B )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.54 => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_neq_le_trans
% 0.29/0.54 thf(fact_829_order__neq__le__trans,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( A != B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_neq_le_trans
% 0.29/0.54 thf(fact_830_order__neq__le__trans,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( A != B )
% 0.29/0.54 => ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ord_less_num @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_neq_le_trans
% 0.29/0.54 thf(fact_831_order__neq__le__trans,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( A != B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_neq_le_trans
% 0.29/0.54 thf(fact_832_order__neq__le__trans,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( A != B )
% 0.29/0.54 => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_neq_le_trans
% 0.29/0.54 thf(fact_833_order__le__neq__trans,axiom,
% 0.29/0.54 ! [A: real,B: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54 => ( ( A != B )
% 0.29/0.54 => ( ord_less_real @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_neq_trans
% 0.29/0.54 thf(fact_834_order__le__neq__trans,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.54 => ( ( A != B )
% 0.29/0.54 => ( ord_less_set_int @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_neq_trans
% 0.29/0.54 thf(fact_835_order__le__neq__trans,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( A != B )
% 0.29/0.54 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_neq_trans
% 0.29/0.54 thf(fact_836_order__le__neq__trans,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( A != B )
% 0.29/0.54 => ( ord_less_num @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_neq_trans
% 0.29/0.54 thf(fact_837_order__le__neq__trans,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( A != B )
% 0.29/0.54 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_neq_trans
% 0.29/0.54 thf(fact_838_order__le__neq__trans,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( A != B )
% 0.29/0.54 => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_neq_trans
% 0.29/0.54 thf(fact_839_order__less__imp__le,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_le
% 0.29/0.54 thf(fact_840_order__less__imp__le,axiom,
% 0.29/0.54 ! [X: set_int,Y: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ X @ Y )
% 0.29/0.54 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_le
% 0.29/0.54 thf(fact_841_order__less__imp__le,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_le
% 0.29/0.54 thf(fact_842_order__less__imp__le,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ord_less_num @ X @ Y )
% 0.29/0.54 => ( ord_less_eq_num @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_le
% 0.29/0.54 thf(fact_843_order__less__imp__le,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X @ Y )
% 0.29/0.54 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_le
% 0.29/0.54 thf(fact_844_order__less__imp__le,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ord_less_int @ X @ Y )
% 0.29/0.54 => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_imp_le
% 0.29/0.54 thf(fact_845_linorder__not__less,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.29/0.54 = ( ord_less_eq_real @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_less
% 0.29/0.54 thf(fact_846_linorder__not__less,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.54 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_less
% 0.29/0.54 thf(fact_847_linorder__not__less,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.29/0.54 = ( ord_less_eq_num @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_less
% 0.29/0.54 thf(fact_848_linorder__not__less,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.54 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_less
% 0.29/0.54 thf(fact_849_linorder__not__less,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.54 = ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_less
% 0.29/0.54 thf(fact_850_linorder__not__le,axiom,
% 0.29/0.54 ! [X: real,Y: real] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 0.29/0.54 = ( ord_less_real @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_le
% 0.29/0.54 thf(fact_851_linorder__not__le,axiom,
% 0.29/0.54 ! [X: rat,Y: rat] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 0.29/0.54 = ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_le
% 0.29/0.54 thf(fact_852_linorder__not__le,axiom,
% 0.29/0.54 ! [X: num,Y: num] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 0.29/0.54 = ( ord_less_num @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_le
% 0.29/0.54 thf(fact_853_linorder__not__le,axiom,
% 0.29/0.54 ! [X: nat,Y: nat] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.29/0.54 = ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_le
% 0.29/0.54 thf(fact_854_linorder__not__le,axiom,
% 0.29/0.54 ! [X: int,Y: int] :
% 0.29/0.54 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 0.29/0.54 = ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.54
% 0.29/0.54 % linorder_not_le
% 0.29/0.54 thf(fact_855_order__less__le,axiom,
% 0.29/0.54 ( ord_less_real
% 0.29/0.54 = ( ^ [X4: real,Y4: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.29/0.54 & ( X4 != Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le
% 0.29/0.54 thf(fact_856_order__less__le,axiom,
% 0.29/0.54 ( ord_less_set_int
% 0.29/0.54 = ( ^ [X4: set_int,Y4: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 0.29/0.54 & ( X4 != Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le
% 0.29/0.54 thf(fact_857_order__less__le,axiom,
% 0.29/0.54 ( ord_less_rat
% 0.29/0.54 = ( ^ [X4: rat,Y4: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.29/0.54 & ( X4 != Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le
% 0.29/0.54 thf(fact_858_order__less__le,axiom,
% 0.29/0.54 ( ord_less_num
% 0.29/0.54 = ( ^ [X4: num,Y4: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.29/0.54 & ( X4 != Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le
% 0.29/0.54 thf(fact_859_order__less__le,axiom,
% 0.29/0.54 ( ord_less_nat
% 0.29/0.54 = ( ^ [X4: nat,Y4: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.29/0.54 & ( X4 != Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le
% 0.29/0.54 thf(fact_860_order__less__le,axiom,
% 0.29/0.54 ( ord_less_int
% 0.29/0.54 = ( ^ [X4: int,Y4: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.29/0.54 & ( X4 != Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_less_le
% 0.29/0.54 thf(fact_861_order__le__less,axiom,
% 0.29/0.54 ( ord_less_eq_real
% 0.29/0.54 = ( ^ [X4: real,Y4: real] :
% 0.29/0.54 ( ( ord_less_real @ X4 @ Y4 )
% 0.29/0.54 | ( X4 = Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less
% 0.29/0.54 thf(fact_862_order__le__less,axiom,
% 0.29/0.54 ( ord_less_eq_set_int
% 0.29/0.54 = ( ^ [X4: set_int,Y4: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ X4 @ Y4 )
% 0.29/0.54 | ( X4 = Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less
% 0.29/0.54 thf(fact_863_order__le__less,axiom,
% 0.29/0.54 ( ord_less_eq_rat
% 0.29/0.54 = ( ^ [X4: rat,Y4: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X4 @ Y4 )
% 0.29/0.54 | ( X4 = Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less
% 0.29/0.54 thf(fact_864_order__le__less,axiom,
% 0.29/0.54 ( ord_less_eq_num
% 0.29/0.54 = ( ^ [X4: num,Y4: num] :
% 0.29/0.54 ( ( ord_less_num @ X4 @ Y4 )
% 0.29/0.54 | ( X4 = Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less
% 0.29/0.54 thf(fact_865_order__le__less,axiom,
% 0.29/0.54 ( ord_less_eq_nat
% 0.29/0.54 = ( ^ [X4: nat,Y4: nat] :
% 0.29/0.54 ( ( ord_less_nat @ X4 @ Y4 )
% 0.29/0.54 | ( X4 = Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less
% 0.29/0.54 thf(fact_866_order__le__less,axiom,
% 0.29/0.54 ( ord_less_eq_int
% 0.29/0.54 = ( ^ [X4: int,Y4: int] :
% 0.29/0.54 ( ( ord_less_int @ X4 @ Y4 )
% 0.29/0.54 | ( X4 = Y4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order_le_less
% 0.29/0.54 thf(fact_867_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [B: real,A: real] :
% 0.29/0.54 ( ( ord_less_real @ B @ A )
% 0.29/0.54 => ( ord_less_eq_real @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_order
% 0.29/0.54 thf(fact_868_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [B: set_int,A: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ B @ A )
% 0.29/0.54 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_order
% 0.29/0.54 thf(fact_869_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [B: rat,A: rat] :
% 0.29/0.54 ( ( ord_less_rat @ B @ A )
% 0.29/0.54 => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_order
% 0.29/0.54 thf(fact_870_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [B: num,A: num] :
% 0.29/0.54 ( ( ord_less_num @ B @ A )
% 0.29/0.54 => ( ord_less_eq_num @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_order
% 0.29/0.54 thf(fact_871_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [B: nat,A: nat] :
% 0.29/0.54 ( ( ord_less_nat @ B @ A )
% 0.29/0.54 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_order
% 0.29/0.54 thf(fact_872_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [B: int,A: int] :
% 0.29/0.54 ( ( ord_less_int @ B @ A )
% 0.29/0.54 => ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_implies_order
% 0.29/0.54 thf(fact_873_order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [A: real,B: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_order
% 0.29/0.54 thf(fact_874_order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ A @ B )
% 0.29/0.54 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_order
% 0.29/0.54 thf(fact_875_order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [A: rat,B: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_order
% 0.29/0.54 thf(fact_876_order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [A: num,B: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ( ord_less_eq_num @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_order
% 0.29/0.54 thf(fact_877_order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [A: nat,B: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_order
% 0.29/0.54 thf(fact_878_order_Ostrict__implies__order,axiom,
% 0.29/0.54 ! [A: int,B: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_implies_order
% 0.29/0.54 thf(fact_879_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_real
% 0.29/0.54 = ( ^ [B7: real,A7: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ B7 @ A7 )
% 0.29/0.54 & ~ ( ord_less_eq_real @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_not
% 0.29/0.54 thf(fact_880_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_set_int
% 0.29/0.54 = ( ^ [B7: set_int,A7: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ B7 @ A7 )
% 0.29/0.54 & ~ ( ord_less_eq_set_int @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_not
% 0.29/0.54 thf(fact_881_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_rat
% 0.29/0.54 = ( ^ [B7: rat,A7: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B7 @ A7 )
% 0.29/0.54 & ~ ( ord_less_eq_rat @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_not
% 0.29/0.54 thf(fact_882_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_num
% 0.29/0.54 = ( ^ [B7: num,A7: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ B7 @ A7 )
% 0.29/0.54 & ~ ( ord_less_eq_num @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_not
% 0.29/0.54 thf(fact_883_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_nat
% 0.29/0.54 = ( ^ [B7: nat,A7: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B7 @ A7 )
% 0.29/0.54 & ~ ( ord_less_eq_nat @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_not
% 0.29/0.54 thf(fact_884_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_int
% 0.29/0.54 = ( ^ [B7: int,A7: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B7 @ A7 )
% 0.29/0.54 & ~ ( ord_less_eq_int @ A7 @ B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_not
% 0.29/0.54 thf(fact_885_dual__order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [B: real,A: real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_real @ C2 @ B )
% 0.29/0.54 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans2
% 0.29/0.54 thf(fact_886_dual__order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [B: set_int,A: set_int,C2: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ C2 @ B )
% 0.29/0.54 => ( ord_less_set_int @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans2
% 0.29/0.54 thf(fact_887_dual__order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_rat @ C2 @ B )
% 0.29/0.54 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans2
% 0.29/0.54 thf(fact_888_dual__order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [B: num,A: num,C2: num] :
% 0.29/0.54 ( ( ord_less_num @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_num @ C2 @ B )
% 0.29/0.54 => ( ord_less_num @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans2
% 0.29/0.54 thf(fact_889_dual__order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_nat @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.29/0.54 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans2
% 0.29/0.54 thf(fact_890_dual__order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [B: int,A: int,C2: int] :
% 0.29/0.54 ( ( ord_less_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_eq_int @ C2 @ B )
% 0.29/0.54 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans2
% 0.29/0.54 thf(fact_891_dual__order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [B: real,A: real,C2: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ B @ A )
% 0.29/0.54 => ( ( ord_less_real @ C2 @ B )
% 0.29/0.54 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans1
% 0.29/0.54 thf(fact_892_dual__order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [B: set_int,A: set_int,C2: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_set_int @ C2 @ B )
% 0.29/0.54 => ( ord_less_set_int @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans1
% 0.29/0.54 thf(fact_893_dual__order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54 => ( ( ord_less_rat @ C2 @ B )
% 0.29/0.54 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans1
% 0.29/0.54 thf(fact_894_dual__order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [B: num,A: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ B @ A )
% 0.29/0.54 => ( ( ord_less_num @ C2 @ B )
% 0.29/0.54 => ( ord_less_num @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans1
% 0.29/0.54 thf(fact_895_dual__order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54 => ( ( ord_less_nat @ C2 @ B )
% 0.29/0.54 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans1
% 0.29/0.54 thf(fact_896_dual__order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [B: int,A: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54 => ( ( ord_less_int @ C2 @ B )
% 0.29/0.54 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_trans1
% 0.29/0.54 thf(fact_897_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_real
% 0.29/0.54 = ( ^ [B7: real,A7: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ B7 @ A7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_order
% 0.29/0.54 thf(fact_898_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_set_int
% 0.29/0.54 = ( ^ [B7: set_int,A7: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ B7 @ A7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_order
% 0.29/0.54 thf(fact_899_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_rat
% 0.29/0.54 = ( ^ [B7: rat,A7: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ B7 @ A7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_order
% 0.29/0.54 thf(fact_900_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_num
% 0.29/0.54 = ( ^ [B7: num,A7: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ B7 @ A7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_order
% 0.29/0.54 thf(fact_901_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_nat
% 0.29/0.54 = ( ^ [B7: nat,A7: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ B7 @ A7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_order
% 0.29/0.54 thf(fact_902_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_int
% 0.29/0.54 = ( ^ [B7: int,A7: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ B7 @ A7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.strict_iff_order
% 0.29/0.54 thf(fact_903_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_real
% 0.29/0.54 = ( ^ [B7: real,A7: real] :
% 0.29/0.54 ( ( ord_less_real @ B7 @ A7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.order_iff_strict
% 0.29/0.54 thf(fact_904_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_set_int
% 0.29/0.54 = ( ^ [B7: set_int,A7: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ B7 @ A7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.order_iff_strict
% 0.29/0.54 thf(fact_905_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_rat
% 0.29/0.54 = ( ^ [B7: rat,A7: rat] :
% 0.29/0.54 ( ( ord_less_rat @ B7 @ A7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.order_iff_strict
% 0.29/0.54 thf(fact_906_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_num
% 0.29/0.54 = ( ^ [B7: num,A7: num] :
% 0.29/0.54 ( ( ord_less_num @ B7 @ A7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.order_iff_strict
% 0.29/0.54 thf(fact_907_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_nat
% 0.29/0.54 = ( ^ [B7: nat,A7: nat] :
% 0.29/0.54 ( ( ord_less_nat @ B7 @ A7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.order_iff_strict
% 0.29/0.54 thf(fact_908_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_int
% 0.29/0.54 = ( ^ [B7: int,A7: int] :
% 0.29/0.54 ( ( ord_less_int @ B7 @ A7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dual_order.order_iff_strict
% 0.29/0.54 thf(fact_909_dense__le__bounded,axiom,
% 0.29/0.54 ! [X: real,Y: real,Z: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ Y )
% 0.29/0.54 => ( ! [W: real] :
% 0.29/0.54 ( ( ord_less_real @ X @ W )
% 0.29/0.54 => ( ( ord_less_real @ W @ Y )
% 0.29/0.54 => ( ord_less_eq_real @ W @ Z ) ) )
% 0.29/0.54 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense_le_bounded
% 0.29/0.54 thf(fact_910_dense__le__bounded,axiom,
% 0.29/0.54 ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ Y )
% 0.29/0.54 => ( ! [W: rat] :
% 0.29/0.54 ( ( ord_less_rat @ X @ W )
% 0.29/0.54 => ( ( ord_less_rat @ W @ Y )
% 0.29/0.54 => ( ord_less_eq_rat @ W @ Z ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense_le_bounded
% 0.29/0.54 thf(fact_911_dense__ge__bounded,axiom,
% 0.29/0.54 ! [Z: real,X: real,Y: real] :
% 0.29/0.54 ( ( ord_less_real @ Z @ X )
% 0.29/0.54 => ( ! [W: real] :
% 0.29/0.54 ( ( ord_less_real @ Z @ W )
% 0.29/0.54 => ( ( ord_less_real @ W @ X )
% 0.29/0.54 => ( ord_less_eq_real @ Y @ W ) ) )
% 0.29/0.54 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense_ge_bounded
% 0.29/0.54 thf(fact_912_dense__ge__bounded,axiom,
% 0.29/0.54 ! [Z: rat,X: rat,Y: rat] :
% 0.29/0.54 ( ( ord_less_rat @ Z @ X )
% 0.29/0.54 => ( ! [W: rat] :
% 0.29/0.54 ( ( ord_less_rat @ Z @ W )
% 0.29/0.54 => ( ( ord_less_rat @ W @ X )
% 0.29/0.54 => ( ord_less_eq_rat @ Y @ W ) ) )
% 0.29/0.54 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense_ge_bounded
% 0.29/0.54 thf(fact_913_order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_real
% 0.29/0.54 = ( ^ [A7: real,B7: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ A7 @ B7 )
% 0.29/0.54 & ~ ( ord_less_eq_real @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_not
% 0.29/0.54 thf(fact_914_order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_set_int
% 0.29/0.54 = ( ^ [A7: set_int,B7: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A7 @ B7 )
% 0.29/0.54 & ~ ( ord_less_eq_set_int @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_not
% 0.29/0.54 thf(fact_915_order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_rat
% 0.29/0.54 = ( ^ [A7: rat,B7: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A7 @ B7 )
% 0.29/0.54 & ~ ( ord_less_eq_rat @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_not
% 0.29/0.54 thf(fact_916_order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_num
% 0.29/0.54 = ( ^ [A7: num,B7: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A7 @ B7 )
% 0.29/0.54 & ~ ( ord_less_eq_num @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_not
% 0.29/0.54 thf(fact_917_order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_nat
% 0.29/0.54 = ( ^ [A7: nat,B7: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A7 @ B7 )
% 0.29/0.54 & ~ ( ord_less_eq_nat @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_not
% 0.29/0.54 thf(fact_918_order_Ostrict__iff__not,axiom,
% 0.29/0.54 ( ord_less_int
% 0.29/0.54 = ( ^ [A7: int,B7: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A7 @ B7 )
% 0.29/0.54 & ~ ( ord_less_eq_int @ B7 @ A7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_not
% 0.29/0.54 thf(fact_919_order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [A: real,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_real @ B @ C2 )
% 0.29/0.54 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans2
% 0.29/0.54 thf(fact_920_order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int,C2: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_set_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_set_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans2
% 0.29/0.54 thf(fact_921_order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.29/0.54 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans2
% 0.29/0.54 thf(fact_922_order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_num @ B @ C2 )
% 0.29/0.54 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans2
% 0.29/0.54 thf(fact_923_order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans2
% 0.29/0.54 thf(fact_924_order_Ostrict__trans2,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_eq_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans2
% 0.29/0.54 thf(fact_925_order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [A: real,B: real,C2: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.54 => ( ( ord_less_real @ B @ C2 )
% 0.29/0.54 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans1
% 0.29/0.54 thf(fact_926_order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [A: set_int,B: set_int,C2: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_set_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_set_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans1
% 0.29/0.54 thf(fact_927_order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54 => ( ( ord_less_rat @ B @ C2 )
% 0.29/0.54 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans1
% 0.29/0.54 thf(fact_928_order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [A: num,B: num,C2: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.54 => ( ( ord_less_num @ B @ C2 )
% 0.29/0.54 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans1
% 0.29/0.54 thf(fact_929_order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54 => ( ( ord_less_nat @ B @ C2 )
% 0.29/0.54 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans1
% 0.29/0.54 thf(fact_930_order_Ostrict__trans1,axiom,
% 0.29/0.54 ! [A: int,B: int,C2: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54 => ( ( ord_less_int @ B @ C2 )
% 0.29/0.54 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_trans1
% 0.29/0.54 thf(fact_931_order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_real
% 0.29/0.54 = ( ^ [A7: real,B7: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ A7 @ B7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_order
% 0.29/0.54 thf(fact_932_order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_set_int
% 0.29/0.54 = ( ^ [A7: set_int,B7: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ A7 @ B7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_order
% 0.29/0.54 thf(fact_933_order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_rat
% 0.29/0.54 = ( ^ [A7: rat,B7: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ A7 @ B7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_order
% 0.29/0.54 thf(fact_934_order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_num
% 0.29/0.54 = ( ^ [A7: num,B7: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ A7 @ B7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_order
% 0.29/0.54 thf(fact_935_order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_nat
% 0.29/0.54 = ( ^ [A7: nat,B7: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ A7 @ B7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_order
% 0.29/0.54 thf(fact_936_order_Ostrict__iff__order,axiom,
% 0.29/0.54 ( ord_less_int
% 0.29/0.54 = ( ^ [A7: int,B7: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ A7 @ B7 )
% 0.29/0.54 & ( A7 != B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.strict_iff_order
% 0.29/0.54 thf(fact_937_order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_real
% 0.29/0.54 = ( ^ [A7: real,B7: real] :
% 0.29/0.54 ( ( ord_less_real @ A7 @ B7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.order_iff_strict
% 0.29/0.54 thf(fact_938_order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_set_int
% 0.29/0.54 = ( ^ [A7: set_int,B7: set_int] :
% 0.29/0.54 ( ( ord_less_set_int @ A7 @ B7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.order_iff_strict
% 0.29/0.54 thf(fact_939_order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_rat
% 0.29/0.54 = ( ^ [A7: rat,B7: rat] :
% 0.29/0.54 ( ( ord_less_rat @ A7 @ B7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.order_iff_strict
% 0.29/0.54 thf(fact_940_order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_num
% 0.29/0.54 = ( ^ [A7: num,B7: num] :
% 0.29/0.54 ( ( ord_less_num @ A7 @ B7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.order_iff_strict
% 0.29/0.54 thf(fact_941_order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_nat
% 0.29/0.54 = ( ^ [A7: nat,B7: nat] :
% 0.29/0.54 ( ( ord_less_nat @ A7 @ B7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.order_iff_strict
% 0.29/0.54 thf(fact_942_order_Oorder__iff__strict,axiom,
% 0.29/0.54 ( ord_less_eq_int
% 0.29/0.54 = ( ^ [A7: int,B7: int] :
% 0.29/0.54 ( ( ord_less_int @ A7 @ B7 )
% 0.29/0.54 | ( A7 = B7 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % order.order_iff_strict
% 0.29/0.54 thf(fact_943_not__le__imp__less,axiom,
% 0.29/0.54 ! [Y: real,X: real] :
% 0.29/0.54 ( ~ ( ord_less_eq_real @ Y @ X )
% 0.29/0.54 => ( ord_less_real @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_le_imp_less
% 0.29/0.54 thf(fact_944_not__le__imp__less,axiom,
% 0.29/0.54 ! [Y: rat,X: rat] :
% 0.29/0.54 ( ~ ( ord_less_eq_rat @ Y @ X )
% 0.29/0.54 => ( ord_less_rat @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_le_imp_less
% 0.29/0.54 thf(fact_945_not__le__imp__less,axiom,
% 0.29/0.54 ! [Y: num,X: num] :
% 0.29/0.54 ( ~ ( ord_less_eq_num @ Y @ X )
% 0.29/0.54 => ( ord_less_num @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_le_imp_less
% 0.29/0.54 thf(fact_946_not__le__imp__less,axiom,
% 0.29/0.54 ! [Y: nat,X: nat] :
% 0.29/0.54 ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.29/0.54 => ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_le_imp_less
% 0.29/0.54 thf(fact_947_not__le__imp__less,axiom,
% 0.29/0.54 ! [Y: int,X: int] :
% 0.29/0.54 ( ~ ( ord_less_eq_int @ Y @ X )
% 0.29/0.54 => ( ord_less_int @ X @ Y ) ) ).
% 0.29/0.54
% 0.29/0.54 % not_le_imp_less
% 0.29/0.54 thf(fact_948_less__le__not__le,axiom,
% 0.29/0.54 ( ord_less_real
% 0.29/0.54 = ( ^ [X4: real,Y4: real] :
% 0.29/0.54 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.29/0.54 & ~ ( ord_less_eq_real @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_le_not_le
% 0.29/0.54 thf(fact_949_less__le__not__le,axiom,
% 0.29/0.54 ( ord_less_set_int
% 0.29/0.54 = ( ^ [X4: set_int,Y4: set_int] :
% 0.29/0.54 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 0.29/0.54 & ~ ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_le_not_le
% 0.29/0.54 thf(fact_950_less__le__not__le,axiom,
% 0.29/0.54 ( ord_less_rat
% 0.29/0.54 = ( ^ [X4: rat,Y4: rat] :
% 0.29/0.54 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.29/0.54 & ~ ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_le_not_le
% 0.29/0.54 thf(fact_951_less__le__not__le,axiom,
% 0.29/0.54 ( ord_less_num
% 0.29/0.54 = ( ^ [X4: num,Y4: num] :
% 0.29/0.54 ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.29/0.54 & ~ ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_le_not_le
% 0.29/0.54 thf(fact_952_less__le__not__le,axiom,
% 0.29/0.54 ( ord_less_nat
% 0.29/0.54 = ( ^ [X4: nat,Y4: nat] :
% 0.29/0.54 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.29/0.54 & ~ ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_le_not_le
% 0.29/0.54 thf(fact_953_less__le__not__le,axiom,
% 0.29/0.54 ( ord_less_int
% 0.29/0.54 = ( ^ [X4: int,Y4: int] :
% 0.29/0.54 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.29/0.54 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 0.29/0.54
% 0.29/0.54 % less_le_not_le
% 0.29/0.54 thf(fact_954_dense__le,axiom,
% 0.29/0.54 ! [Y: real,Z: real] :
% 0.29/0.54 ( ! [X3: real] :
% 0.29/0.54 ( ( ord_less_real @ X3 @ Y )
% 0.29/0.54 => ( ord_less_eq_real @ X3 @ Z ) )
% 0.29/0.54 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 0.29/0.54
% 0.29/0.54 % dense_le
% 0.29/0.54 thf(fact_955_dense__le,axiom,
% 0.29/0.54 ! [Y: rat,Z: rat] :
% 0.29/0.54 ( ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X3 @ Y )
% 0.29/0.55 => ( ord_less_eq_rat @ X3 @ Z ) )
% 0.29/0.55 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.29/0.55
% 0.29/0.55 % dense_le
% 0.29/0.55 thf(fact_956_dense__ge,axiom,
% 0.29/0.55 ! [Z: real,Y: real] :
% 0.29/0.55 ( ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ Z @ X3 )
% 0.29/0.55 => ( ord_less_eq_real @ Y @ X3 ) )
% 0.29/0.55 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 0.29/0.55
% 0.29/0.55 % dense_ge
% 0.29/0.55 thf(fact_957_dense__ge,axiom,
% 0.29/0.55 ! [Z: rat,Y: rat] :
% 0.29/0.55 ( ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z @ X3 )
% 0.29/0.55 => ( ord_less_eq_rat @ Y @ X3 ) )
% 0.29/0.55 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.29/0.55
% 0.29/0.55 % dense_ge
% 0.29/0.55 thf(fact_958_antisym__conv2,axiom,
% 0.29/0.55 ! [X: real,Y: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ X @ Y )
% 0.29/0.55 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv2
% 0.29/0.55 thf(fact_959_antisym__conv2,axiom,
% 0.29/0.55 ! [X: set_int,Y: set_int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ X @ Y )
% 0.29/0.55 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv2
% 0.29/0.55 thf(fact_960_antisym__conv2,axiom,
% 0.29/0.55 ! [X: rat,Y: rat] :
% 0.29/0.55 ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.55 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv2
% 0.29/0.55 thf(fact_961_antisym__conv2,axiom,
% 0.29/0.55 ! [X: num,Y: num] :
% 0.29/0.55 ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.55 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv2
% 0.29/0.55 thf(fact_962_antisym__conv2,axiom,
% 0.29/0.55 ! [X: nat,Y: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.55 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv2
% 0.29/0.55 thf(fact_963_antisym__conv2,axiom,
% 0.29/0.55 ! [X: int,Y: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.55 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv2
% 0.29/0.55 thf(fact_964_antisym__conv1,axiom,
% 0.29/0.55 ! [X: real,Y: real] :
% 0.29/0.55 ( ~ ( ord_less_real @ X @ Y )
% 0.29/0.55 => ( ( ord_less_eq_real @ X @ Y )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv1
% 0.29/0.55 thf(fact_965_antisym__conv1,axiom,
% 0.29/0.55 ! [X: set_int,Y: set_int] :
% 0.29/0.55 ( ~ ( ord_less_set_int @ X @ Y )
% 0.29/0.55 => ( ( ord_less_eq_set_int @ X @ Y )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv1
% 0.29/0.55 thf(fact_966_antisym__conv1,axiom,
% 0.29/0.55 ! [X: rat,Y: rat] :
% 0.29/0.55 ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.55 => ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv1
% 0.29/0.55 thf(fact_967_antisym__conv1,axiom,
% 0.29/0.55 ! [X: num,Y: num] :
% 0.29/0.55 ( ~ ( ord_less_num @ X @ Y )
% 0.29/0.55 => ( ( ord_less_eq_num @ X @ Y )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv1
% 0.29/0.55 thf(fact_968_antisym__conv1,axiom,
% 0.29/0.55 ! [X: nat,Y: nat] :
% 0.29/0.55 ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.55 => ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv1
% 0.29/0.55 thf(fact_969_antisym__conv1,axiom,
% 0.29/0.55 ! [X: int,Y: int] :
% 0.29/0.55 ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.55 => ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.55 = ( X = Y ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % antisym_conv1
% 0.29/0.55 thf(fact_970_nless__le,axiom,
% 0.29/0.55 ! [A: real,B: real] :
% 0.29/0.55 ( ( ~ ( ord_less_real @ A @ B ) )
% 0.29/0.55 = ( ~ ( ord_less_eq_real @ A @ B )
% 0.29/0.55 | ( A = B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nless_le
% 0.29/0.55 thf(fact_971_nless__le,axiom,
% 0.29/0.55 ! [A: set_int,B: set_int] :
% 0.29/0.55 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 0.29/0.55 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 0.29/0.55 | ( A = B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nless_le
% 0.29/0.55 thf(fact_972_nless__le,axiom,
% 0.29/0.55 ! [A: rat,B: rat] :
% 0.29/0.55 ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.29/0.55 = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.29/0.55 | ( A = B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nless_le
% 0.29/0.55 thf(fact_973_nless__le,axiom,
% 0.29/0.55 ! [A: num,B: num] :
% 0.29/0.55 ( ( ~ ( ord_less_num @ A @ B ) )
% 0.29/0.55 = ( ~ ( ord_less_eq_num @ A @ B )
% 0.29/0.55 | ( A = B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nless_le
% 0.29/0.55 thf(fact_974_nless__le,axiom,
% 0.29/0.55 ! [A: nat,B: nat] :
% 0.29/0.55 ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.29/0.55 = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.55 | ( A = B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nless_le
% 0.29/0.55 thf(fact_975_nless__le,axiom,
% 0.29/0.55 ! [A: int,B: int] :
% 0.29/0.55 ( ( ~ ( ord_less_int @ A @ B ) )
% 0.29/0.55 = ( ~ ( ord_less_eq_int @ A @ B )
% 0.29/0.55 | ( A = B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nless_le
% 0.29/0.55 thf(fact_976_leI,axiom,
% 0.29/0.55 ! [X: real,Y: real] :
% 0.29/0.55 ( ~ ( ord_less_real @ X @ Y )
% 0.29/0.55 => ( ord_less_eq_real @ Y @ X ) ) ).
% 0.29/0.55
% 0.29/0.55 % leI
% 0.29/0.55 thf(fact_977_leI,axiom,
% 0.29/0.55 ! [X: rat,Y: rat] :
% 0.29/0.55 ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.55 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.55
% 0.29/0.55 % leI
% 0.29/0.55 thf(fact_978_leI,axiom,
% 0.29/0.55 ! [X: num,Y: num] :
% 0.29/0.55 ( ~ ( ord_less_num @ X @ Y )
% 0.29/0.55 => ( ord_less_eq_num @ Y @ X ) ) ).
% 0.29/0.55
% 0.29/0.55 % leI
% 0.29/0.55 thf(fact_979_leI,axiom,
% 0.29/0.55 ! [X: nat,Y: nat] :
% 0.29/0.55 ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.55 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.55
% 0.29/0.55 % leI
% 0.29/0.55 thf(fact_980_leI,axiom,
% 0.29/0.55 ! [X: int,Y: int] :
% 0.29/0.55 ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.55 => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.55
% 0.29/0.55 % leI
% 0.29/0.55 thf(fact_981_leD,axiom,
% 0.29/0.55 ! [Y: real,X: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ Y @ X )
% 0.29/0.55 => ~ ( ord_less_real @ X @ Y ) ) ).
% 0.29/0.55
% 0.29/0.55 % leD
% 0.29/0.55 thf(fact_982_leD,axiom,
% 0.29/0.55 ! [Y: set_int,X: set_int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ Y @ X )
% 0.29/0.55 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 0.29/0.55
% 0.29/0.55 % leD
% 0.29/0.55 thf(fact_983_leD,axiom,
% 0.29/0.55 ! [Y: rat,X: rat] :
% 0.29/0.55 ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.55 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 0.29/0.55
% 0.29/0.55 % leD
% 0.29/0.55 thf(fact_984_leD,axiom,
% 0.29/0.55 ! [Y: num,X: num] :
% 0.29/0.55 ( ( ord_less_eq_num @ Y @ X )
% 0.29/0.55 => ~ ( ord_less_num @ X @ Y ) ) ).
% 0.29/0.55
% 0.29/0.55 % leD
% 0.29/0.55 thf(fact_985_leD,axiom,
% 0.29/0.55 ! [Y: nat,X: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.55 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.55
% 0.29/0.55 % leD
% 0.29/0.55 thf(fact_986_leD,axiom,
% 0.29/0.55 ! [Y: int,X: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.55 => ~ ( ord_less_int @ X @ Y ) ) ).
% 0.29/0.55
% 0.29/0.55 % leD
% 0.29/0.55 thf(fact_987_bot_Oextremum__uniqueI,axiom,
% 0.29/0.55 ! [A: set_nat] :
% 0.29/0.55 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.29/0.55 => ( A = bot_bot_set_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_uniqueI
% 0.29/0.55 thf(fact_988_bot_Oextremum__uniqueI,axiom,
% 0.29/0.55 ! [A: assn] :
% 0.29/0.55 ( ( ord_less_eq_assn @ A @ bot_bot_assn )
% 0.29/0.55 => ( A = bot_bot_assn ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_uniqueI
% 0.29/0.55 thf(fact_989_bot_Oextremum__uniqueI,axiom,
% 0.29/0.55 ! [A: set_o] :
% 0.29/0.55 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 0.29/0.55 => ( A = bot_bot_set_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_uniqueI
% 0.29/0.55 thf(fact_990_bot_Oextremum__uniqueI,axiom,
% 0.29/0.55 ! [A: set_int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.29/0.55 => ( A = bot_bot_set_int ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_uniqueI
% 0.29/0.55 thf(fact_991_bot_Oextremum__uniqueI,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.29/0.55 => ( A = bot_bot_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_uniqueI
% 0.29/0.55 thf(fact_992_bot_Oextremum__unique,axiom,
% 0.29/0.55 ! [A: set_nat] :
% 0.29/0.55 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.29/0.55 = ( A = bot_bot_set_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_unique
% 0.29/0.55 thf(fact_993_bot_Oextremum__unique,axiom,
% 0.29/0.55 ! [A: assn] :
% 0.29/0.55 ( ( ord_less_eq_assn @ A @ bot_bot_assn )
% 0.29/0.55 = ( A = bot_bot_assn ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_unique
% 0.29/0.55 thf(fact_994_bot_Oextremum__unique,axiom,
% 0.29/0.55 ! [A: set_o] :
% 0.29/0.55 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 0.29/0.55 = ( A = bot_bot_set_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_unique
% 0.29/0.55 thf(fact_995_bot_Oextremum__unique,axiom,
% 0.29/0.55 ! [A: set_int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.29/0.55 = ( A = bot_bot_set_int ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_unique
% 0.29/0.55 thf(fact_996_bot_Oextremum__unique,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.29/0.55 = ( A = bot_bot_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_unique
% 0.29/0.55 thf(fact_997_bot_Oextremum,axiom,
% 0.29/0.55 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum
% 0.29/0.55 thf(fact_998_bot_Oextremum,axiom,
% 0.29/0.55 ! [A: assn] : ( ord_less_eq_assn @ bot_bot_assn @ A ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum
% 0.29/0.55 thf(fact_999_bot_Oextremum,axiom,
% 0.29/0.55 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum
% 0.29/0.55 thf(fact_1000_bot_Oextremum,axiom,
% 0.29/0.55 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum
% 0.29/0.55 thf(fact_1001_bot_Oextremum,axiom,
% 0.29/0.55 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum
% 0.29/0.55 thf(fact_1002_bot_Onot__eq__extremum,axiom,
% 0.29/0.55 ! [A: set_nat] :
% 0.29/0.55 ( ( A != bot_bot_set_nat )
% 0.29/0.55 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.not_eq_extremum
% 0.29/0.55 thf(fact_1003_bot_Onot__eq__extremum,axiom,
% 0.29/0.55 ! [A: assn] :
% 0.29/0.55 ( ( A != bot_bot_assn )
% 0.29/0.55 = ( ord_less_assn @ bot_bot_assn @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.not_eq_extremum
% 0.29/0.55 thf(fact_1004_bot_Onot__eq__extremum,axiom,
% 0.29/0.55 ! [A: set_int] :
% 0.29/0.55 ( ( A != bot_bot_set_int )
% 0.29/0.55 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.not_eq_extremum
% 0.29/0.55 thf(fact_1005_bot_Onot__eq__extremum,axiom,
% 0.29/0.55 ! [A: set_o] :
% 0.29/0.55 ( ( A != bot_bot_set_o )
% 0.29/0.55 = ( ord_less_set_o @ bot_bot_set_o @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.not_eq_extremum
% 0.29/0.55 thf(fact_1006_bot_Onot__eq__extremum,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ( ( A != bot_bot_nat )
% 0.29/0.55 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot.not_eq_extremum
% 0.29/0.55 thf(fact_1007_bot_Oextremum__strict,axiom,
% 0.29/0.55 ! [A: set_nat] :
% 0.29/0.55 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_strict
% 0.29/0.55 thf(fact_1008_bot_Oextremum__strict,axiom,
% 0.29/0.55 ! [A: assn] :
% 0.29/0.55 ~ ( ord_less_assn @ A @ bot_bot_assn ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_strict
% 0.29/0.55 thf(fact_1009_bot_Oextremum__strict,axiom,
% 0.29/0.55 ! [A: set_int] :
% 0.29/0.55 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_strict
% 0.29/0.55 thf(fact_1010_bot_Oextremum__strict,axiom,
% 0.29/0.55 ! [A: set_o] :
% 0.29/0.55 ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_strict
% 0.29/0.55 thf(fact_1011_bot_Oextremum__strict,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.29/0.55
% 0.29/0.55 % bot.extremum_strict
% 0.29/0.55 thf(fact_1012_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 0.29/0.55 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.minNull.simps(1)
% 0.29/0.55 thf(fact_1013_deg1Leaf,axiom,
% 0.29/0.55 ! [T: vEBT_VEBT] :
% 0.29/0.55 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.29/0.55 = ( ? [A7: $o,B7: $o] :
% 0.29/0.55 ( T
% 0.29/0.55 = ( vEBT_Leaf @ A7 @ B7 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % deg1Leaf
% 0.29/0.55 thf(fact_1014_deg__1__Leaf,axiom,
% 0.29/0.55 ! [T: vEBT_VEBT] :
% 0.29/0.55 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.29/0.55 => ? [A3: $o,B3: $o] :
% 0.29/0.55 ( T
% 0.29/0.55 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % deg_1_Leaf
% 0.29/0.55 thf(fact_1015_deg__1__Leafy,axiom,
% 0.29/0.55 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.55 => ( ( N = one_one_nat )
% 0.29/0.55 => ? [A3: $o,B3: $o] :
% 0.29/0.55 ( T
% 0.29/0.55 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % deg_1_Leafy
% 0.29/0.55 thf(fact_1016_finite__nat__set__iff__bounded__le,axiom,
% 0.29/0.55 ( finite_finite_nat
% 0.29/0.55 = ( ^ [N7: set_nat] :
% 0.29/0.55 ? [M5: nat] :
% 0.29/0.55 ! [X4: nat] :
% 0.29/0.55 ( ( member_nat @ X4 @ N7 )
% 0.29/0.55 => ( ord_less_eq_nat @ X4 @ M5 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_nat_set_iff_bounded_le
% 0.29/0.55 thf(fact_1017_infinite__nat__iff__unbounded__le,axiom,
% 0.29/0.55 ! [S3: set_nat] :
% 0.29/0.55 ( ( ~ ( finite_finite_nat @ S3 ) )
% 0.29/0.55 = ( ! [M5: nat] :
% 0.29/0.55 ? [N6: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ M5 @ N6 )
% 0.29/0.55 & ( member_nat @ N6 @ S3 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % infinite_nat_iff_unbounded_le
% 0.29/0.55 thf(fact_1018_finite__nat__set__iff__bounded,axiom,
% 0.29/0.55 ( finite_finite_nat
% 0.29/0.55 = ( ^ [N7: set_nat] :
% 0.29/0.55 ? [M5: nat] :
% 0.29/0.55 ! [X4: nat] :
% 0.29/0.55 ( ( member_nat @ X4 @ N7 )
% 0.29/0.55 => ( ord_less_nat @ X4 @ M5 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_nat_set_iff_bounded
% 0.29/0.55 thf(fact_1019_infinite__nat__iff__unbounded,axiom,
% 0.29/0.55 ! [S3: set_nat] :
% 0.29/0.55 ( ( ~ ( finite_finite_nat @ S3 ) )
% 0.29/0.55 = ( ! [M5: nat] :
% 0.29/0.55 ? [N6: nat] :
% 0.29/0.55 ( ( ord_less_nat @ M5 @ N6 )
% 0.29/0.55 & ( member_nat @ N6 @ S3 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % infinite_nat_iff_unbounded
% 0.29/0.55 thf(fact_1020_bounded__nat__set__is__finite,axiom,
% 0.29/0.55 ! [N8: set_nat,N: nat] :
% 0.29/0.55 ( ! [X3: nat] :
% 0.29/0.55 ( ( member_nat @ X3 @ N8 )
% 0.29/0.55 => ( ord_less_nat @ X3 @ N ) )
% 0.29/0.55 => ( finite_finite_nat @ N8 ) ) ).
% 0.29/0.55
% 0.29/0.55 % bounded_nat_set_is_finite
% 0.29/0.55 thf(fact_1021_unbounded__k__infinite,axiom,
% 0.29/0.55 ! [K: nat,S3: set_nat] :
% 0.29/0.55 ( ! [M3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ K @ M3 )
% 0.29/0.55 => ? [N9: nat] :
% 0.29/0.55 ( ( ord_less_nat @ M3 @ N9 )
% 0.29/0.55 & ( member_nat @ N9 @ S3 ) ) )
% 0.29/0.55 => ~ ( finite_finite_nat @ S3 ) ) ).
% 0.29/0.55
% 0.29/0.55 % unbounded_k_infinite
% 0.29/0.55 thf(fact_1022_VEBT__internal_Oheight_Ocases,axiom,
% 0.29/0.55 ! [X: vEBT_VEBT] :
% 0.29/0.55 ( ! [A3: $o,B3: $o] :
% 0.29/0.55 ( X
% 0.29/0.55 != ( vEBT_Leaf @ A3 @ B3 ) )
% 0.29/0.55 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.29/0.55 ( X
% 0.29/0.55 != ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.height.cases
% 0.29/0.55 thf(fact_1023_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_complex,F: complex > real] :
% 0.29/0.55 ( ( finite3207457112153483333omplex @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_complex )
% 0.29/0.55 => ~ ? [X5: complex] :
% 0.29/0.55 ( ( member_complex @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic8794016678065449205x_real @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1024_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_Code_integer,F: code_integer > real] :
% 0.29/0.55 ( ( finite6017078050557962740nteger @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.29/0.55 => ~ ? [X5: code_integer] :
% 0.29/0.55 ( ( member_Code_integer @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic2659822949269061924r_real @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1025_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_nat,F: nat > real] :
% 0.29/0.55 ( ( finite_finite_nat @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_nat )
% 0.29/0.55 => ~ ? [X5: nat] :
% 0.29/0.55 ( ( member_nat @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic488527866317076247t_real @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1026_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_int,F: int > real] :
% 0.29/0.55 ( ( finite_finite_int @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_int )
% 0.29/0.55 => ~ ? [X5: int] :
% 0.29/0.55 ( ( member_int @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic2675449441010098035t_real @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1027_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_o,F: $o > real] :
% 0.29/0.55 ( ( finite_finite_o @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_o )
% 0.29/0.55 => ~ ? [X5: $o] :
% 0.29/0.55 ( ( member_o @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic8697145971487455083o_real @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1028_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_complex,F: complex > rat] :
% 0.29/0.55 ( ( finite3207457112153483333omplex @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_complex )
% 0.29/0.55 => ~ ? [X5: complex] :
% 0.29/0.55 ( ( member_complex @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1029_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_Code_integer,F: code_integer > rat] :
% 0.29/0.55 ( ( finite6017078050557962740nteger @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.29/0.55 => ~ ? [X5: code_integer] :
% 0.29/0.55 ( ( member_Code_integer @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic5439806495466278992er_rat @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1030_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_nat,F: nat > rat] :
% 0.29/0.55 ( ( finite_finite_nat @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_nat )
% 0.29/0.55 => ~ ? [X5: nat] :
% 0.29/0.55 ( ( member_nat @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic6811802900495863747at_rat @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1031_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_int,F: int > rat] :
% 0.29/0.55 ( ( finite_finite_int @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_int )
% 0.29/0.55 => ~ ? [X5: int] :
% 0.29/0.55 ( ( member_int @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1032_arg__min__if__finite_I2_J,axiom,
% 0.29/0.55 ! [S3: set_o,F: $o > rat] :
% 0.29/0.55 ( ( finite_finite_o @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_o )
% 0.29/0.55 => ~ ? [X5: $o] :
% 0.29/0.55 ( ( member_o @ X5 @ S3 )
% 0.29/0.55 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S3 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_if_finite(2)
% 0.29/0.55 thf(fact_1033_subsetI,axiom,
% 0.29/0.55 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.55 ( ! [X3: nat] :
% 0.29/0.55 ( ( member_nat @ X3 @ A4 )
% 0.29/0.55 => ( member_nat @ X3 @ B4 ) )
% 0.29/0.55 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetI
% 0.29/0.55 thf(fact_1034_subsetI,axiom,
% 0.29/0.55 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.55 ( ! [X3: vEBT_VEBT] :
% 0.29/0.55 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.29/0.55 => ( member_VEBT_VEBT @ X3 @ B4 ) )
% 0.29/0.55 => ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetI
% 0.29/0.55 thf(fact_1035_subsetI,axiom,
% 0.29/0.55 ! [A4: set_real,B4: set_real] :
% 0.29/0.55 ( ! [X3: real] :
% 0.29/0.55 ( ( member_real @ X3 @ A4 )
% 0.29/0.55 => ( member_real @ X3 @ B4 ) )
% 0.29/0.55 => ( ord_less_eq_set_real @ A4 @ B4 ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetI
% 0.29/0.55 thf(fact_1036_subsetI,axiom,
% 0.29/0.55 ! [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.55 ( ! [X3: set_nat] :
% 0.29/0.55 ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.55 => ( member_set_nat @ X3 @ B4 ) )
% 0.29/0.55 => ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetI
% 0.29/0.55 thf(fact_1037_subsetI,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int] :
% 0.29/0.55 ( ! [X3: int] :
% 0.29/0.55 ( ( member_int @ X3 @ A4 )
% 0.29/0.55 => ( member_int @ X3 @ B4 ) )
% 0.29/0.55 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetI
% 0.29/0.55 thf(fact_1038_subset__antisym,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.55 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.29/0.55 => ( A4 = B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_antisym
% 0.29/0.55 thf(fact_1039_less__one,axiom,
% 0.29/0.55 ! [N: nat] :
% 0.29/0.55 ( ( ord_less_nat @ N @ one_one_nat )
% 0.29/0.55 = ( N = zero_zero_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % less_one
% 0.29/0.55 thf(fact_1040_subset__Collect__conv,axiom,
% 0.29/0.55 ! [S3: set_complex,P2: complex > $o] :
% 0.29/0.55 ( ( ord_le211207098394363844omplex @ S3 @ ( collect_complex @ P2 ) )
% 0.29/0.55 = ( ! [X4: complex] :
% 0.29/0.55 ( ( member_complex @ X4 @ S3 )
% 0.29/0.55 => ( P2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_Collect_conv
% 0.29/0.55 thf(fact_1041_subset__Collect__conv,axiom,
% 0.29/0.55 ! [S3: set_list_nat,P2: list_nat > $o] :
% 0.29/0.55 ( ( ord_le6045566169113846134st_nat @ S3 @ ( collect_list_nat @ P2 ) )
% 0.29/0.55 = ( ! [X4: list_nat] :
% 0.29/0.55 ( ( member_list_nat @ X4 @ S3 )
% 0.29/0.55 => ( P2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_Collect_conv
% 0.29/0.55 thf(fact_1042_subset__Collect__conv,axiom,
% 0.29/0.55 ! [S3: set_set_nat,P2: set_nat > $o] :
% 0.29/0.55 ( ( ord_le6893508408891458716et_nat @ S3 @ ( collect_set_nat @ P2 ) )
% 0.29/0.55 = ( ! [X4: set_nat] :
% 0.29/0.55 ( ( member_set_nat @ X4 @ S3 )
% 0.29/0.55 => ( P2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_Collect_conv
% 0.29/0.55 thf(fact_1043_subset__Collect__conv,axiom,
% 0.29/0.55 ! [S3: set_nat,P2: nat > $o] :
% 0.29/0.55 ( ( ord_less_eq_set_nat @ S3 @ ( collect_nat @ P2 ) )
% 0.29/0.55 = ( ! [X4: nat] :
% 0.29/0.55 ( ( member_nat @ X4 @ S3 )
% 0.29/0.55 => ( P2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_Collect_conv
% 0.29/0.55 thf(fact_1044_subset__Collect__conv,axiom,
% 0.29/0.55 ! [S3: set_int,P2: int > $o] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ S3 @ ( collect_int @ P2 ) )
% 0.29/0.55 = ( ! [X4: int] :
% 0.29/0.55 ( ( member_int @ X4 @ S3 )
% 0.29/0.55 => ( P2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_Collect_conv
% 0.29/0.55 thf(fact_1045_in__mono,axiom,
% 0.29/0.55 ! [A4: set_nat,B4: set_nat,X: nat] :
% 0.29/0.55 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.55 => ( ( member_nat @ X @ A4 )
% 0.29/0.55 => ( member_nat @ X @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % in_mono
% 0.29/0.55 thf(fact_1046_in__mono,axiom,
% 0.29/0.55 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.29/0.55 ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.29/0.55 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.55 => ( member_VEBT_VEBT @ X @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % in_mono
% 0.29/0.55 thf(fact_1047_in__mono,axiom,
% 0.29/0.55 ! [A4: set_real,B4: set_real,X: real] :
% 0.29/0.55 ( ( ord_less_eq_set_real @ A4 @ B4 )
% 0.29/0.55 => ( ( member_real @ X @ A4 )
% 0.29/0.55 => ( member_real @ X @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % in_mono
% 0.29/0.55 thf(fact_1048_in__mono,axiom,
% 0.29/0.55 ! [A4: set_set_nat,B4: set_set_nat,X: set_nat] :
% 0.29/0.55 ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 0.29/0.55 => ( ( member_set_nat @ X @ A4 )
% 0.29/0.55 => ( member_set_nat @ X @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % in_mono
% 0.29/0.55 thf(fact_1049_in__mono,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int,X: int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.55 => ( ( member_int @ X @ A4 )
% 0.29/0.55 => ( member_int @ X @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % in_mono
% 0.29/0.55 thf(fact_1050_subsetD,axiom,
% 0.29/0.55 ! [A4: set_nat,B4: set_nat,C2: nat] :
% 0.29/0.55 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.55 => ( ( member_nat @ C2 @ A4 )
% 0.29/0.55 => ( member_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetD
% 0.29/0.55 thf(fact_1051_subsetD,axiom,
% 0.29/0.55 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,C2: vEBT_VEBT] :
% 0.29/0.55 ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.29/0.55 => ( ( member_VEBT_VEBT @ C2 @ A4 )
% 0.29/0.55 => ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetD
% 0.29/0.55 thf(fact_1052_subsetD,axiom,
% 0.29/0.55 ! [A4: set_real,B4: set_real,C2: real] :
% 0.29/0.55 ( ( ord_less_eq_set_real @ A4 @ B4 )
% 0.29/0.55 => ( ( member_real @ C2 @ A4 )
% 0.29/0.55 => ( member_real @ C2 @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetD
% 0.29/0.55 thf(fact_1053_subsetD,axiom,
% 0.29/0.55 ! [A4: set_set_nat,B4: set_set_nat,C2: set_nat] :
% 0.29/0.55 ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 0.29/0.55 => ( ( member_set_nat @ C2 @ A4 )
% 0.29/0.55 => ( member_set_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetD
% 0.29/0.55 thf(fact_1054_subsetD,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int,C2: int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.55 => ( ( member_int @ C2 @ A4 )
% 0.29/0.55 => ( member_int @ C2 @ B4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subsetD
% 0.29/0.55 thf(fact_1055_equalityE,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int] :
% 0.29/0.55 ( ( A4 = B4 )
% 0.29/0.55 => ~ ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.55 => ~ ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % equalityE
% 0.29/0.55 thf(fact_1056_subset__eq,axiom,
% 0.29/0.55 ( ord_less_eq_set_nat
% 0.29/0.55 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.29/0.55 ! [X4: nat] :
% 0.29/0.55 ( ( member_nat @ X4 @ A6 )
% 0.29/0.55 => ( member_nat @ X4 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_eq
% 0.29/0.55 thf(fact_1057_subset__eq,axiom,
% 0.29/0.55 ( ord_le4337996190870823476T_VEBT
% 0.29/0.55 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.29/0.55 ! [X4: vEBT_VEBT] :
% 0.29/0.55 ( ( member_VEBT_VEBT @ X4 @ A6 )
% 0.29/0.55 => ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_eq
% 0.29/0.55 thf(fact_1058_subset__eq,axiom,
% 0.29/0.55 ( ord_less_eq_set_real
% 0.29/0.55 = ( ^ [A6: set_real,B6: set_real] :
% 0.29/0.55 ! [X4: real] :
% 0.29/0.55 ( ( member_real @ X4 @ A6 )
% 0.29/0.55 => ( member_real @ X4 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_eq
% 0.29/0.55 thf(fact_1059_subset__eq,axiom,
% 0.29/0.55 ( ord_le6893508408891458716et_nat
% 0.29/0.55 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.29/0.55 ! [X4: set_nat] :
% 0.29/0.55 ( ( member_set_nat @ X4 @ A6 )
% 0.29/0.55 => ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_eq
% 0.29/0.55 thf(fact_1060_subset__eq,axiom,
% 0.29/0.55 ( ord_less_eq_set_int
% 0.29/0.55 = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.55 ! [X4: int] :
% 0.29/0.55 ( ( member_int @ X4 @ A6 )
% 0.29/0.55 => ( member_int @ X4 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_eq
% 0.29/0.55 thf(fact_1061_equalityD1,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int] :
% 0.29/0.55 ( ( A4 = B4 )
% 0.29/0.55 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 0.29/0.55
% 0.29/0.55 % equalityD1
% 0.29/0.55 thf(fact_1062_Set_OequalityD2,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int] :
% 0.29/0.55 ( ( A4 = B4 )
% 0.29/0.55 => ( ord_less_eq_set_int @ B4 @ A4 ) ) ).
% 0.29/0.55
% 0.29/0.55 % Set.equalityD2
% 0.29/0.55 thf(fact_1063_subset__iff,axiom,
% 0.29/0.55 ( ord_less_eq_set_nat
% 0.29/0.55 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.29/0.55 ! [T2: nat] :
% 0.29/0.55 ( ( member_nat @ T2 @ A6 )
% 0.29/0.55 => ( member_nat @ T2 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_iff
% 0.29/0.55 thf(fact_1064_subset__iff,axiom,
% 0.29/0.55 ( ord_le4337996190870823476T_VEBT
% 0.29/0.55 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.29/0.55 ! [T2: vEBT_VEBT] :
% 0.29/0.55 ( ( member_VEBT_VEBT @ T2 @ A6 )
% 0.29/0.55 => ( member_VEBT_VEBT @ T2 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_iff
% 0.29/0.55 thf(fact_1065_subset__iff,axiom,
% 0.29/0.55 ( ord_less_eq_set_real
% 0.29/0.55 = ( ^ [A6: set_real,B6: set_real] :
% 0.29/0.55 ! [T2: real] :
% 0.29/0.55 ( ( member_real @ T2 @ A6 )
% 0.29/0.55 => ( member_real @ T2 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_iff
% 0.29/0.55 thf(fact_1066_subset__iff,axiom,
% 0.29/0.55 ( ord_le6893508408891458716et_nat
% 0.29/0.55 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.29/0.55 ! [T2: set_nat] :
% 0.29/0.55 ( ( member_set_nat @ T2 @ A6 )
% 0.29/0.55 => ( member_set_nat @ T2 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_iff
% 0.29/0.55 thf(fact_1067_subset__iff,axiom,
% 0.29/0.55 ( ord_less_eq_set_int
% 0.29/0.55 = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.55 ! [T2: int] :
% 0.29/0.55 ( ( member_int @ T2 @ A6 )
% 0.29/0.55 => ( member_int @ T2 @ B6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_iff
% 0.29/0.55 thf(fact_1068_subset__refl,axiom,
% 0.29/0.55 ! [A4: set_int] : ( ord_less_eq_set_int @ A4 @ A4 ) ).
% 0.29/0.55
% 0.29/0.55 % subset_refl
% 0.29/0.55 thf(fact_1069_Collect__mono,axiom,
% 0.29/0.55 ! [P2: complex > $o,Q2: complex > $o] :
% 0.29/0.55 ( ! [X3: complex] :
% 0.29/0.55 ( ( P2 @ X3 )
% 0.29/0.55 => ( Q2 @ X3 ) )
% 0.29/0.55 => ( ord_le211207098394363844omplex @ ( collect_complex @ P2 ) @ ( collect_complex @ Q2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono
% 0.29/0.55 thf(fact_1070_Collect__mono,axiom,
% 0.29/0.55 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 0.29/0.55 ( ! [X3: list_nat] :
% 0.29/0.55 ( ( P2 @ X3 )
% 0.29/0.55 => ( Q2 @ X3 ) )
% 0.29/0.55 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono
% 0.29/0.55 thf(fact_1071_Collect__mono,axiom,
% 0.29/0.55 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 0.29/0.55 ( ! [X3: set_nat] :
% 0.29/0.55 ( ( P2 @ X3 )
% 0.29/0.55 => ( Q2 @ X3 ) )
% 0.29/0.55 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono
% 0.29/0.55 thf(fact_1072_Collect__mono,axiom,
% 0.29/0.55 ! [P2: nat > $o,Q2: nat > $o] :
% 0.29/0.55 ( ! [X3: nat] :
% 0.29/0.55 ( ( P2 @ X3 )
% 0.29/0.55 => ( Q2 @ X3 ) )
% 0.29/0.55 => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono
% 0.29/0.55 thf(fact_1073_Collect__mono,axiom,
% 0.29/0.55 ! [P2: int > $o,Q2: int > $o] :
% 0.29/0.55 ( ! [X3: int] :
% 0.29/0.55 ( ( P2 @ X3 )
% 0.29/0.55 => ( Q2 @ X3 ) )
% 0.29/0.55 => ( ord_less_eq_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono
% 0.29/0.55 thf(fact_1074_subset__trans,axiom,
% 0.29/0.55 ! [A4: set_int,B4: set_int,C3: set_int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.55 => ( ( ord_less_eq_set_int @ B4 @ C3 )
% 0.29/0.55 => ( ord_less_eq_set_int @ A4 @ C3 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % subset_trans
% 0.29/0.55 thf(fact_1075_set__eq__subset,axiom,
% 0.29/0.55 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 0.29/0.55 = ( ^ [A6: set_int,B6: set_int] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 0.29/0.55 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % set_eq_subset
% 0.29/0.55 thf(fact_1076_Collect__mono__iff,axiom,
% 0.29/0.55 ! [P2: complex > $o,Q2: complex > $o] :
% 0.29/0.55 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P2 ) @ ( collect_complex @ Q2 ) )
% 0.29/0.55 = ( ! [X4: complex] :
% 0.29/0.55 ( ( P2 @ X4 )
% 0.29/0.55 => ( Q2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono_iff
% 0.29/0.55 thf(fact_1077_Collect__mono__iff,axiom,
% 0.29/0.55 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 0.29/0.55 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) )
% 0.29/0.55 = ( ! [X4: list_nat] :
% 0.29/0.55 ( ( P2 @ X4 )
% 0.29/0.55 => ( Q2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono_iff
% 0.29/0.55 thf(fact_1078_Collect__mono__iff,axiom,
% 0.29/0.55 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 0.29/0.55 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) )
% 0.29/0.55 = ( ! [X4: set_nat] :
% 0.29/0.55 ( ( P2 @ X4 )
% 0.29/0.55 => ( Q2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono_iff
% 0.29/0.55 thf(fact_1079_Collect__mono__iff,axiom,
% 0.29/0.55 ! [P2: nat > $o,Q2: nat > $o] :
% 0.29/0.55 ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) )
% 0.29/0.55 = ( ! [X4: nat] :
% 0.29/0.55 ( ( P2 @ X4 )
% 0.29/0.55 => ( Q2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono_iff
% 0.29/0.55 thf(fact_1080_Collect__mono__iff,axiom,
% 0.29/0.55 ! [P2: int > $o,Q2: int > $o] :
% 0.29/0.55 ( ( ord_less_eq_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) )
% 0.29/0.55 = ( ! [X4: int] :
% 0.29/0.55 ( ( P2 @ X4 )
% 0.29/0.55 => ( Q2 @ X4 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_mono_iff
% 0.29/0.55 thf(fact_1081_one__reorient,axiom,
% 0.29/0.55 ! [X: uint32] :
% 0.29/0.55 ( ( one_one_uint32 = X )
% 0.29/0.55 = ( X = one_one_uint32 ) ) ).
% 0.29/0.55
% 0.29/0.55 % one_reorient
% 0.29/0.55 thf(fact_1082_one__reorient,axiom,
% 0.29/0.55 ! [X: real] :
% 0.29/0.55 ( ( one_one_real = X )
% 0.29/0.55 = ( X = one_one_real ) ) ).
% 0.29/0.55
% 0.29/0.55 % one_reorient
% 0.29/0.55 thf(fact_1083_one__reorient,axiom,
% 0.29/0.55 ! [X: rat] :
% 0.29/0.55 ( ( one_one_rat = X )
% 0.29/0.55 = ( X = one_one_rat ) ) ).
% 0.29/0.55
% 0.29/0.55 % one_reorient
% 0.29/0.55 thf(fact_1084_one__reorient,axiom,
% 0.29/0.55 ! [X: nat] :
% 0.29/0.55 ( ( one_one_nat = X )
% 0.29/0.55 = ( X = one_one_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % one_reorient
% 0.29/0.55 thf(fact_1085_one__reorient,axiom,
% 0.29/0.55 ! [X: int] :
% 0.29/0.55 ( ( one_one_int = X )
% 0.29/0.55 = ( X = one_one_int ) ) ).
% 0.29/0.55
% 0.29/0.55 % one_reorient
% 0.29/0.55 thf(fact_1086_one__natural_Orsp,axiom,
% 0.29/0.55 one_one_nat = one_one_nat ).
% 0.29/0.55
% 0.29/0.55 % one_natural.rsp
% 0.29/0.55 thf(fact_1087_One__nat__def,axiom,
% 0.29/0.55 ( one_one_nat
% 0.29/0.55 = ( suc @ zero_zero_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % One_nat_def
% 0.29/0.55 thf(fact_1088_nat__geq__1__eq__neqz,axiom,
% 0.29/0.55 ! [X: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 0.29/0.55 = ( X != zero_zero_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % nat_geq_1_eq_neqz
% 0.29/0.55 thf(fact_1089_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 0.29/0.55 ! [Uu2: $o,Uv2: $o,D: nat] :
% 0.29/0.55 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D )
% 0.29/0.55 = ( D = one_one_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.valid'.simps(1)
% 0.29/0.55 thf(fact_1090_nat__induct__non__zero,axiom,
% 0.29/0.55 ! [N: nat,P2: nat > $o] :
% 0.29/0.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55 => ( ( P2 @ one_one_nat )
% 0.29/0.55 => ( ! [N2: nat] :
% 0.29/0.55 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.29/0.55 => ( ( P2 @ N2 )
% 0.29/0.55 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.29/0.55 => ( P2 @ N ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nat_induct_non_zero
% 0.29/0.55 thf(fact_1091_bounded__Max__nat,axiom,
% 0.29/0.55 ! [P2: nat > $o,X: nat,M7: nat] :
% 0.29/0.55 ( ( P2 @ X )
% 0.29/0.55 => ( ! [X3: nat] :
% 0.29/0.55 ( ( P2 @ X3 )
% 0.29/0.55 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 0.29/0.55 => ~ ! [M3: nat] :
% 0.29/0.55 ( ( P2 @ M3 )
% 0.29/0.55 => ~ ! [X5: nat] :
% 0.29/0.55 ( ( P2 @ X5 )
% 0.29/0.55 => ( ord_less_eq_nat @ X5 @ M3 ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % bounded_Max_nat
% 0.29/0.55 thf(fact_1092_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 0.29/0.55 ! [A: $o,B: $o,X: nat] :
% 0.29/0.55 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.55 = ( ( ( X = zero_zero_nat )
% 0.29/0.55 => A )
% 0.29/0.55 & ( ( X != zero_zero_nat )
% 0.29/0.55 => ( ( ( X = one_one_nat )
% 0.29/0.55 => B )
% 0.29/0.55 & ( X = one_one_nat ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.naive_member.simps(1)
% 0.29/0.55 thf(fact_1093_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_VEBT_VEBT,R2: vEBT_VEBT > vEBT_VEBT > $o] :
% 0.29/0.55 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.29/0.55 => ( ! [X3: vEBT_VEBT] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: vEBT_VEBT,Y3: vEBT_VEBT,Z3: vEBT_VEBT] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: vEBT_VEBT] :
% 0.29/0.55 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: vEBT_VEBT] :
% 0.29/0.55 ( ( member_VEBT_VEBT @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1094_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_real,R2: real > real > $o] :
% 0.29/0.55 ( ( finite_finite_real @ A4 )
% 0.29/0.55 => ( ! [X3: real] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: real,Y3: real,Z3: real] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: real] :
% 0.29/0.55 ( ( member_real @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: real] :
% 0.29/0.55 ( ( member_real @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bot_set_real ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1095_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_set_nat,R2: set_nat > set_nat > $o] :
% 0.29/0.55 ( ( finite1152437895449049373et_nat @ A4 )
% 0.29/0.55 => ( ! [X3: set_nat] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: set_nat,Y3: set_nat,Z3: set_nat] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: set_nat] :
% 0.29/0.55 ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: set_nat] :
% 0.29/0.55 ( ( member_set_nat @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bot_set_set_nat ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1096_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_complex,R2: complex > complex > $o] :
% 0.29/0.55 ( ( finite3207457112153483333omplex @ A4 )
% 0.29/0.55 => ( ! [X3: complex] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: complex,Y3: complex,Z3: complex] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: complex] :
% 0.29/0.55 ( ( member_complex @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: complex] :
% 0.29/0.55 ( ( member_complex @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bot_set_complex ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1097_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_Code_integer,R2: code_integer > code_integer > $o] :
% 0.29/0.55 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.55 => ( ! [X3: code_integer] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: code_integer,Y3: code_integer,Z3: code_integer] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: code_integer] :
% 0.29/0.55 ( ( member_Code_integer @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: code_integer] :
% 0.29/0.55 ( ( member_Code_integer @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1098_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_nat,R2: nat > nat > $o] :
% 0.29/0.55 ( ( finite_finite_nat @ A4 )
% 0.29/0.55 => ( ! [X3: nat] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: nat] :
% 0.29/0.55 ( ( member_nat @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: nat] :
% 0.29/0.55 ( ( member_nat @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bot_set_nat ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1099_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_int,R2: int > int > $o] :
% 0.29/0.55 ( ( finite_finite_int @ A4 )
% 0.29/0.55 => ( ! [X3: int] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: int,Y3: int,Z3: int] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: int] :
% 0.29/0.55 ( ( member_int @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: int] :
% 0.29/0.55 ( ( member_int @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bot_set_int ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1100_finite__transitivity__chain,axiom,
% 0.29/0.55 ! [A4: set_o,R2: $o > $o > $o] :
% 0.29/0.55 ( ( finite_finite_o @ A4 )
% 0.29/0.55 => ( ! [X3: $o] :
% 0.29/0.55 ~ ( R2 @ X3 @ X3 )
% 0.29/0.55 => ( ! [X3: $o,Y3: $o,Z3: $o] :
% 0.29/0.55 ( ( R2 @ X3 @ Y3 )
% 0.29/0.55 => ( ( R2 @ Y3 @ Z3 )
% 0.29/0.55 => ( R2 @ X3 @ Z3 ) ) )
% 0.29/0.55 => ( ! [X3: $o] :
% 0.29/0.55 ( ( member_o @ X3 @ A4 )
% 0.29/0.55 => ? [Y5: $o] :
% 0.29/0.55 ( ( member_o @ Y5 @ A4 )
% 0.29/0.55 & ( R2 @ X3 @ Y5 ) ) )
% 0.29/0.55 => ( A4 = bot_bot_set_o ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % finite_transitivity_chain
% 0.29/0.55 thf(fact_1101_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.29/0.55 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.55 => ( ( member_VEBT_VEBT @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( F @ ( lattic6139528642216935859BT_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1102_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_real,Y: real,F: real > rat] :
% 0.29/0.55 ( ( finite_finite_real @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_real )
% 0.29/0.55 => ( ( member_real @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( F @ ( lattic4420706379359479199al_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1103_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_complex,Y: complex,F: complex > rat] :
% 0.29/0.55 ( ( finite3207457112153483333omplex @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_complex )
% 0.29/0.55 => ( ( member_complex @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1104_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_Code_integer,Y: code_integer,F: code_integer > rat] :
% 0.29/0.55 ( ( finite6017078050557962740nteger @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.29/0.55 => ( ( member_Code_integer @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( F @ ( lattic5439806495466278992er_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1105_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_nat,Y: nat,F: nat > rat] :
% 0.29/0.55 ( ( finite_finite_nat @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_nat )
% 0.29/0.55 => ( ( member_nat @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( F @ ( lattic6811802900495863747at_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1106_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_int,Y: int,F: int > rat] :
% 0.29/0.55 ( ( finite_finite_int @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_int )
% 0.29/0.55 => ( ( member_int @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1107_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_o,Y: $o,F: $o > rat] :
% 0.29/0.55 ( ( finite_finite_o @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_o )
% 0.29/0.55 => ( ( member_o @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1108_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > num] :
% 0.29/0.55 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.55 => ( ( member_VEBT_VEBT @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_num @ ( F @ ( lattic3331990488459210229BT_num @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1109_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_real,Y: real,F: real > num] :
% 0.29/0.55 ( ( finite_finite_real @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_real )
% 0.29/0.55 => ( ( member_real @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_num @ ( F @ ( lattic1613168225601753569al_num @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1110_arg__min__least,axiom,
% 0.29/0.55 ! [S3: set_complex,Y: complex,F: complex > num] :
% 0.29/0.55 ( ( finite3207457112153483333omplex @ S3 )
% 0.29/0.55 => ( ( S3 != bot_bot_set_complex )
% 0.29/0.55 => ( ( member_complex @ Y @ S3 )
% 0.29/0.55 => ( ord_less_eq_num @ ( F @ ( lattic1922116423962787043ex_num @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % arg_min_least
% 0.29/0.55 thf(fact_1111_minNull__delete__time__bound_H,axiom,
% 0.29/0.55 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.55 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 0.29/0.55 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) @ one_one_nat ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minNull_delete_time_bound'
% 0.29/0.55 thf(fact_1112_vebt__member__code_I1_J,axiom,
% 0.29/0.55 ! [A: $o,B: $o,X: nat] :
% 0.29/0.55 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.55 = ( ( ( X = zero_zero_nat )
% 0.29/0.55 => A )
% 0.29/0.55 & ( ( X != zero_zero_nat )
% 0.29/0.55 => ( ( ( X = one_one_nat )
% 0.29/0.55 => B )
% 0.29/0.55 & ( X = one_one_nat ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % vebt_member_code(1)
% 0.29/0.55 thf(fact_1113_vebt__delete__code_I1_J,axiom,
% 0.29/0.55 ! [X: nat,A: $o,B: $o] :
% 0.29/0.55 ( ( ( X = zero_zero_nat )
% 0.29/0.55 => ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.55 = ( vEBT_Leaf @ $false @ B ) ) )
% 0.29/0.55 & ( ( X != zero_zero_nat )
% 0.29/0.55 => ( ( ( X = one_one_nat )
% 0.29/0.55 => ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.55 = ( vEBT_Leaf @ A @ $false ) ) )
% 0.29/0.55 & ( ( X != one_one_nat )
% 0.29/0.55 => ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.55 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % vebt_delete_code(1)
% 0.29/0.55 thf(fact_1114_not__one__less__zero,axiom,
% 0.29/0.55 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_less_zero
% 0.29/0.55 thf(fact_1115_not__one__less__zero,axiom,
% 0.29/0.55 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_less_zero
% 0.29/0.55 thf(fact_1116_not__one__less__zero,axiom,
% 0.29/0.55 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_less_zero
% 0.29/0.55 thf(fact_1117_not__one__less__zero,axiom,
% 0.29/0.55 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_less_zero
% 0.29/0.55 thf(fact_1118_zero__less__one,axiom,
% 0.29/0.55 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one
% 0.29/0.55 thf(fact_1119_zero__less__one,axiom,
% 0.29/0.55 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one
% 0.29/0.55 thf(fact_1120_zero__less__one,axiom,
% 0.29/0.55 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one
% 0.29/0.55 thf(fact_1121_zero__less__one,axiom,
% 0.29/0.55 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one
% 0.29/0.55 thf(fact_1122_less__numeral__extra_I1_J,axiom,
% 0.29/0.55 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(1)
% 0.29/0.55 thf(fact_1123_less__numeral__extra_I1_J,axiom,
% 0.29/0.55 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(1)
% 0.29/0.55 thf(fact_1124_less__numeral__extra_I1_J,axiom,
% 0.29/0.55 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(1)
% 0.29/0.55 thf(fact_1125_less__numeral__extra_I1_J,axiom,
% 0.29/0.55 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(1)
% 0.29/0.55 thf(fact_1126_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one_class.zero_le_one
% 0.29/0.55 thf(fact_1127_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one_class.zero_le_one
% 0.29/0.55 thf(fact_1128_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one_class.zero_le_one
% 0.29/0.55 thf(fact_1129_zero__less__one__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55
% 0.29/0.55 % zero_less_one_class.zero_le_one
% 0.29/0.55 thf(fact_1130_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.29/0.55
% 0.29/0.55 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55 thf(fact_1131_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.29/0.55
% 0.29/0.55 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55 thf(fact_1132_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.29/0.55
% 0.29/0.55 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55 thf(fact_1133_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.29/0.55 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.29/0.55
% 0.29/0.55 % linordered_nonzero_semiring_class.zero_le_one
% 0.29/0.55 thf(fact_1134_not__one__le__zero,axiom,
% 0.29/0.55 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_le_zero
% 0.29/0.55 thf(fact_1135_not__one__le__zero,axiom,
% 0.29/0.55 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_le_zero
% 0.29/0.55 thf(fact_1136_not__one__le__zero,axiom,
% 0.29/0.55 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_le_zero
% 0.29/0.55 thf(fact_1137_not__one__le__zero,axiom,
% 0.29/0.55 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.29/0.55
% 0.29/0.55 % not_one_le_zero
% 0.29/0.55 thf(fact_1138_bot__empty__eq,axiom,
% 0.29/0.55 ( bot_bot_VEBT_VEBT_o
% 0.29/0.55 = ( ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot_empty_eq
% 0.29/0.55 thf(fact_1139_bot__empty__eq,axiom,
% 0.29/0.55 ( bot_bot_real_o
% 0.29/0.55 = ( ^ [X4: real] : ( member_real @ X4 @ bot_bot_set_real ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot_empty_eq
% 0.29/0.55 thf(fact_1140_bot__empty__eq,axiom,
% 0.29/0.55 ( bot_bot_set_nat_o
% 0.29/0.55 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot_empty_eq
% 0.29/0.55 thf(fact_1141_bot__empty__eq,axiom,
% 0.29/0.55 ( bot_bot_nat_o
% 0.29/0.55 = ( ^ [X4: nat] : ( member_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot_empty_eq
% 0.29/0.55 thf(fact_1142_bot__empty__eq,axiom,
% 0.29/0.55 ( bot_bot_int_o
% 0.29/0.55 = ( ^ [X4: int] : ( member_int @ X4 @ bot_bot_set_int ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot_empty_eq
% 0.29/0.55 thf(fact_1143_bot__empty__eq,axiom,
% 0.29/0.55 ( bot_bot_o_o
% 0.29/0.55 = ( ^ [X4: $o] : ( member_o @ X4 @ bot_bot_set_o ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % bot_empty_eq
% 0.29/0.55 thf(fact_1144_Collect__empty__eq__bot,axiom,
% 0.29/0.55 ! [P2: complex > $o] :
% 0.29/0.55 ( ( ( collect_complex @ P2 )
% 0.29/0.55 = bot_bot_set_complex )
% 0.29/0.55 = ( P2 = bot_bot_complex_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_empty_eq_bot
% 0.29/0.55 thf(fact_1145_Collect__empty__eq__bot,axiom,
% 0.29/0.55 ! [P2: list_nat > $o] :
% 0.29/0.55 ( ( ( collect_list_nat @ P2 )
% 0.29/0.55 = bot_bot_set_list_nat )
% 0.29/0.55 = ( P2 = bot_bot_list_nat_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_empty_eq_bot
% 0.29/0.55 thf(fact_1146_Collect__empty__eq__bot,axiom,
% 0.29/0.55 ! [P2: set_nat > $o] :
% 0.29/0.55 ( ( ( collect_set_nat @ P2 )
% 0.29/0.55 = bot_bot_set_set_nat )
% 0.29/0.55 = ( P2 = bot_bot_set_nat_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_empty_eq_bot
% 0.29/0.55 thf(fact_1147_Collect__empty__eq__bot,axiom,
% 0.29/0.55 ! [P2: nat > $o] :
% 0.29/0.55 ( ( ( collect_nat @ P2 )
% 0.29/0.55 = bot_bot_set_nat )
% 0.29/0.55 = ( P2 = bot_bot_nat_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_empty_eq_bot
% 0.29/0.55 thf(fact_1148_Collect__empty__eq__bot,axiom,
% 0.29/0.55 ! [P2: int > $o] :
% 0.29/0.55 ( ( ( collect_int @ P2 )
% 0.29/0.55 = bot_bot_set_int )
% 0.29/0.55 = ( P2 = bot_bot_int_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_empty_eq_bot
% 0.29/0.55 thf(fact_1149_Collect__empty__eq__bot,axiom,
% 0.29/0.55 ! [P2: $o > $o] :
% 0.29/0.55 ( ( ( collect_o @ P2 )
% 0.29/0.55 = bot_bot_set_o )
% 0.29/0.55 = ( P2 = bot_bot_o_o ) ) ).
% 0.29/0.55
% 0.29/0.55 % Collect_empty_eq_bot
% 0.29/0.55 thf(fact_1150_assn__basic__inequalities_I3_J,axiom,
% 0.29/0.55 bot_bot_assn != one_one_assn ).
% 0.29/0.55
% 0.29/0.55 % assn_basic_inequalities(3)
% 0.29/0.55 thf(fact_1151_linorder__neqE__linordered__idom,axiom,
% 0.29/0.55 ! [X: real,Y: real] :
% 0.29/0.55 ( ( X != Y )
% 0.29/0.55 => ( ~ ( ord_less_real @ X @ Y )
% 0.29/0.55 => ( ord_less_real @ Y @ X ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % linorder_neqE_linordered_idom
% 0.29/0.55 thf(fact_1152_linorder__neqE__linordered__idom,axiom,
% 0.29/0.55 ! [X: rat,Y: rat] :
% 0.29/0.55 ( ( X != Y )
% 0.29/0.55 => ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.55 => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % linorder_neqE_linordered_idom
% 0.29/0.55 thf(fact_1153_linorder__neqE__linordered__idom,axiom,
% 0.29/0.55 ! [X: int,Y: int] :
% 0.29/0.55 ( ( X != Y )
% 0.29/0.55 => ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.55 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % linorder_neqE_linordered_idom
% 0.29/0.55 thf(fact_1154_subrelI,axiom,
% 0.29/0.55 ! [R: set_Pr1773385645901665561uint32,S: set_Pr1773385645901665561uint32] :
% 0.29/0.55 ( ! [X3: uint32,Y3: uint32] :
% 0.29/0.55 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ R )
% 0.29/0.55 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ S ) )
% 0.29/0.55 => ( ord_le6429528607962791097uint32 @ R @ S ) ) ).
% 0.29/0.55
% 0.29/0.55 % subrelI
% 0.29/0.55 thf(fact_1155_subrelI,axiom,
% 0.29/0.55 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.55 ( ! [X3: nat,Y3: nat] :
% 0.29/0.55 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 0.29/0.55 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.55 => ( ord_le3146513528884898305at_nat @ R @ S ) ) ).
% 0.29/0.55
% 0.29/0.55 % subrelI
% 0.29/0.55 thf(fact_1156_subrelI,axiom,
% 0.29/0.55 ! [R: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 0.29/0.55 ( ! [X3: int,Y3: int] :
% 0.29/0.55 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R )
% 0.29/0.55 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ S ) )
% 0.29/0.55 => ( ord_le2843351958646193337nt_int @ R @ S ) ) ).
% 0.29/0.55
% 0.29/0.55 % subrelI
% 0.29/0.55 thf(fact_1157_subrelI,axiom,
% 0.29/0.55 ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 0.29/0.55 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 0.29/0.55 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.55 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.55 => ( ord_le5966269811547037844et_nat @ R @ S ) ) ).
% 0.29/0.55
% 0.29/0.55 % subrelI
% 0.29/0.55 thf(fact_1158_subrelI,axiom,
% 0.29/0.55 ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 0.29/0.55 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 0.29/0.55 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.55 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.55 => ( ord_le4763372923235995152et_nat @ R @ S ) ) ).
% 0.29/0.55
% 0.29/0.55 % subrelI
% 0.29/0.55 thf(fact_1159_mod__emp__simp,axiom,
% 0.29/0.55 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % mod_emp_simp
% 0.29/0.55 thf(fact_1160_le__numeral__extra_I3_J,axiom,
% 0.29/0.55 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(3)
% 0.29/0.55 thf(fact_1161_le__numeral__extra_I3_J,axiom,
% 0.29/0.55 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(3)
% 0.29/0.55 thf(fact_1162_le__numeral__extra_I3_J,axiom,
% 0.29/0.55 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(3)
% 0.29/0.55 thf(fact_1163_le__numeral__extra_I3_J,axiom,
% 0.29/0.55 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(3)
% 0.29/0.55 thf(fact_1164_less__numeral__extra_I3_J,axiom,
% 0.29/0.55 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(3)
% 0.29/0.55 thf(fact_1165_less__numeral__extra_I3_J,axiom,
% 0.29/0.55 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(3)
% 0.29/0.55 thf(fact_1166_less__numeral__extra_I3_J,axiom,
% 0.29/0.55 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(3)
% 0.29/0.55 thf(fact_1167_less__numeral__extra_I3_J,axiom,
% 0.29/0.55 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(3)
% 0.29/0.55 thf(fact_1168_zero__neq__one,axiom,
% 0.29/0.55 zero_zero_uint32 != one_one_uint32 ).
% 0.29/0.55
% 0.29/0.55 % zero_neq_one
% 0.29/0.55 thf(fact_1169_zero__neq__one,axiom,
% 0.29/0.55 zero_zero_real != one_one_real ).
% 0.29/0.55
% 0.29/0.55 % zero_neq_one
% 0.29/0.55 thf(fact_1170_zero__neq__one,axiom,
% 0.29/0.55 zero_zero_rat != one_one_rat ).
% 0.29/0.55
% 0.29/0.55 % zero_neq_one
% 0.29/0.55 thf(fact_1171_zero__neq__one,axiom,
% 0.29/0.55 zero_zero_nat != one_one_nat ).
% 0.29/0.55
% 0.29/0.55 % zero_neq_one
% 0.29/0.55 thf(fact_1172_zero__neq__one,axiom,
% 0.29/0.55 zero_zero_int != one_one_int ).
% 0.29/0.55
% 0.29/0.55 % zero_neq_one
% 0.29/0.55 thf(fact_1173_le__numeral__extra_I4_J,axiom,
% 0.29/0.55 ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(4)
% 0.29/0.55 thf(fact_1174_le__numeral__extra_I4_J,axiom,
% 0.29/0.55 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(4)
% 0.29/0.55 thf(fact_1175_le__numeral__extra_I4_J,axiom,
% 0.29/0.55 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(4)
% 0.29/0.55 thf(fact_1176_le__numeral__extra_I4_J,axiom,
% 0.29/0.55 ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.29/0.55
% 0.29/0.55 % le_numeral_extra(4)
% 0.29/0.55 thf(fact_1177_less__numeral__extra_I4_J,axiom,
% 0.29/0.55 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(4)
% 0.29/0.55 thf(fact_1178_less__numeral__extra_I4_J,axiom,
% 0.29/0.55 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(4)
% 0.29/0.55 thf(fact_1179_less__numeral__extra_I4_J,axiom,
% 0.29/0.55 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(4)
% 0.29/0.55 thf(fact_1180_less__numeral__extra_I4_J,axiom,
% 0.29/0.55 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.29/0.55
% 0.29/0.55 % less_numeral_extra(4)
% 0.29/0.55 thf(fact_1181_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I2_J,axiom,
% 0.29/0.55 ! [A: $o,B: $o] :
% 0.29/0.55 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.55 = one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(2)
% 0.29/0.55 thf(fact_1182_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I1_J,axiom,
% 0.29/0.55 ! [A: $o,B: $o] :
% 0.29/0.55 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.29/0.55 = one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(1)
% 0.29/0.55 thf(fact_1183_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I3_J,axiom,
% 0.29/0.55 ! [A: $o,B: $o,N: nat] :
% 0.29/0.55 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.29/0.55 = one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(3)
% 0.29/0.55 thf(fact_1184_nat__descend__induct,axiom,
% 0.29/0.55 ! [N: nat,P2: nat > $o,M: nat] :
% 0.29/0.55 ( ! [K2: nat] :
% 0.29/0.55 ( ( ord_less_nat @ N @ K2 )
% 0.29/0.55 => ( P2 @ K2 ) )
% 0.29/0.55 => ( ! [K2: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ K2 @ N )
% 0.29/0.55 => ( ! [I4: nat] :
% 0.29/0.55 ( ( ord_less_nat @ K2 @ I4 )
% 0.29/0.55 => ( P2 @ I4 ) )
% 0.29/0.55 => ( P2 @ K2 ) ) )
% 0.29/0.55 => ( P2 @ M ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % nat_descend_induct
% 0.29/0.55 thf(fact_1185_exists__least__lemma,axiom,
% 0.29/0.55 ! [P2: nat > $o] :
% 0.29/0.55 ( ~ ( P2 @ zero_zero_nat )
% 0.29/0.55 => ( ? [X_12: nat] : ( P2 @ X_12 )
% 0.29/0.55 => ? [N2: nat] :
% 0.29/0.55 ( ~ ( P2 @ N2 )
% 0.29/0.55 & ( P2 @ ( suc @ N2 ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % exists_least_lemma
% 0.29/0.55 thf(fact_1186_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Ocases,axiom,
% 0.29/0.55 ! [X: nat] :
% 0.29/0.55 ( ( X != zero_zero_nat )
% 0.29/0.55 => ( ( X
% 0.29/0.55 != ( suc @ zero_zero_nat ) )
% 0.29/0.55 => ~ ! [Va: nat] :
% 0.29/0.55 ( X
% 0.29/0.55 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.cases
% 0.29/0.55 thf(fact_1187_list__decode_Ocases,axiom,
% 0.29/0.55 ! [X: nat] :
% 0.29/0.55 ( ( X != zero_zero_nat )
% 0.29/0.55 => ~ ! [N2: nat] :
% 0.29/0.55 ( X
% 0.29/0.55 != ( suc @ N2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % list_decode.cases
% 0.29/0.55 thf(fact_1188_mod__h__bot__iff_I4_J,axiom,
% 0.29/0.55 ! [Q3: array_VEBT_VEBTi,Y: list_VEBT_VEBTi,H2: heap_e7401611519738050253t_unit] :
% 0.29/0.55 ~ ( rep_assn @ ( snga_assn_VEBT_VEBTi @ Q3 @ Y ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % mod_h_bot_iff(4)
% 0.29/0.55 thf(fact_1189_complete__interval,axiom,
% 0.29/0.55 ! [A: real,B: real,P2: real > $o] :
% 0.29/0.55 ( ( ord_less_real @ A @ B )
% 0.29/0.55 => ( ( P2 @ A )
% 0.29/0.55 => ( ~ ( P2 @ B )
% 0.29/0.55 => ? [C: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ A @ C )
% 0.29/0.55 & ( ord_less_eq_real @ C @ B )
% 0.29/0.55 & ! [X5: real] :
% 0.29/0.55 ( ( ( ord_less_eq_real @ A @ X5 )
% 0.29/0.55 & ( ord_less_real @ X5 @ C ) )
% 0.29/0.55 => ( P2 @ X5 ) )
% 0.29/0.55 & ! [D3: real] :
% 0.29/0.55 ( ! [X3: real] :
% 0.29/0.55 ( ( ( ord_less_eq_real @ A @ X3 )
% 0.29/0.55 & ( ord_less_real @ X3 @ D3 ) )
% 0.29/0.55 => ( P2 @ X3 ) )
% 0.29/0.55 => ( ord_less_eq_real @ D3 @ C ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % complete_interval
% 0.29/0.55 thf(fact_1190_complete__interval,axiom,
% 0.29/0.55 ! [A: nat,B: nat,P2: nat > $o] :
% 0.29/0.55 ( ( ord_less_nat @ A @ B )
% 0.29/0.55 => ( ( P2 @ A )
% 0.29/0.55 => ( ~ ( P2 @ B )
% 0.29/0.55 => ? [C: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.55 & ( ord_less_eq_nat @ C @ B )
% 0.29/0.55 & ! [X5: nat] :
% 0.29/0.55 ( ( ( ord_less_eq_nat @ A @ X5 )
% 0.29/0.55 & ( ord_less_nat @ X5 @ C ) )
% 0.29/0.55 => ( P2 @ X5 ) )
% 0.29/0.55 & ! [D3: nat] :
% 0.29/0.55 ( ! [X3: nat] :
% 0.29/0.55 ( ( ( ord_less_eq_nat @ A @ X3 )
% 0.29/0.55 & ( ord_less_nat @ X3 @ D3 ) )
% 0.29/0.55 => ( P2 @ X3 ) )
% 0.29/0.55 => ( ord_less_eq_nat @ D3 @ C ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % complete_interval
% 0.29/0.55 thf(fact_1191_complete__interval,axiom,
% 0.29/0.55 ! [A: int,B: int,P2: int > $o] :
% 0.29/0.55 ( ( ord_less_int @ A @ B )
% 0.29/0.55 => ( ( P2 @ A )
% 0.29/0.55 => ( ~ ( P2 @ B )
% 0.29/0.55 => ? [C: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ A @ C )
% 0.29/0.55 & ( ord_less_eq_int @ C @ B )
% 0.29/0.55 & ! [X5: int] :
% 0.29/0.55 ( ( ( ord_less_eq_int @ A @ X5 )
% 0.29/0.55 & ( ord_less_int @ X5 @ C ) )
% 0.29/0.55 => ( P2 @ X5 ) )
% 0.29/0.55 & ! [D3: int] :
% 0.29/0.55 ( ! [X3: int] :
% 0.29/0.55 ( ( ( ord_less_eq_int @ A @ X3 )
% 0.29/0.55 & ( ord_less_int @ X3 @ D3 ) )
% 0.29/0.55 => ( P2 @ X3 ) )
% 0.29/0.55 => ( ord_less_eq_int @ D3 @ C ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % complete_interval
% 0.29/0.55 thf(fact_1192_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.55 ! [B2: real,A2: real] :
% 0.29/0.55 ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 0.29/0.55 = ( ord_less_real @ A2 @ B2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(3)
% 0.29/0.55 thf(fact_1193_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.55 ! [B2: rat,A2: rat] :
% 0.29/0.55 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 0.29/0.55 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(3)
% 0.29/0.55 thf(fact_1194_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.55 ! [B2: num,A2: num] :
% 0.29/0.55 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 0.29/0.55 = ( ord_less_num @ A2 @ B2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(3)
% 0.29/0.55 thf(fact_1195_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.55 ! [B2: nat,A2: nat] :
% 0.29/0.55 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 0.29/0.55 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(3)
% 0.29/0.55 thf(fact_1196_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.55 ! [B2: int,A2: int] :
% 0.29/0.55 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 0.29/0.55 = ( ord_less_int @ A2 @ B2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(3)
% 0.29/0.55 thf(fact_1197_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.55 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(2)
% 0.29/0.55 thf(fact_1198_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.55 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(2)
% 0.29/0.55 thf(fact_1199_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.55 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(2)
% 0.29/0.55 thf(fact_1200_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.55 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(2)
% 0.29/0.55 thf(fact_1201_verit__comp__simplify1_I2_J,axiom,
% 0.29/0.55 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(2)
% 0.29/0.55 thf(fact_1202_verit__la__disequality,axiom,
% 0.29/0.55 ! [A: rat,B: rat] :
% 0.29/0.55 ( ( A = B )
% 0.29/0.55 | ~ ( ord_less_eq_rat @ A @ B )
% 0.29/0.55 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_la_disequality
% 0.29/0.55 thf(fact_1203_verit__la__disequality,axiom,
% 0.29/0.55 ! [A: num,B: num] :
% 0.29/0.55 ( ( A = B )
% 0.29/0.55 | ~ ( ord_less_eq_num @ A @ B )
% 0.29/0.55 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_la_disequality
% 0.29/0.55 thf(fact_1204_verit__la__disequality,axiom,
% 0.29/0.55 ! [A: nat,B: nat] :
% 0.29/0.55 ( ( A = B )
% 0.29/0.55 | ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.55 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_la_disequality
% 0.29/0.55 thf(fact_1205_verit__la__disequality,axiom,
% 0.29/0.55 ! [A: int,B: int] :
% 0.29/0.55 ( ( A = B )
% 0.29/0.55 | ~ ( ord_less_eq_int @ A @ B )
% 0.29/0.55 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % verit_la_disequality
% 0.29/0.55 thf(fact_1206_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.55 ! [A: real] :
% 0.29/0.55 ~ ( ord_less_real @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(1)
% 0.29/0.55 thf(fact_1207_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.55 ! [A: rat] :
% 0.29/0.55 ~ ( ord_less_rat @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(1)
% 0.29/0.55 thf(fact_1208_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.55 ! [A: num] :
% 0.29/0.55 ~ ( ord_less_num @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(1)
% 0.29/0.55 thf(fact_1209_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ~ ( ord_less_nat @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(1)
% 0.29/0.55 thf(fact_1210_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.55 ! [A: int] :
% 0.29/0.55 ~ ( ord_less_int @ A @ A ) ).
% 0.29/0.55
% 0.29/0.55 % verit_comp_simplify1(1)
% 0.29/0.55 thf(fact_1211_ex__gt__or__lt,axiom,
% 0.29/0.55 ! [A: real] :
% 0.29/0.55 ? [B3: real] :
% 0.29/0.55 ( ( ord_less_real @ A @ B3 )
% 0.29/0.55 | ( ord_less_real @ B3 @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % ex_gt_or_lt
% 0.29/0.55 thf(fact_1212_minf_I8_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.55 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(8)
% 0.29/0.55 thf(fact_1213_minf_I8_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.55 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(8)
% 0.29/0.55 thf(fact_1214_minf_I8_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.55 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(8)
% 0.29/0.55 thf(fact_1215_minf_I8_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.55 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(8)
% 0.29/0.55 thf(fact_1216_minf_I8_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.55 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(8)
% 0.29/0.55 thf(fact_1217_minf_I6_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.55 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(6)
% 0.29/0.55 thf(fact_1218_minf_I6_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.55 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(6)
% 0.29/0.55 thf(fact_1219_minf_I6_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.55 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(6)
% 0.29/0.55 thf(fact_1220_minf_I6_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.55 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(6)
% 0.29/0.55 thf(fact_1221_minf_I6_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.55 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(6)
% 0.29/0.55 thf(fact_1222_pinf_I8_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(8)
% 0.29/0.55 thf(fact_1223_pinf_I8_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(8)
% 0.29/0.55 thf(fact_1224_pinf_I8_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(8)
% 0.29/0.55 thf(fact_1225_pinf_I8_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(8)
% 0.29/0.55 thf(fact_1226_pinf_I8_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(8)
% 0.29/0.55 thf(fact_1227_pinf_I6_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(6)
% 0.29/0.55 thf(fact_1228_pinf_I6_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(6)
% 0.29/0.55 thf(fact_1229_pinf_I6_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(6)
% 0.29/0.55 thf(fact_1230_pinf_I6_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(6)
% 0.29/0.55 thf(fact_1231_pinf_I6_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(6)
% 0.29/0.55 thf(fact_1232_field__lbound__gt__zero,axiom,
% 0.29/0.55 ! [D1: real,D22: real] :
% 0.29/0.55 ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.29/0.55 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 0.29/0.55 => ? [E: real] :
% 0.29/0.55 ( ( ord_less_real @ zero_zero_real @ E )
% 0.29/0.55 & ( ord_less_real @ E @ D1 )
% 0.29/0.55 & ( ord_less_real @ E @ D22 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % field_lbound_gt_zero
% 0.29/0.55 thf(fact_1233_field__lbound__gt__zero,axiom,
% 0.29/0.55 ! [D1: rat,D22: rat] :
% 0.29/0.55 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 0.29/0.55 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 0.29/0.55 => ? [E: rat] :
% 0.29/0.55 ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.29/0.55 & ( ord_less_rat @ E @ D1 )
% 0.29/0.55 & ( ord_less_rat @ E @ D22 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % field_lbound_gt_zero
% 0.29/0.55 thf(fact_1234_dbl__inc__simps_I2_J,axiom,
% 0.29/0.55 ( ( neg_nu4269007558841261821uint32 @ zero_zero_uint32 )
% 0.29/0.55 = one_one_uint32 ) ).
% 0.29/0.55
% 0.29/0.55 % dbl_inc_simps(2)
% 0.29/0.55 thf(fact_1235_dbl__inc__simps_I2_J,axiom,
% 0.29/0.55 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 0.29/0.55 = one_one_real ) ).
% 0.29/0.55
% 0.29/0.55 % dbl_inc_simps(2)
% 0.29/0.55 thf(fact_1236_dbl__inc__simps_I2_J,axiom,
% 0.29/0.55 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.29/0.55 = one_one_rat ) ).
% 0.29/0.55
% 0.29/0.55 % dbl_inc_simps(2)
% 0.29/0.55 thf(fact_1237_dbl__inc__simps_I2_J,axiom,
% 0.29/0.55 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.29/0.55 = one_one_int ) ).
% 0.29/0.55
% 0.29/0.55 % dbl_inc_simps(2)
% 0.29/0.55 thf(fact_1238_VEBT_Osize__gen_I2_J,axiom,
% 0.29/0.55 ! [X21: $o,X22: $o] :
% 0.29/0.55 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 0.29/0.55 = zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT.size_gen(2)
% 0.29/0.55 thf(fact_1239_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J,axiom,
% 0.29/0.55 ! [A: $o,B: $o] :
% 0.29/0.55 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.55 = one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(2)
% 0.29/0.55 thf(fact_1240_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I6_J,axiom,
% 0.29/0.55 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.55 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 0.29/0.55 = one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(6)
% 0.29/0.55 thf(fact_1241_frac__eq,axiom,
% 0.29/0.55 ! [X: real] :
% 0.29/0.55 ( ( ( archim2898591450579166408c_real @ X )
% 0.29/0.55 = X )
% 0.29/0.55 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.29/0.55 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % frac_eq
% 0.29/0.55 thf(fact_1242_frac__eq,axiom,
% 0.29/0.55 ! [X: rat] :
% 0.29/0.55 ( ( ( archimedean_frac_rat @ X )
% 0.29/0.55 = X )
% 0.29/0.55 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.29/0.55 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % frac_eq
% 0.29/0.55 thf(fact_1243_Suc__diff__1,axiom,
% 0.29/0.55 ! [N: nat] :
% 0.29/0.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.29/0.55 = N ) ) ).
% 0.29/0.55
% 0.29/0.55 % Suc_diff_1
% 0.29/0.55 thf(fact_1244_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.55 ! [A: rat] :
% 0.29/0.55 ( ( minus_minus_rat @ A @ A )
% 0.29/0.55 = zero_zero_rat ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.55 thf(fact_1245_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.55 ! [A: uint32] :
% 0.29/0.55 ( ( minus_minus_uint32 @ A @ A )
% 0.29/0.55 = zero_zero_uint32 ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.55 thf(fact_1246_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.55 ! [A: real] :
% 0.29/0.55 ( ( minus_minus_real @ A @ A )
% 0.29/0.55 = zero_zero_real ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.55 thf(fact_1247_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ A @ A )
% 0.29/0.55 = zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.55 thf(fact_1248_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.55 ! [A: int] :
% 0.29/0.55 ( ( minus_minus_int @ A @ A )
% 0.29/0.55 = zero_zero_int ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.55 thf(fact_1249_diff__zero,axiom,
% 0.29/0.55 ! [A: rat] :
% 0.29/0.55 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_zero
% 0.29/0.55 thf(fact_1250_diff__zero,axiom,
% 0.29/0.55 ! [A: uint32] :
% 0.29/0.55 ( ( minus_minus_uint32 @ A @ zero_zero_uint32 )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_zero
% 0.29/0.55 thf(fact_1251_diff__zero,axiom,
% 0.29/0.55 ! [A: real] :
% 0.29/0.55 ( ( minus_minus_real @ A @ zero_zero_real )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_zero
% 0.29/0.55 thf(fact_1252_diff__zero,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_zero
% 0.29/0.55 thf(fact_1253_diff__zero,axiom,
% 0.29/0.55 ! [A: int] :
% 0.29/0.55 ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_zero
% 0.29/0.55 thf(fact_1254_zero__diff,axiom,
% 0.29/0.55 ! [A: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.29/0.55 = zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % zero_diff
% 0.29/0.55 thf(fact_1255_diff__0__right,axiom,
% 0.29/0.55 ! [A: rat] :
% 0.29/0.55 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_0_right
% 0.29/0.55 thf(fact_1256_diff__0__right,axiom,
% 0.29/0.55 ! [A: uint32] :
% 0.29/0.55 ( ( minus_minus_uint32 @ A @ zero_zero_uint32 )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_0_right
% 0.29/0.55 thf(fact_1257_diff__0__right,axiom,
% 0.29/0.55 ! [A: real] :
% 0.29/0.55 ( ( minus_minus_real @ A @ zero_zero_real )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_0_right
% 0.29/0.55 thf(fact_1258_diff__0__right,axiom,
% 0.29/0.55 ! [A: int] :
% 0.29/0.55 ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.55 = A ) ).
% 0.29/0.55
% 0.29/0.55 % diff_0_right
% 0.29/0.55 thf(fact_1259_diff__self,axiom,
% 0.29/0.55 ! [A: rat] :
% 0.29/0.55 ( ( minus_minus_rat @ A @ A )
% 0.29/0.55 = zero_zero_rat ) ).
% 0.29/0.55
% 0.29/0.55 % diff_self
% 0.29/0.55 thf(fact_1260_diff__self,axiom,
% 0.29/0.55 ! [A: uint32] :
% 0.29/0.55 ( ( minus_minus_uint32 @ A @ A )
% 0.29/0.55 = zero_zero_uint32 ) ).
% 0.29/0.55
% 0.29/0.55 % diff_self
% 0.29/0.55 thf(fact_1261_diff__self,axiom,
% 0.29/0.55 ! [A: real] :
% 0.29/0.55 ( ( minus_minus_real @ A @ A )
% 0.29/0.55 = zero_zero_real ) ).
% 0.29/0.55
% 0.29/0.55 % diff_self
% 0.29/0.55 thf(fact_1262_diff__self,axiom,
% 0.29/0.55 ! [A: int] :
% 0.29/0.55 ( ( minus_minus_int @ A @ A )
% 0.29/0.55 = zero_zero_int ) ).
% 0.29/0.55
% 0.29/0.55 % diff_self
% 0.29/0.55 thf(fact_1263_Suc__diff__diff,axiom,
% 0.29/0.55 ! [M: nat,N: nat,K: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.29/0.55 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.29/0.55
% 0.29/0.55 % Suc_diff_diff
% 0.29/0.55 thf(fact_1264_diff__Suc__Suc,axiom,
% 0.29/0.55 ! [M: nat,N: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.55 = ( minus_minus_nat @ M @ N ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_Suc_Suc
% 0.29/0.55 thf(fact_1265_diff__self__eq__0,axiom,
% 0.29/0.55 ! [M: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ M @ M )
% 0.29/0.55 = zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % diff_self_eq_0
% 0.29/0.55 thf(fact_1266_diff__0__eq__0,axiom,
% 0.29/0.55 ! [N: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.29/0.55 = zero_zero_nat ) ).
% 0.29/0.55
% 0.29/0.55 % diff_0_eq_0
% 0.29/0.55 thf(fact_1267_diff__diff__cancel,axiom,
% 0.29/0.55 ! [I: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ I @ N )
% 0.29/0.55 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.29/0.55 = I ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_diff_cancel
% 0.29/0.55 thf(fact_1268_zero__comp__diff__simps_I1_J,axiom,
% 0.29/0.55 ! [A: real,B: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.55 = ( ord_less_eq_real @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_comp_diff_simps(1)
% 0.29/0.55 thf(fact_1269_zero__comp__diff__simps_I1_J,axiom,
% 0.29/0.55 ! [A: rat,B: rat] :
% 0.29/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.55 = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_comp_diff_simps(1)
% 0.29/0.55 thf(fact_1270_zero__comp__diff__simps_I1_J,axiom,
% 0.29/0.55 ! [A: int,B: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.55 = ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_comp_diff_simps(1)
% 0.29/0.55 thf(fact_1271_diff__ge__0__iff__ge,axiom,
% 0.29/0.55 ! [A: real,B: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.55 = ( ord_less_eq_real @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_ge_0_iff_ge
% 0.29/0.55 thf(fact_1272_diff__ge__0__iff__ge,axiom,
% 0.29/0.55 ! [A: rat,B: rat] :
% 0.29/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.55 = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_ge_0_iff_ge
% 0.29/0.55 thf(fact_1273_diff__ge__0__iff__ge,axiom,
% 0.29/0.55 ! [A: int,B: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.55 = ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_ge_0_iff_ge
% 0.29/0.55 thf(fact_1274_zero__comp__diff__simps_I2_J,axiom,
% 0.29/0.55 ! [A: real,B: real] :
% 0.29/0.55 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.55 = ( ord_less_real @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_comp_diff_simps(2)
% 0.29/0.55 thf(fact_1275_zero__comp__diff__simps_I2_J,axiom,
% 0.29/0.55 ! [A: rat,B: rat] :
% 0.29/0.55 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.55 = ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_comp_diff_simps(2)
% 0.29/0.55 thf(fact_1276_zero__comp__diff__simps_I2_J,axiom,
% 0.29/0.55 ! [A: int,B: int] :
% 0.29/0.55 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.55 = ( ord_less_int @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_comp_diff_simps(2)
% 0.29/0.55 thf(fact_1277_diff__gt__0__iff__gt,axiom,
% 0.29/0.55 ! [A: real,B: real] :
% 0.29/0.55 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.55 = ( ord_less_real @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_gt_0_iff_gt
% 0.29/0.55 thf(fact_1278_diff__gt__0__iff__gt,axiom,
% 0.29/0.55 ! [A: rat,B: rat] :
% 0.29/0.55 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.55 = ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_gt_0_iff_gt
% 0.29/0.55 thf(fact_1279_diff__gt__0__iff__gt,axiom,
% 0.29/0.55 ! [A: int,B: int] :
% 0.29/0.55 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.55 = ( ord_less_int @ B @ A ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_gt_0_iff_gt
% 0.29/0.55 thf(fact_1280_diff__numeral__special_I9_J,axiom,
% 0.29/0.55 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.29/0.55 = zero_zero_rat ) ).
% 0.29/0.55
% 0.29/0.55 % diff_numeral_special(9)
% 0.29/0.55 thf(fact_1281_diff__numeral__special_I9_J,axiom,
% 0.29/0.55 ( ( minus_minus_uint32 @ one_one_uint32 @ one_one_uint32 )
% 0.29/0.55 = zero_zero_uint32 ) ).
% 0.29/0.55
% 0.29/0.55 % diff_numeral_special(9)
% 0.29/0.55 thf(fact_1282_diff__numeral__special_I9_J,axiom,
% 0.29/0.55 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 0.29/0.55 = zero_zero_real ) ).
% 0.29/0.55
% 0.29/0.55 % diff_numeral_special(9)
% 0.29/0.55 thf(fact_1283_diff__numeral__special_I9_J,axiom,
% 0.29/0.55 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.29/0.55 = zero_zero_int ) ).
% 0.29/0.55
% 0.29/0.55 % diff_numeral_special(9)
% 0.29/0.55 thf(fact_1284_zero__less__diff,axiom,
% 0.29/0.55 ! [N: nat,M: nat] :
% 0.29/0.55 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.29/0.55 = ( ord_less_nat @ M @ N ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_less_diff
% 0.29/0.55 thf(fact_1285_diff__Suc__1,axiom,
% 0.29/0.55 ! [N: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.29/0.55 = N ) ).
% 0.29/0.55
% 0.29/0.55 % diff_Suc_1
% 0.29/0.55 thf(fact_1286_diff__is__0__eq_H,axiom,
% 0.29/0.55 ! [M: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.55 => ( ( minus_minus_nat @ M @ N )
% 0.29/0.55 = zero_zero_nat ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_is_0_eq'
% 0.29/0.55 thf(fact_1287_diff__is__0__eq,axiom,
% 0.29/0.55 ! [M: nat,N: nat] :
% 0.29/0.55 ( ( ( minus_minus_nat @ M @ N )
% 0.29/0.55 = zero_zero_nat )
% 0.29/0.55 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_is_0_eq
% 0.29/0.55 thf(fact_1288_Suc__pred,axiom,
% 0.29/0.55 ! [N: nat] :
% 0.29/0.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.55 = N ) ) ).
% 0.29/0.55
% 0.29/0.55 % Suc_pred
% 0.29/0.55 thf(fact_1289_Suc__diff,axiom,
% 0.29/0.55 ! [M: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.55 => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.29/0.55 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 0.29/0.55 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Suc_diff
% 0.29/0.55 thf(fact_1290_diff__eq__diff__eq,axiom,
% 0.29/0.55 ! [A: uint32,B: uint32,C2: uint32,D: uint32] :
% 0.29/0.55 ( ( ( minus_minus_uint32 @ A @ B )
% 0.29/0.55 = ( minus_minus_uint32 @ C2 @ D ) )
% 0.29/0.55 => ( ( A = B )
% 0.29/0.55 = ( C2 = D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_eq
% 0.29/0.55 thf(fact_1291_diff__eq__diff__eq,axiom,
% 0.29/0.55 ! [A: real,B: real,C2: real,D: real] :
% 0.29/0.55 ( ( ( minus_minus_real @ A @ B )
% 0.29/0.55 = ( minus_minus_real @ C2 @ D ) )
% 0.29/0.55 => ( ( A = B )
% 0.29/0.55 = ( C2 = D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_eq
% 0.29/0.55 thf(fact_1292_diff__eq__diff__eq,axiom,
% 0.29/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.29/0.55 ( ( ( minus_minus_int @ A @ B )
% 0.29/0.55 = ( minus_minus_int @ C2 @ D ) )
% 0.29/0.55 => ( ( A = B )
% 0.29/0.55 = ( C2 = D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_eq
% 0.29/0.55 thf(fact_1293_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.55 ! [A: uint32,C2: uint32,B: uint32] :
% 0.29/0.55 ( ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ C2 ) @ B )
% 0.29/0.55 = ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ C2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.55 thf(fact_1294_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.55 ! [A: real,C2: real,B: real] :
% 0.29/0.55 ( ( minus_minus_real @ ( minus_minus_real @ A @ C2 ) @ B )
% 0.29/0.55 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.55 thf(fact_1295_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.55 ! [A: nat,C2: nat,B: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B )
% 0.29/0.55 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.55 thf(fact_1296_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.55 ! [A: int,C2: int,B: int] :
% 0.29/0.55 ( ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B )
% 0.29/0.55 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 ) ) ).
% 0.29/0.55
% 0.29/0.55 % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.55 thf(fact_1297_diff__commute,axiom,
% 0.29/0.55 ! [I: nat,J: nat,K: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/0.55 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_commute
% 0.29/0.55 thf(fact_1298_le__some__optE,axiom,
% 0.29/0.55 ! [M: set_int,X: option_set_int] :
% 0.29/0.55 ( ( ord_le353528952715127954et_int @ ( some_set_int @ M ) @ X )
% 0.29/0.55 => ~ ! [M8: set_int] :
% 0.29/0.55 ( ( X
% 0.29/0.55 = ( some_set_int @ M8 ) )
% 0.29/0.55 => ~ ( ord_less_eq_set_int @ M @ M8 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_some_optE
% 0.29/0.55 thf(fact_1299_le__some__optE,axiom,
% 0.29/0.55 ! [M: rat,X: option_rat] :
% 0.29/0.55 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M ) @ X )
% 0.29/0.55 => ~ ! [M8: rat] :
% 0.29/0.55 ( ( X
% 0.29/0.55 = ( some_rat @ M8 ) )
% 0.29/0.55 => ~ ( ord_less_eq_rat @ M @ M8 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_some_optE
% 0.29/0.55 thf(fact_1300_le__some__optE,axiom,
% 0.29/0.55 ! [M: num,X: option_num] :
% 0.29/0.55 ( ( ord_le6622620407824499402on_num @ ( some_num @ M ) @ X )
% 0.29/0.55 => ~ ! [M8: num] :
% 0.29/0.55 ( ( X
% 0.29/0.55 = ( some_num @ M8 ) )
% 0.29/0.55 => ~ ( ord_less_eq_num @ M @ M8 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_some_optE
% 0.29/0.55 thf(fact_1301_le__some__optE,axiom,
% 0.29/0.55 ! [M: nat,X: option_nat] :
% 0.29/0.55 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M ) @ X )
% 0.29/0.55 => ~ ! [M8: nat] :
% 0.29/0.55 ( ( X
% 0.29/0.55 = ( some_nat @ M8 ) )
% 0.29/0.55 => ~ ( ord_less_eq_nat @ M @ M8 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_some_optE
% 0.29/0.55 thf(fact_1302_le__some__optE,axiom,
% 0.29/0.55 ! [M: int,X: option_int] :
% 0.29/0.55 ( ( ord_le1736525451366464988on_int @ ( some_int @ M ) @ X )
% 0.29/0.55 => ~ ! [M8: int] :
% 0.29/0.55 ( ( X
% 0.29/0.55 = ( some_int @ M8 ) )
% 0.29/0.55 => ~ ( ord_less_eq_int @ M @ M8 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_some_optE
% 0.29/0.55 thf(fact_1303_eq__iff__diff__eq__0,axiom,
% 0.29/0.55 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 0.29/0.55 = ( ^ [A7: rat,B7: rat] :
% 0.29/0.55 ( ( minus_minus_rat @ A7 @ B7 )
% 0.29/0.55 = zero_zero_rat ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % eq_iff_diff_eq_0
% 0.29/0.55 thf(fact_1304_eq__iff__diff__eq__0,axiom,
% 0.29/0.55 ( ( ^ [Y6: uint32,Z4: uint32] : ( Y6 = Z4 ) )
% 0.29/0.55 = ( ^ [A7: uint32,B7: uint32] :
% 0.29/0.55 ( ( minus_minus_uint32 @ A7 @ B7 )
% 0.29/0.55 = zero_zero_uint32 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % eq_iff_diff_eq_0
% 0.29/0.55 thf(fact_1305_eq__iff__diff__eq__0,axiom,
% 0.29/0.55 ( ( ^ [Y6: real,Z4: real] : ( Y6 = Z4 ) )
% 0.29/0.55 = ( ^ [A7: real,B7: real] :
% 0.29/0.55 ( ( minus_minus_real @ A7 @ B7 )
% 0.29/0.55 = zero_zero_real ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % eq_iff_diff_eq_0
% 0.29/0.55 thf(fact_1306_eq__iff__diff__eq__0,axiom,
% 0.29/0.55 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.29/0.55 = ( ^ [A7: int,B7: int] :
% 0.29/0.55 ( ( minus_minus_int @ A7 @ B7 )
% 0.29/0.55 = zero_zero_int ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % eq_iff_diff_eq_0
% 0.29/0.55 thf(fact_1307_diff__mono,axiom,
% 0.29/0.55 ! [A: real,B: real,D: real,C2: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55 => ( ( ord_less_eq_real @ D @ C2 )
% 0.29/0.55 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_mono
% 0.29/0.55 thf(fact_1308_diff__mono,axiom,
% 0.29/0.55 ! [A: rat,B: rat,D: rat,C2: rat] :
% 0.29/0.55 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55 => ( ( ord_less_eq_rat @ D @ C2 )
% 0.29/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_mono
% 0.29/0.55 thf(fact_1309_diff__mono,axiom,
% 0.29/0.55 ! [A: int,B: int,D: int,C2: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55 => ( ( ord_less_eq_int @ D @ C2 )
% 0.29/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_mono
% 0.29/0.55 thf(fact_1310_diff__left__mono,axiom,
% 0.29/0.55 ! [B: real,A: real,C2: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ B @ A )
% 0.29/0.55 => ( ord_less_eq_real @ ( minus_minus_real @ C2 @ A ) @ ( minus_minus_real @ C2 @ B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_left_mono
% 0.29/0.55 thf(fact_1311_diff__left__mono,axiom,
% 0.29/0.55 ! [B: rat,A: rat,C2: rat] :
% 0.29/0.55 ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_left_mono
% 0.29/0.55 thf(fact_1312_diff__left__mono,axiom,
% 0.29/0.55 ! [B: int,A: int,C2: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_left_mono
% 0.29/0.55 thf(fact_1313_diff__right__mono,axiom,
% 0.29/0.55 ! [A: real,B: real,C2: real] :
% 0.29/0.55 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ C2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_right_mono
% 0.29/0.55 thf(fact_1314_diff__right__mono,axiom,
% 0.29/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.55 ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_right_mono
% 0.29/0.55 thf(fact_1315_diff__right__mono,axiom,
% 0.29/0.55 ! [A: int,B: int,C2: int] :
% 0.29/0.55 ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_right_mono
% 0.29/0.55 thf(fact_1316_diff__eq__diff__less__eq,axiom,
% 0.29/0.55 ! [A: real,B: real,C2: real,D: real] :
% 0.29/0.55 ( ( ( minus_minus_real @ A @ B )
% 0.29/0.55 = ( minus_minus_real @ C2 @ D ) )
% 0.29/0.55 => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.55 = ( ord_less_eq_real @ C2 @ D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_less_eq
% 0.29/0.55 thf(fact_1317_diff__eq__diff__less__eq,axiom,
% 0.29/0.55 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.29/0.55 ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.55 = ( minus_minus_rat @ C2 @ D ) )
% 0.29/0.55 => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55 = ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_less_eq
% 0.29/0.55 thf(fact_1318_diff__eq__diff__less__eq,axiom,
% 0.29/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.29/0.55 ( ( ( minus_minus_int @ A @ B )
% 0.29/0.55 = ( minus_minus_int @ C2 @ D ) )
% 0.29/0.55 => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55 = ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_less_eq
% 0.29/0.55 thf(fact_1319_diff__strict__right__mono,axiom,
% 0.29/0.55 ! [A: real,B: real,C2: real] :
% 0.29/0.55 ( ( ord_less_real @ A @ B )
% 0.29/0.55 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ C2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_right_mono
% 0.29/0.55 thf(fact_1320_diff__strict__right__mono,axiom,
% 0.29/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.55 ( ( ord_less_rat @ A @ B )
% 0.29/0.55 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_right_mono
% 0.29/0.55 thf(fact_1321_diff__strict__right__mono,axiom,
% 0.29/0.55 ! [A: int,B: int,C2: int] :
% 0.29/0.55 ( ( ord_less_int @ A @ B )
% 0.29/0.55 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_right_mono
% 0.29/0.55 thf(fact_1322_diff__strict__left__mono,axiom,
% 0.29/0.55 ! [B: real,A: real,C2: real] :
% 0.29/0.55 ( ( ord_less_real @ B @ A )
% 0.29/0.55 => ( ord_less_real @ ( minus_minus_real @ C2 @ A ) @ ( minus_minus_real @ C2 @ B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_left_mono
% 0.29/0.55 thf(fact_1323_diff__strict__left__mono,axiom,
% 0.29/0.55 ! [B: rat,A: rat,C2: rat] :
% 0.29/0.55 ( ( ord_less_rat @ B @ A )
% 0.29/0.55 => ( ord_less_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_left_mono
% 0.29/0.55 thf(fact_1324_diff__strict__left__mono,axiom,
% 0.29/0.55 ! [B: int,A: int,C2: int] :
% 0.29/0.55 ( ( ord_less_int @ B @ A )
% 0.29/0.55 => ( ord_less_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_left_mono
% 0.29/0.55 thf(fact_1325_diff__eq__diff__less,axiom,
% 0.29/0.55 ! [A: real,B: real,C2: real,D: real] :
% 0.29/0.55 ( ( ( minus_minus_real @ A @ B )
% 0.29/0.55 = ( minus_minus_real @ C2 @ D ) )
% 0.29/0.55 => ( ( ord_less_real @ A @ B )
% 0.29/0.55 = ( ord_less_real @ C2 @ D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_less
% 0.29/0.55 thf(fact_1326_diff__eq__diff__less,axiom,
% 0.29/0.55 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.29/0.55 ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.55 = ( minus_minus_rat @ C2 @ D ) )
% 0.29/0.55 => ( ( ord_less_rat @ A @ B )
% 0.29/0.55 = ( ord_less_rat @ C2 @ D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_less
% 0.29/0.55 thf(fact_1327_diff__eq__diff__less,axiom,
% 0.29/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.29/0.55 ( ( ( minus_minus_int @ A @ B )
% 0.29/0.55 = ( minus_minus_int @ C2 @ D ) )
% 0.29/0.55 => ( ( ord_less_int @ A @ B )
% 0.29/0.55 = ( ord_less_int @ C2 @ D ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_eq_diff_less
% 0.29/0.55 thf(fact_1328_diff__strict__mono,axiom,
% 0.29/0.55 ! [A: real,B: real,D: real,C2: real] :
% 0.29/0.55 ( ( ord_less_real @ A @ B )
% 0.29/0.55 => ( ( ord_less_real @ D @ C2 )
% 0.29/0.55 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_mono
% 0.29/0.55 thf(fact_1329_diff__strict__mono,axiom,
% 0.29/0.55 ! [A: rat,B: rat,D: rat,C2: rat] :
% 0.29/0.55 ( ( ord_less_rat @ A @ B )
% 0.29/0.55 => ( ( ord_less_rat @ D @ C2 )
% 0.29/0.55 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_mono
% 0.29/0.55 thf(fact_1330_diff__strict__mono,axiom,
% 0.29/0.55 ! [A: int,B: int,D: int,C2: int] :
% 0.29/0.55 ( ( ord_less_int @ A @ B )
% 0.29/0.55 => ( ( ord_less_int @ D @ C2 )
% 0.29/0.55 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_strict_mono
% 0.29/0.55 thf(fact_1331_zero__induct__lemma,axiom,
% 0.29/0.55 ! [P2: nat > $o,K: nat,I: nat] :
% 0.29/0.55 ( ( P2 @ K )
% 0.29/0.55 => ( ! [N2: nat] :
% 0.29/0.55 ( ( P2 @ ( suc @ N2 ) )
% 0.29/0.55 => ( P2 @ N2 ) )
% 0.29/0.55 => ( P2 @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % zero_induct_lemma
% 0.29/0.55 thf(fact_1332_diffs0__imp__equal,axiom,
% 0.29/0.55 ! [M: nat,N: nat] :
% 0.29/0.55 ( ( ( minus_minus_nat @ M @ N )
% 0.29/0.55 = zero_zero_nat )
% 0.29/0.55 => ( ( ( minus_minus_nat @ N @ M )
% 0.29/0.55 = zero_zero_nat )
% 0.29/0.55 => ( M = N ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diffs0_imp_equal
% 0.29/0.55 thf(fact_1333_minus__nat_Odiff__0,axiom,
% 0.29/0.55 ! [M: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.29/0.55 = M ) ).
% 0.29/0.55
% 0.29/0.55 % minus_nat.diff_0
% 0.29/0.55 thf(fact_1334_less__imp__diff__less,axiom,
% 0.29/0.55 ! [J: nat,K: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_nat @ J @ K )
% 0.29/0.55 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.29/0.55
% 0.29/0.55 % less_imp_diff_less
% 0.29/0.55 thf(fact_1335_diff__less__mono2,axiom,
% 0.29/0.55 ! [M: nat,N: nat,L: nat] :
% 0.29/0.55 ( ( ord_less_nat @ M @ N )
% 0.29/0.55 => ( ( ord_less_nat @ M @ L )
% 0.29/0.55 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_less_mono2
% 0.29/0.55 thf(fact_1336_eq__diff__iff,axiom,
% 0.29/0.55 ! [K: nat,M: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.55 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.55 => ( ( ( minus_minus_nat @ M @ K )
% 0.29/0.55 = ( minus_minus_nat @ N @ K ) )
% 0.29/0.55 = ( M = N ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % eq_diff_iff
% 0.29/0.55 thf(fact_1337_le__diff__iff,axiom,
% 0.29/0.55 ! [K: nat,M: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.55 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.55 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.55 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_diff_iff
% 0.29/0.55 thf(fact_1338_Nat_Odiff__diff__eq,axiom,
% 0.29/0.55 ! [K: nat,M: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.55 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.55 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.55 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Nat.diff_diff_eq
% 0.29/0.55 thf(fact_1339_diff__le__mono,axiom,
% 0.29/0.55 ! [M: nat,N: nat,L: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.55 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_le_mono
% 0.29/0.55 thf(fact_1340_diff__le__self,axiom,
% 0.29/0.55 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.29/0.55
% 0.29/0.55 % diff_le_self
% 0.29/0.55 thf(fact_1341_le__diff__iff_H,axiom,
% 0.29/0.55 ! [A: nat,C2: nat,B: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ A @ C2 )
% 0.29/0.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.29/0.55 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C2 @ A ) @ ( minus_minus_nat @ C2 @ B ) )
% 0.29/0.55 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_diff_iff'
% 0.29/0.55 thf(fact_1342_diff__le__mono2,axiom,
% 0.29/0.55 ! [M: nat,N: nat,L: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.55 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_le_mono2
% 0.29/0.55 thf(fact_1343_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J,axiom,
% 0.29/0.55 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.55 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 0.29/0.55 = one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(5)
% 0.29/0.55 thf(fact_1344_le__iff__diff__le__0,axiom,
% 0.29/0.55 ( ord_less_eq_real
% 0.29/0.55 = ( ^ [A7: real,B7: real] : ( ord_less_eq_real @ ( minus_minus_real @ A7 @ B7 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_iff_diff_le_0
% 0.29/0.55 thf(fact_1345_le__iff__diff__le__0,axiom,
% 0.29/0.55 ( ord_less_eq_rat
% 0.29/0.55 = ( ^ [A7: rat,B7: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A7 @ B7 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_iff_diff_le_0
% 0.29/0.55 thf(fact_1346_le__iff__diff__le__0,axiom,
% 0.29/0.55 ( ord_less_eq_int
% 0.29/0.55 = ( ^ [A7: int,B7: int] : ( ord_less_eq_int @ ( minus_minus_int @ A7 @ B7 ) @ zero_zero_int ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % le_iff_diff_le_0
% 0.29/0.55 thf(fact_1347_less__iff__diff__less__0,axiom,
% 0.29/0.55 ( ord_less_real
% 0.29/0.55 = ( ^ [A7: real,B7: real] : ( ord_less_real @ ( minus_minus_real @ A7 @ B7 ) @ zero_zero_real ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % less_iff_diff_less_0
% 0.29/0.55 thf(fact_1348_less__iff__diff__less__0,axiom,
% 0.29/0.55 ( ord_less_rat
% 0.29/0.55 = ( ^ [A7: rat,B7: rat] : ( ord_less_rat @ ( minus_minus_rat @ A7 @ B7 ) @ zero_zero_rat ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % less_iff_diff_less_0
% 0.29/0.55 thf(fact_1349_less__iff__diff__less__0,axiom,
% 0.29/0.55 ( ord_less_int
% 0.29/0.55 = ( ^ [A7: int,B7: int] : ( ord_less_int @ ( minus_minus_int @ A7 @ B7 ) @ zero_zero_int ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % less_iff_diff_less_0
% 0.29/0.55 thf(fact_1350_Suc__to__right,axiom,
% 0.29/0.55 ! [N: nat,M: nat] :
% 0.29/0.55 ( ( ( suc @ N )
% 0.29/0.55 = M )
% 0.29/0.55 => ( N
% 0.29/0.55 = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Suc_to_right
% 0.29/0.55 thf(fact_1351_diff__less__Suc,axiom,
% 0.29/0.55 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_less_Suc
% 0.29/0.55 thf(fact_1352_Suc__diff__Suc,axiom,
% 0.29/0.55 ! [N: nat,M: nat] :
% 0.29/0.55 ( ( ord_less_nat @ N @ M )
% 0.29/0.55 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.29/0.55 = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Suc_diff_Suc
% 0.29/0.55 thf(fact_1353_diff__less,axiom,
% 0.29/0.55 ! [N: nat,M: nat] :
% 0.29/0.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.29/0.55 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_less
% 0.29/0.55 thf(fact_1354_Suc__diff__le,axiom,
% 0.29/0.55 ! [N: nat,M: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.55 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.29/0.55 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % Suc_diff_le
% 0.29/0.55 thf(fact_1355_diff__Suc__eq__diff__pred,axiom,
% 0.29/0.55 ! [M: nat,N: nat] :
% 0.29/0.55 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.29/0.55 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_Suc_eq_diff_pred
% 0.29/0.55 thf(fact_1356_less__diff__iff,axiom,
% 0.29/0.55 ! [K: nat,M: nat,N: nat] :
% 0.29/0.55 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.55 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.55 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.55 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % less_diff_iff
% 0.29/0.55 thf(fact_1357_diff__less__mono,axiom,
% 0.29/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.55 ( ( ord_less_nat @ A @ B )
% 0.29/0.55 => ( ( ord_less_eq_nat @ C2 @ A )
% 0.29/0.55 => ( ord_less_nat @ ( minus_minus_nat @ A @ C2 ) @ ( minus_minus_nat @ B @ C2 ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_less_mono
% 0.29/0.55 thf(fact_1358_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J,axiom,
% 0.29/0.55 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.55 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 0.29/0.55 = one_one_nat ) ).
% 0.29/0.55
% 0.29/0.55 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(6)
% 0.29/0.55 thf(fact_1359_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 0.29/0.55 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.29/0.55 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 0.29/0.55
% 0.29/0.55 % VEBT_internal.minNull.simps(5)
% 0.29/0.55 thf(fact_1360_frac__ge__0,axiom,
% 0.29/0.55 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 0.29/0.55
% 0.29/0.55 % frac_ge_0
% 0.29/0.55 thf(fact_1361_frac__ge__0,axiom,
% 0.29/0.55 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 0.29/0.55
% 0.29/0.55 % frac_ge_0
% 0.29/0.55 thf(fact_1362_frac__lt__1,axiom,
% 0.29/0.55 ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 0.29/0.55
% 0.29/0.55 % frac_lt_1
% 0.29/0.55 thf(fact_1363_frac__lt__1,axiom,
% 0.29/0.55 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 0.29/0.55
% 0.29/0.55 % frac_lt_1
% 0.29/0.55 thf(fact_1364_diff__Suc__less,axiom,
% 0.29/0.55 ! [N: nat,I: nat] :
% 0.29/0.55 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.55 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 0.29/0.55
% 0.29/0.55 % diff_Suc_less
% 0.29/0.55 thf(fact_1365_pinf_I1_J,axiom,
% 0.29/0.55 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 0.29/0.55 ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(1)
% 0.29/0.55 thf(fact_1366_pinf_I1_J,axiom,
% 0.29/0.55 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 0.29/0.55 ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(1)
% 0.29/0.55 thf(fact_1367_pinf_I1_J,axiom,
% 0.29/0.55 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 0.29/0.55 ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(1)
% 0.29/0.55 thf(fact_1368_pinf_I1_J,axiom,
% 0.29/0.55 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 0.29/0.55 ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(1)
% 0.29/0.55 thf(fact_1369_pinf_I1_J,axiom,
% 0.29/0.55 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 0.29/0.55 ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(1)
% 0.29/0.55 thf(fact_1370_pinf_I2_J,axiom,
% 0.29/0.55 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 0.29/0.55 ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(2)
% 0.29/0.55 thf(fact_1371_pinf_I2_J,axiom,
% 0.29/0.55 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 0.29/0.55 ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(2)
% 0.29/0.55 thf(fact_1372_pinf_I2_J,axiom,
% 0.29/0.55 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 0.29/0.55 ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(2)
% 0.29/0.55 thf(fact_1373_pinf_I2_J,axiom,
% 0.29/0.55 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 0.29/0.55 ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(2)
% 0.29/0.55 thf(fact_1374_pinf_I2_J,axiom,
% 0.29/0.55 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 0.29/0.55 ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ Z5 @ X3 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ Z5 @ X3 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(2)
% 0.29/0.55 thf(fact_1375_pinf_I3_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(3)
% 0.29/0.55 thf(fact_1376_pinf_I3_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(3)
% 0.29/0.55 thf(fact_1377_pinf_I3_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(3)
% 0.29/0.55 thf(fact_1378_pinf_I3_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(3)
% 0.29/0.55 thf(fact_1379_pinf_I3_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(3)
% 0.29/0.55 thf(fact_1380_pinf_I4_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(4)
% 0.29/0.55 thf(fact_1381_pinf_I4_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(4)
% 0.29/0.55 thf(fact_1382_pinf_I4_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(4)
% 0.29/0.55 thf(fact_1383_pinf_I4_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(4)
% 0.29/0.55 thf(fact_1384_pinf_I4_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(4)
% 0.29/0.55 thf(fact_1385_pinf_I5_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(5)
% 0.29/0.55 thf(fact_1386_pinf_I5_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(5)
% 0.29/0.55 thf(fact_1387_pinf_I5_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(5)
% 0.29/0.55 thf(fact_1388_pinf_I5_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(5)
% 0.29/0.55 thf(fact_1389_pinf_I5_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(5)
% 0.29/0.55 thf(fact_1390_pinf_I7_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_real @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(7)
% 0.29/0.55 thf(fact_1391_pinf_I7_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_rat @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(7)
% 0.29/0.55 thf(fact_1392_pinf_I7_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_num @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(7)
% 0.29/0.55 thf(fact_1393_pinf_I7_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_nat @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(7)
% 0.29/0.55 thf(fact_1394_pinf_I7_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ Z3 @ X5 )
% 0.29/0.55 => ( ord_less_int @ T @ X5 ) ) ).
% 0.29/0.55
% 0.29/0.55 % pinf(7)
% 0.29/0.55 thf(fact_1395_minf_I1_J,axiom,
% 0.29/0.55 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 0.29/0.55 ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(1)
% 0.29/0.55 thf(fact_1396_minf_I1_J,axiom,
% 0.29/0.55 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 0.29/0.55 ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(1)
% 0.29/0.55 thf(fact_1397_minf_I1_J,axiom,
% 0.29/0.55 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 0.29/0.55 ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(1)
% 0.29/0.55 thf(fact_1398_minf_I1_J,axiom,
% 0.29/0.55 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 0.29/0.55 ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(1)
% 0.29/0.55 thf(fact_1399_minf_I1_J,axiom,
% 0.29/0.55 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 0.29/0.55 ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 & ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(1)
% 0.29/0.55 thf(fact_1400_minf_I2_J,axiom,
% 0.29/0.55 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 0.29/0.55 ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: real] :
% 0.29/0.55 ! [X3: real] :
% 0.29/0.55 ( ( ord_less_real @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(2)
% 0.29/0.55 thf(fact_1401_minf_I2_J,axiom,
% 0.29/0.55 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 0.29/0.55 ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: rat] :
% 0.29/0.55 ! [X3: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(2)
% 0.29/0.55 thf(fact_1402_minf_I2_J,axiom,
% 0.29/0.55 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 0.29/0.55 ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: num] :
% 0.29/0.55 ! [X3: num] :
% 0.29/0.55 ( ( ord_less_num @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(2)
% 0.29/0.55 thf(fact_1403_minf_I2_J,axiom,
% 0.29/0.55 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 0.29/0.55 ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: nat] :
% 0.29/0.55 ! [X3: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(2)
% 0.29/0.55 thf(fact_1404_minf_I2_J,axiom,
% 0.29/0.55 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 0.29/0.55 ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ X3 @ Z5 )
% 0.29/0.55 => ( ( P2 @ X3 )
% 0.29/0.55 = ( P6 @ X3 ) ) )
% 0.29/0.55 => ( ? [Z5: int] :
% 0.29/0.55 ! [X3: int] :
% 0.29/0.55 ( ( ord_less_int @ X3 @ Z5 )
% 0.29/0.55 => ( ( Q2 @ X3 )
% 0.29/0.55 = ( Q4 @ X3 ) ) )
% 0.29/0.55 => ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.55 => ( ( ( P2 @ X5 )
% 0.29/0.55 | ( Q2 @ X5 ) )
% 0.29/0.55 = ( ( P6 @ X5 )
% 0.29/0.55 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(2)
% 0.29/0.55 thf(fact_1405_minf_I3_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(3)
% 0.29/0.55 thf(fact_1406_minf_I3_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(3)
% 0.29/0.55 thf(fact_1407_minf_I3_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(3)
% 0.29/0.55 thf(fact_1408_minf_I3_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(3)
% 0.29/0.55 thf(fact_1409_minf_I3_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(3)
% 0.29/0.55 thf(fact_1410_minf_I4_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.55 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(4)
% 0.29/0.55 thf(fact_1411_minf_I4_J,axiom,
% 0.29/0.55 ! [T: rat] :
% 0.29/0.55 ? [Z3: rat] :
% 0.29/0.55 ! [X5: rat] :
% 0.29/0.55 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(4)
% 0.29/0.55 thf(fact_1412_minf_I4_J,axiom,
% 0.29/0.55 ! [T: num] :
% 0.29/0.55 ? [Z3: num] :
% 0.29/0.55 ! [X5: num] :
% 0.29/0.55 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(4)
% 0.29/0.55 thf(fact_1413_minf_I4_J,axiom,
% 0.29/0.55 ! [T: nat] :
% 0.29/0.55 ? [Z3: nat] :
% 0.29/0.55 ! [X5: nat] :
% 0.29/0.55 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(4)
% 0.29/0.55 thf(fact_1414_minf_I4_J,axiom,
% 0.29/0.55 ! [T: int] :
% 0.29/0.55 ? [Z3: int] :
% 0.29/0.55 ! [X5: int] :
% 0.29/0.55 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.55 => ( X5 != T ) ) ).
% 0.29/0.55
% 0.29/0.55 % minf(4)
% 0.29/0.55 thf(fact_1415_minf_I5_J,axiom,
% 0.29/0.55 ! [T: real] :
% 0.29/0.55 ? [Z3: real] :
% 0.29/0.55 ! [X5: real] :
% 0.29/0.56 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.56 => ( ord_less_real @ X5 @ T ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(5)
% 0.29/0.56 thf(fact_1416_minf_I5_J,axiom,
% 0.29/0.56 ! [T: rat] :
% 0.29/0.56 ? [Z3: rat] :
% 0.29/0.56 ! [X5: rat] :
% 0.29/0.56 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.56 => ( ord_less_rat @ X5 @ T ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(5)
% 0.29/0.56 thf(fact_1417_minf_I5_J,axiom,
% 0.29/0.56 ! [T: num] :
% 0.29/0.56 ? [Z3: num] :
% 0.29/0.56 ! [X5: num] :
% 0.29/0.56 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.56 => ( ord_less_num @ X5 @ T ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(5)
% 0.29/0.56 thf(fact_1418_minf_I5_J,axiom,
% 0.29/0.56 ! [T: nat] :
% 0.29/0.56 ? [Z3: nat] :
% 0.29/0.56 ! [X5: nat] :
% 0.29/0.56 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.56 => ( ord_less_nat @ X5 @ T ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(5)
% 0.29/0.56 thf(fact_1419_minf_I5_J,axiom,
% 0.29/0.56 ! [T: int] :
% 0.29/0.56 ? [Z3: int] :
% 0.29/0.56 ! [X5: int] :
% 0.29/0.56 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.56 => ( ord_less_int @ X5 @ T ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(5)
% 0.29/0.56 thf(fact_1420_minf_I7_J,axiom,
% 0.29/0.56 ! [T: real] :
% 0.29/0.56 ? [Z3: real] :
% 0.29/0.56 ! [X5: real] :
% 0.29/0.56 ( ( ord_less_real @ X5 @ Z3 )
% 0.29/0.56 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(7)
% 0.29/0.56 thf(fact_1421_minf_I7_J,axiom,
% 0.29/0.56 ! [T: rat] :
% 0.29/0.56 ? [Z3: rat] :
% 0.29/0.56 ! [X5: rat] :
% 0.29/0.56 ( ( ord_less_rat @ X5 @ Z3 )
% 0.29/0.56 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(7)
% 0.29/0.56 thf(fact_1422_minf_I7_J,axiom,
% 0.29/0.56 ! [T: num] :
% 0.29/0.56 ? [Z3: num] :
% 0.29/0.56 ! [X5: num] :
% 0.29/0.56 ( ( ord_less_num @ X5 @ Z3 )
% 0.29/0.56 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(7)
% 0.29/0.56 thf(fact_1423_minf_I7_J,axiom,
% 0.29/0.56 ! [T: nat] :
% 0.29/0.56 ? [Z3: nat] :
% 0.29/0.56 ! [X5: nat] :
% 0.29/0.56 ( ( ord_less_nat @ X5 @ Z3 )
% 0.29/0.56 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(7)
% 0.29/0.56 thf(fact_1424_minf_I7_J,axiom,
% 0.29/0.56 ! [T: int] :
% 0.29/0.56 ? [Z3: int] :
% 0.29/0.56 ! [X5: int] :
% 0.29/0.56 ( ( ord_less_int @ X5 @ Z3 )
% 0.29/0.56 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 0.29/0.56
% 0.29/0.56 % minf(7)
% 0.29/0.56 thf(fact_1425_vebt__delete_Osimps_I5_J,axiom,
% 0.29/0.56 ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 0.29/0.56 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 0.29/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 0.29/0.56
% 0.29/0.56 % vebt_delete.simps(5)
% 0.29/0.56 thf(fact_1426_vebt__member_Osimps_I3_J,axiom,
% 0.29/0.56 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.29/0.56 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X ) ).
% 0.29/0.56
% 0.29/0.56 % vebt_member.simps(3)
% 0.29/0.56 thf(fact_1427_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT] :
% 0.29/0.56 ( ~ ( vEBT_VEBT_minNull @ X )
% 0.29/0.56 => ( ! [Uv: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.56 => ( ! [Uu: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.56 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.minNull.elims(3)
% 0.29/0.56 thf(fact_1428_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 0.29/0.56 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 0.29/0.56 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 0.29/0.56 = ( ( X = Mi )
% 0.29/0.56 | ( X = Ma ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.membermima.simps(3)
% 0.29/0.56 thf(fact_1429_nz__le__conv__less,axiom,
% 0.29/0.56 ! [K: nat,M: nat] :
% 0.29/0.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.29/0.56 => ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.56 => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % nz_le_conv_less
% 0.29/0.56 thf(fact_1430_Suc__pred_H,axiom,
% 0.29/0.56 ! [N: nat] :
% 0.29/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.56 => ( N
% 0.29/0.56 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Suc_pred'
% 0.29/0.56 thf(fact_1431_Suc__diff__eq__diff__pred,axiom,
% 0.29/0.56 ! [N: nat,M: nat] :
% 0.29/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.56 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.29/0.56 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Suc_diff_eq_diff_pred
% 0.29/0.56 thf(fact_1432_Suc__n__minus__m__eq,axiom,
% 0.29/0.56 ! [M: nat,N: nat] :
% 0.29/0.56 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.56 => ( ( ord_less_nat @ one_one_nat @ M )
% 0.29/0.56 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 0.29/0.56 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Suc_n_minus_m_eq
% 0.29/0.56 thf(fact_1433_vebt__delete_Osimps_I6_J,axiom,
% 0.29/0.56 ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 0.29/0.56 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 0.29/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 0.29/0.56
% 0.29/0.56 % vebt_delete.simps(6)
% 0.29/0.56 thf(fact_1434_vebt__member_Osimps_I4_J,axiom,
% 0.29/0.56 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.29/0.56 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 0.29/0.56
% 0.29/0.56 % vebt_member.simps(4)
% 0.29/0.56 thf(fact_1435_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I5_J,axiom,
% 0.29/0.56 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.56 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 0.29/0.56 = one_one_nat ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(5)
% 0.29/0.56 thf(fact_1436_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J,axiom,
% 0.29/0.56 ! [A: $o,B: $o,N: nat] :
% 0.29/0.56 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.29/0.56 = one_one_nat ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(3)
% 0.29/0.56 thf(fact_1437_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J,axiom,
% 0.29/0.56 ! [A: $o,B: $o] :
% 0.29/0.56 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.29/0.56 = one_one_nat ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(1)
% 0.29/0.56 thf(fact_1438_less__option__Some,axiom,
% 0.29/0.56 ! [X: real,Y: real] :
% 0.29/0.56 ( ( ord_less_option_real @ ( some_real @ X ) @ ( some_real @ Y ) )
% 0.29/0.56 = ( ord_less_real @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_Some
% 0.29/0.56 thf(fact_1439_less__option__Some,axiom,
% 0.29/0.56 ! [X: rat,Y: rat] :
% 0.29/0.56 ( ( ord_less_option_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 0.29/0.56 = ( ord_less_rat @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_Some
% 0.29/0.56 thf(fact_1440_less__option__Some,axiom,
% 0.29/0.56 ! [X: num,Y: num] :
% 0.29/0.56 ( ( ord_less_option_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 0.29/0.56 = ( ord_less_num @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_Some
% 0.29/0.56 thf(fact_1441_less__option__Some,axiom,
% 0.29/0.56 ! [X: nat,Y: nat] :
% 0.29/0.56 ( ( ord_less_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.29/0.56 = ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_Some
% 0.29/0.56 thf(fact_1442_less__option__Some,axiom,
% 0.29/0.56 ! [X: int,Y: int] :
% 0.29/0.56 ( ( ord_less_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 0.29/0.56 = ( ord_less_int @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_Some
% 0.29/0.56 thf(fact_1443_less__eq__option__Some,axiom,
% 0.29/0.56 ! [X: set_int,Y: set_int] :
% 0.29/0.56 ( ( ord_le353528952715127954et_int @ ( some_set_int @ X ) @ ( some_set_int @ Y ) )
% 0.29/0.56 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_Some
% 0.29/0.56 thf(fact_1444_less__eq__option__Some,axiom,
% 0.29/0.56 ! [X: rat,Y: rat] :
% 0.29/0.56 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 0.29/0.56 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_Some
% 0.29/0.56 thf(fact_1445_less__eq__option__Some,axiom,
% 0.29/0.56 ! [X: num,Y: num] :
% 0.29/0.56 ( ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 0.29/0.56 = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_Some
% 0.29/0.56 thf(fact_1446_less__eq__option__Some,axiom,
% 0.29/0.56 ! [X: nat,Y: nat] :
% 0.29/0.56 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.29/0.56 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_Some
% 0.29/0.56 thf(fact_1447_less__eq__option__Some,axiom,
% 0.29/0.56 ! [X: int,Y: int] :
% 0.29/0.56 ( ( ord_le1736525451366464988on_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 0.29/0.56 = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_Some
% 0.29/0.56 thf(fact_1448_mi__eq__ma__no__ch,axiom,
% 0.29/0.56 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.56 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 0.29/0.56 => ( ( Mi = Ma )
% 0.29/0.56 => ( ! [X5: vEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.56 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 0.29/0.56 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % mi_eq_ma_no_ch
% 0.29/0.56 thf(fact_1449_diff__shunt__var,axiom,
% 0.29/0.56 ! [X: assn,Y: assn] :
% 0.29/0.56 ( ( ( minus_minus_assn @ X @ Y )
% 0.29/0.56 = bot_bot_assn )
% 0.29/0.56 = ( ord_less_eq_assn @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % diff_shunt_var
% 0.29/0.56 thf(fact_1450_diff__shunt__var,axiom,
% 0.29/0.56 ! [X: set_o,Y: set_o] :
% 0.29/0.56 ( ( ( minus_minus_set_o @ X @ Y )
% 0.29/0.56 = bot_bot_set_o )
% 0.29/0.56 = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % diff_shunt_var
% 0.29/0.56 thf(fact_1451_diff__shunt__var,axiom,
% 0.29/0.56 ! [X: set_nat,Y: set_nat] :
% 0.29/0.56 ( ( ( minus_minus_set_nat @ X @ Y )
% 0.29/0.56 = bot_bot_set_nat )
% 0.29/0.56 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % diff_shunt_var
% 0.29/0.56 thf(fact_1452_diff__shunt__var,axiom,
% 0.29/0.56 ! [X: set_int,Y: set_int] :
% 0.29/0.56 ( ( ( minus_minus_set_int @ X @ Y )
% 0.29/0.56 = bot_bot_set_int )
% 0.29/0.56 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.29/0.56
% 0.29/0.56 % diff_shunt_var
% 0.29/0.56 thf(fact_1453_prod__decode__aux_Osimps,axiom,
% 0.29/0.56 ( nat_prod_decode_aux
% 0.29/0.56 = ( ^ [K3: nat,M5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M5 @ K3 ) @ ( product_Pair_nat_nat @ M5 @ ( minus_minus_nat @ K3 @ M5 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M5 @ ( suc @ K3 ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % prod_decode_aux.simps
% 0.29/0.56 thf(fact_1454_prod__decode__aux_Oelims,axiom,
% 0.29/0.56 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 0.29/0.56 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.29/0.56 = Y )
% 0.29/0.56 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.29/0.56 => ( Y
% 0.29/0.56 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.29/0.56 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.29/0.56 => ( Y
% 0.29/0.56 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % prod_decode_aux.elims
% 0.29/0.56 thf(fact_1455_VEBT__internal_Omembermima_Ocases,axiom,
% 0.29/0.56 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.56 ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 0.29/0.56 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz2: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz2 ) )
% 0.29/0.56 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 0.29/0.56 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ X3 ) )
% 0.29/0.56 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X3 ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.membermima.cases
% 0.29/0.56 thf(fact_1456_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Ocases,axiom,
% 0.29/0.56 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.56 ( ! [A3: $o,B3: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) )
% 0.29/0.56 => ( ! [A3: $o,B3: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.56 => ( ! [A3: $o,B3: $o,N2: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) )
% 0.29/0.56 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Uu ) )
% 0.29/0.56 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ X3 ) )
% 0.29/0.56 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 0.29/0.56 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.cases
% 0.29/0.56 thf(fact_1457_diff__diff__less,axiom,
% 0.29/0.56 ! [I: nat,M: nat,N: nat] :
% 0.29/0.56 ( ( ord_less_nat @ I @ ( minus_minus_nat @ M @ ( minus_minus_nat @ M @ N ) ) )
% 0.29/0.56 = ( ( ord_less_nat @ I @ M )
% 0.29/0.56 & ( ord_less_nat @ I @ N ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % diff_diff_less
% 0.29/0.56 thf(fact_1458_Diff__empty,axiom,
% 0.29/0.56 ! [A4: set_int] :
% 0.29/0.56 ( ( minus_minus_set_int @ A4 @ bot_bot_set_int )
% 0.29/0.56 = A4 ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_empty
% 0.29/0.56 thf(fact_1459_Diff__empty,axiom,
% 0.29/0.56 ! [A4: set_o] :
% 0.29/0.56 ( ( minus_minus_set_o @ A4 @ bot_bot_set_o )
% 0.29/0.56 = A4 ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_empty
% 0.29/0.56 thf(fact_1460_Diff__empty,axiom,
% 0.29/0.56 ! [A4: set_nat] :
% 0.29/0.56 ( ( minus_minus_set_nat @ A4 @ bot_bot_set_nat )
% 0.29/0.56 = A4 ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_empty
% 0.29/0.56 thf(fact_1461_empty__Diff,axiom,
% 0.29/0.56 ! [A4: set_int] :
% 0.29/0.56 ( ( minus_minus_set_int @ bot_bot_set_int @ A4 )
% 0.29/0.56 = bot_bot_set_int ) ).
% 0.29/0.56
% 0.29/0.56 % empty_Diff
% 0.29/0.56 thf(fact_1462_empty__Diff,axiom,
% 0.29/0.56 ! [A4: set_o] :
% 0.29/0.56 ( ( minus_minus_set_o @ bot_bot_set_o @ A4 )
% 0.29/0.56 = bot_bot_set_o ) ).
% 0.29/0.56
% 0.29/0.56 % empty_Diff
% 0.29/0.56 thf(fact_1463_empty__Diff,axiom,
% 0.29/0.56 ! [A4: set_nat] :
% 0.29/0.56 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A4 )
% 0.29/0.56 = bot_bot_set_nat ) ).
% 0.29/0.56
% 0.29/0.56 % empty_Diff
% 0.29/0.56 thf(fact_1464_Diff__cancel,axiom,
% 0.29/0.56 ! [A4: set_int] :
% 0.29/0.56 ( ( minus_minus_set_int @ A4 @ A4 )
% 0.29/0.56 = bot_bot_set_int ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_cancel
% 0.29/0.56 thf(fact_1465_Diff__cancel,axiom,
% 0.29/0.56 ! [A4: set_o] :
% 0.29/0.56 ( ( minus_minus_set_o @ A4 @ A4 )
% 0.29/0.56 = bot_bot_set_o ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_cancel
% 0.29/0.56 thf(fact_1466_Diff__cancel,axiom,
% 0.29/0.56 ! [A4: set_nat] :
% 0.29/0.56 ( ( minus_minus_set_nat @ A4 @ A4 )
% 0.29/0.56 = bot_bot_set_nat ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_cancel
% 0.29/0.56 thf(fact_1467_finite__Diff,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ A4 )
% 0.29/0.56 => ( finite_finite_int @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff
% 0.29/0.56 thf(fact_1468_finite__Diff,axiom,
% 0.29/0.56 ! [A4: set_complex,B4: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ A4 )
% 0.29/0.56 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff
% 0.29/0.56 thf(fact_1469_finite__Diff,axiom,
% 0.29/0.56 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.56 => ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff
% 0.29/0.56 thf(fact_1470_finite__Diff,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ A4 )
% 0.29/0.56 => ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff
% 0.29/0.56 thf(fact_1471_finite__Diff2,axiom,
% 0.29/0.56 ! [B4: set_int,A4: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ B4 )
% 0.29/0.56 => ( ( finite_finite_int @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.29/0.56 = ( finite_finite_int @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff2
% 0.29/0.56 thf(fact_1472_finite__Diff2,axiom,
% 0.29/0.56 ! [B4: set_complex,A4: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ B4 )
% 0.29/0.56 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 0.29/0.56 = ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff2
% 0.29/0.56 thf(fact_1473_finite__Diff2,axiom,
% 0.29/0.56 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ B4 )
% 0.29/0.56 => ( ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 0.29/0.56 = ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff2
% 0.29/0.56 thf(fact_1474_finite__Diff2,axiom,
% 0.29/0.56 ! [B4: set_nat,A4: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ B4 )
% 0.29/0.56 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.29/0.56 = ( finite_finite_nat @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff2
% 0.29/0.56 thf(fact_1475_Diff__eq__empty__iff,axiom,
% 0.29/0.56 ! [A4: set_o,B4: set_o] :
% 0.29/0.56 ( ( ( minus_minus_set_o @ A4 @ B4 )
% 0.29/0.56 = bot_bot_set_o )
% 0.29/0.56 = ( ord_less_eq_set_o @ A4 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_eq_empty_iff
% 0.29/0.56 thf(fact_1476_Diff__eq__empty__iff,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( ( minus_minus_set_nat @ A4 @ B4 )
% 0.29/0.56 = bot_bot_set_nat )
% 0.29/0.56 = ( ord_less_eq_set_nat @ A4 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_eq_empty_iff
% 0.29/0.56 thf(fact_1477_Diff__eq__empty__iff,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( ( minus_minus_set_int @ A4 @ B4 )
% 0.29/0.56 = bot_bot_set_int )
% 0.29/0.56 = ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_eq_empty_iff
% 0.29/0.56 thf(fact_1478_lesseq__shift,axiom,
% 0.29/0.56 ( ord_less_eq_nat
% 0.29/0.56 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % lesseq_shift
% 0.29/0.56 thf(fact_1479_less__eq__option__None__code,axiom,
% 0.29/0.56 ! [X: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_None_code
% 0.29/0.56 thf(fact_1480_less__option__None,axiom,
% 0.29/0.56 ! [X: option_nat] :
% 0.29/0.56 ~ ( ord_less_option_nat @ X @ none_nat ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_None
% 0.29/0.56 thf(fact_1481_not__Some__eq2,axiom,
% 0.29/0.56 ! [V2: option3972171592325465343uint32] :
% 0.29/0.56 ( ( ! [X4: uint32,Y4: uint32] :
% 0.29/0.56 ( V2
% 0.29/0.56 != ( some_P6695178580830101022uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) ) ) )
% 0.29/0.56 = ( V2 = none_P7441528354948028570uint32 ) ) ).
% 0.29/0.56
% 0.29/0.56 % not_Some_eq2
% 0.29/0.56 thf(fact_1482_not__Some__eq2,axiom,
% 0.29/0.56 ! [V2: option4624381673175914239nt_int] :
% 0.29/0.56 ( ( ! [X4: int,Y4: int] :
% 0.29/0.56 ( V2
% 0.29/0.56 != ( some_P4184893108420464158nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) ) ) )
% 0.29/0.56 = ( V2 = none_P2377608414092835994nt_int ) ) ).
% 0.29/0.56
% 0.29/0.56 % not_Some_eq2
% 0.29/0.56 thf(fact_1483_not__Some__eq2,axiom,
% 0.29/0.56 ! [V2: option5190343406534369742et_nat] :
% 0.29/0.56 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] :
% 0.29/0.56 ( V2
% 0.29/0.56 != ( some_P750831030444334937et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) ) ) )
% 0.29/0.56 = ( V2 = none_P4972525538344268765et_nat ) ) ).
% 0.29/0.56
% 0.29/0.56 % not_Some_eq2
% 0.29/0.56 thf(fact_1484_not__Some__eq2,axiom,
% 0.29/0.56 ! [V2: option2860828798490689354et_nat] :
% 0.29/0.56 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] :
% 0.29/0.56 ( V2
% 0.29/0.56 != ( some_P1630309045189364437et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) ) ) )
% 0.29/0.56 = ( V2 = none_P199884684680593241et_nat ) ) ).
% 0.29/0.56
% 0.29/0.56 % not_Some_eq2
% 0.29/0.56 thf(fact_1485_not__Some__eq2,axiom,
% 0.29/0.56 ! [V2: option4927543243414619207at_nat] :
% 0.29/0.56 ( ( ! [X4: nat,Y4: nat] :
% 0.29/0.56 ( V2
% 0.29/0.56 != ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) ) )
% 0.29/0.56 = ( V2 = none_P5556105721700978146at_nat ) ) ).
% 0.29/0.56
% 0.29/0.56 % not_Some_eq2
% 0.29/0.56 thf(fact_1486_less__eq__option__Some__None,axiom,
% 0.29/0.56 ! [X: nat] :
% 0.29/0.56 ~ ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ none_nat ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_Some_None
% 0.29/0.56 thf(fact_1487_less__option__None__Some__code,axiom,
% 0.29/0.56 ! [X: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_None_Some_code
% 0.29/0.56 thf(fact_1488_less__eq__option__None,axiom,
% 0.29/0.56 ! [X: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_None
% 0.29/0.56 thf(fact_1489_less__eq__option__None__is__None,axiom,
% 0.29/0.56 ! [X: option_nat] :
% 0.29/0.56 ( ( ord_le5914376470875661696on_nat @ X @ none_nat )
% 0.29/0.56 => ( X = none_nat ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_eq_option_None_is_None
% 0.29/0.56 thf(fact_1490_less__option__None__Some,axiom,
% 0.29/0.56 ! [X: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_None_Some
% 0.29/0.56 thf(fact_1491_less__option__None__is__Some,axiom,
% 0.29/0.56 ! [X: option_nat] :
% 0.29/0.56 ( ( ord_less_option_nat @ none_nat @ X )
% 0.29/0.56 => ? [Z3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 = ( some_nat @ Z3 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % less_option_None_is_Some
% 0.29/0.56 thf(fact_1492_Diff__infinite__finite,axiom,
% 0.29/0.56 ! [T3: set_int,S3: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ T3 )
% 0.29/0.56 => ( ~ ( finite_finite_int @ S3 )
% 0.29/0.56 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S3 @ T3 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_infinite_finite
% 0.29/0.56 thf(fact_1493_Diff__infinite__finite,axiom,
% 0.29/0.56 ! [T3: set_complex,S3: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ T3 )
% 0.29/0.56 => ( ~ ( finite3207457112153483333omplex @ S3 )
% 0.29/0.56 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S3 @ T3 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_infinite_finite
% 0.29/0.56 thf(fact_1494_Diff__infinite__finite,axiom,
% 0.29/0.56 ! [T3: set_Code_integer,S3: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ T3 )
% 0.29/0.56 => ( ~ ( finite6017078050557962740nteger @ S3 )
% 0.29/0.56 => ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ S3 @ T3 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_infinite_finite
% 0.29/0.56 thf(fact_1495_Diff__infinite__finite,axiom,
% 0.29/0.56 ! [T3: set_nat,S3: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ T3 )
% 0.29/0.56 => ( ~ ( finite_finite_nat @ S3 )
% 0.29/0.56 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S3 @ T3 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_infinite_finite
% 0.29/0.56 thf(fact_1496_Diff__mono,axiom,
% 0.29/0.56 ! [A4: set_nat,C3: set_nat,D4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 0.29/0.56 => ( ( ord_less_eq_set_nat @ D4 @ B4 )
% 0.29/0.56 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ ( minus_minus_set_nat @ C3 @ D4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_mono
% 0.29/0.56 thf(fact_1497_Diff__mono,axiom,
% 0.29/0.56 ! [A4: set_int,C3: set_int,D4: set_int,B4: set_int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ A4 @ C3 )
% 0.29/0.56 => ( ( ord_less_eq_set_int @ D4 @ B4 )
% 0.29/0.56 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B4 ) @ ( minus_minus_set_int @ C3 @ D4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_mono
% 0.29/0.56 thf(fact_1498_Diff__subset,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ A4 ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_subset
% 0.29/0.56 thf(fact_1499_Diff__subset,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B4 ) @ A4 ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_subset
% 0.29/0.56 thf(fact_1500_double__diff,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat,C3: set_nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.56 => ( ( ord_less_eq_set_nat @ B4 @ C3 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C3 @ A4 ) )
% 0.29/0.56 = A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % double_diff
% 0.29/0.56 thf(fact_1501_double__diff,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int,C3: set_int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.56 => ( ( ord_less_eq_set_int @ B4 @ C3 )
% 0.29/0.56 => ( ( minus_minus_set_int @ B4 @ ( minus_minus_set_int @ C3 @ A4 ) )
% 0.29/0.56 = A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % double_diff
% 0.29/0.56 thf(fact_1502_psubset__imp__ex__mem,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( ord_le3480810397992357184T_VEBT @ A4 @ B4 )
% 0.29/0.56 => ? [B3: vEBT_VEBT] : ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % psubset_imp_ex_mem
% 0.29/0.56 thf(fact_1503_psubset__imp__ex__mem,axiom,
% 0.29/0.56 ! [A4: set_real,B4: set_real] :
% 0.29/0.56 ( ( ord_less_set_real @ A4 @ B4 )
% 0.29/0.56 => ? [B3: real] : ( member_real @ B3 @ ( minus_minus_set_real @ B4 @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % psubset_imp_ex_mem
% 0.29/0.56 thf(fact_1504_psubset__imp__ex__mem,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( ord_less_set_int @ A4 @ B4 )
% 0.29/0.56 => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B4 @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % psubset_imp_ex_mem
% 0.29/0.56 thf(fact_1505_psubset__imp__ex__mem,axiom,
% 0.29/0.56 ! [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( ord_less_set_set_nat @ A4 @ B4 )
% 0.29/0.56 => ? [B3: set_nat] : ( member_set_nat @ B3 @ ( minus_2163939370556025621et_nat @ B4 @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % psubset_imp_ex_mem
% 0.29/0.56 thf(fact_1506_psubset__imp__ex__mem,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( ord_less_set_nat @ A4 @ B4 )
% 0.29/0.56 => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B4 @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % psubset_imp_ex_mem
% 0.29/0.56 thf(fact_1507_subset__minus__empty,axiom,
% 0.29/0.56 ! [A4: set_o,B4: set_o] :
% 0.29/0.56 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_o @ A4 @ B4 )
% 0.29/0.56 = bot_bot_set_o ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_minus_empty
% 0.29/0.56 thf(fact_1508_subset__minus__empty,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ A4 @ B4 )
% 0.29/0.56 = bot_bot_set_nat ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_minus_empty
% 0.29/0.56 thf(fact_1509_subset__minus__empty,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_int @ A4 @ B4 )
% 0.29/0.56 = bot_bot_set_int ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_minus_empty
% 0.29/0.56 thf(fact_1510_vebt__delete_Osimps_I4_J,axiom,
% 0.29/0.56 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 0.29/0.56 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu2 )
% 0.29/0.56 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 0.29/0.56
% 0.29/0.56 % vebt_delete.simps(4)
% 0.29/0.56 thf(fact_1511_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 0.29/0.56 ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.minNull.simps(4)
% 0.29/0.56 thf(fact_1512_vebt__member_Osimps_I2_J,axiom,
% 0.29/0.56 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X: nat] :
% 0.29/0.56 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X ) ).
% 0.29/0.56
% 0.29/0.56 % vebt_member.simps(2)
% 0.29/0.56 thf(fact_1513_vebt__member__code_I2_J,axiom,
% 0.29/0.56 ! [T: nat,R: list_VEBT_VEBT,E2: vEBT_VEBT,X: nat] :
% 0.29/0.56 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ T @ R @ E2 ) @ X ) ).
% 0.29/0.56
% 0.29/0.56 % vebt_member_code(2)
% 0.29/0.56 thf(fact_1514_bijective__def,axiom,
% 0.29/0.56 ( biject2923219584331114343uint32
% 0.29/0.56 = ( ^ [R3: set_Pr1773385645901665561uint32] :
% 0.29/0.56 ( ! [X4: uint32,Y4: uint32,Z2: uint32] :
% 0.29/0.56 ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R3 )
% 0.29/0.56 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( Y4 = Z2 ) )
% 0.29/0.56 & ! [X4: uint32,Y4: uint32,Z2: uint32] :
% 0.29/0.56 ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Z2 ) @ R3 )
% 0.29/0.56 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( X4 = Y4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % bijective_def
% 0.29/0.56 thf(fact_1515_bijective__def,axiom,
% 0.29/0.56 ( bijective_nat_nat
% 0.29/0.56 = ( ^ [R3: set_Pr1261947904930325089at_nat] :
% 0.29/0.56 ( ! [X4: nat,Y4: nat,Z2: nat] :
% 0.29/0.56 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R3 )
% 0.29/0.56 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( Y4 = Z2 ) )
% 0.29/0.56 & ! [X4: nat,Y4: nat,Z2: nat] :
% 0.29/0.56 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Z2 ) @ R3 )
% 0.29/0.56 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( X4 = Y4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % bijective_def
% 0.29/0.56 thf(fact_1516_bijective__def,axiom,
% 0.29/0.56 ( bijective_int_int
% 0.29/0.56 = ( ^ [R3: set_Pr958786334691620121nt_int] :
% 0.29/0.56 ( ! [X4: int,Y4: int,Z2: int] :
% 0.29/0.56 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R3 )
% 0.29/0.56 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( Y4 = Z2 ) )
% 0.29/0.56 & ! [X4: int,Y4: int,Z2: int] :
% 0.29/0.56 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z2 ) @ R3 )
% 0.29/0.56 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( X4 = Y4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % bijective_def
% 0.29/0.56 thf(fact_1517_bijective__def,axiom,
% 0.29/0.56 ( biject2615096655818420098et_nat
% 0.29/0.56 = ( ^ [R3: set_Pr3286484037609594932et_nat] :
% 0.29/0.56 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat,Z2: produc3658429121746597890et_nat] :
% 0.29/0.56 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R3 )
% 0.29/0.56 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( Y4 = Z2 ) )
% 0.29/0.56 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z2: produc3658429121746597890et_nat] :
% 0.29/0.56 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z2 ) @ R3 )
% 0.29/0.56 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( X4 = Y4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % bijective_def
% 0.29/0.56 thf(fact_1518_bijective__def,axiom,
% 0.29/0.56 ( biject1468766312547416318et_nat
% 0.29/0.56 = ( ^ [R3: set_Pr8536935166611901872et_nat] :
% 0.29/0.56 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat,Z2: produc3925858234332021118et_nat] :
% 0.29/0.56 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R3 )
% 0.29/0.56 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( Y4 = Z2 ) )
% 0.29/0.56 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z2: produc3925858234332021118et_nat] :
% 0.29/0.56 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z2 ) @ R3 )
% 0.29/0.56 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y4 @ Z2 ) @ R3 ) )
% 0.29/0.56 => ( X4 = Y4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % bijective_def
% 0.29/0.56 thf(fact_1519_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT] :
% 0.29/0.56 ( ( vEBT_VEBT_minNull @ X )
% 0.29/0.56 => ( ( X
% 0.29/0.56 != ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.56 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.minNull.elims(2)
% 0.29/0.56 thf(fact_1520_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 0.29/0.56 ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz: nat] :
% 0.29/0.56 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.membermima.simps(2)
% 0.29/0.56 thf(fact_1521_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J,axiom,
% 0.29/0.56 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 0.29/0.56 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu2 )
% 0.29/0.56 = one_one_nat ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(4)
% 0.29/0.56 thf(fact_1522_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I4_J,axiom,
% 0.29/0.56 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 0.29/0.56 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu2 )
% 0.29/0.56 = one_one_nat ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(4)
% 0.29/0.56 thf(fact_1523_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,Y: $o] :
% 0.29/0.56 ( ( ( vEBT_VEBT_minNull @ X )
% 0.29/0.56 = Y )
% 0.29/0.56 => ( ( ( X
% 0.29/0.56 = ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.56 => ~ Y )
% 0.29/0.56 => ( ( ? [Uv: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 = ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.56 => Y )
% 0.29/0.56 => ( ( ? [Uu: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 = ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.56 => Y )
% 0.29/0.56 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.29/0.56 => ~ Y )
% 0.29/0.56 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.29/0.56 => Y ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % VEBT_internal.minNull.elims(1)
% 0.29/0.56 thf(fact_1524_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 0.29/0.56 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.56 ( ! [Uu: $o,Uv: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) )
% 0.29/0.56 => ( ! [A3: $o,Uw: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 0.29/0.56 => ( ! [A3: $o,B3: $o,Va: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) )
% 0.29/0.56 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Vb2 ) )
% 0.29/0.56 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf ) )
% 0.29/0.56 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 0.29/0.56 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.cases
% 0.29/0.56 thf(fact_1525_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 0.29/0.56 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.56 ( ! [Uu: $o,B3: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) )
% 0.29/0.56 => ( ! [Uv: $o,Uw: $o,N2: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) )
% 0.29/0.56 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Va3 ) )
% 0.29/0.56 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve ) )
% 0.29/0.56 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 0.29/0.56 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.cases
% 0.29/0.56 thf(fact_1526_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 0.29/0.56 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.56 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.29/0.56 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ X3 ) )
% 0.29/0.56 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ X3 ) )
% 0.29/0.56 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 0.29/0.56 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.cases
% 0.29/0.56 thf(fact_1527_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 0.29/0.56 ! [X: produc9072475918466114483BT_nat] :
% 0.29/0.56 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.29/0.56 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X3 ) )
% 0.29/0.56 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ X3 ) )
% 0.29/0.56 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 0.29/0.56 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 0.29/0.56 thf(fact_1528_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT] :
% 0.29/0.56 ( ! [A3: $o,B3: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Leaf @ A3 @ B3 ) )
% 0.29/0.56 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.56 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.cases
% 0.29/0.56 thf(fact_1529_List_Ofinite__set,axiom,
% 0.29/0.56 ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 0.29/0.56
% 0.29/0.56 % List.finite_set
% 0.29/0.56 thf(fact_1530_List_Ofinite__set,axiom,
% 0.29/0.56 ! [Xs: list_real] : ( finite_finite_real @ ( set_real2 @ Xs ) ) ).
% 0.29/0.56
% 0.29/0.56 % List.finite_set
% 0.29/0.56 thf(fact_1531_List_Ofinite__set,axiom,
% 0.29/0.56 ! [Xs: list_o] : ( finite_finite_o @ ( set_o2 @ Xs ) ) ).
% 0.29/0.56
% 0.29/0.56 % List.finite_set
% 0.29/0.56 thf(fact_1532_List_Ofinite__set,axiom,
% 0.29/0.56 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 0.29/0.56
% 0.29/0.56 % List.finite_set
% 0.29/0.56 thf(fact_1533_List_Ofinite__set,axiom,
% 0.29/0.56 ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 0.29/0.56
% 0.29/0.56 % List.finite_set
% 0.29/0.56 thf(fact_1534_List_Ofinite__set,axiom,
% 0.29/0.56 ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 0.29/0.56
% 0.29/0.56 % List.finite_set
% 0.29/0.56 thf(fact_1535_List_Ofinite__set,axiom,
% 0.29/0.56 ! [Xs: list_Code_integer] : ( finite6017078050557962740nteger @ ( set_Code_integer2 @ Xs ) ) ).
% 0.29/0.56
% 0.29/0.56 % List.finite_set
% 0.29/0.56 thf(fact_1536_delete__correct,axiom,
% 0.29/0.56 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.56 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.56 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 0.29/0.56 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % delete_correct
% 0.29/0.56 thf(fact_1537_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT] :
% 0.29/0.56 ( ( X
% 0.29/0.56 != ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.56 => ( ! [Uv: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.56 => ( ! [Uu: $o] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.56 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.29/0.56 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.56 ( X
% 0.29/0.56 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.cases
% 0.29/0.56 thf(fact_1538_insertCI,axiom,
% 0.29/0.56 ! [A: $o,B4: set_o,B: $o] :
% 0.29/0.56 ( ( ~ ( member_o @ A @ B4 )
% 0.29/0.56 => ( A = B ) )
% 0.29/0.56 => ( member_o @ A @ ( insert_o @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertCI
% 0.29/0.56 thf(fact_1539_insertCI,axiom,
% 0.29/0.56 ! [A: nat,B4: set_nat,B: nat] :
% 0.29/0.56 ( ( ~ ( member_nat @ A @ B4 )
% 0.29/0.56 => ( A = B ) )
% 0.29/0.56 => ( member_nat @ A @ ( insert_nat @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertCI
% 0.29/0.56 thf(fact_1540_insertCI,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,B4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.29/0.56 ( ( ~ ( member_VEBT_VEBT @ A @ B4 )
% 0.29/0.56 => ( A = B ) )
% 0.29/0.56 => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertCI
% 0.29/0.56 thf(fact_1541_insertCI,axiom,
% 0.29/0.56 ! [A: real,B4: set_real,B: real] :
% 0.29/0.56 ( ( ~ ( member_real @ A @ B4 )
% 0.29/0.56 => ( A = B ) )
% 0.29/0.56 => ( member_real @ A @ ( insert_real @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertCI
% 0.29/0.56 thf(fact_1542_insertCI,axiom,
% 0.29/0.56 ! [A: int,B4: set_int,B: int] :
% 0.29/0.56 ( ( ~ ( member_int @ A @ B4 )
% 0.29/0.56 => ( A = B ) )
% 0.29/0.56 => ( member_int @ A @ ( insert_int @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertCI
% 0.29/0.56 thf(fact_1543_insertCI,axiom,
% 0.29/0.56 ! [A: set_nat,B4: set_set_nat,B: set_nat] :
% 0.29/0.56 ( ( ~ ( member_set_nat @ A @ B4 )
% 0.29/0.56 => ( A = B ) )
% 0.29/0.56 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertCI
% 0.29/0.56 thf(fact_1544_insert__iff,axiom,
% 0.29/0.56 ! [A: $o,B: $o,A4: set_o] :
% 0.29/0.56 ( ( member_o @ A @ ( insert_o @ B @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 | ( member_o @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_iff
% 0.29/0.56 thf(fact_1545_insert__iff,axiom,
% 0.29/0.56 ! [A: nat,B: nat,A4: set_nat] :
% 0.29/0.56 ( ( member_nat @ A @ ( insert_nat @ B @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 | ( member_nat @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_iff
% 0.29/0.56 thf(fact_1546_insert__iff,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,B: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 | ( member_VEBT_VEBT @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_iff
% 0.29/0.56 thf(fact_1547_insert__iff,axiom,
% 0.29/0.56 ! [A: real,B: real,A4: set_real] :
% 0.29/0.56 ( ( member_real @ A @ ( insert_real @ B @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 | ( member_real @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_iff
% 0.29/0.56 thf(fact_1548_insert__iff,axiom,
% 0.29/0.56 ! [A: int,B: int,A4: set_int] :
% 0.29/0.56 ( ( member_int @ A @ ( insert_int @ B @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 | ( member_int @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_iff
% 0.29/0.56 thf(fact_1549_insert__iff,axiom,
% 0.29/0.56 ! [A: set_nat,B: set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 | ( member_set_nat @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_iff
% 0.29/0.56 thf(fact_1550_insert__absorb2,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat] :
% 0.29/0.56 ( ( insert_nat @ X @ ( insert_nat @ X @ A4 ) )
% 0.29/0.56 = ( insert_nat @ X @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb2
% 0.29/0.56 thf(fact_1551_insert__absorb2,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( insert_VEBT_VEBT @ X @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.29/0.56 = ( insert_VEBT_VEBT @ X @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb2
% 0.29/0.56 thf(fact_1552_insert__absorb2,axiom,
% 0.29/0.56 ! [X: int,A4: set_int] :
% 0.29/0.56 ( ( insert_int @ X @ ( insert_int @ X @ A4 ) )
% 0.29/0.56 = ( insert_int @ X @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb2
% 0.29/0.56 thf(fact_1553_insert__absorb2,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o] :
% 0.29/0.56 ( ( insert_o @ X @ ( insert_o @ X @ A4 ) )
% 0.29/0.56 = ( insert_o @ X @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb2
% 0.29/0.56 thf(fact_1554_DiffI,axiom,
% 0.29/0.56 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ C2 @ A4 )
% 0.29/0.56 => ( ~ ( member_VEBT_VEBT @ C2 @ B4 )
% 0.29/0.56 => ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffI
% 0.29/0.56 thf(fact_1555_DiffI,axiom,
% 0.29/0.56 ! [C2: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ( member_real @ C2 @ A4 )
% 0.29/0.56 => ( ~ ( member_real @ C2 @ B4 )
% 0.29/0.56 => ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffI
% 0.29/0.56 thf(fact_1556_DiffI,axiom,
% 0.29/0.56 ! [C2: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( member_int @ C2 @ A4 )
% 0.29/0.56 => ( ~ ( member_int @ C2 @ B4 )
% 0.29/0.56 => ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffI
% 0.29/0.56 thf(fact_1557_DiffI,axiom,
% 0.29/0.56 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ C2 @ A4 )
% 0.29/0.56 => ( ~ ( member_set_nat @ C2 @ B4 )
% 0.29/0.56 => ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffI
% 0.29/0.56 thf(fact_1558_DiffI,axiom,
% 0.29/0.56 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( member_nat @ C2 @ A4 )
% 0.29/0.56 => ( ~ ( member_nat @ C2 @ B4 )
% 0.29/0.56 => ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffI
% 0.29/0.56 thf(fact_1559_Diff__iff,axiom,
% 0.29/0.56 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 0.29/0.56 = ( ( member_VEBT_VEBT @ C2 @ A4 )
% 0.29/0.56 & ~ ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_iff
% 0.29/0.56 thf(fact_1560_Diff__iff,axiom,
% 0.29/0.56 ! [C2: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 0.29/0.56 = ( ( member_real @ C2 @ A4 )
% 0.29/0.56 & ~ ( member_real @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_iff
% 0.29/0.56 thf(fact_1561_Diff__iff,axiom,
% 0.29/0.56 ! [C2: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.29/0.56 = ( ( member_int @ C2 @ A4 )
% 0.29/0.56 & ~ ( member_int @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_iff
% 0.29/0.56 thf(fact_1562_Diff__iff,axiom,
% 0.29/0.56 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 0.29/0.56 = ( ( member_set_nat @ C2 @ A4 )
% 0.29/0.56 & ~ ( member_set_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_iff
% 0.29/0.56 thf(fact_1563_Diff__iff,axiom,
% 0.29/0.56 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.29/0.56 = ( ( member_nat @ C2 @ A4 )
% 0.29/0.56 & ~ ( member_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_iff
% 0.29/0.56 thf(fact_1564_Diff__idemp,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_nat @ A4 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_idemp
% 0.29/0.56 thf(fact_1565_set__vebt__delete,axiom,
% 0.29/0.56 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.56 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.56 => ( ( vEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 0.29/0.56 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % set_vebt_delete
% 0.29/0.56 thf(fact_1566_delete__correct_H,axiom,
% 0.29/0.56 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.56 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.56 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 0.29/0.56 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % delete_correct'
% 0.29/0.56 thf(fact_1567_singletonI,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonI
% 0.29/0.56 thf(fact_1568_singletonI,axiom,
% 0.29/0.56 ! [A: real] : ( member_real @ A @ ( insert_real @ A @ bot_bot_set_real ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonI
% 0.29/0.56 thf(fact_1569_singletonI,axiom,
% 0.29/0.56 ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonI
% 0.29/0.56 thf(fact_1570_singletonI,axiom,
% 0.29/0.56 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonI
% 0.29/0.56 thf(fact_1571_singletonI,axiom,
% 0.29/0.56 ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonI
% 0.29/0.56 thf(fact_1572_singletonI,axiom,
% 0.29/0.56 ! [A: $o] : ( member_o @ A @ ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonI
% 0.29/0.56 thf(fact_1573_finite__insert,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ ( insert_VEBT_VEBT @ A @ A4 ) )
% 0.29/0.56 = ( finite5795047828879050333T_VEBT @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_insert
% 0.29/0.56 thf(fact_1574_finite__insert,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o] :
% 0.29/0.56 ( ( finite_finite_o @ ( insert_o @ A @ A4 ) )
% 0.29/0.56 = ( finite_finite_o @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_insert
% 0.29/0.56 thf(fact_1575_finite__insert,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ ( insert_nat @ A @ A4 ) )
% 0.29/0.56 = ( finite_finite_nat @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_insert
% 0.29/0.56 thf(fact_1576_finite__insert,axiom,
% 0.29/0.56 ! [A: int,A4: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ ( insert_int @ A @ A4 ) )
% 0.29/0.56 = ( finite_finite_int @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_insert
% 0.29/0.56 thf(fact_1577_finite__insert,axiom,
% 0.29/0.56 ! [A: complex,A4: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ ( insert_complex @ A @ A4 ) )
% 0.29/0.56 = ( finite3207457112153483333omplex @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_insert
% 0.29/0.56 thf(fact_1578_finite__insert,axiom,
% 0.29/0.56 ! [A: code_integer,A4: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ ( insert_Code_integer @ A @ A4 ) )
% 0.29/0.56 = ( finite6017078050557962740nteger @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_insert
% 0.29/0.56 thf(fact_1579_insert__subset,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o,B4: set_o] :
% 0.29/0.56 ( ( ord_less_eq_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( ( member_o @ X @ B4 )
% 0.29/0.56 & ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subset
% 0.29/0.56 thf(fact_1580_insert__subset,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( ( member_nat @ X @ B4 )
% 0.29/0.56 & ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subset
% 0.29/0.56 thf(fact_1581_insert__subset,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( ( member_VEBT_VEBT @ X @ B4 )
% 0.29/0.56 & ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subset
% 0.29/0.56 thf(fact_1582_insert__subset,axiom,
% 0.29/0.56 ! [X: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ( ord_less_eq_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( ( member_real @ X @ B4 )
% 0.29/0.56 & ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subset
% 0.29/0.56 thf(fact_1583_insert__subset,axiom,
% 0.29/0.56 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( ( member_set_nat @ X @ B4 )
% 0.29/0.56 & ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subset
% 0.29/0.56 thf(fact_1584_insert__subset,axiom,
% 0.29/0.56 ! [X: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( ( member_int @ X @ B4 )
% 0.29/0.56 & ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subset
% 0.29/0.56 thf(fact_1585_Diff__insert0,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o,B4: set_o] :
% 0.29/0.56 ( ~ ( member_o @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_o @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert0
% 0.29/0.56 thf(fact_1586_Diff__insert0,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ( ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 0.29/0.56 = ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert0
% 0.29/0.56 thf(fact_1587_Diff__insert0,axiom,
% 0.29/0.56 ! [X: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ~ ( member_real @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_real @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert0
% 0.29/0.56 thf(fact_1588_Diff__insert0,axiom,
% 0.29/0.56 ! [X: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ~ ( member_int @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert0
% 0.29/0.56 thf(fact_1589_Diff__insert0,axiom,
% 0.29/0.56 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ~ ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ( ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 0.29/0.56 = ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert0
% 0.29/0.56 thf(fact_1590_Diff__insert0,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ~ ( member_nat @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert0
% 0.29/0.56 thf(fact_1591_insert__Diff1,axiom,
% 0.29/0.56 ! [X: $o,B4: set_o,A4: set_o] :
% 0.29/0.56 ( ( member_o @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_o @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff1
% 0.29/0.56 thf(fact_1592_insert__Diff1,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,B4: set_VEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ X @ B4 )
% 0.29/0.56 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff1
% 0.29/0.56 thf(fact_1593_insert__Diff1,axiom,
% 0.29/0.56 ! [X: real,B4: set_real,A4: set_real] :
% 0.29/0.56 ( ( member_real @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_real @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff1
% 0.29/0.56 thf(fact_1594_insert__Diff1,axiom,
% 0.29/0.56 ! [X: int,B4: set_int,A4: set_int] :
% 0.29/0.56 ( ( member_int @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff1
% 0.29/0.56 thf(fact_1595_insert__Diff1,axiom,
% 0.29/0.56 ! [X: set_nat,B4: set_set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ X @ B4 )
% 0.29/0.56 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff1
% 0.29/0.56 thf(fact_1596_insert__Diff1,axiom,
% 0.29/0.56 ! [X: nat,B4: set_nat,A4: set_nat] :
% 0.29/0.56 ( ( member_nat @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff1
% 0.29/0.56 thf(fact_1597_singleton__insert__inj__eq_H,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.29/0.56 ( ( ( insert_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 = ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq'
% 0.29/0.56 thf(fact_1598_singleton__insert__inj__eq_H,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat,B: nat] :
% 0.29/0.56 ( ( ( insert_nat @ A @ A4 )
% 0.29/0.56 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq'
% 0.29/0.56 thf(fact_1599_singleton__insert__inj__eq_H,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o,B: $o] :
% 0.29/0.56 ( ( ( insert_o @ A @ A4 )
% 0.29/0.56 = ( insert_o @ B @ bot_bot_set_o ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq'
% 0.29/0.56 thf(fact_1600_singleton__insert__inj__eq_H,axiom,
% 0.29/0.56 ! [A: int,A4: set_int,B: int] :
% 0.29/0.56 ( ( ( insert_int @ A @ A4 )
% 0.29/0.56 = ( insert_int @ B @ bot_bot_set_int ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq'
% 0.29/0.56 thf(fact_1601_singleton__insert__inj__eq,axiom,
% 0.29/0.56 ! [B: vEBT_VEBT,A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 = ( insert_VEBT_VEBT @ A @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq
% 0.29/0.56 thf(fact_1602_singleton__insert__inj__eq,axiom,
% 0.29/0.56 ! [B: nat,A: nat,A4: set_nat] :
% 0.29/0.56 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 0.29/0.56 = ( insert_nat @ A @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq
% 0.29/0.56 thf(fact_1603_singleton__insert__inj__eq,axiom,
% 0.29/0.56 ! [B: $o,A: $o,A4: set_o] :
% 0.29/0.56 ( ( ( insert_o @ B @ bot_bot_set_o )
% 0.29/0.56 = ( insert_o @ A @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq
% 0.29/0.56 thf(fact_1604_singleton__insert__inj__eq,axiom,
% 0.29/0.56 ! [B: int,A: int,A4: set_int] :
% 0.29/0.56 ( ( ( insert_int @ B @ bot_bot_set_int )
% 0.29/0.56 = ( insert_int @ A @ A4 ) )
% 0.29/0.56 = ( ( A = B )
% 0.29/0.56 & ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_insert_inj_eq
% 0.29/0.56 thf(fact_1605_insert__Diff__single,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.29/0.56 = ( insert_VEBT_VEBT @ A @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_single
% 0.29/0.56 thf(fact_1606_insert__Diff__single,axiom,
% 0.29/0.56 ! [A: int,A4: set_int] :
% 0.29/0.56 ( ( insert_int @ A @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.29/0.56 = ( insert_int @ A @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_single
% 0.29/0.56 thf(fact_1607_insert__Diff__single,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o] :
% 0.29/0.56 ( ( insert_o @ A @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.29/0.56 = ( insert_o @ A @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_single
% 0.29/0.56 thf(fact_1608_insert__Diff__single,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat] :
% 0.29/0.56 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.29/0.56 = ( insert_nat @ A @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_single
% 0.29/0.56 thf(fact_1609_finite__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) ) )
% 0.29/0.56 = ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff_insert
% 0.29/0.56 thf(fact_1610_finite__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_o,A: $o,B4: set_o] :
% 0.29/0.56 ( ( finite_finite_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) ) )
% 0.29/0.56 = ( finite_finite_o @ ( minus_minus_set_o @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff_insert
% 0.29/0.56 thf(fact_1611_finite__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_int,A: int,B4: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) ) )
% 0.29/0.56 = ( finite_finite_int @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff_insert
% 0.29/0.56 thf(fact_1612_finite__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_complex,A: complex,B4: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ B4 ) ) )
% 0.29/0.56 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff_insert
% 0.29/0.56 thf(fact_1613_finite__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_Code_integer,A: code_integer,B4: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ B4 ) ) )
% 0.29/0.56 = ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff_insert
% 0.29/0.56 thf(fact_1614_finite__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_nat,A: nat,B4: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) ) )
% 0.29/0.56 = ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_Diff_insert
% 0.29/0.56 thf(fact_1615_DiffE,axiom,
% 0.29/0.56 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( ( member_VEBT_VEBT @ C2 @ A4 )
% 0.29/0.56 => ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffE
% 0.29/0.56 thf(fact_1616_DiffE,axiom,
% 0.29/0.56 ! [C2: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( ( member_real @ C2 @ A4 )
% 0.29/0.56 => ( member_real @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffE
% 0.29/0.56 thf(fact_1617_DiffE,axiom,
% 0.29/0.56 ! [C2: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( ( member_int @ C2 @ A4 )
% 0.29/0.56 => ( member_int @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffE
% 0.29/0.56 thf(fact_1618_DiffE,axiom,
% 0.29/0.56 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( ( member_set_nat @ C2 @ A4 )
% 0.29/0.56 => ( member_set_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffE
% 0.29/0.56 thf(fact_1619_DiffE,axiom,
% 0.29/0.56 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( ( member_nat @ C2 @ A4 )
% 0.29/0.56 => ( member_nat @ C2 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffE
% 0.29/0.56 thf(fact_1620_DiffD1,axiom,
% 0.29/0.56 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 0.29/0.56 => ( member_VEBT_VEBT @ C2 @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD1
% 0.29/0.56 thf(fact_1621_DiffD1,axiom,
% 0.29/0.56 ! [C2: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 0.29/0.56 => ( member_real @ C2 @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD1
% 0.29/0.56 thf(fact_1622_DiffD1,axiom,
% 0.29/0.56 ! [C2: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.29/0.56 => ( member_int @ C2 @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD1
% 0.29/0.56 thf(fact_1623_DiffD1,axiom,
% 0.29/0.56 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 0.29/0.56 => ( member_set_nat @ C2 @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD1
% 0.29/0.56 thf(fact_1624_DiffD1,axiom,
% 0.29/0.56 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.29/0.56 => ( member_nat @ C2 @ A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD1
% 0.29/0.56 thf(fact_1625_DiffD2,axiom,
% 0.29/0.56 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( member_VEBT_VEBT @ C2 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD2
% 0.29/0.56 thf(fact_1626_DiffD2,axiom,
% 0.29/0.56 ! [C2: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( member_real @ C2 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD2
% 0.29/0.56 thf(fact_1627_DiffD2,axiom,
% 0.29/0.56 ! [C2: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( member_int @ C2 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD2
% 0.29/0.56 thf(fact_1628_DiffD2,axiom,
% 0.29/0.56 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( member_set_nat @ C2 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD2
% 0.29/0.56 thf(fact_1629_DiffD2,axiom,
% 0.29/0.56 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.29/0.56 => ~ ( member_nat @ C2 @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % DiffD2
% 0.29/0.56 thf(fact_1630_insert__Diff__if,axiom,
% 0.29/0.56 ! [X: $o,B4: set_o,A4: set_o] :
% 0.29/0.56 ( ( ( member_o @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_o @ A4 @ B4 ) ) )
% 0.29/0.56 & ( ~ ( member_o @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( insert_o @ X @ ( minus_minus_set_o @ A4 @ B4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_if
% 0.29/0.56 thf(fact_1631_insert__Diff__if,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,B4: set_VEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( ( member_VEBT_VEBT @ X @ B4 )
% 0.29/0.56 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) )
% 0.29/0.56 & ( ~ ( member_VEBT_VEBT @ X @ B4 )
% 0.29/0.56 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_if
% 0.29/0.56 thf(fact_1632_insert__Diff__if,axiom,
% 0.29/0.56 ! [X: real,B4: set_real,A4: set_real] :
% 0.29/0.56 ( ( ( member_real @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_real @ A4 @ B4 ) ) )
% 0.29/0.56 & ( ~ ( member_real @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( insert_real @ X @ ( minus_minus_set_real @ A4 @ B4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_if
% 0.29/0.56 thf(fact_1633_insert__Diff__if,axiom,
% 0.29/0.56 ! [X: int,B4: set_int,A4: set_int] :
% 0.29/0.56 ( ( ( member_int @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_int @ A4 @ B4 ) ) )
% 0.29/0.56 & ( ~ ( member_int @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( insert_int @ X @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_if
% 0.29/0.56 thf(fact_1634_insert__Diff__if,axiom,
% 0.29/0.56 ! [X: set_nat,B4: set_set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( ( member_set_nat @ X @ B4 )
% 0.29/0.56 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) )
% 0.29/0.56 & ( ~ ( member_set_nat @ X @ B4 )
% 0.29/0.56 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_if
% 0.29/0.56 thf(fact_1635_insert__Diff__if,axiom,
% 0.29/0.56 ! [X: nat,B4: set_nat,A4: set_nat] :
% 0.29/0.56 ( ( ( member_nat @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( minus_minus_set_nat @ A4 @ B4 ) ) )
% 0.29/0.56 & ( ~ ( member_nat @ X @ B4 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 0.29/0.56 = ( insert_nat @ X @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff_if
% 0.29/0.56 thf(fact_1636_insertE,axiom,
% 0.29/0.56 ! [A: $o,B: $o,A4: set_o] :
% 0.29/0.56 ( ( member_o @ A @ ( insert_o @ B @ A4 ) )
% 0.29/0.56 => ( ( A = ( ~ B ) )
% 0.29/0.56 => ( member_o @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertE
% 0.29/0.56 thf(fact_1637_insertE,axiom,
% 0.29/0.56 ! [A: nat,B: nat,A4: set_nat] :
% 0.29/0.56 ( ( member_nat @ A @ ( insert_nat @ B @ A4 ) )
% 0.29/0.56 => ( ( A != B )
% 0.29/0.56 => ( member_nat @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertE
% 0.29/0.56 thf(fact_1638_insertE,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,B: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A4 ) )
% 0.29/0.56 => ( ( A != B )
% 0.29/0.56 => ( member_VEBT_VEBT @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertE
% 0.29/0.56 thf(fact_1639_insertE,axiom,
% 0.29/0.56 ! [A: real,B: real,A4: set_real] :
% 0.29/0.56 ( ( member_real @ A @ ( insert_real @ B @ A4 ) )
% 0.29/0.56 => ( ( A != B )
% 0.29/0.56 => ( member_real @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertE
% 0.29/0.56 thf(fact_1640_insertE,axiom,
% 0.29/0.56 ! [A: int,B: int,A4: set_int] :
% 0.29/0.56 ( ( member_int @ A @ ( insert_int @ B @ A4 ) )
% 0.29/0.56 => ( ( A != B )
% 0.29/0.56 => ( member_int @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertE
% 0.29/0.56 thf(fact_1641_insertE,axiom,
% 0.29/0.56 ! [A: set_nat,B: set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A4 ) )
% 0.29/0.56 => ( ( A != B )
% 0.29/0.56 => ( member_set_nat @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertE
% 0.29/0.56 thf(fact_1642_insertI1,axiom,
% 0.29/0.56 ! [A: $o,B4: set_o] : ( member_o @ A @ ( insert_o @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI1
% 0.29/0.56 thf(fact_1643_insertI1,axiom,
% 0.29/0.56 ! [A: nat,B4: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI1
% 0.29/0.56 thf(fact_1644_insertI1,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,B4: set_VEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI1
% 0.29/0.56 thf(fact_1645_insertI1,axiom,
% 0.29/0.56 ! [A: real,B4: set_real] : ( member_real @ A @ ( insert_real @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI1
% 0.29/0.56 thf(fact_1646_insertI1,axiom,
% 0.29/0.56 ! [A: int,B4: set_int] : ( member_int @ A @ ( insert_int @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI1
% 0.29/0.56 thf(fact_1647_insertI1,axiom,
% 0.29/0.56 ! [A: set_nat,B4: set_set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI1
% 0.29/0.56 thf(fact_1648_insertI2,axiom,
% 0.29/0.56 ! [A: $o,B4: set_o,B: $o] :
% 0.29/0.56 ( ( member_o @ A @ B4 )
% 0.29/0.56 => ( member_o @ A @ ( insert_o @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI2
% 0.29/0.56 thf(fact_1649_insertI2,axiom,
% 0.29/0.56 ! [A: nat,B4: set_nat,B: nat] :
% 0.29/0.56 ( ( member_nat @ A @ B4 )
% 0.29/0.56 => ( member_nat @ A @ ( insert_nat @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI2
% 0.29/0.56 thf(fact_1650_insertI2,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,B4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ A @ B4 )
% 0.29/0.56 => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI2
% 0.29/0.56 thf(fact_1651_insertI2,axiom,
% 0.29/0.56 ! [A: real,B4: set_real,B: real] :
% 0.29/0.56 ( ( member_real @ A @ B4 )
% 0.29/0.56 => ( member_real @ A @ ( insert_real @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI2
% 0.29/0.56 thf(fact_1652_insertI2,axiom,
% 0.29/0.56 ! [A: int,B4: set_int,B: int] :
% 0.29/0.56 ( ( member_int @ A @ B4 )
% 0.29/0.56 => ( member_int @ A @ ( insert_int @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI2
% 0.29/0.56 thf(fact_1653_insertI2,axiom,
% 0.29/0.56 ! [A: set_nat,B4: set_set_nat,B: set_nat] :
% 0.29/0.56 ( ( member_set_nat @ A @ B4 )
% 0.29/0.56 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insertI2
% 0.29/0.56 thf(fact_1654_Set_Oset__insert,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o] :
% 0.29/0.56 ( ( member_o @ X @ A4 )
% 0.29/0.56 => ~ ! [B8: set_o] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_o @ X @ B8 ) )
% 0.29/0.56 => ( member_o @ X @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Set.set_insert
% 0.29/0.56 thf(fact_1655_Set_Oset__insert,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat] :
% 0.29/0.56 ( ( member_nat @ X @ A4 )
% 0.29/0.56 => ~ ! [B8: set_nat] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_nat @ X @ B8 ) )
% 0.29/0.56 => ( member_nat @ X @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Set.set_insert
% 0.29/0.56 thf(fact_1656_Set_Oset__insert,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ~ ! [B8: set_VEBT_VEBT] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_VEBT_VEBT @ X @ B8 ) )
% 0.29/0.56 => ( member_VEBT_VEBT @ X @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Set.set_insert
% 0.29/0.56 thf(fact_1657_Set_Oset__insert,axiom,
% 0.29/0.56 ! [X: real,A4: set_real] :
% 0.29/0.56 ( ( member_real @ X @ A4 )
% 0.29/0.56 => ~ ! [B8: set_real] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_real @ X @ B8 ) )
% 0.29/0.56 => ( member_real @ X @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Set.set_insert
% 0.29/0.56 thf(fact_1658_Set_Oset__insert,axiom,
% 0.29/0.56 ! [X: int,A4: set_int] :
% 0.29/0.56 ( ( member_int @ X @ A4 )
% 0.29/0.56 => ~ ! [B8: set_int] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_int @ X @ B8 ) )
% 0.29/0.56 => ( member_int @ X @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Set.set_insert
% 0.29/0.56 thf(fact_1659_Set_Oset__insert,axiom,
% 0.29/0.56 ! [X: set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ~ ! [B8: set_set_nat] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_set_nat @ X @ B8 ) )
% 0.29/0.56 => ( member_set_nat @ X @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Set.set_insert
% 0.29/0.56 thf(fact_1660_insert__ident,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o,B4: set_o] :
% 0.29/0.56 ( ~ ( member_o @ X @ A4 )
% 0.29/0.56 => ( ~ ( member_o @ X @ B4 )
% 0.29/0.56 => ( ( ( insert_o @ X @ A4 )
% 0.29/0.56 = ( insert_o @ X @ B4 ) )
% 0.29/0.56 = ( A4 = B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_ident
% 0.29/0.56 thf(fact_1661_insert__ident,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ~ ( member_nat @ X @ A4 )
% 0.29/0.56 => ( ~ ( member_nat @ X @ B4 )
% 0.29/0.56 => ( ( ( insert_nat @ X @ A4 )
% 0.29/0.56 = ( insert_nat @ X @ B4 ) )
% 0.29/0.56 = ( A4 = B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_ident
% 0.29/0.56 thf(fact_1662_insert__ident,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ( ~ ( member_VEBT_VEBT @ X @ B4 )
% 0.29/0.56 => ( ( ( insert_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 = ( insert_VEBT_VEBT @ X @ B4 ) )
% 0.29/0.56 = ( A4 = B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_ident
% 0.29/0.56 thf(fact_1663_insert__ident,axiom,
% 0.29/0.56 ! [X: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ~ ( member_real @ X @ A4 )
% 0.29/0.56 => ( ~ ( member_real @ X @ B4 )
% 0.29/0.56 => ( ( ( insert_real @ X @ A4 )
% 0.29/0.56 = ( insert_real @ X @ B4 ) )
% 0.29/0.56 = ( A4 = B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_ident
% 0.29/0.56 thf(fact_1664_insert__ident,axiom,
% 0.29/0.56 ! [X: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ~ ( member_int @ X @ A4 )
% 0.29/0.56 => ( ~ ( member_int @ X @ B4 )
% 0.29/0.56 => ( ( ( insert_int @ X @ A4 )
% 0.29/0.56 = ( insert_int @ X @ B4 ) )
% 0.29/0.56 = ( A4 = B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_ident
% 0.29/0.56 thf(fact_1665_insert__ident,axiom,
% 0.29/0.56 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ~ ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ( ~ ( member_set_nat @ X @ B4 )
% 0.29/0.56 => ( ( ( insert_set_nat @ X @ A4 )
% 0.29/0.56 = ( insert_set_nat @ X @ B4 ) )
% 0.29/0.56 = ( A4 = B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_ident
% 0.29/0.56 thf(fact_1666_insert__absorb,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o] :
% 0.29/0.56 ( ( member_o @ A @ A4 )
% 0.29/0.56 => ( ( insert_o @ A @ A4 )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb
% 0.29/0.56 thf(fact_1667_insert__absorb,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat] :
% 0.29/0.56 ( ( member_nat @ A @ A4 )
% 0.29/0.56 => ( ( insert_nat @ A @ A4 )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb
% 0.29/0.56 thf(fact_1668_insert__absorb,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 => ( ( insert_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb
% 0.29/0.56 thf(fact_1669_insert__absorb,axiom,
% 0.29/0.56 ! [A: real,A4: set_real] :
% 0.29/0.56 ( ( member_real @ A @ A4 )
% 0.29/0.56 => ( ( insert_real @ A @ A4 )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb
% 0.29/0.56 thf(fact_1670_insert__absorb,axiom,
% 0.29/0.56 ! [A: int,A4: set_int] :
% 0.29/0.56 ( ( member_int @ A @ A4 )
% 0.29/0.56 => ( ( insert_int @ A @ A4 )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb
% 0.29/0.56 thf(fact_1671_insert__absorb,axiom,
% 0.29/0.56 ! [A: set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ A @ A4 )
% 0.29/0.56 => ( ( insert_set_nat @ A @ A4 )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_absorb
% 0.29/0.56 thf(fact_1672_insert__eq__iff,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o,B: $o,B4: set_o] :
% 0.29/0.56 ( ~ ( member_o @ A @ A4 )
% 0.29/0.56 => ( ~ ( member_o @ B @ B4 )
% 0.29/0.56 => ( ( ( insert_o @ A @ A4 )
% 0.29/0.56 = ( insert_o @ B @ B4 ) )
% 0.29/0.56 = ( ( ( A = B )
% 0.29/0.56 => ( A4 = B4 ) )
% 0.29/0.56 & ( ( A = ( ~ B ) )
% 0.29/0.56 => ? [C4: set_o] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_o @ B @ C4 ) )
% 0.29/0.56 & ~ ( member_o @ B @ C4 )
% 0.29/0.56 & ( B4
% 0.29/0.56 = ( insert_o @ A @ C4 ) )
% 0.29/0.56 & ~ ( member_o @ A @ C4 ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_eq_iff
% 0.29/0.56 thf(fact_1673_insert__eq__iff,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat,B: nat,B4: set_nat] :
% 0.29/0.56 ( ~ ( member_nat @ A @ A4 )
% 0.29/0.56 => ( ~ ( member_nat @ B @ B4 )
% 0.29/0.56 => ( ( ( insert_nat @ A @ A4 )
% 0.29/0.56 = ( insert_nat @ B @ B4 ) )
% 0.29/0.56 = ( ( ( A = B )
% 0.29/0.56 => ( A4 = B4 ) )
% 0.29/0.56 & ( ( A != B )
% 0.29/0.56 => ? [C4: set_nat] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_nat @ B @ C4 ) )
% 0.29/0.56 & ~ ( member_nat @ B @ C4 )
% 0.29/0.56 & ( B4
% 0.29/0.56 = ( insert_nat @ A @ C4 ) )
% 0.29/0.56 & ~ ( member_nat @ A @ C4 ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_eq_iff
% 0.29/0.56 thf(fact_1674_insert__eq__iff,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 => ( ~ ( member_VEBT_VEBT @ B @ B4 )
% 0.29/0.56 => ( ( ( insert_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 = ( insert_VEBT_VEBT @ B @ B4 ) )
% 0.29/0.56 = ( ( ( A = B )
% 0.29/0.56 => ( A4 = B4 ) )
% 0.29/0.56 & ( ( A != B )
% 0.29/0.56 => ? [C4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_VEBT_VEBT @ B @ C4 ) )
% 0.29/0.56 & ~ ( member_VEBT_VEBT @ B @ C4 )
% 0.29/0.56 & ( B4
% 0.29/0.56 = ( insert_VEBT_VEBT @ A @ C4 ) )
% 0.29/0.56 & ~ ( member_VEBT_VEBT @ A @ C4 ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_eq_iff
% 0.29/0.56 thf(fact_1675_insert__eq__iff,axiom,
% 0.29/0.56 ! [A: real,A4: set_real,B: real,B4: set_real] :
% 0.29/0.56 ( ~ ( member_real @ A @ A4 )
% 0.29/0.56 => ( ~ ( member_real @ B @ B4 )
% 0.29/0.56 => ( ( ( insert_real @ A @ A4 )
% 0.29/0.56 = ( insert_real @ B @ B4 ) )
% 0.29/0.56 = ( ( ( A = B )
% 0.29/0.56 => ( A4 = B4 ) )
% 0.29/0.56 & ( ( A != B )
% 0.29/0.56 => ? [C4: set_real] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_real @ B @ C4 ) )
% 0.29/0.56 & ~ ( member_real @ B @ C4 )
% 0.29/0.56 & ( B4
% 0.29/0.56 = ( insert_real @ A @ C4 ) )
% 0.29/0.56 & ~ ( member_real @ A @ C4 ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_eq_iff
% 0.29/0.56 thf(fact_1676_insert__eq__iff,axiom,
% 0.29/0.56 ! [A: int,A4: set_int,B: int,B4: set_int] :
% 0.29/0.56 ( ~ ( member_int @ A @ A4 )
% 0.29/0.56 => ( ~ ( member_int @ B @ B4 )
% 0.29/0.56 => ( ( ( insert_int @ A @ A4 )
% 0.29/0.56 = ( insert_int @ B @ B4 ) )
% 0.29/0.56 = ( ( ( A = B )
% 0.29/0.56 => ( A4 = B4 ) )
% 0.29/0.56 & ( ( A != B )
% 0.29/0.56 => ? [C4: set_int] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_int @ B @ C4 ) )
% 0.29/0.56 & ~ ( member_int @ B @ C4 )
% 0.29/0.56 & ( B4
% 0.29/0.56 = ( insert_int @ A @ C4 ) )
% 0.29/0.56 & ~ ( member_int @ A @ C4 ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_eq_iff
% 0.29/0.56 thf(fact_1677_insert__eq__iff,axiom,
% 0.29/0.56 ! [A: set_nat,A4: set_set_nat,B: set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ~ ( member_set_nat @ A @ A4 )
% 0.29/0.56 => ( ~ ( member_set_nat @ B @ B4 )
% 0.29/0.56 => ( ( ( insert_set_nat @ A @ A4 )
% 0.29/0.56 = ( insert_set_nat @ B @ B4 ) )
% 0.29/0.56 = ( ( ( A = B )
% 0.29/0.56 => ( A4 = B4 ) )
% 0.29/0.56 & ( ( A != B )
% 0.29/0.56 => ? [C4: set_set_nat] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_set_nat @ B @ C4 ) )
% 0.29/0.56 & ~ ( member_set_nat @ B @ C4 )
% 0.29/0.56 & ( B4
% 0.29/0.56 = ( insert_set_nat @ A @ C4 ) )
% 0.29/0.56 & ~ ( member_set_nat @ A @ C4 ) ) ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_eq_iff
% 0.29/0.56 thf(fact_1678_insert__commute,axiom,
% 0.29/0.56 ! [X: nat,Y: nat,A4: set_nat] :
% 0.29/0.56 ( ( insert_nat @ X @ ( insert_nat @ Y @ A4 ) )
% 0.29/0.56 = ( insert_nat @ Y @ ( insert_nat @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_commute
% 0.29/0.56 thf(fact_1679_insert__commute,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,Y: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( insert_VEBT_VEBT @ X @ ( insert_VEBT_VEBT @ Y @ A4 ) )
% 0.29/0.56 = ( insert_VEBT_VEBT @ Y @ ( insert_VEBT_VEBT @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_commute
% 0.29/0.56 thf(fact_1680_insert__commute,axiom,
% 0.29/0.56 ! [X: int,Y: int,A4: set_int] :
% 0.29/0.56 ( ( insert_int @ X @ ( insert_int @ Y @ A4 ) )
% 0.29/0.56 = ( insert_int @ Y @ ( insert_int @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_commute
% 0.29/0.56 thf(fact_1681_insert__commute,axiom,
% 0.29/0.56 ! [X: $o,Y: $o,A4: set_o] :
% 0.29/0.56 ( ( insert_o @ X @ ( insert_o @ Y @ A4 ) )
% 0.29/0.56 = ( insert_o @ Y @ ( insert_o @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_commute
% 0.29/0.56 thf(fact_1682_mk__disjoint__insert,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o] :
% 0.29/0.56 ( ( member_o @ A @ A4 )
% 0.29/0.56 => ? [B8: set_o] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_o @ A @ B8 ) )
% 0.29/0.56 & ~ ( member_o @ A @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % mk_disjoint_insert
% 0.29/0.56 thf(fact_1683_mk__disjoint__insert,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat] :
% 0.29/0.56 ( ( member_nat @ A @ A4 )
% 0.29/0.56 => ? [B8: set_nat] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_nat @ A @ B8 ) )
% 0.29/0.56 & ~ ( member_nat @ A @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % mk_disjoint_insert
% 0.29/0.56 thf(fact_1684_mk__disjoint__insert,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 => ? [B8: set_VEBT_VEBT] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_VEBT_VEBT @ A @ B8 ) )
% 0.29/0.56 & ~ ( member_VEBT_VEBT @ A @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % mk_disjoint_insert
% 0.29/0.56 thf(fact_1685_mk__disjoint__insert,axiom,
% 0.29/0.56 ! [A: real,A4: set_real] :
% 0.29/0.56 ( ( member_real @ A @ A4 )
% 0.29/0.56 => ? [B8: set_real] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_real @ A @ B8 ) )
% 0.29/0.56 & ~ ( member_real @ A @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % mk_disjoint_insert
% 0.29/0.56 thf(fact_1686_mk__disjoint__insert,axiom,
% 0.29/0.56 ! [A: int,A4: set_int] :
% 0.29/0.56 ( ( member_int @ A @ A4 )
% 0.29/0.56 => ? [B8: set_int] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_int @ A @ B8 ) )
% 0.29/0.56 & ~ ( member_int @ A @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % mk_disjoint_insert
% 0.29/0.56 thf(fact_1687_mk__disjoint__insert,axiom,
% 0.29/0.56 ! [A: set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ A @ A4 )
% 0.29/0.56 => ? [B8: set_set_nat] :
% 0.29/0.56 ( ( A4
% 0.29/0.56 = ( insert_set_nat @ A @ B8 ) )
% 0.29/0.56 & ~ ( member_set_nat @ A @ B8 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % mk_disjoint_insert
% 0.29/0.56 thf(fact_1688_singleton__inject,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,B: vEBT_VEBT] :
% 0.29/0.56 ( ( ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 = ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 => ( A = B ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_inject
% 0.29/0.56 thf(fact_1689_singleton__inject,axiom,
% 0.29/0.56 ! [A: nat,B: nat] :
% 0.29/0.56 ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 0.29/0.56 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.29/0.56 => ( A = B ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_inject
% 0.29/0.56 thf(fact_1690_singleton__inject,axiom,
% 0.29/0.56 ! [A: int,B: int] :
% 0.29/0.56 ( ( ( insert_int @ A @ bot_bot_set_int )
% 0.29/0.56 = ( insert_int @ B @ bot_bot_set_int ) )
% 0.29/0.56 => ( A = B ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_inject
% 0.29/0.56 thf(fact_1691_singleton__inject,axiom,
% 0.29/0.56 ! [A: $o,B: $o] :
% 0.29/0.56 ( ( ( insert_o @ A @ bot_bot_set_o )
% 0.29/0.56 = ( insert_o @ B @ bot_bot_set_o ) )
% 0.29/0.56 => ( A = B ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_inject
% 0.29/0.56 thf(fact_1692_insert__not__empty,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( insert_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 != bot_bo8194388402131092736T_VEBT ) ).
% 0.29/0.56
% 0.29/0.56 % insert_not_empty
% 0.29/0.56 thf(fact_1693_insert__not__empty,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat] :
% 0.29/0.56 ( ( insert_nat @ A @ A4 )
% 0.29/0.56 != bot_bot_set_nat ) ).
% 0.29/0.56
% 0.29/0.56 % insert_not_empty
% 0.29/0.56 thf(fact_1694_insert__not__empty,axiom,
% 0.29/0.56 ! [A: int,A4: set_int] :
% 0.29/0.56 ( ( insert_int @ A @ A4 )
% 0.29/0.56 != bot_bot_set_int ) ).
% 0.29/0.56
% 0.29/0.56 % insert_not_empty
% 0.29/0.56 thf(fact_1695_insert__not__empty,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o] :
% 0.29/0.56 ( ( insert_o @ A @ A4 )
% 0.29/0.56 != bot_bot_set_o ) ).
% 0.29/0.56
% 0.29/0.56 % insert_not_empty
% 0.29/0.56 thf(fact_1696_doubleton__eq__iff,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,B: vEBT_VEBT,C2: vEBT_VEBT,D: vEBT_VEBT] :
% 0.29/0.56 ( ( ( insert_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 = ( insert_VEBT_VEBT @ C2 @ ( insert_VEBT_VEBT @ D @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.29/0.56 = ( ( ( A = C2 )
% 0.29/0.56 & ( B = D ) )
% 0.29/0.56 | ( ( A = D )
% 0.29/0.56 & ( B = C2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % doubleton_eq_iff
% 0.29/0.56 thf(fact_1697_doubleton__eq__iff,axiom,
% 0.29/0.56 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.29/0.56 ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.29/0.56 = ( insert_nat @ C2 @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 0.29/0.56 = ( ( ( A = C2 )
% 0.29/0.56 & ( B = D ) )
% 0.29/0.56 | ( ( A = D )
% 0.29/0.56 & ( B = C2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % doubleton_eq_iff
% 0.29/0.56 thf(fact_1698_doubleton__eq__iff,axiom,
% 0.29/0.56 ! [A: int,B: int,C2: int,D: int] :
% 0.29/0.56 ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 0.29/0.56 = ( insert_int @ C2 @ ( insert_int @ D @ bot_bot_set_int ) ) )
% 0.29/0.56 = ( ( ( A = C2 )
% 0.29/0.56 & ( B = D ) )
% 0.29/0.56 | ( ( A = D )
% 0.29/0.56 & ( B = C2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % doubleton_eq_iff
% 0.29/0.56 thf(fact_1699_doubleton__eq__iff,axiom,
% 0.29/0.56 ! [A: $o,B: $o,C2: $o,D: $o] :
% 0.29/0.56 ( ( ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) )
% 0.29/0.56 = ( insert_o @ C2 @ ( insert_o @ D @ bot_bot_set_o ) ) )
% 0.29/0.56 = ( ( ( A = C2 )
% 0.29/0.56 & ( B = D ) )
% 0.29/0.56 | ( ( A = D )
% 0.29/0.56 & ( B = C2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % doubleton_eq_iff
% 0.29/0.56 thf(fact_1700_singleton__iff,axiom,
% 0.29/0.56 ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 = ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_iff
% 0.29/0.56 thf(fact_1701_singleton__iff,axiom,
% 0.29/0.56 ! [B: real,A: real] :
% 0.29/0.56 ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 0.29/0.56 = ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_iff
% 0.29/0.56 thf(fact_1702_singleton__iff,axiom,
% 0.29/0.56 ! [B: set_nat,A: set_nat] :
% 0.29/0.56 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 0.29/0.56 = ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_iff
% 0.29/0.56 thf(fact_1703_singleton__iff,axiom,
% 0.29/0.56 ! [B: nat,A: nat] :
% 0.29/0.56 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.29/0.56 = ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_iff
% 0.29/0.56 thf(fact_1704_singleton__iff,axiom,
% 0.29/0.56 ! [B: int,A: int] :
% 0.29/0.56 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.29/0.56 = ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_iff
% 0.29/0.56 thf(fact_1705_singleton__iff,axiom,
% 0.29/0.56 ! [B: $o,A: $o] :
% 0.29/0.56 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 0.29/0.56 = ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singleton_iff
% 0.29/0.56 thf(fact_1706_singletonD,axiom,
% 0.29/0.56 ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 => ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonD
% 0.29/0.56 thf(fact_1707_singletonD,axiom,
% 0.29/0.56 ! [B: real,A: real] :
% 0.29/0.56 ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 0.29/0.56 => ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonD
% 0.29/0.56 thf(fact_1708_singletonD,axiom,
% 0.29/0.56 ! [B: set_nat,A: set_nat] :
% 0.29/0.56 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 0.29/0.56 => ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonD
% 0.29/0.56 thf(fact_1709_singletonD,axiom,
% 0.29/0.56 ! [B: nat,A: nat] :
% 0.29/0.56 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.29/0.56 => ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonD
% 0.29/0.56 thf(fact_1710_singletonD,axiom,
% 0.29/0.56 ! [B: int,A: int] :
% 0.29/0.56 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.29/0.56 => ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonD
% 0.29/0.56 thf(fact_1711_singletonD,axiom,
% 0.29/0.56 ! [B: $o,A: $o] :
% 0.29/0.56 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 0.29/0.56 => ( B = A ) ) ).
% 0.29/0.56
% 0.29/0.56 % singletonD
% 0.29/0.56 thf(fact_1712_insert__minus__eq,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,Y: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( X != Y )
% 0.29/0.56 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ ( insert_VEBT_VEBT @ Y @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ Y @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_minus_eq
% 0.29/0.56 thf(fact_1713_insert__minus__eq,axiom,
% 0.29/0.56 ! [X: int,Y: int,A4: set_int] :
% 0.29/0.56 ( ( X != Y )
% 0.29/0.56 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 0.29/0.56 = ( insert_int @ X @ ( minus_minus_set_int @ A4 @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_minus_eq
% 0.29/0.56 thf(fact_1714_insert__minus__eq,axiom,
% 0.29/0.56 ! [X: $o,Y: $o,A4: set_o] :
% 0.29/0.56 ( ( X != Y )
% 0.29/0.56 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 0.29/0.56 = ( insert_o @ X @ ( minus_minus_set_o @ A4 @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_minus_eq
% 0.29/0.56 thf(fact_1715_insert__minus__eq,axiom,
% 0.29/0.56 ! [X: nat,Y: nat,A4: set_nat] :
% 0.29/0.56 ( ( X != Y )
% 0.29/0.56 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 0.29/0.56 = ( insert_nat @ X @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_minus_eq
% 0.29/0.56 thf(fact_1716_set__minus__singleton__eq,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,X6: set_VEBT_VEBT] :
% 0.29/0.56 ( ~ ( member_VEBT_VEBT @ X @ X6 )
% 0.29/0.56 => ( ( minus_5127226145743854075T_VEBT @ X6 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 = X6 ) ) ).
% 0.29/0.56
% 0.29/0.56 % set_minus_singleton_eq
% 0.29/0.56 thf(fact_1717_set__minus__singleton__eq,axiom,
% 0.29/0.56 ! [X: real,X6: set_real] :
% 0.29/0.56 ( ~ ( member_real @ X @ X6 )
% 0.29/0.56 => ( ( minus_minus_set_real @ X6 @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.29/0.56 = X6 ) ) ).
% 0.29/0.56
% 0.29/0.56 % set_minus_singleton_eq
% 0.29/0.56 thf(fact_1718_set__minus__singleton__eq,axiom,
% 0.29/0.56 ! [X: set_nat,X6: set_set_nat] :
% 0.29/0.56 ( ~ ( member_set_nat @ X @ X6 )
% 0.29/0.56 => ( ( minus_2163939370556025621et_nat @ X6 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.29/0.56 = X6 ) ) ).
% 0.29/0.56
% 0.29/0.56 % set_minus_singleton_eq
% 0.29/0.56 thf(fact_1719_set__minus__singleton__eq,axiom,
% 0.29/0.56 ! [X: int,X6: set_int] :
% 0.29/0.56 ( ~ ( member_int @ X @ X6 )
% 0.29/0.56 => ( ( minus_minus_set_int @ X6 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.29/0.56 = X6 ) ) ).
% 0.29/0.56
% 0.29/0.56 % set_minus_singleton_eq
% 0.29/0.56 thf(fact_1720_set__minus__singleton__eq,axiom,
% 0.29/0.56 ! [X: $o,X6: set_o] :
% 0.29/0.56 ( ~ ( member_o @ X @ X6 )
% 0.29/0.56 => ( ( minus_minus_set_o @ X6 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.29/0.56 = X6 ) ) ).
% 0.29/0.56
% 0.29/0.56 % set_minus_singleton_eq
% 0.29/0.56 thf(fact_1721_set__minus__singleton__eq,axiom,
% 0.29/0.56 ! [X: nat,X6: set_nat] :
% 0.29/0.56 ( ~ ( member_nat @ X @ X6 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ X6 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.29/0.56 = X6 ) ) ).
% 0.29/0.56
% 0.29/0.56 % set_minus_singleton_eq
% 0.29/0.56 thf(fact_1722_Diff__insert__absorb,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert_absorb
% 0.29/0.56 thf(fact_1723_Diff__insert__absorb,axiom,
% 0.29/0.56 ! [X: real,A4: set_real] :
% 0.29/0.56 ( ~ ( member_real @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert_absorb
% 0.29/0.56 thf(fact_1724_Diff__insert__absorb,axiom,
% 0.29/0.56 ! [X: set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ~ ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert_absorb
% 0.29/0.56 thf(fact_1725_Diff__insert__absorb,axiom,
% 0.29/0.56 ! [X: int,A4: set_int] :
% 0.29/0.56 ( ~ ( member_int @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert_absorb
% 0.29/0.56 thf(fact_1726_Diff__insert__absorb,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o] :
% 0.29/0.56 ( ~ ( member_o @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert_absorb
% 0.29/0.56 thf(fact_1727_Diff__insert__absorb,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat] :
% 0.29/0.56 ( ~ ( member_nat @ X @ A4 )
% 0.29/0.56 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert_absorb
% 0.29/0.56 thf(fact_1728_Diff__insert2,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 0.29/0.56 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert2
% 0.29/0.56 thf(fact_1729_Diff__insert2,axiom,
% 0.29/0.56 ! [A4: set_int,A: int,B4: set_int] :
% 0.29/0.56 ( ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert2
% 0.29/0.56 thf(fact_1730_Diff__insert2,axiom,
% 0.29/0.56 ! [A4: set_o,A: $o,B4: set_o] :
% 0.29/0.56 ( ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert2
% 0.29/0.56 thf(fact_1731_Diff__insert2,axiom,
% 0.29/0.56 ! [A4: set_nat,A: nat,B4: set_nat] :
% 0.29/0.56 ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert2
% 0.29/0.56 thf(fact_1732_insert__Diff,axiom,
% 0.29/0.56 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ A @ A4 )
% 0.29/0.56 => ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff
% 0.29/0.56 thf(fact_1733_insert__Diff,axiom,
% 0.29/0.56 ! [A: real,A4: set_real] :
% 0.29/0.56 ( ( member_real @ A @ A4 )
% 0.29/0.56 => ( ( insert_real @ A @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff
% 0.29/0.56 thf(fact_1734_insert__Diff,axiom,
% 0.29/0.56 ! [A: set_nat,A4: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ A @ A4 )
% 0.29/0.56 => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff
% 0.29/0.56 thf(fact_1735_insert__Diff,axiom,
% 0.29/0.56 ! [A: int,A4: set_int] :
% 0.29/0.56 ( ( member_int @ A @ A4 )
% 0.29/0.56 => ( ( insert_int @ A @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff
% 0.29/0.56 thf(fact_1736_insert__Diff,axiom,
% 0.29/0.56 ! [A: $o,A4: set_o] :
% 0.29/0.56 ( ( member_o @ A @ A4 )
% 0.29/0.56 => ( ( insert_o @ A @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff
% 0.29/0.56 thf(fact_1737_insert__Diff,axiom,
% 0.29/0.56 ! [A: nat,A4: set_nat] :
% 0.29/0.56 ( ( member_nat @ A @ A4 )
% 0.29/0.56 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.29/0.56 = A4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_Diff
% 0.29/0.56 thf(fact_1738_Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 0.29/0.56 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert
% 0.29/0.56 thf(fact_1739_Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_int,A: int,B4: set_int] :
% 0.29/0.56 ( ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ B4 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert
% 0.29/0.56 thf(fact_1740_Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_o,A: $o,B4: set_o] :
% 0.29/0.56 ( ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ B4 ) @ ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert
% 0.29/0.56 thf(fact_1741_Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_nat,A: nat,B4: set_nat] :
% 0.29/0.56 ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) )
% 0.29/0.56 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % Diff_insert
% 0.29/0.56 thf(fact_1742_finite_OinsertI,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.29/0.56 => ( finite5795047828879050333T_VEBT @ ( insert_VEBT_VEBT @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.insertI
% 0.29/0.56 thf(fact_1743_finite_OinsertI,axiom,
% 0.29/0.56 ! [A4: set_o,A: $o] :
% 0.29/0.56 ( ( finite_finite_o @ A4 )
% 0.29/0.56 => ( finite_finite_o @ ( insert_o @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.insertI
% 0.29/0.56 thf(fact_1744_finite_OinsertI,axiom,
% 0.29/0.56 ! [A4: set_nat,A: nat] :
% 0.29/0.56 ( ( finite_finite_nat @ A4 )
% 0.29/0.56 => ( finite_finite_nat @ ( insert_nat @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.insertI
% 0.29/0.56 thf(fact_1745_finite_OinsertI,axiom,
% 0.29/0.56 ! [A4: set_int,A: int] :
% 0.29/0.56 ( ( finite_finite_int @ A4 )
% 0.29/0.56 => ( finite_finite_int @ ( insert_int @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.insertI
% 0.29/0.56 thf(fact_1746_finite_OinsertI,axiom,
% 0.29/0.56 ! [A4: set_complex,A: complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ A4 )
% 0.29/0.56 => ( finite3207457112153483333omplex @ ( insert_complex @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.insertI
% 0.29/0.56 thf(fact_1747_finite_OinsertI,axiom,
% 0.29/0.56 ! [A4: set_Code_integer,A: code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.56 => ( finite6017078050557962740nteger @ ( insert_Code_integer @ A @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.insertI
% 0.29/0.56 thf(fact_1748_subset__insertI2,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat,B: nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.56 => ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI2
% 0.29/0.56 thf(fact_1749_subset__insertI2,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.29/0.56 ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.29/0.56 => ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI2
% 0.29/0.56 thf(fact_1750_subset__insertI2,axiom,
% 0.29/0.56 ! [A4: set_o,B4: set_o,B: $o] :
% 0.29/0.56 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 0.29/0.56 => ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI2
% 0.29/0.56 thf(fact_1751_subset__insertI2,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int,B: int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.56 => ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI2
% 0.29/0.56 thf(fact_1752_subset__insertI,axiom,
% 0.29/0.56 ! [B4: set_nat,A: nat] : ( ord_less_eq_set_nat @ B4 @ ( insert_nat @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI
% 0.29/0.56 thf(fact_1753_subset__insertI,axiom,
% 0.29/0.56 ! [B4: set_VEBT_VEBT,A: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ B4 @ ( insert_VEBT_VEBT @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI
% 0.29/0.56 thf(fact_1754_subset__insertI,axiom,
% 0.29/0.56 ! [B4: set_o,A: $o] : ( ord_less_eq_set_o @ B4 @ ( insert_o @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI
% 0.29/0.56 thf(fact_1755_subset__insertI,axiom,
% 0.29/0.56 ! [B4: set_int,A: int] : ( ord_less_eq_set_int @ B4 @ ( insert_int @ A @ B4 ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insertI
% 0.29/0.56 thf(fact_1756_subset__insert,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o,B4: set_o] :
% 0.29/0.56 ( ~ ( member_o @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 0.29/0.56 = ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert
% 0.29/0.56 thf(fact_1757_subset__insert,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat,B4: set_nat] :
% 0.29/0.56 ( ~ ( member_nat @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 0.29/0.56 = ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert
% 0.29/0.56 thf(fact_1758_subset__insert,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 0.29/0.56 = ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert
% 0.29/0.56 thf(fact_1759_subset__insert,axiom,
% 0.29/0.56 ! [X: real,A4: set_real,B4: set_real] :
% 0.29/0.56 ( ~ ( member_real @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 0.29/0.56 = ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert
% 0.29/0.56 thf(fact_1760_subset__insert,axiom,
% 0.29/0.56 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ~ ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ( ( ord_le6893508408891458716et_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 0.29/0.56 = ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert
% 0.29/0.56 thf(fact_1761_subset__insert,axiom,
% 0.29/0.56 ! [X: int,A4: set_int,B4: set_int] :
% 0.29/0.56 ( ~ ( member_int @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 0.29/0.56 = ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert
% 0.29/0.56 thf(fact_1762_insert__mono,axiom,
% 0.29/0.56 ! [C3: set_nat,D4: set_nat,A: nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ C3 @ D4 )
% 0.29/0.56 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C3 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_mono
% 0.29/0.56 thf(fact_1763_insert__mono,axiom,
% 0.29/0.56 ! [C3: set_VEBT_VEBT,D4: set_VEBT_VEBT,A: vEBT_VEBT] :
% 0.29/0.56 ( ( ord_le4337996190870823476T_VEBT @ C3 @ D4 )
% 0.29/0.56 => ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ A @ C3 ) @ ( insert_VEBT_VEBT @ A @ D4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_mono
% 0.29/0.56 thf(fact_1764_insert__mono,axiom,
% 0.29/0.56 ! [C3: set_o,D4: set_o,A: $o] :
% 0.29/0.56 ( ( ord_less_eq_set_o @ C3 @ D4 )
% 0.29/0.56 => ( ord_less_eq_set_o @ ( insert_o @ A @ C3 ) @ ( insert_o @ A @ D4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_mono
% 0.29/0.56 thf(fact_1765_insert__mono,axiom,
% 0.29/0.56 ! [C3: set_int,D4: set_int,A: int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ C3 @ D4 )
% 0.29/0.56 => ( ord_less_eq_set_int @ ( insert_int @ A @ C3 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_mono
% 0.29/0.56 thf(fact_1766_insert__subsetI,axiom,
% 0.29/0.56 ! [X: $o,A4: set_o,X6: set_o] :
% 0.29/0.56 ( ( member_o @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_o @ X6 @ A4 )
% 0.29/0.56 => ( ord_less_eq_set_o @ ( insert_o @ X @ X6 ) @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subsetI
% 0.29/0.56 thf(fact_1767_insert__subsetI,axiom,
% 0.29/0.56 ! [X: nat,A4: set_nat,X6: set_nat] :
% 0.29/0.56 ( ( member_nat @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_nat @ X6 @ A4 )
% 0.29/0.56 => ( ord_less_eq_set_nat @ ( insert_nat @ X @ X6 ) @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subsetI
% 0.29/0.56 thf(fact_1768_insert__subsetI,axiom,
% 0.29/0.56 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,X6: set_VEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ( ( ord_le4337996190870823476T_VEBT @ X6 @ A4 )
% 0.29/0.56 => ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X @ X6 ) @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subsetI
% 0.29/0.56 thf(fact_1769_insert__subsetI,axiom,
% 0.29/0.56 ! [X: real,A4: set_real,X6: set_real] :
% 0.29/0.56 ( ( member_real @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_real @ X6 @ A4 )
% 0.29/0.56 => ( ord_less_eq_set_real @ ( insert_real @ X @ X6 ) @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subsetI
% 0.29/0.56 thf(fact_1770_insert__subsetI,axiom,
% 0.29/0.56 ! [X: set_nat,A4: set_set_nat,X6: set_set_nat] :
% 0.29/0.56 ( ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ( ( ord_le6893508408891458716et_nat @ X6 @ A4 )
% 0.29/0.56 => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ X6 ) @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subsetI
% 0.29/0.56 thf(fact_1771_insert__subsetI,axiom,
% 0.29/0.56 ! [X: int,A4: set_int,X6: set_int] :
% 0.29/0.56 ( ( member_int @ X @ A4 )
% 0.29/0.56 => ( ( ord_less_eq_set_int @ X6 @ A4 )
% 0.29/0.56 => ( ord_less_eq_set_int @ ( insert_int @ X @ X6 ) @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % insert_subsetI
% 0.29/0.56 thf(fact_1772_subset__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_o,B4: set_o,X: $o,C3: set_o] :
% 0.29/0.56 ( ( ord_less_eq_set_o @ A4 @ ( minus_minus_set_o @ B4 @ ( insert_o @ X @ C3 ) ) )
% 0.29/0.56 = ( ( ord_less_eq_set_o @ A4 @ ( minus_minus_set_o @ B4 @ C3 ) )
% 0.29/0.56 & ~ ( member_o @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_Diff_insert
% 0.29/0.56 thf(fact_1773_subset__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,X: vEBT_VEBT,C3: set_VEBT_VEBT] :
% 0.29/0.56 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ B4 @ ( insert_VEBT_VEBT @ X @ C3 ) ) )
% 0.29/0.56 = ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ B4 @ C3 ) )
% 0.29/0.56 & ~ ( member_VEBT_VEBT @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_Diff_insert
% 0.29/0.56 thf(fact_1774_subset__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_real,B4: set_real,X: real,C3: set_real] :
% 0.29/0.56 ( ( ord_less_eq_set_real @ A4 @ ( minus_minus_set_real @ B4 @ ( insert_real @ X @ C3 ) ) )
% 0.29/0.56 = ( ( ord_less_eq_set_real @ A4 @ ( minus_minus_set_real @ B4 @ C3 ) )
% 0.29/0.56 & ~ ( member_real @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_Diff_insert
% 0.29/0.56 thf(fact_1775_subset__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_set_nat,B4: set_set_nat,X: set_nat,C3: set_set_nat] :
% 0.29/0.56 ( ( ord_le6893508408891458716et_nat @ A4 @ ( minus_2163939370556025621et_nat @ B4 @ ( insert_set_nat @ X @ C3 ) ) )
% 0.29/0.56 = ( ( ord_le6893508408891458716et_nat @ A4 @ ( minus_2163939370556025621et_nat @ B4 @ C3 ) )
% 0.29/0.56 & ~ ( member_set_nat @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_Diff_insert
% 0.29/0.56 thf(fact_1776_subset__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_nat,B4: set_nat,X: nat,C3: set_nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ A4 @ ( minus_minus_set_nat @ B4 @ ( insert_nat @ X @ C3 ) ) )
% 0.29/0.56 = ( ( ord_less_eq_set_nat @ A4 @ ( minus_minus_set_nat @ B4 @ C3 ) )
% 0.29/0.56 & ~ ( member_nat @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_Diff_insert
% 0.29/0.56 thf(fact_1777_subset__Diff__insert,axiom,
% 0.29/0.56 ! [A4: set_int,B4: set_int,X: int,C3: set_int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ A4 @ ( minus_minus_set_int @ B4 @ ( insert_int @ X @ C3 ) ) )
% 0.29/0.56 = ( ( ord_less_eq_set_int @ A4 @ ( minus_minus_set_int @ B4 @ C3 ) )
% 0.29/0.56 & ~ ( member_int @ X @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_Diff_insert
% 0.29/0.56 thf(fact_1778_finite_Ocases,axiom,
% 0.29/0.56 ! [A: set_VEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ A )
% 0.29/0.56 => ( ( A != bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 => ~ ! [A5: set_VEBT_VEBT] :
% 0.29/0.56 ( ? [A3: vEBT_VEBT] :
% 0.29/0.56 ( A
% 0.29/0.56 = ( insert_VEBT_VEBT @ A3 @ A5 ) )
% 0.29/0.56 => ~ ( finite5795047828879050333T_VEBT @ A5 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.cases
% 0.29/0.56 thf(fact_1779_finite_Ocases,axiom,
% 0.29/0.56 ! [A: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ A )
% 0.29/0.56 => ( ( A != bot_bot_set_complex )
% 0.29/0.56 => ~ ! [A5: set_complex] :
% 0.29/0.56 ( ? [A3: complex] :
% 0.29/0.56 ( A
% 0.29/0.56 = ( insert_complex @ A3 @ A5 ) )
% 0.29/0.56 => ~ ( finite3207457112153483333omplex @ A5 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.cases
% 0.29/0.56 thf(fact_1780_finite_Ocases,axiom,
% 0.29/0.56 ! [A: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ A )
% 0.29/0.56 => ( ( A != bot_bo3990330152332043303nteger )
% 0.29/0.56 => ~ ! [A5: set_Code_integer] :
% 0.29/0.56 ( ? [A3: code_integer] :
% 0.29/0.56 ( A
% 0.29/0.56 = ( insert_Code_integer @ A3 @ A5 ) )
% 0.29/0.56 => ~ ( finite6017078050557962740nteger @ A5 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.cases
% 0.29/0.56 thf(fact_1781_finite_Ocases,axiom,
% 0.29/0.56 ! [A: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ A )
% 0.29/0.56 => ( ( A != bot_bot_set_nat )
% 0.29/0.56 => ~ ! [A5: set_nat] :
% 0.29/0.56 ( ? [A3: nat] :
% 0.29/0.56 ( A
% 0.29/0.56 = ( insert_nat @ A3 @ A5 ) )
% 0.29/0.56 => ~ ( finite_finite_nat @ A5 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.cases
% 0.29/0.56 thf(fact_1782_finite_Ocases,axiom,
% 0.29/0.56 ! [A: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ A )
% 0.29/0.56 => ( ( A != bot_bot_set_int )
% 0.29/0.56 => ~ ! [A5: set_int] :
% 0.29/0.56 ( ? [A3: int] :
% 0.29/0.56 ( A
% 0.29/0.56 = ( insert_int @ A3 @ A5 ) )
% 0.29/0.56 => ~ ( finite_finite_int @ A5 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.cases
% 0.29/0.56 thf(fact_1783_finite_Ocases,axiom,
% 0.29/0.56 ! [A: set_o] :
% 0.29/0.56 ( ( finite_finite_o @ A )
% 0.29/0.56 => ( ( A != bot_bot_set_o )
% 0.29/0.56 => ~ ! [A5: set_o] :
% 0.29/0.56 ( ? [A3: $o] :
% 0.29/0.56 ( A
% 0.29/0.56 = ( insert_o @ A3 @ A5 ) )
% 0.29/0.56 => ~ ( finite_finite_o @ A5 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.cases
% 0.29/0.56 thf(fact_1784_finite_Osimps,axiom,
% 0.29/0.56 ( finite5795047828879050333T_VEBT
% 0.29/0.56 = ( ^ [A7: set_VEBT_VEBT] :
% 0.29/0.56 ( ( A7 = bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 | ? [A6: set_VEBT_VEBT,B7: vEBT_VEBT] :
% 0.29/0.56 ( ( A7
% 0.29/0.56 = ( insert_VEBT_VEBT @ B7 @ A6 ) )
% 0.29/0.56 & ( finite5795047828879050333T_VEBT @ A6 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.simps
% 0.29/0.56 thf(fact_1785_finite_Osimps,axiom,
% 0.29/0.56 ( finite3207457112153483333omplex
% 0.29/0.56 = ( ^ [A7: set_complex] :
% 0.29/0.56 ( ( A7 = bot_bot_set_complex )
% 0.29/0.56 | ? [A6: set_complex,B7: complex] :
% 0.29/0.56 ( ( A7
% 0.29/0.56 = ( insert_complex @ B7 @ A6 ) )
% 0.29/0.56 & ( finite3207457112153483333omplex @ A6 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.simps
% 0.29/0.56 thf(fact_1786_finite_Osimps,axiom,
% 0.29/0.56 ( finite6017078050557962740nteger
% 0.29/0.56 = ( ^ [A7: set_Code_integer] :
% 0.29/0.56 ( ( A7 = bot_bo3990330152332043303nteger )
% 0.29/0.56 | ? [A6: set_Code_integer,B7: code_integer] :
% 0.29/0.56 ( ( A7
% 0.29/0.56 = ( insert_Code_integer @ B7 @ A6 ) )
% 0.29/0.56 & ( finite6017078050557962740nteger @ A6 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.simps
% 0.29/0.56 thf(fact_1787_finite_Osimps,axiom,
% 0.29/0.56 ( finite_finite_nat
% 0.29/0.56 = ( ^ [A7: set_nat] :
% 0.29/0.56 ( ( A7 = bot_bot_set_nat )
% 0.29/0.56 | ? [A6: set_nat,B7: nat] :
% 0.29/0.56 ( ( A7
% 0.29/0.56 = ( insert_nat @ B7 @ A6 ) )
% 0.29/0.56 & ( finite_finite_nat @ A6 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.simps
% 0.29/0.56 thf(fact_1788_finite_Osimps,axiom,
% 0.29/0.56 ( finite_finite_int
% 0.29/0.56 = ( ^ [A7: set_int] :
% 0.29/0.56 ( ( A7 = bot_bot_set_int )
% 0.29/0.56 | ? [A6: set_int,B7: int] :
% 0.29/0.56 ( ( A7
% 0.29/0.56 = ( insert_int @ B7 @ A6 ) )
% 0.29/0.56 & ( finite_finite_int @ A6 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.simps
% 0.29/0.56 thf(fact_1789_finite_Osimps,axiom,
% 0.29/0.56 ( finite_finite_o
% 0.29/0.56 = ( ^ [A7: set_o] :
% 0.29/0.56 ( ( A7 = bot_bot_set_o )
% 0.29/0.56 | ? [A6: set_o,B7: $o] :
% 0.29/0.56 ( ( A7
% 0.29/0.56 = ( insert_o @ B7 @ A6 ) )
% 0.29/0.56 & ( finite_finite_o @ A6 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite.simps
% 0.29/0.56 thf(fact_1790_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 => ( ! [X3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.29/0.56 => ( ~ ( member_VEBT_VEBT @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1791_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_real,P2: set_real > $o] :
% 0.29/0.56 ( ( finite_finite_real @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.56 => ( ! [X3: real,F3: set_real] :
% 0.29/0.56 ( ( finite_finite_real @ F3 )
% 0.29/0.56 => ( ~ ( member_real @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_real @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1792_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_set_nat,P2: set_set_nat > $o] :
% 0.29/0.56 ( ( finite1152437895449049373et_nat @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_set_nat )
% 0.29/0.56 => ( ! [X3: set_nat,F3: set_set_nat] :
% 0.29/0.56 ( ( finite1152437895449049373et_nat @ F3 )
% 0.29/0.56 => ( ~ ( member_set_nat @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_set_nat @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1793_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_complex,P2: set_complex > $o] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.56 => ( ! [X3: complex,F3: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ F3 )
% 0.29/0.56 => ( ~ ( member_complex @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_complex @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1794_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.56 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ F3 )
% 0.29/0.56 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1795_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_nat,P2: set_nat > $o] :
% 0.29/0.56 ( ( finite_finite_nat @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.56 => ( ! [X3: nat,F3: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ F3 )
% 0.29/0.56 => ( ~ ( member_nat @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_nat @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1796_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_int,P2: set_int > $o] :
% 0.29/0.56 ( ( finite_finite_int @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.56 => ( ! [X3: int,F3: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ F3 )
% 0.29/0.56 => ( ~ ( member_int @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_int @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1797_finite__induct,axiom,
% 0.29/0.56 ! [F2: set_o,P2: set_o > $o] :
% 0.29/0.56 ( ( finite_finite_o @ F2 )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.56 => ( ! [X3: $o,F3: set_o] :
% 0.29/0.56 ( ( finite_finite_o @ F3 )
% 0.29/0.56 => ( ~ ( member_o @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_o @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_induct
% 0.29/0.56 thf(fact_1798_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 => ( ! [X3: vEBT_VEBT] : ( P2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 => ( ! [X3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 => ( ~ ( member_VEBT_VEBT @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1799_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_real,P2: set_real > $o] :
% 0.29/0.56 ( ( finite_finite_real @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bot_set_real )
% 0.29/0.56 => ( ! [X3: real] : ( P2 @ ( insert_real @ X3 @ bot_bot_set_real ) )
% 0.29/0.56 => ( ! [X3: real,F3: set_real] :
% 0.29/0.56 ( ( finite_finite_real @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bot_set_real )
% 0.29/0.56 => ( ~ ( member_real @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_real @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1800_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_set_nat,P2: set_set_nat > $o] :
% 0.29/0.56 ( ( finite1152437895449049373et_nat @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bot_set_set_nat )
% 0.29/0.56 => ( ! [X3: set_nat] : ( P2 @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) )
% 0.29/0.56 => ( ! [X3: set_nat,F3: set_set_nat] :
% 0.29/0.56 ( ( finite1152437895449049373et_nat @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bot_set_set_nat )
% 0.29/0.56 => ( ~ ( member_set_nat @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_set_nat @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1801_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_complex,P2: set_complex > $o] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bot_set_complex )
% 0.29/0.56 => ( ! [X3: complex] : ( P2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) )
% 0.29/0.56 => ( ! [X3: complex,F3: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bot_set_complex )
% 0.29/0.56 => ( ~ ( member_complex @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_complex @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1802_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bo3990330152332043303nteger )
% 0.29/0.56 => ( ! [X3: code_integer] : ( P2 @ ( insert_Code_integer @ X3 @ bot_bo3990330152332043303nteger ) )
% 0.29/0.56 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bo3990330152332043303nteger )
% 0.29/0.56 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1803_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_nat,P2: set_nat > $o] :
% 0.29/0.56 ( ( finite_finite_nat @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bot_set_nat )
% 0.29/0.56 => ( ! [X3: nat] : ( P2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.29/0.56 => ( ! [X3: nat,F3: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bot_set_nat )
% 0.29/0.56 => ( ~ ( member_nat @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_nat @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1804_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_int,P2: set_int > $o] :
% 0.29/0.56 ( ( finite_finite_int @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bot_set_int )
% 0.29/0.56 => ( ! [X3: int] : ( P2 @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 0.29/0.56 => ( ! [X3: int,F3: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bot_set_int )
% 0.29/0.56 => ( ~ ( member_int @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_int @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1805_finite__ne__induct,axiom,
% 0.29/0.56 ! [F2: set_o,P2: set_o > $o] :
% 0.29/0.56 ( ( finite_finite_o @ F2 )
% 0.29/0.56 => ( ( F2 != bot_bot_set_o )
% 0.29/0.56 => ( ! [X3: $o] : ( P2 @ ( insert_o @ X3 @ bot_bot_set_o ) )
% 0.29/0.56 => ( ! [X3: $o,F3: set_o] :
% 0.29/0.56 ( ( finite_finite_o @ F3 )
% 0.29/0.56 => ( ( F3 != bot_bot_set_o )
% 0.29/0.56 => ( ~ ( member_o @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_o @ X3 @ F3 ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_ne_induct
% 0.29/0.56 thf(fact_1806_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_VEBT_VEBT > $o,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ! [A5: set_VEBT_VEBT] :
% 0.29/0.56 ( ~ ( finite5795047828879050333T_VEBT @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 => ( ! [X3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.29/0.56 => ( ~ ( member_VEBT_VEBT @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1807_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_real > $o,A4: set_real] :
% 0.29/0.56 ( ! [A5: set_real] :
% 0.29/0.56 ( ~ ( finite_finite_real @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.56 => ( ! [X3: real,F3: set_real] :
% 0.29/0.56 ( ( finite_finite_real @ F3 )
% 0.29/0.56 => ( ~ ( member_real @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_real @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1808_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_set_nat > $o,A4: set_set_nat] :
% 0.29/0.56 ( ! [A5: set_set_nat] :
% 0.29/0.56 ( ~ ( finite1152437895449049373et_nat @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_set_nat )
% 0.29/0.56 => ( ! [X3: set_nat,F3: set_set_nat] :
% 0.29/0.56 ( ( finite1152437895449049373et_nat @ F3 )
% 0.29/0.56 => ( ~ ( member_set_nat @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_set_nat @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1809_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_complex > $o,A4: set_complex] :
% 0.29/0.56 ( ! [A5: set_complex] :
% 0.29/0.56 ( ~ ( finite3207457112153483333omplex @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.56 => ( ! [X3: complex,F3: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ F3 )
% 0.29/0.56 => ( ~ ( member_complex @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_complex @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1810_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_Code_integer > $o,A4: set_Code_integer] :
% 0.29/0.56 ( ! [A5: set_Code_integer] :
% 0.29/0.56 ( ~ ( finite6017078050557962740nteger @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.56 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ F3 )
% 0.29/0.56 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1811_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_nat > $o,A4: set_nat] :
% 0.29/0.56 ( ! [A5: set_nat] :
% 0.29/0.56 ( ~ ( finite_finite_nat @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.56 => ( ! [X3: nat,F3: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ F3 )
% 0.29/0.56 => ( ~ ( member_nat @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_nat @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1812_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_int > $o,A4: set_int] :
% 0.29/0.56 ( ! [A5: set_int] :
% 0.29/0.56 ( ~ ( finite_finite_int @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.56 => ( ! [X3: int,F3: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ F3 )
% 0.29/0.56 => ( ~ ( member_int @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_int @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1813_infinite__finite__induct,axiom,
% 0.29/0.56 ! [P2: set_o > $o,A4: set_o] :
% 0.29/0.56 ( ! [A5: set_o] :
% 0.29/0.56 ( ~ ( finite_finite_o @ A5 )
% 0.29/0.56 => ( P2 @ A5 ) )
% 0.29/0.56 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.56 => ( ! [X3: $o,F3: set_o] :
% 0.29/0.56 ( ( finite_finite_o @ F3 )
% 0.29/0.56 => ( ~ ( member_o @ X3 @ F3 )
% 0.29/0.56 => ( ( P2 @ F3 )
% 0.29/0.56 => ( P2 @ ( insert_o @ X3 @ F3 ) ) ) ) )
% 0.29/0.56 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_finite_induct
% 0.29/0.56 thf(fact_1814_infinite__remove,axiom,
% 0.29/0.56 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT] :
% 0.29/0.56 ( ~ ( finite5795047828879050333T_VEBT @ S3 )
% 0.29/0.56 => ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_remove
% 0.29/0.56 thf(fact_1815_infinite__remove,axiom,
% 0.29/0.56 ! [S3: set_complex,A: complex] :
% 0.29/0.56 ( ~ ( finite3207457112153483333omplex @ S3 )
% 0.29/0.56 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_remove
% 0.29/0.56 thf(fact_1816_infinite__remove,axiom,
% 0.29/0.56 ! [S3: set_Code_integer,A: code_integer] :
% 0.29/0.56 ( ~ ( finite6017078050557962740nteger @ S3 )
% 0.29/0.56 => ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_remove
% 0.29/0.56 thf(fact_1817_infinite__remove,axiom,
% 0.29/0.56 ! [S3: set_int,A: int] :
% 0.29/0.56 ( ~ ( finite_finite_int @ S3 )
% 0.29/0.56 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_remove
% 0.29/0.56 thf(fact_1818_infinite__remove,axiom,
% 0.29/0.56 ! [S3: set_o,A: $o] :
% 0.29/0.56 ( ~ ( finite_finite_o @ S3 )
% 0.29/0.56 => ~ ( finite_finite_o @ ( minus_minus_set_o @ S3 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_remove
% 0.29/0.56 thf(fact_1819_infinite__remove,axiom,
% 0.29/0.56 ! [S3: set_nat,A: nat] :
% 0.29/0.56 ( ~ ( finite_finite_nat @ S3 )
% 0.29/0.56 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_remove
% 0.29/0.56 thf(fact_1820_infinite__coinduct,axiom,
% 0.29/0.56 ! [X6: set_VEBT_VEBT > $o,A4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( X6 @ A4 )
% 0.29/0.56 => ( ! [A5: set_VEBT_VEBT] :
% 0.29/0.56 ( ( X6 @ A5 )
% 0.29/0.56 => ? [X5: vEBT_VEBT] :
% 0.29/0.56 ( ( member_VEBT_VEBT @ X5 @ A5 )
% 0.29/0.56 & ( ( X6 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.29/0.56 | ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.29/0.56 => ~ ( finite5795047828879050333T_VEBT @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_coinduct
% 0.29/0.56 thf(fact_1821_infinite__coinduct,axiom,
% 0.29/0.56 ! [X6: set_complex > $o,A4: set_complex] :
% 0.29/0.56 ( ( X6 @ A4 )
% 0.29/0.56 => ( ! [A5: set_complex] :
% 0.29/0.56 ( ( X6 @ A5 )
% 0.29/0.56 => ? [X5: complex] :
% 0.29/0.56 ( ( member_complex @ X5 @ A5 )
% 0.29/0.56 & ( ( X6 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) )
% 0.29/0.56 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) ) ) )
% 0.29/0.56 => ~ ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_coinduct
% 0.29/0.56 thf(fact_1822_infinite__coinduct,axiom,
% 0.29/0.56 ! [X6: set_Code_integer > $o,A4: set_Code_integer] :
% 0.29/0.56 ( ( X6 @ A4 )
% 0.29/0.56 => ( ! [A5: set_Code_integer] :
% 0.29/0.56 ( ( X6 @ A5 )
% 0.29/0.56 => ? [X5: code_integer] :
% 0.29/0.56 ( ( member_Code_integer @ X5 @ A5 )
% 0.29/0.56 & ( ( X6 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) )
% 0.29/0.56 | ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 0.29/0.56 => ~ ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_coinduct
% 0.29/0.56 thf(fact_1823_infinite__coinduct,axiom,
% 0.29/0.56 ! [X6: set_int > $o,A4: set_int] :
% 0.29/0.56 ( ( X6 @ A4 )
% 0.29/0.56 => ( ! [A5: set_int] :
% 0.29/0.56 ( ( X6 @ A5 )
% 0.29/0.56 => ? [X5: int] :
% 0.29/0.56 ( ( member_int @ X5 @ A5 )
% 0.29/0.56 & ( ( X6 @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) )
% 0.29/0.56 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) ) ) )
% 0.29/0.56 => ~ ( finite_finite_int @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_coinduct
% 0.29/0.56 thf(fact_1824_infinite__coinduct,axiom,
% 0.29/0.56 ! [X6: set_o > $o,A4: set_o] :
% 0.29/0.56 ( ( X6 @ A4 )
% 0.29/0.56 => ( ! [A5: set_o] :
% 0.29/0.56 ( ( X6 @ A5 )
% 0.29/0.56 => ? [X5: $o] :
% 0.29/0.56 ( ( member_o @ X5 @ A5 )
% 0.29/0.56 & ( ( X6 @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) )
% 0.29/0.56 | ~ ( finite_finite_o @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) ) ) )
% 0.29/0.56 => ~ ( finite_finite_o @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_coinduct
% 0.29/0.56 thf(fact_1825_infinite__coinduct,axiom,
% 0.29/0.56 ! [X6: set_nat > $o,A4: set_nat] :
% 0.29/0.56 ( ( X6 @ A4 )
% 0.29/0.56 => ( ! [A5: set_nat] :
% 0.29/0.56 ( ( X6 @ A5 )
% 0.29/0.56 => ? [X5: nat] :
% 0.29/0.56 ( ( member_nat @ X5 @ A5 )
% 0.29/0.56 & ( ( X6 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
% 0.29/0.56 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ) )
% 0.29/0.56 => ~ ( finite_finite_nat @ A4 ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % infinite_coinduct
% 0.29/0.56 thf(fact_1826_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: vEBT_VEBT,A5: set_VEBT_VEBT] :
% 0.29/0.56 ( ( finite5795047828879050333T_VEBT @ A5 )
% 0.29/0.56 => ( ( member_VEBT_VEBT @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ A3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1827_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_real,P2: set_real > $o] :
% 0.29/0.56 ( ( finite_finite_real @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: real,A5: set_real] :
% 0.29/0.56 ( ( finite_finite_real @ A5 )
% 0.29/0.56 => ( ( member_real @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_minus_set_real @ A5 @ ( insert_real @ A3 @ bot_bot_set_real ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bot_set_real ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1828_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_set_nat,P2: set_set_nat > $o] :
% 0.29/0.56 ( ( finite1152437895449049373et_nat @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: set_nat,A5: set_set_nat] :
% 0.29/0.56 ( ( finite1152437895449049373et_nat @ A5 )
% 0.29/0.56 => ( ( member_set_nat @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ A3 @ bot_bot_set_set_nat ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bot_set_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1829_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_complex,P2: set_complex > $o] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: complex,A5: set_complex] :
% 0.29/0.56 ( ( finite3207457112153483333omplex @ A5 )
% 0.29/0.56 => ( ( member_complex @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ A3 @ bot_bot_set_complex ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bot_set_complex ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1830_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: code_integer,A5: set_Code_integer] :
% 0.29/0.56 ( ( finite6017078050557962740nteger @ A5 )
% 0.29/0.56 => ( ( member_Code_integer @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ A3 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1831_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_int,P2: set_int > $o] :
% 0.29/0.56 ( ( finite_finite_int @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: int,A5: set_int] :
% 0.29/0.56 ( ( finite_finite_int @ A5 )
% 0.29/0.56 => ( ( member_int @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_minus_set_int @ A5 @ ( insert_int @ A3 @ bot_bot_set_int ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1832_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_o,P2: set_o > $o] :
% 0.29/0.56 ( ( finite_finite_o @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: $o,A5: set_o] :
% 0.29/0.56 ( ( finite_finite_o @ A5 )
% 0.29/0.56 => ( ( member_o @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_minus_set_o @ A5 @ ( insert_o @ A3 @ bot_bot_set_o ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1833_finite__empty__induct,axiom,
% 0.29/0.56 ! [A4: set_nat,P2: set_nat > $o] :
% 0.29/0.56 ( ( finite_finite_nat @ A4 )
% 0.29/0.56 => ( ( P2 @ A4 )
% 0.29/0.56 => ( ! [A3: nat,A5: set_nat] :
% 0.29/0.56 ( ( finite_finite_nat @ A5 )
% 0.29/0.56 => ( ( member_nat @ A3 @ A5 )
% 0.29/0.56 => ( ( P2 @ A5 )
% 0.29/0.56 => ( P2 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ A3 @ bot_bot_set_nat ) ) ) ) ) )
% 0.29/0.56 => ( P2 @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % finite_empty_induct
% 0.29/0.56 thf(fact_1834_subset__singleton__iff,axiom,
% 0.29/0.56 ! [X6: set_VEBT_VEBT,A: vEBT_VEBT] :
% 0.29/0.56 ( ( ord_le4337996190870823476T_VEBT @ X6 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 = ( ( X6 = bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 | ( X6
% 0.29/0.56 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singleton_iff
% 0.29/0.56 thf(fact_1835_subset__singleton__iff,axiom,
% 0.29/0.56 ! [X6: set_nat,A: nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ X6 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.29/0.56 = ( ( X6 = bot_bot_set_nat )
% 0.29/0.56 | ( X6
% 0.29/0.56 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singleton_iff
% 0.29/0.56 thf(fact_1836_subset__singleton__iff,axiom,
% 0.29/0.56 ! [X6: set_o,A: $o] :
% 0.29/0.56 ( ( ord_less_eq_set_o @ X6 @ ( insert_o @ A @ bot_bot_set_o ) )
% 0.29/0.56 = ( ( X6 = bot_bot_set_o )
% 0.29/0.56 | ( X6
% 0.29/0.56 = ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singleton_iff
% 0.29/0.56 thf(fact_1837_subset__singleton__iff,axiom,
% 0.29/0.56 ! [X6: set_int,A: int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ X6 @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.29/0.56 = ( ( X6 = bot_bot_set_int )
% 0.29/0.56 | ( X6
% 0.29/0.56 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singleton_iff
% 0.29/0.56 thf(fact_1838_subset__singletonD,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.29/0.56 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.56 => ( ( A4 = bot_bo8194388402131092736T_VEBT )
% 0.29/0.56 | ( A4
% 0.29/0.56 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singletonD
% 0.29/0.56 thf(fact_1839_subset__singletonD,axiom,
% 0.29/0.56 ! [A4: set_nat,X: nat] :
% 0.29/0.56 ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.29/0.56 => ( ( A4 = bot_bot_set_nat )
% 0.29/0.56 | ( A4
% 0.29/0.56 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singletonD
% 0.29/0.56 thf(fact_1840_subset__singletonD,axiom,
% 0.29/0.56 ! [A4: set_o,X: $o] :
% 0.29/0.56 ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.29/0.56 => ( ( A4 = bot_bot_set_o )
% 0.29/0.56 | ( A4
% 0.29/0.56 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singletonD
% 0.29/0.56 thf(fact_1841_subset__singletonD,axiom,
% 0.29/0.56 ! [A4: set_int,X: int] :
% 0.29/0.56 ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.29/0.56 => ( ( A4 = bot_bot_set_int )
% 0.29/0.56 | ( A4
% 0.29/0.56 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_singletonD
% 0.29/0.56 thf(fact_1842_subset__insert__iff,axiom,
% 0.29/0.56 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.56 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 0.29/0.56 = ( ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) )
% 0.29/0.56 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.56 => ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert_iff
% 0.29/0.56 thf(fact_1843_subset__insert__iff,axiom,
% 0.29/0.56 ! [A4: set_real,X: real,B4: set_real] :
% 0.29/0.56 ( ( ord_less_eq_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 0.29/0.56 = ( ( ( member_real @ X @ A4 )
% 0.29/0.56 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B4 ) )
% 0.29/0.56 & ( ~ ( member_real @ X @ A4 )
% 0.29/0.56 => ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert_iff
% 0.29/0.56 thf(fact_1844_subset__insert__iff,axiom,
% 0.29/0.56 ! [A4: set_set_nat,X: set_nat,B4: set_set_nat] :
% 0.29/0.56 ( ( ord_le6893508408891458716et_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 0.29/0.56 = ( ( ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B4 ) )
% 0.29/0.56 & ( ~ ( member_set_nat @ X @ A4 )
% 0.29/0.56 => ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ) ).
% 0.29/0.56
% 0.29/0.56 % subset_insert_iff
% 0.29/0.57 thf(fact_1845_subset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o,B4: set_o] :
% 0.29/0.57 ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_o @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_o @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_insert_iff
% 0.29/0.57 thf(fact_1846_subset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat,B4: set_nat] :
% 0.29/0.57 ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_insert_iff
% 0.29/0.57 thf(fact_1847_subset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int,B4: set_int] :
% 0.29/0.57 ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_int @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_int @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_insert_iff
% 0.29/0.57 thf(fact_1848_Diff__single__insert,axiom,
% 0.29/0.57 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.57 ( ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 )
% 0.29/0.57 => ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Diff_single_insert
% 0.29/0.57 thf(fact_1849_Diff__single__insert,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o,B4: set_o] :
% 0.29/0.57 ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 )
% 0.29/0.57 => ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Diff_single_insert
% 0.29/0.57 thf(fact_1850_Diff__single__insert,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat,B4: set_nat] :
% 0.29/0.57 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 )
% 0.29/0.57 => ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Diff_single_insert
% 0.29/0.57 thf(fact_1851_Diff__single__insert,axiom,
% 0.29/0.57 ! [A4: set_int,X: int,B4: set_int] :
% 0.29/0.57 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 )
% 0.29/0.57 => ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Diff_single_insert
% 0.29/0.57 thf(fact_1852_remove__subset,axiom,
% 0.29/0.57 ! [X: vEBT_VEBT,S3: set_VEBT_VEBT] :
% 0.29/0.57 ( ( member_VEBT_VEBT @ X @ S3 )
% 0.29/0.57 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ S3 ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_subset
% 0.29/0.57 thf(fact_1853_remove__subset,axiom,
% 0.29/0.57 ! [X: real,S3: set_real] :
% 0.29/0.57 ( ( member_real @ X @ S3 )
% 0.29/0.57 => ( ord_less_set_real @ ( minus_minus_set_real @ S3 @ ( insert_real @ X @ bot_bot_set_real ) ) @ S3 ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_subset
% 0.29/0.57 thf(fact_1854_remove__subset,axiom,
% 0.29/0.57 ! [X: set_nat,S3: set_set_nat] :
% 0.29/0.57 ( ( member_set_nat @ X @ S3 )
% 0.29/0.57 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ S3 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ S3 ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_subset
% 0.29/0.57 thf(fact_1855_remove__subset,axiom,
% 0.29/0.57 ! [X: int,S3: set_int] :
% 0.29/0.57 ( ( member_int @ X @ S3 )
% 0.29/0.57 => ( ord_less_set_int @ ( minus_minus_set_int @ S3 @ ( insert_int @ X @ bot_bot_set_int ) ) @ S3 ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_subset
% 0.29/0.57 thf(fact_1856_remove__subset,axiom,
% 0.29/0.57 ! [X: $o,S3: set_o] :
% 0.29/0.57 ( ( member_o @ X @ S3 )
% 0.29/0.57 => ( ord_less_set_o @ ( minus_minus_set_o @ S3 @ ( insert_o @ X @ bot_bot_set_o ) ) @ S3 ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_subset
% 0.29/0.57 thf(fact_1857_remove__subset,axiom,
% 0.29/0.57 ! [X: nat,S3: set_nat] :
% 0.29/0.57 ( ( member_nat @ X @ S3 )
% 0.29/0.57 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S3 ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_subset
% 0.29/0.57 thf(fact_1858_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ! [X3: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ S5 )
% 0.29/0.57 => ( ! [Y5: vEBT_VEBT] :
% 0.29/0.57 ( ( member_VEBT_VEBT @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1859_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_real,P2: set_real > $o,F: real > rat] :
% 0.29/0.57 ( ( finite_finite_real @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ! [X3: real,S5: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ S5 )
% 0.29/0.57 => ( ! [Y5: real] :
% 0.29/0.57 ( ( member_real @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_real @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1860_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_complex,P2: set_complex > $o,F: complex > rat] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.57 => ( ! [X3: complex,S5: set_complex] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ S5 )
% 0.29/0.57 => ( ! [Y5: complex] :
% 0.29/0.57 ( ( member_complex @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_complex @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1861_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_Code_integer,P2: set_Code_integer > $o,F: code_integer > rat] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [X3: code_integer,S5: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ S5 )
% 0.29/0.57 => ( ! [Y5: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_Code_integer @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1862_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_nat,P2: set_nat > $o,F: nat > rat] :
% 0.29/0.57 ( ( finite_finite_nat @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ! [X3: nat,S5: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ S5 )
% 0.29/0.57 => ( ! [Y5: nat] :
% 0.29/0.57 ( ( member_nat @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_nat @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1863_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_int,P2: set_int > $o,F: int > rat] :
% 0.29/0.57 ( ( finite_finite_int @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ! [X3: int,S5: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ S5 )
% 0.29/0.57 => ( ! [Y5: int] :
% 0.29/0.57 ( ( member_int @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_int @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1864_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_o,P2: set_o > $o,F: $o > rat] :
% 0.29/0.57 ( ( finite_finite_o @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ! [X3: $o,S5: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ S5 )
% 0.29/0.57 => ( ! [Y5: $o] :
% 0.29/0.57 ( ( member_o @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_o @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1865_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ! [X3: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ S5 )
% 0.29/0.57 => ( ! [Y5: vEBT_VEBT] :
% 0.29/0.57 ( ( member_VEBT_VEBT @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1866_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_real,P2: set_real > $o,F: real > num] :
% 0.29/0.57 ( ( finite_finite_real @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ! [X3: real,S5: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ S5 )
% 0.29/0.57 => ( ! [Y5: real] :
% 0.29/0.57 ( ( member_real @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_real @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1867_finite__ranking__induct,axiom,
% 0.29/0.57 ! [S3: set_complex,P2: set_complex > $o,F: complex > num] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.57 => ( ! [X3: complex,S5: set_complex] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ S5 )
% 0.29/0.57 => ( ! [Y5: complex] :
% 0.29/0.57 ( ( member_complex @ Y5 @ S5 )
% 0.29/0.57 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 0.29/0.57 => ( ( P2 @ S5 )
% 0.29/0.57 => ( P2 @ ( insert_complex @ X3 @ S5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_ranking_induct
% 0.29/0.57 thf(fact_1868_finite__linorder__max__induct,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [B3: code_integer,A5: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A5 )
% 0.29/0.57 => ( ! [X5: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X5 @ A5 )
% 0.29/0.57 => ( ord_le6747313008572928689nteger @ X5 @ B3 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_Code_integer @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_max_induct
% 0.29/0.57 thf(fact_1869_finite__linorder__max__induct,axiom,
% 0.29/0.57 ! [A4: set_o,P2: set_o > $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ! [B3: $o,A5: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ A5 )
% 0.29/0.57 => ( ! [X5: $o] :
% 0.29/0.57 ( ( member_o @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_o @ X5 @ B3 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_o @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_max_induct
% 0.29/0.57 thf(fact_1870_finite__linorder__max__induct,axiom,
% 0.29/0.57 ! [A4: set_real,P2: set_real > $o] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ! [B3: real,A5: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ A5 )
% 0.29/0.57 => ( ! [X5: real] :
% 0.29/0.57 ( ( member_real @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_real @ X5 @ B3 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_real @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_max_induct
% 0.29/0.57 thf(fact_1871_finite__linorder__max__induct,axiom,
% 0.29/0.57 ! [A4: set_rat,P2: set_rat > $o] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_rat )
% 0.29/0.57 => ( ! [B3: rat,A5: set_rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A5 )
% 0.29/0.57 => ( ! [X5: rat] :
% 0.29/0.57 ( ( member_rat @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_rat @ X5 @ B3 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_rat @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_max_induct
% 0.29/0.57 thf(fact_1872_finite__linorder__max__induct,axiom,
% 0.29/0.57 ! [A4: set_num,P2: set_num > $o] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_num )
% 0.29/0.57 => ( ! [B3: num,A5: set_num] :
% 0.29/0.57 ( ( finite_finite_num @ A5 )
% 0.29/0.57 => ( ! [X5: num] :
% 0.29/0.57 ( ( member_num @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_num @ X5 @ B3 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_num @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_max_induct
% 0.29/0.57 thf(fact_1873_finite__linorder__max__induct,axiom,
% 0.29/0.57 ! [A4: set_nat,P2: set_nat > $o] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ! [B3: nat,A5: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A5 )
% 0.29/0.57 => ( ! [X5: nat] :
% 0.29/0.57 ( ( member_nat @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_nat @ X5 @ B3 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_nat @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_max_induct
% 0.29/0.57 thf(fact_1874_finite__linorder__max__induct,axiom,
% 0.29/0.57 ! [A4: set_int,P2: set_int > $o] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ! [B3: int,A5: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A5 )
% 0.29/0.57 => ( ! [X5: int] :
% 0.29/0.57 ( ( member_int @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_int @ X5 @ B3 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_int @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_max_induct
% 0.29/0.57 thf(fact_1875_finite__linorder__min__induct,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [B3: code_integer,A5: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A5 )
% 0.29/0.57 => ( ! [X5: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X5 @ A5 )
% 0.29/0.57 => ( ord_le6747313008572928689nteger @ B3 @ X5 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_Code_integer @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_min_induct
% 0.29/0.57 thf(fact_1876_finite__linorder__min__induct,axiom,
% 0.29/0.57 ! [A4: set_o,P2: set_o > $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ! [B3: $o,A5: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ A5 )
% 0.29/0.57 => ( ! [X5: $o] :
% 0.29/0.57 ( ( member_o @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_o @ B3 @ X5 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_o @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_min_induct
% 0.29/0.57 thf(fact_1877_finite__linorder__min__induct,axiom,
% 0.29/0.57 ! [A4: set_real,P2: set_real > $o] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ! [B3: real,A5: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ A5 )
% 0.29/0.57 => ( ! [X5: real] :
% 0.29/0.57 ( ( member_real @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_real @ B3 @ X5 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_real @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_min_induct
% 0.29/0.57 thf(fact_1878_finite__linorder__min__induct,axiom,
% 0.29/0.57 ! [A4: set_rat,P2: set_rat > $o] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_rat )
% 0.29/0.57 => ( ! [B3: rat,A5: set_rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A5 )
% 0.29/0.57 => ( ! [X5: rat] :
% 0.29/0.57 ( ( member_rat @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_rat @ B3 @ X5 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_rat @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_min_induct
% 0.29/0.57 thf(fact_1879_finite__linorder__min__induct,axiom,
% 0.29/0.57 ! [A4: set_num,P2: set_num > $o] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_num )
% 0.29/0.57 => ( ! [B3: num,A5: set_num] :
% 0.29/0.57 ( ( finite_finite_num @ A5 )
% 0.29/0.57 => ( ! [X5: num] :
% 0.29/0.57 ( ( member_num @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_num @ B3 @ X5 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_num @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_min_induct
% 0.29/0.57 thf(fact_1880_finite__linorder__min__induct,axiom,
% 0.29/0.57 ! [A4: set_nat,P2: set_nat > $o] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ! [B3: nat,A5: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A5 )
% 0.29/0.57 => ( ! [X5: nat] :
% 0.29/0.57 ( ( member_nat @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_nat @ B3 @ X5 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_nat @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_min_induct
% 0.29/0.57 thf(fact_1881_finite__linorder__min__induct,axiom,
% 0.29/0.57 ! [A4: set_int,P2: set_int > $o] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ! [B3: int,A5: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A5 )
% 0.29/0.57 => ( ! [X5: int] :
% 0.29/0.57 ( ( member_int @ X5 @ A5 )
% 0.29/0.57 => ( ord_less_int @ B3 @ X5 ) )
% 0.29/0.57 => ( ( P2 @ A5 )
% 0.29/0.57 => ( P2 @ ( insert_int @ B3 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_linorder_min_induct
% 0.29/0.57 thf(fact_1882_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_VEBT_VEBT,A4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ F2 )
% 0.29/0.57 => ( ( ord_le4337996190870823476T_VEBT @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ! [A3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.29/0.57 => ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_VEBT_VEBT @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_VEBT_VEBT @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1883_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_real,A4: set_real,P2: set_real > $o] :
% 0.29/0.57 ( ( finite_finite_real @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_real @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ! [A3: real,F3: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ F3 )
% 0.29/0.57 => ( ( member_real @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_real @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_real @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1884_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_set_nat,A4: set_set_nat,P2: set_set_nat > $o] :
% 0.29/0.57 ( ( finite1152437895449049373et_nat @ F2 )
% 0.29/0.57 => ( ( ord_le6893508408891458716et_nat @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_set_nat )
% 0.29/0.57 => ( ! [A3: set_nat,F3: set_set_nat] :
% 0.29/0.57 ( ( finite1152437895449049373et_nat @ F3 )
% 0.29/0.57 => ( ( member_set_nat @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_set_nat @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_set_nat @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1885_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_complex,A4: set_complex,P2: set_complex > $o] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ F2 )
% 0.29/0.57 => ( ( ord_le211207098394363844omplex @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.57 => ( ! [A3: complex,F3: set_complex] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ F3 )
% 0.29/0.57 => ( ( member_complex @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_complex @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_complex @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1886_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_Code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ F2 )
% 0.29/0.57 => ( ( ord_le7084787975880047091nteger @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [A3: code_integer,F3: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ F3 )
% 0.29/0.57 => ( ( member_Code_integer @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_Code_integer @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_Code_integer @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1887_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_nat,A4: set_nat,P2: set_nat > $o] :
% 0.29/0.57 ( ( finite_finite_nat @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_nat @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ! [A3: nat,F3: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ F3 )
% 0.29/0.57 => ( ( member_nat @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_nat @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_nat @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1888_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_o,A4: set_o,P2: set_o > $o] :
% 0.29/0.57 ( ( finite_finite_o @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_o @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ! [A3: $o,F3: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ F3 )
% 0.29/0.57 => ( ( member_o @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_o @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_o @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1889_finite__subset__induct,axiom,
% 0.29/0.57 ! [F2: set_int,A4: set_int,P2: set_int > $o] :
% 0.29/0.57 ( ( finite_finite_int @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_int @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ! [A3: int,F3: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ F3 )
% 0.29/0.57 => ( ( member_int @ A3 @ A4 )
% 0.29/0.57 => ( ~ ( member_int @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_int @ A3 @ F3 ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct
% 0.29/0.57 thf(fact_1890_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_VEBT_VEBT,A4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ F2 )
% 0.29/0.57 => ( ( ord_le4337996190870823476T_VEBT @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ! [A3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ F3 )
% 0.29/0.57 => ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_VEBT_VEBT @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_VEBT_VEBT @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1891_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_real,A4: set_real,P2: set_real > $o] :
% 0.29/0.57 ( ( finite_finite_real @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_real @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ! [A3: real,F3: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ F3 )
% 0.29/0.57 => ( ( member_real @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_less_eq_set_real @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_real @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_real @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1892_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_set_nat,A4: set_set_nat,P2: set_set_nat > $o] :
% 0.29/0.57 ( ( finite1152437895449049373et_nat @ F2 )
% 0.29/0.57 => ( ( ord_le6893508408891458716et_nat @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_set_nat )
% 0.29/0.57 => ( ! [A3: set_nat,F3: set_set_nat] :
% 0.29/0.57 ( ( finite1152437895449049373et_nat @ F3 )
% 0.29/0.57 => ( ( member_set_nat @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_le6893508408891458716et_nat @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_set_nat @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_set_nat @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1893_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_complex,A4: set_complex,P2: set_complex > $o] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ F2 )
% 0.29/0.57 => ( ( ord_le211207098394363844omplex @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.57 => ( ! [A3: complex,F3: set_complex] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ F3 )
% 0.29/0.57 => ( ( member_complex @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_le211207098394363844omplex @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_complex @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_complex @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1894_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_Code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ F2 )
% 0.29/0.57 => ( ( ord_le7084787975880047091nteger @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [A3: code_integer,F3: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ F3 )
% 0.29/0.57 => ( ( member_Code_integer @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_le7084787975880047091nteger @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_Code_integer @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_Code_integer @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1895_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_nat,A4: set_nat,P2: set_nat > $o] :
% 0.29/0.57 ( ( finite_finite_nat @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_nat @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ! [A3: nat,F3: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ F3 )
% 0.29/0.57 => ( ( member_nat @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_less_eq_set_nat @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_nat @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_nat @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1896_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_o,A4: set_o,P2: set_o > $o] :
% 0.29/0.57 ( ( finite_finite_o @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_o @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ! [A3: $o,F3: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ F3 )
% 0.29/0.57 => ( ( member_o @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_less_eq_set_o @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_o @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_o @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1897_finite__subset__induct_H,axiom,
% 0.29/0.57 ! [F2: set_int,A4: set_int,P2: set_int > $o] :
% 0.29/0.57 ( ( finite_finite_int @ F2 )
% 0.29/0.57 => ( ( ord_less_eq_set_int @ F2 @ A4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ! [A3: int,F3: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ F3 )
% 0.29/0.57 => ( ( member_int @ A3 @ A4 )
% 0.29/0.57 => ( ( ord_less_eq_set_int @ F3 @ A4 )
% 0.29/0.57 => ( ~ ( member_int @ A3 @ F3 )
% 0.29/0.57 => ( ( P2 @ F3 )
% 0.29/0.57 => ( P2 @ ( insert_int @ A3 @ F3 ) ) ) ) ) ) )
% 0.29/0.57 => ( P2 @ F2 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_subset_induct'
% 0.29/0.57 thf(fact_1898_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_VEBT_VEBT > $o,B4: set_VEBT_VEBT] :
% 0.29/0.57 ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ( ~ ( finite5795047828879050333T_VEBT @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_VEBT_VEBT] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ( ord_le4337996190870823476T_VEBT @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: vEBT_VEBT] :
% 0.29/0.57 ( ( member_VEBT_VEBT @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1899_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_real > $o,B4: set_real] :
% 0.29/0.57 ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ( ~ ( finite_finite_real @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_eq_set_real @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: real] :
% 0.29/0.57 ( ( member_real @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_real @ A5 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1900_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_set_nat > $o,B4: set_set_nat] :
% 0.29/0.57 ( ( P2 @ bot_bot_set_set_nat )
% 0.29/0.57 => ( ( ~ ( finite1152437895449049373et_nat @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_set_nat] :
% 0.29/0.57 ( ( finite1152437895449049373et_nat @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_set_nat )
% 0.29/0.57 => ( ( ord_le6893508408891458716et_nat @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: set_nat] :
% 0.29/0.57 ( ( member_set_nat @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1901_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_complex > $o,B4: set_complex] :
% 0.29/0.57 ( ( P2 @ bot_bot_set_complex )
% 0.29/0.57 => ( ( ~ ( finite3207457112153483333omplex @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_complex] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_complex )
% 0.29/0.57 => ( ( ord_le211207098394363844omplex @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: complex] :
% 0.29/0.57 ( ( member_complex @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1902_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_Code_integer > $o,B4: set_Code_integer] :
% 0.29/0.57 ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ~ ( finite6017078050557962740nteger @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le7084787975880047091nteger @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1903_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_o > $o,B4: set_o] :
% 0.29/0.57 ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ( ~ ( finite_finite_o @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_set_o @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: $o] :
% 0.29/0.57 ( ( member_o @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1904_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_nat > $o,B4: set_nat] :
% 0.29/0.57 ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ( ~ ( finite_finite_nat @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: nat] :
% 0.29/0.57 ( ( member_nat @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1905_remove__induct,axiom,
% 0.29/0.57 ! [P2: set_int > $o,B4: set_int] :
% 0.29/0.57 ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ( ~ ( finite_finite_int @ B4 )
% 0.29/0.57 => ( P2 @ B4 ) )
% 0.29/0.57 => ( ! [A5: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_set_int @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: int] :
% 0.29/0.57 ( ( member_int @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % remove_induct
% 0.29/0.57 thf(fact_1906_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ! [A5: set_VEBT_VEBT] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ( ord_le4337996190870823476T_VEBT @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: vEBT_VEBT] :
% 0.29/0.57 ( ( member_VEBT_VEBT @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1907_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_real,P2: set_real > $o] :
% 0.29/0.57 ( ( finite_finite_real @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_real )
% 0.29/0.57 => ( ! [A5: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_eq_set_real @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: real] :
% 0.29/0.57 ( ( member_real @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_real @ A5 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1908_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_set_nat,P2: set_set_nat > $o] :
% 0.29/0.57 ( ( finite1152437895449049373et_nat @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_set_nat )
% 0.29/0.57 => ( ! [A5: set_set_nat] :
% 0.29/0.57 ( ( finite1152437895449049373et_nat @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_set_nat )
% 0.29/0.57 => ( ( ord_le6893508408891458716et_nat @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: set_nat] :
% 0.29/0.57 ( ( member_set_nat @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1909_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_complex,P2: set_complex > $o] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.57 => ( ! [A5: set_complex] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_complex )
% 0.29/0.57 => ( ( ord_le211207098394363844omplex @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: complex] :
% 0.29/0.57 ( ( member_complex @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1910_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [A5: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le7084787975880047091nteger @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1911_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_o,P2: set_o > $o] :
% 0.29/0.57 ( ( finite_finite_o @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ! [A5: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_set_o @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: $o] :
% 0.29/0.57 ( ( member_o @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1912_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_nat,P2: set_nat > $o] :
% 0.29/0.57 ( ( finite_finite_nat @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ! [A5: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: nat] :
% 0.29/0.57 ( ( member_nat @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1913_finite__remove__induct,axiom,
% 0.29/0.57 ! [B4: set_int,P2: set_int > $o] :
% 0.29/0.57 ( ( finite_finite_int @ B4 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ! [A5: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A5 )
% 0.29/0.57 => ( ( A5 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_set_int @ A5 @ B4 )
% 0.29/0.57 => ( ! [X5: int] :
% 0.29/0.57 ( ( member_int @ X5 @ A5 )
% 0.29/0.57 => ( P2 @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 0.29/0.57 => ( P2 @ A5 ) ) ) ) )
% 0.29/0.57 => ( P2 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_remove_induct
% 0.29/0.57 thf(fact_1914_finite__induct__select,axiom,
% 0.29/0.57 ! [S3: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 0.29/0.57 => ( ! [T4: set_VEBT_VEBT] :
% 0.29/0.57 ( ( ord_le3480810397992357184T_VEBT @ T4 @ S3 )
% 0.29/0.57 => ( ( P2 @ T4 )
% 0.29/0.57 => ? [X5: vEBT_VEBT] :
% 0.29/0.57 ( ( member_VEBT_VEBT @ X5 @ ( minus_5127226145743854075T_VEBT @ S3 @ T4 ) )
% 0.29/0.57 & ( P2 @ ( insert_VEBT_VEBT @ X5 @ T4 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_induct_select
% 0.29/0.57 thf(fact_1915_finite__induct__select,axiom,
% 0.29/0.57 ! [S3: set_complex,P2: set_complex > $o] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_complex )
% 0.29/0.57 => ( ! [T4: set_complex] :
% 0.29/0.57 ( ( ord_less_set_complex @ T4 @ S3 )
% 0.29/0.57 => ( ( P2 @ T4 )
% 0.29/0.57 => ? [X5: complex] :
% 0.29/0.57 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ S3 @ T4 ) )
% 0.29/0.57 & ( P2 @ ( insert_complex @ X5 @ T4 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_induct_select
% 0.29/0.57 thf(fact_1916_finite__induct__select,axiom,
% 0.29/0.57 ! [S3: set_Code_integer,P2: set_Code_integer > $o] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [T4: set_Code_integer] :
% 0.29/0.57 ( ( ord_le1307284697595431911nteger @ T4 @ S3 )
% 0.29/0.57 => ( ( P2 @ T4 )
% 0.29/0.57 => ? [X5: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X5 @ ( minus_2355218937544613996nteger @ S3 @ T4 ) )
% 0.29/0.57 & ( P2 @ ( insert_Code_integer @ X5 @ T4 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_induct_select
% 0.29/0.57 thf(fact_1917_finite__induct__select,axiom,
% 0.29/0.57 ! [S3: set_int,P2: set_int > $o] :
% 0.29/0.57 ( ( finite_finite_int @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_int )
% 0.29/0.57 => ( ! [T4: set_int] :
% 0.29/0.57 ( ( ord_less_set_int @ T4 @ S3 )
% 0.29/0.57 => ( ( P2 @ T4 )
% 0.29/0.57 => ? [X5: int] :
% 0.29/0.57 ( ( member_int @ X5 @ ( minus_minus_set_int @ S3 @ T4 ) )
% 0.29/0.57 & ( P2 @ ( insert_int @ X5 @ T4 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_induct_select
% 0.29/0.57 thf(fact_1918_finite__induct__select,axiom,
% 0.29/0.57 ! [S3: set_o,P2: set_o > $o] :
% 0.29/0.57 ( ( finite_finite_o @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_o )
% 0.29/0.57 => ( ! [T4: set_o] :
% 0.29/0.57 ( ( ord_less_set_o @ T4 @ S3 )
% 0.29/0.57 => ( ( P2 @ T4 )
% 0.29/0.57 => ? [X5: $o] :
% 0.29/0.57 ( ( member_o @ X5 @ ( minus_minus_set_o @ S3 @ T4 ) )
% 0.29/0.57 & ( P2 @ ( insert_o @ X5 @ T4 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_induct_select
% 0.29/0.57 thf(fact_1919_finite__induct__select,axiom,
% 0.29/0.57 ! [S3: set_nat,P2: set_nat > $o] :
% 0.29/0.57 ( ( finite_finite_nat @ S3 )
% 0.29/0.57 => ( ( P2 @ bot_bot_set_nat )
% 0.29/0.57 => ( ! [T4: set_nat] :
% 0.29/0.57 ( ( ord_less_set_nat @ T4 @ S3 )
% 0.29/0.57 => ( ( P2 @ T4 )
% 0.29/0.57 => ? [X5: nat] :
% 0.29/0.57 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ S3 @ T4 ) )
% 0.29/0.57 & ( P2 @ ( insert_nat @ X5 @ T4 ) ) ) ) )
% 0.29/0.57 => ( P2 @ S3 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_induct_select
% 0.29/0.57 thf(fact_1920_psubset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.57 ( ( ord_le3480810397992357184T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_VEBT_VEBT @ X @ B4 )
% 0.29/0.57 => ( ord_le3480810397992357184T_VEBT @ A4 @ B4 ) )
% 0.29/0.57 & ( ~ ( member_VEBT_VEBT @ X @ B4 )
% 0.29/0.57 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.57 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.57 => ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % psubset_insert_iff
% 0.29/0.57 thf(fact_1921_psubset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_real,X: real,B4: set_real] :
% 0.29/0.57 ( ( ord_less_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_real @ X @ B4 )
% 0.29/0.57 => ( ord_less_set_real @ A4 @ B4 ) )
% 0.29/0.57 & ( ~ ( member_real @ X @ B4 )
% 0.29/0.57 => ( ( ( member_real @ X @ A4 )
% 0.29/0.57 => ( ord_less_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_real @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % psubset_insert_iff
% 0.29/0.57 thf(fact_1922_psubset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_set_nat,X: set_nat,B4: set_set_nat] :
% 0.29/0.57 ( ( ord_less_set_set_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_set_nat @ X @ B4 )
% 0.29/0.57 => ( ord_less_set_set_nat @ A4 @ B4 ) )
% 0.29/0.57 & ( ~ ( member_set_nat @ X @ B4 )
% 0.29/0.57 => ( ( ( member_set_nat @ X @ A4 )
% 0.29/0.57 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_set_nat @ X @ A4 )
% 0.29/0.57 => ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % psubset_insert_iff
% 0.29/0.57 thf(fact_1923_psubset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o,B4: set_o] :
% 0.29/0.57 ( ( ord_less_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_o @ X @ B4 )
% 0.29/0.57 => ( ord_less_set_o @ A4 @ B4 ) )
% 0.29/0.57 & ( ~ ( member_o @ X @ B4 )
% 0.29/0.57 => ( ( ( member_o @ X @ A4 )
% 0.29/0.57 => ( ord_less_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_o @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % psubset_insert_iff
% 0.29/0.57 thf(fact_1924_psubset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat,B4: set_nat] :
% 0.29/0.57 ( ( ord_less_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_nat @ X @ B4 )
% 0.29/0.57 => ( ord_less_set_nat @ A4 @ B4 ) )
% 0.29/0.57 & ( ~ ( member_nat @ X @ B4 )
% 0.29/0.57 => ( ( ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % psubset_insert_iff
% 0.29/0.57 thf(fact_1925_psubset__insert__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int,B4: set_int] :
% 0.29/0.57 ( ( ord_less_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 0.29/0.57 = ( ( ( member_int @ X @ B4 )
% 0.29/0.57 => ( ord_less_set_int @ A4 @ B4 ) )
% 0.29/0.57 & ( ~ ( member_int @ X @ B4 )
% 0.29/0.57 => ( ( ( member_int @ X @ A4 )
% 0.29/0.57 => ( ord_less_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) )
% 0.29/0.57 & ( ~ ( member_int @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % psubset_insert_iff
% 0.29/0.57 thf(fact_1926_finite__list,axiom,
% 0.29/0.57 ! [A4: set_VEBT_VEBT] :
% 0.29/0.57 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.29/0.57 => ? [Xs3: list_VEBT_VEBT] :
% 0.29/0.57 ( ( set_VEBT_VEBT2 @ Xs3 )
% 0.29/0.57 = A4 ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_list
% 0.29/0.57 thf(fact_1927_finite__list,axiom,
% 0.29/0.57 ! [A4: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ? [Xs3: list_real] :
% 0.29/0.57 ( ( set_real2 @ Xs3 )
% 0.29/0.57 = A4 ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_list
% 0.29/0.57 thf(fact_1928_finite__list,axiom,
% 0.29/0.57 ! [A4: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ? [Xs3: list_o] :
% 0.29/0.57 ( ( set_o2 @ Xs3 )
% 0.29/0.57 = A4 ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_list
% 0.29/0.57 thf(fact_1929_finite__list,axiom,
% 0.29/0.57 ! [A4: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ? [Xs3: list_nat] :
% 0.29/0.57 ( ( set_nat2 @ Xs3 )
% 0.29/0.57 = A4 ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_list
% 0.29/0.57 thf(fact_1930_finite__list,axiom,
% 0.29/0.57 ! [A4: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ? [Xs3: list_int] :
% 0.29/0.57 ( ( set_int2 @ Xs3 )
% 0.29/0.57 = A4 ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_list
% 0.29/0.57 thf(fact_1931_finite__list,axiom,
% 0.29/0.57 ! [A4: set_complex] :
% 0.29/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.29/0.57 => ? [Xs3: list_complex] :
% 0.29/0.57 ( ( set_complex2 @ Xs3 )
% 0.29/0.57 = A4 ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_list
% 0.29/0.57 thf(fact_1932_finite__list,axiom,
% 0.29/0.57 ! [A4: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ? [Xs3: list_Code_integer] :
% 0.29/0.57 ( ( set_Code_integer2 @ Xs3 )
% 0.29/0.57 = A4 ) ) ).
% 0.29/0.57
% 0.29/0.57 % finite_list
% 0.29/0.57 thf(fact_1933_subset__code_I1_J,axiom,
% 0.29/0.57 ! [Xs: list_set_nat,B4: set_set_nat] :
% 0.29/0.57 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B4 )
% 0.29/0.57 = ( ! [X4: set_nat] :
% 0.29/0.57 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 0.29/0.57 => ( member_set_nat @ X4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_code(1)
% 0.29/0.57 thf(fact_1934_subset__code_I1_J,axiom,
% 0.29/0.57 ! [Xs: list_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.29/0.57 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B4 )
% 0.29/0.57 = ( ! [X4: vEBT_VEBT] :
% 0.29/0.57 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.29/0.57 => ( member_VEBT_VEBT @ X4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_code(1)
% 0.29/0.57 thf(fact_1935_subset__code_I1_J,axiom,
% 0.29/0.57 ! [Xs: list_nat,B4: set_nat] :
% 0.29/0.57 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B4 )
% 0.29/0.57 = ( ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.29/0.57 => ( member_nat @ X4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_code(1)
% 0.29/0.57 thf(fact_1936_subset__code_I1_J,axiom,
% 0.29/0.57 ! [Xs: list_real,B4: set_real] :
% 0.29/0.57 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B4 )
% 0.29/0.57 = ( ! [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 0.29/0.57 => ( member_real @ X4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_code(1)
% 0.29/0.57 thf(fact_1937_subset__code_I1_J,axiom,
% 0.29/0.57 ! [Xs: list_o,B4: set_o] :
% 0.29/0.57 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ B4 )
% 0.29/0.57 = ( ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.29/0.57 => ( member_o @ X4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_code(1)
% 0.29/0.57 thf(fact_1938_subset__code_I1_J,axiom,
% 0.29/0.57 ! [Xs: list_int,B4: set_int] :
% 0.29/0.57 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B4 )
% 0.29/0.57 = ( ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.29/0.57 => ( member_int @ X4 @ B4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % subset_code(1)
% 0.29/0.57 thf(fact_1939_geqmaxNone,axiom,
% 0.29/0.57 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.57 => ( ( ord_less_eq_nat @ Ma @ X )
% 0.29/0.57 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.29/0.57 = none_nat ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % geqmaxNone
% 0.29/0.57 thf(fact_1940_pred__corr,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.29/0.57 = ( some_nat @ Px ) )
% 0.29/0.57 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % pred_corr
% 0.29/0.57 thf(fact_1941_pred__correct,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.29/0.57 = ( some_nat @ Sx ) )
% 0.29/0.57 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % pred_correct
% 0.29/0.57 thf(fact_1942_set__vebt__pred,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.29/0.57 = ( some_nat @ Px ) )
% 0.29/0.57 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % set_vebt_pred
% 0.29/0.57 thf(fact_1943_succ__corr,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.29/0.57 = ( some_nat @ Sx ) )
% 0.29/0.57 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % succ_corr
% 0.29/0.57 thf(fact_1944_succ__correct,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.29/0.57 = ( some_nat @ Sx ) )
% 0.29/0.57 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % succ_correct
% 0.29/0.57 thf(fact_1945_maxt__sound,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.29/0.57 => ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % maxt_sound
% 0.29/0.57 thf(fact_1946_maxt__corr,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ X ) )
% 0.29/0.57 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % maxt_corr
% 0.29/0.57 thf(fact_1947_set__vebt__maxt,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ X ) )
% 0.29/0.57 = ( vEBT_VEBT_max_in_set @ ( vEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % set_vebt_maxt
% 0.29/0.57 thf(fact_1948_mint__sound,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.29/0.57 => ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = ( some_nat @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % mint_sound
% 0.29/0.57 thf(fact_1949_maxbmo,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,X: nat] :
% 0.29/0.57 ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ X ) )
% 0.29/0.57 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 0.29/0.57
% 0.29/0.57 % maxbmo
% 0.29/0.57 thf(fact_1950_minNullmin,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT] :
% 0.29/0.57 ( ( vEBT_VEBT_minNull @ T )
% 0.29/0.57 => ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = none_nat ) ) ).
% 0.29/0.57
% 0.29/0.57 % minNullmin
% 0.29/0.57 thf(fact_1951_minminNull,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT] :
% 0.29/0.57 ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = none_nat )
% 0.29/0.57 => ( vEBT_VEBT_minNull @ T ) ) ).
% 0.29/0.57
% 0.29/0.57 % minminNull
% 0.29/0.57 thf(fact_1952_vebt__minNull__mint,axiom,
% 0.29/0.57 ( vEBT_VEBT_minNull
% 0.29/0.57 = ( ^ [T2: vEBT_VEBT] :
% 0.29/0.57 ( ( vEBT_vebt_mint @ T2 )
% 0.29/0.57 = none_nat ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_minNull_mint
% 0.29/0.57 thf(fact_1953_mint__member,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = ( some_nat @ Maxi ) )
% 0.29/0.57 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % mint_member
% 0.29/0.57 thf(fact_1954_maxt__member,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ Maxi ) )
% 0.29/0.57 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % maxt_member
% 0.29/0.57 thf(fact_1955_mint__corr__help,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = ( some_nat @ Mini ) )
% 0.29/0.57 => ( ( vEBT_vebt_member @ T @ X )
% 0.29/0.57 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % mint_corr_help
% 0.29/0.57 thf(fact_1956_maxt__corr__help,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ Maxi ) )
% 0.29/0.57 => ( ( vEBT_vebt_member @ T @ X )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % maxt_corr_help
% 0.29/0.57 thf(fact_1957_set__vebt__mint_H,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = ( some_nat @ X ) )
% 0.29/0.57 = ( ( member_nat @ X @ ( vEBT_set_vebt @ T ) )
% 0.29/0.57 & ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ ( vEBT_set_vebt @ T ) )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ X4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % set_vebt_mint'
% 0.29/0.57 thf(fact_1958_set__vebt__maxt_H,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ X ) )
% 0.29/0.57 = ( ( member_nat @ X @ ( vEBT_set_vebt @ T ) )
% 0.29/0.57 & ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ ( vEBT_set_vebt @ T ) )
% 0.29/0.57 => ( ord_less_eq_nat @ X4 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % set_vebt_maxt'
% 0.29/0.57 thf(fact_1959_mint__corr__help__empty,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = none_nat )
% 0.29/0.57 => ( ( vEBT_VEBT_set_vebt @ T )
% 0.29/0.57 = bot_bot_set_nat ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % mint_corr_help_empty
% 0.29/0.57 thf(fact_1960_maxt__corr__help__empty,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = none_nat )
% 0.29/0.57 => ( ( vEBT_VEBT_set_vebt @ T )
% 0.29/0.57 = bot_bot_set_nat ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % maxt_corr_help_empty
% 0.29/0.57 thf(fact_1961_set__vebt__mint,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = ( some_nat @ X ) )
% 0.29/0.57 = ( vEBT_VEBT_min_in_set @ ( vEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % set_vebt_mint
% 0.29/0.57 thf(fact_1962_mint__corr,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = ( some_nat @ X ) )
% 0.29/0.57 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % mint_corr
% 0.29/0.57 thf(fact_1963_vebt__succ_Osimps_I2_J,axiom,
% 0.29/0.57 ! [Uv2: $o,Uw2: $o,N: nat] :
% 0.29/0.57 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_succ.simps(2)
% 0.29/0.57 thf(fact_1964_vebt__pred_Osimps_I1_J,axiom,
% 0.29/0.57 ! [Uu2: $o,Uv2: $o] :
% 0.29/0.57 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_pred.simps(1)
% 0.29/0.57 thf(fact_1965_vebt__succ_Osimps_I3_J,axiom,
% 0.29/0.57 ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 0.29/0.57 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz ) @ Va2 )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_succ.simps(3)
% 0.29/0.57 thf(fact_1966_vebt__pred_Osimps_I4_J,axiom,
% 0.29/0.57 ! [Uy2: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 0.29/0.57 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz @ Va2 ) @ Vb )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_pred.simps(4)
% 0.29/0.57 thf(fact_1967_vebt__succ_Osimps_I4_J,axiom,
% 0.29/0.57 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 0.29/0.57 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_succ.simps(4)
% 0.29/0.57 thf(fact_1968_vebt__pred_Osimps_I5_J,axiom,
% 0.29/0.57 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 0.29/0.57 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_pred.simps(5)
% 0.29/0.57 thf(fact_1969_vebt__succ_Osimps_I5_J,axiom,
% 0.29/0.57 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 0.29/0.57 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_succ.simps(5)
% 0.29/0.57 thf(fact_1970_vebt__pred_Osimps_I6_J,axiom,
% 0.29/0.57 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 0.29/0.57 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_pred.simps(6)
% 0.29/0.57 thf(fact_1971_vebt__succ_Osimps_I1_J,axiom,
% 0.29/0.57 ! [B: $o,Uu2: $o] :
% 0.29/0.57 ( ( B
% 0.29/0.57 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ B
% 0.29/0.57 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.29/0.57 = none_nat ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_succ.simps(1)
% 0.29/0.57 thf(fact_1972_vebt__succ__code_I1_J,axiom,
% 0.29/0.57 ! [B: $o,X: nat,A: $o] :
% 0.29/0.57 ( ( ( B
% 0.29/0.57 & ( X = zero_zero_nat ) )
% 0.29/0.57 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ ( B
% 0.29/0.57 & ( X = zero_zero_nat ) )
% 0.29/0.57 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = none_nat ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_succ_code(1)
% 0.29/0.57 thf(fact_1973_vebt__pred_Osimps_I2_J,axiom,
% 0.29/0.57 ! [A: $o,Uw2: $o] :
% 0.29/0.57 ( ( A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.57 = none_nat ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_pred.simps(2)
% 0.29/0.57 thf(fact_1974_vebt__pred__code,axiom,
% 0.29/0.57 ! [X: nat,A: $o,B: $o] :
% 0.29/0.57 ( ( ( X = zero_zero_nat )
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = none_nat ) )
% 0.29/0.57 & ( ( X != zero_zero_nat )
% 0.29/0.57 => ( ( ( X = one_one_nat )
% 0.29/0.57 => ( ( A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = none_nat ) ) ) )
% 0.29/0.57 & ( ( X != one_one_nat )
% 0.29/0.57 => ( ( B
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ B
% 0.29/0.57 => ( ( A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.57 = none_nat ) ) ) ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_pred_code
% 0.29/0.57 thf(fact_1975_vebt__pred_Osimps_I3_J,axiom,
% 0.29/0.57 ! [B: $o,A: $o,Va2: nat] :
% 0.29/0.57 ( ( B
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ B
% 0.29/0.57 => ( ( A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A
% 0.29/0.57 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.57 = none_nat ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_pred.simps(3)
% 0.29/0.57 thf(fact_1976_vebt__maxt_Oelims,axiom,
% 0.29/0.57 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.29/0.57 ( ( ( vEBT_vebt_maxt @ X )
% 0.29/0.57 = Y )
% 0.29/0.57 => ( ! [A3: $o,B3: $o] :
% 0.29/0.57 ( ( X
% 0.29/0.57 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.29/0.57 => ~ ( ( B3
% 0.29/0.57 => ( Y
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ B3
% 0.29/0.57 => ( ( A3
% 0.29/0.57 => ( Y
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A3
% 0.29/0.57 => ( Y = none_nat ) ) ) ) ) )
% 0.29/0.57 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.57 ( X
% 0.29/0.57 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.57 => ( Y != none_nat ) )
% 0.29/0.57 => ~ ! [Mi2: nat,Ma2: nat] :
% 0.29/0.57 ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.29/0.57 ( X
% 0.29/0.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.29/0.57 => ( Y
% 0.29/0.57 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_maxt.elims
% 0.29/0.57 thf(fact_1977_vebt__mint_Oelims,axiom,
% 0.29/0.57 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.29/0.57 ( ( ( vEBT_vebt_mint @ X )
% 0.29/0.57 = Y )
% 0.29/0.57 => ( ! [A3: $o,B3: $o] :
% 0.29/0.57 ( ( X
% 0.29/0.57 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.29/0.57 => ~ ( ( A3
% 0.29/0.57 => ( Y
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A3
% 0.29/0.57 => ( ( B3
% 0.29/0.57 => ( Y
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ B3
% 0.29/0.57 => ( Y = none_nat ) ) ) ) ) )
% 0.29/0.57 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.57 ( X
% 0.29/0.57 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.57 => ( Y != none_nat ) )
% 0.29/0.57 => ~ ! [Mi2: nat] :
% 0.29/0.57 ( ? [Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.29/0.57 ( X
% 0.29/0.57 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.29/0.57 => ( Y
% 0.29/0.57 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_mint.elims
% 0.29/0.57 thf(fact_1978_vebt__maxt_Osimps_I1_J,axiom,
% 0.29/0.57 ! [B: $o,A: $o] :
% 0.29/0.57 ( ( B
% 0.29/0.57 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ B
% 0.29/0.57 => ( ( A
% 0.29/0.57 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A
% 0.29/0.57 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.57 = none_nat ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_maxt.simps(1)
% 0.29/0.57 thf(fact_1979_vebt__mint_Osimps_I1_J,axiom,
% 0.29/0.57 ! [A: $o,B: $o] :
% 0.29/0.57 ( ( A
% 0.29/0.57 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.57 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.57 & ( ~ A
% 0.29/0.57 => ( ( B
% 0.29/0.57 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.57 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.57 & ( ~ B
% 0.29/0.57 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.57 = none_nat ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_mint.simps(1)
% 0.29/0.57 thf(fact_1980_vebt__maxt_Osimps_I3_J,axiom,
% 0.29/0.57 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.29/0.57 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.29/0.57 = ( some_nat @ Ma ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_maxt.simps(3)
% 0.29/0.57 thf(fact_1981_vebt__mint_Osimps_I3_J,axiom,
% 0.29/0.57 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.29/0.57 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.29/0.57 = ( some_nat @ Mi ) ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_mint.simps(3)
% 0.29/0.57 thf(fact_1982_set__vebt__mint_H_H,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( ( vEBT_set_vebt @ T )
% 0.29/0.57 = bot_bot_set_nat )
% 0.29/0.57 => ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = none_nat ) )
% 0.29/0.57 & ( ( ( vEBT_set_vebt @ T )
% 0.29/0.57 != bot_bot_set_nat )
% 0.29/0.57 => ( ( vEBT_vebt_mint @ T )
% 0.29/0.57 = ( some_nat @ ( lattic8721135487736765967in_nat @ ( vEBT_set_vebt @ T ) ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % set_vebt_mint''
% 0.29/0.57 thf(fact_1983_set__vebt__maxt_H_H,axiom,
% 0.29/0.57 ! [T: vEBT_VEBT,N: nat] :
% 0.29/0.57 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.57 => ( ( ( ( vEBT_set_vebt @ T )
% 0.29/0.57 = bot_bot_set_nat )
% 0.29/0.57 => ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = none_nat ) )
% 0.29/0.57 & ( ( ( vEBT_set_vebt @ T )
% 0.29/0.57 != bot_bot_set_nat )
% 0.29/0.57 => ( ( vEBT_vebt_maxt @ T )
% 0.29/0.57 = ( some_nat @ ( lattic8265883725875713057ax_nat @ ( vEBT_set_vebt @ T ) ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % set_vebt_maxt''
% 0.29/0.57 thf(fact_1984_vebt__maxt_Osimps_I2_J,axiom,
% 0.29/0.57 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.29/0.57 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_maxt.simps(2)
% 0.29/0.57 thf(fact_1985_vebt__mint_Osimps_I2_J,axiom,
% 0.29/0.57 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.29/0.57 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.29/0.57 = none_nat ) ).
% 0.29/0.57
% 0.29/0.57 % vebt_mint.simps(2)
% 0.29/0.57 thf(fact_1986_Max__singleton,axiom,
% 0.29/0.57 ! [X: int] :
% 0.29/0.57 ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.29/0.57 = X ) ).
% 0.29/0.57
% 0.29/0.57 % Max_singleton
% 0.29/0.57 thf(fact_1987_Max__singleton,axiom,
% 0.29/0.57 ! [X: $o] :
% 0.29/0.57 ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.29/0.57 = X ) ).
% 0.29/0.57
% 0.29/0.57 % Max_singleton
% 0.29/0.57 thf(fact_1988_Max__singleton,axiom,
% 0.29/0.57 ! [X: nat] :
% 0.29/0.57 ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.29/0.57 = X ) ).
% 0.29/0.57
% 0.29/0.57 % Max_singleton
% 0.29/0.57 thf(fact_1989_Min__singleton,axiom,
% 0.29/0.57 ! [X: int] :
% 0.29/0.57 ( ( lattic8718645017227715691in_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.29/0.57 = X ) ).
% 0.29/0.57
% 0.29/0.57 % Min_singleton
% 0.29/0.57 thf(fact_1990_Min__singleton,axiom,
% 0.29/0.57 ! [X: $o] :
% 0.29/0.57 ( ( lattic1973801136483472281_Min_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.29/0.57 = X ) ).
% 0.29/0.57
% 0.29/0.57 % Min_singleton
% 0.29/0.57 thf(fact_1991_Min__singleton,axiom,
% 0.29/0.57 ! [X: nat] :
% 0.29/0.57 ( ( lattic8721135487736765967in_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.29/0.57 = X ) ).
% 0.29/0.57
% 0.29/0.57 % Min_singleton
% 0.29/0.57 thf(fact_1992_Max_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.bounded_iff
% 0.29/0.57 thf(fact_1993_Max_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.bounded_iff
% 0.29/0.57 thf(fact_1994_Max_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.bounded_iff
% 0.29/0.57 thf(fact_1995_Max_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.bounded_iff
% 0.29/0.57 thf(fact_1996_Max_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.bounded_iff
% 0.29/0.57 thf(fact_1997_Max_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.bounded_iff
% 0.29/0.57 thf(fact_1998_Max__less__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le6747313008572928689nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le6747313008572928689nteger @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_less_iff
% 0.29/0.57 thf(fact_1999_Max__less__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_o @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_less_iff
% 0.29/0.57 thf(fact_2000_Max__less__iff,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_real @ ( lattic4275903605611617917x_real @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_real @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_less_iff
% 0.29/0.57 thf(fact_2001_Max__less__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_rat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_less_iff
% 0.29/0.57 thf(fact_2002_Max__less__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_num @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_less_iff
% 0.29/0.57 thf(fact_2003_Max__less__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_int @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_less_iff
% 0.29/0.57 thf(fact_2004_Max__less__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X )
% 0.29/0.57 = ( ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_nat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_less_iff
% 0.29/0.57 thf(fact_2005_Min_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) )
% 0.29/0.57 = ( ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.bounded_iff
% 0.29/0.57 thf(fact_2006_Min_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) )
% 0.29/0.57 = ( ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.bounded_iff
% 0.29/0.57 thf(fact_2007_Min_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) )
% 0.29/0.57 = ( ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.bounded_iff
% 0.29/0.57 thf(fact_2008_Min_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_eq_num @ X @ ( lattic5278467273892544601in_num @ A4 ) )
% 0.29/0.57 = ( ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.bounded_iff
% 0.29/0.57 thf(fact_2009_Min_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A4 ) )
% 0.29/0.57 = ( ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.bounded_iff
% 0.29/0.57 thf(fact_2010_Min_Obounded__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) )
% 0.29/0.57 = ( ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.bounded_iff
% 0.29/0.57 thf(fact_2011_Min__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le6747313008572928689nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) )
% 0.29/0.57 = ( ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le6747313008572928689nteger @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_gr_iff
% 0.29/0.57 thf(fact_2012_Min__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) )
% 0.29/0.57 = ( ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_o @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_gr_iff
% 0.29/0.57 thf(fact_2013_Min__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_real @ X @ ( lattic3629708407755379051n_real @ A4 ) )
% 0.29/0.57 = ( ! [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_real @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_gr_iff
% 0.29/0.57 thf(fact_2014_Min__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) )
% 0.29/0.57 = ( ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_rat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_gr_iff
% 0.29/0.57 thf(fact_2015_Min__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_num @ X @ ( lattic5278467273892544601in_num @ A4 ) )
% 0.29/0.57 = ( ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_num @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_gr_iff
% 0.29/0.57 thf(fact_2016_Min__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_int @ X @ ( lattic8718645017227715691in_int @ A4 ) )
% 0.29/0.57 = ( ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_int @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_gr_iff
% 0.29/0.57 thf(fact_2017_Min__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) )
% 0.29/0.57 = ( ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_nat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_gr_iff
% 0.29/0.57 thf(fact_2018_Min_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_real,A: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( member_real @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ ( lattic3629708407755379051n_real @ A4 ) @ A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.coboundedI
% 0.29/0.57 thf(fact_2019_Min_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,A: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( member_Code_integer @ A @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ A4 ) @ A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.coboundedI
% 0.29/0.57 thf(fact_2020_Min_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_rat,A: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( member_rat @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.coboundedI
% 0.29/0.57 thf(fact_2021_Min_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_num,A: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( member_num @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ A4 ) @ A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.coboundedI
% 0.29/0.57 thf(fact_2022_Min_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_int,A: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( member_int @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ A4 ) @ A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.coboundedI
% 0.29/0.57 thf(fact_2023_Min_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_nat,A: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( member_nat @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.coboundedI
% 0.29/0.57 thf(fact_2024_Min__eqI,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ! [Y3: real] :
% 0.29/0.57 ( ( member_real @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ X @ Y3 ) )
% 0.29/0.57 => ( ( member_real @ X @ A4 )
% 0.29/0.57 => ( ( lattic3629708407755379051n_real @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eqI
% 0.29/0.57 thf(fact_2025_Min__eqI,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ! [Y3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ Y3 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X @ Y3 ) )
% 0.29/0.57 => ( ( member_Code_integer @ X @ A4 )
% 0.29/0.57 => ( ( lattic1063845414844153500nteger @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eqI
% 0.29/0.57 thf(fact_2026_Min__eqI,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ! [Y3: rat] :
% 0.29/0.57 ( ( member_rat @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X @ Y3 ) )
% 0.29/0.57 => ( ( member_rat @ X @ A4 )
% 0.29/0.57 => ( ( lattic8086005427650270231in_rat @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eqI
% 0.29/0.57 thf(fact_2027_Min__eqI,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ! [Y3: num] :
% 0.29/0.57 ( ( member_num @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X @ Y3 ) )
% 0.29/0.57 => ( ( member_num @ X @ A4 )
% 0.29/0.57 => ( ( lattic5278467273892544601in_num @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eqI
% 0.29/0.57 thf(fact_2028_Min__eqI,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ! [Y3: int] :
% 0.29/0.57 ( ( member_int @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X @ Y3 ) )
% 0.29/0.57 => ( ( member_int @ X @ A4 )
% 0.29/0.57 => ( ( lattic8718645017227715691in_int @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eqI
% 0.29/0.57 thf(fact_2029_Min__eqI,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ! [Y3: nat] :
% 0.29/0.57 ( ( member_nat @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ Y3 ) )
% 0.29/0.57 => ( ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ( lattic8721135487736765967in_nat @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eqI
% 0.29/0.57 thf(fact_2030_Min__le,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( member_real @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ ( lattic3629708407755379051n_real @ A4 ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le
% 0.29/0.57 thf(fact_2031_Min__le,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( member_Code_integer @ X @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ A4 ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le
% 0.29/0.57 thf(fact_2032_Min__le,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( member_rat @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le
% 0.29/0.57 thf(fact_2033_Min__le,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( member_num @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ A4 ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le
% 0.29/0.57 thf(fact_2034_Min__le,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( member_int @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ A4 ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le
% 0.29/0.57 thf(fact_2035_Min__le,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ X ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le
% 0.29/0.57 thf(fact_2036_Min__in,axiom,
% 0.29/0.57 ! [A4: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( member_real @ ( lattic3629708407755379051n_real @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_in
% 0.29/0.57 thf(fact_2037_Min__in,axiom,
% 0.29/0.57 ! [A4: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( member_Code_integer @ ( lattic1063845414844153500nteger @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_in
% 0.29/0.57 thf(fact_2038_Min__in,axiom,
% 0.29/0.57 ! [A4: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( member_int @ ( lattic8718645017227715691in_int @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_in
% 0.29/0.57 thf(fact_2039_Min__in,axiom,
% 0.29/0.57 ! [A4: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( member_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_in
% 0.29/0.57 thf(fact_2040_Min__in,axiom,
% 0.29/0.57 ! [A4: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( member_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_in
% 0.29/0.57 thf(fact_2041_Max_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_real,A: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( member_real @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ A @ ( lattic4275903605611617917x_real @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.coboundedI
% 0.29/0.57 thf(fact_2042_Max_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,A: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( member_Code_integer @ A @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ A @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.coboundedI
% 0.29/0.57 thf(fact_2043_Max_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_rat,A: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( member_rat @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ A @ ( lattic7630753665789217321ax_rat @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.coboundedI
% 0.29/0.57 thf(fact_2044_Max_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_num,A: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( member_num @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ A @ ( lattic4823215512031491691ax_num @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.coboundedI
% 0.29/0.57 thf(fact_2045_Max_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_int,A: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( member_int @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ A @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.coboundedI
% 0.29/0.57 thf(fact_2046_Max_OcoboundedI,axiom,
% 0.29/0.57 ! [A4: set_nat,A: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( member_nat @ A @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ A @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.coboundedI
% 0.29/0.57 thf(fact_2047_Max__eq__if,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( finite6017078050557962740nteger @ B4 )
% 0.29/0.57 => ( ! [X3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X3 @ A4 )
% 0.29/0.57 => ? [Xa: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ Xa @ B4 )
% 0.29/0.57 & ( ord_le3102999989581377725nteger @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ! [X3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X3 @ B4 )
% 0.29/0.57 => ? [Xa: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ Xa @ A4 )
% 0.29/0.57 & ( ord_le3102999989581377725nteger @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ( lattic4901227151466704046nteger @ A4 )
% 0.29/0.57 = ( lattic4901227151466704046nteger @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_if
% 0.29/0.57 thf(fact_2048_Max__eq__if,axiom,
% 0.29/0.57 ! [A4: set_rat,B4: set_rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( finite_finite_rat @ B4 )
% 0.29/0.57 => ( ! [X3: rat] :
% 0.29/0.57 ( ( member_rat @ X3 @ A4 )
% 0.29/0.57 => ? [Xa: rat] :
% 0.29/0.57 ( ( member_rat @ Xa @ B4 )
% 0.29/0.57 & ( ord_less_eq_rat @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ! [X3: rat] :
% 0.29/0.57 ( ( member_rat @ X3 @ B4 )
% 0.29/0.57 => ? [Xa: rat] :
% 0.29/0.57 ( ( member_rat @ Xa @ A4 )
% 0.29/0.57 & ( ord_less_eq_rat @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ( lattic7630753665789217321ax_rat @ A4 )
% 0.29/0.57 = ( lattic7630753665789217321ax_rat @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_if
% 0.29/0.57 thf(fact_2049_Max__eq__if,axiom,
% 0.29/0.57 ! [A4: set_num,B4: set_num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( finite_finite_num @ B4 )
% 0.29/0.57 => ( ! [X3: num] :
% 0.29/0.57 ( ( member_num @ X3 @ A4 )
% 0.29/0.57 => ? [Xa: num] :
% 0.29/0.57 ( ( member_num @ Xa @ B4 )
% 0.29/0.57 & ( ord_less_eq_num @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ! [X3: num] :
% 0.29/0.57 ( ( member_num @ X3 @ B4 )
% 0.29/0.57 => ? [Xa: num] :
% 0.29/0.57 ( ( member_num @ Xa @ A4 )
% 0.29/0.57 & ( ord_less_eq_num @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ( lattic4823215512031491691ax_num @ A4 )
% 0.29/0.57 = ( lattic4823215512031491691ax_num @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_if
% 0.29/0.57 thf(fact_2050_Max__eq__if,axiom,
% 0.29/0.57 ! [A4: set_int,B4: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( finite_finite_int @ B4 )
% 0.29/0.57 => ( ! [X3: int] :
% 0.29/0.57 ( ( member_int @ X3 @ A4 )
% 0.29/0.57 => ? [Xa: int] :
% 0.29/0.57 ( ( member_int @ Xa @ B4 )
% 0.29/0.57 & ( ord_less_eq_int @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ! [X3: int] :
% 0.29/0.57 ( ( member_int @ X3 @ B4 )
% 0.29/0.57 => ? [Xa: int] :
% 0.29/0.57 ( ( member_int @ Xa @ A4 )
% 0.29/0.57 & ( ord_less_eq_int @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ( lattic8263393255366662781ax_int @ A4 )
% 0.29/0.57 = ( lattic8263393255366662781ax_int @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_if
% 0.29/0.57 thf(fact_2051_Max__eq__if,axiom,
% 0.29/0.57 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( finite_finite_nat @ B4 )
% 0.29/0.57 => ( ! [X3: nat] :
% 0.29/0.57 ( ( member_nat @ X3 @ A4 )
% 0.29/0.57 => ? [Xa: nat] :
% 0.29/0.57 ( ( member_nat @ Xa @ B4 )
% 0.29/0.57 & ( ord_less_eq_nat @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ! [X3: nat] :
% 0.29/0.57 ( ( member_nat @ X3 @ B4 )
% 0.29/0.57 => ? [Xa: nat] :
% 0.29/0.57 ( ( member_nat @ Xa @ A4 )
% 0.29/0.57 & ( ord_less_eq_nat @ X3 @ Xa ) ) )
% 0.29/0.57 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 0.29/0.57 = ( lattic8265883725875713057ax_nat @ B4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_if
% 0.29/0.57 thf(fact_2052_Max__eqI,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ! [Y3: real] :
% 0.29/0.57 ( ( member_real @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ Y3 @ X ) )
% 0.29/0.57 => ( ( member_real @ X @ A4 )
% 0.29/0.57 => ( ( lattic4275903605611617917x_real @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eqI
% 0.29/0.57 thf(fact_2053_Max__eqI,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ! [Y3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ Y3 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ Y3 @ X ) )
% 0.29/0.57 => ( ( member_Code_integer @ X @ A4 )
% 0.29/0.57 => ( ( lattic4901227151466704046nteger @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eqI
% 0.29/0.57 thf(fact_2054_Max__eqI,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ! [Y3: rat] :
% 0.29/0.57 ( ( member_rat @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ Y3 @ X ) )
% 0.29/0.57 => ( ( member_rat @ X @ A4 )
% 0.29/0.57 => ( ( lattic7630753665789217321ax_rat @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eqI
% 0.29/0.57 thf(fact_2055_Max__eqI,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ! [Y3: num] :
% 0.29/0.57 ( ( member_num @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ Y3 @ X ) )
% 0.29/0.57 => ( ( member_num @ X @ A4 )
% 0.29/0.57 => ( ( lattic4823215512031491691ax_num @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eqI
% 0.29/0.57 thf(fact_2056_Max__eqI,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ! [Y3: int] :
% 0.29/0.57 ( ( member_int @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ Y3 @ X ) )
% 0.29/0.57 => ( ( member_int @ X @ A4 )
% 0.29/0.57 => ( ( lattic8263393255366662781ax_int @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eqI
% 0.29/0.57 thf(fact_2057_Max__eqI,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ! [Y3: nat] :
% 0.29/0.57 ( ( member_nat @ Y3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ Y3 @ X ) )
% 0.29/0.57 => ( ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 0.29/0.57 = X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eqI
% 0.29/0.57 thf(fact_2058_Max__ge,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( member_real @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ X @ ( lattic4275903605611617917x_real @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge
% 0.29/0.57 thf(fact_2059_Max__ge,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( member_Code_integer @ X @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge
% 0.29/0.57 thf(fact_2060_Max__ge,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( member_rat @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X @ ( lattic7630753665789217321ax_rat @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge
% 0.29/0.57 thf(fact_2061_Max__ge,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( member_num @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X @ ( lattic4823215512031491691ax_num @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge
% 0.29/0.57 thf(fact_2062_Max__ge,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( member_int @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge
% 0.29/0.57 thf(fact_2063_Max__ge,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( member_nat @ X @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge
% 0.29/0.57 thf(fact_2064_Max__in,axiom,
% 0.29/0.57 ! [A4: set_real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( member_real @ ( lattic4275903605611617917x_real @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_in
% 0.29/0.57 thf(fact_2065_Max__in,axiom,
% 0.29/0.57 ! [A4: set_Code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( member_Code_integer @ ( lattic4901227151466704046nteger @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_in
% 0.29/0.57 thf(fact_2066_Max__in,axiom,
% 0.29/0.57 ! [A4: set_int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( member_int @ ( lattic8263393255366662781ax_int @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_in
% 0.29/0.57 thf(fact_2067_Max__in,axiom,
% 0.29/0.57 ! [A4: set_o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( member_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_in
% 0.29/0.57 thf(fact_2068_Max__in,axiom,
% 0.29/0.57 ! [A4: set_nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( member_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ A4 ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_in
% 0.29/0.57 thf(fact_2069_Min__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_real,M: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ( lattic3629708407755379051n_real @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_real @ M @ A4 )
% 0.29/0.57 & ! [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eq_iff
% 0.29/0.57 thf(fact_2070_Min__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,M: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ( lattic1063845414844153500nteger @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_Code_integer @ M @ A4 )
% 0.29/0.57 & ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eq_iff
% 0.29/0.57 thf(fact_2071_Min__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_o,M: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ( lattic1973801136483472281_Min_o @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_o @ M @ A4 )
% 0.29/0.57 & ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eq_iff
% 0.29/0.57 thf(fact_2072_Min__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,M: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ( lattic8086005427650270231in_rat @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_rat @ M @ A4 )
% 0.29/0.57 & ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eq_iff
% 0.29/0.57 thf(fact_2073_Min__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_num,M: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ( lattic5278467273892544601in_num @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_num @ M @ A4 )
% 0.29/0.57 & ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eq_iff
% 0.29/0.57 thf(fact_2074_Min__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_int,M: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ( lattic8718645017227715691in_int @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_int @ M @ A4 )
% 0.29/0.57 & ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eq_iff
% 0.29/0.57 thf(fact_2075_Min__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,M: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ( lattic8721135487736765967in_nat @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_nat @ M @ A4 )
% 0.29/0.57 & ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_eq_iff
% 0.29/0.57 thf(fact_2076_Min__le__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 & ( ord_le3102999989581377725nteger @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le_iff
% 0.29/0.57 thf(fact_2077_Min__le__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_o @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le_iff
% 0.29/0.57 thf(fact_2078_Min__le__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_rat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le_iff
% 0.29/0.57 thf(fact_2079_Min__le__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_num @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le_iff
% 0.29/0.57 thf(fact_2080_Min__le__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_int @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le_iff
% 0.29/0.57 thf(fact_2081_Min__le__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_nat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_le_iff
% 0.29/0.57 thf(fact_2082_eq__Min__iff,axiom,
% 0.29/0.57 ! [A4: set_real,M: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic3629708407755379051n_real @ A4 ) )
% 0.29/0.57 = ( ( member_real @ M @ A4 )
% 0.29/0.57 & ! [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Min_iff
% 0.29/0.57 thf(fact_2083_eq__Min__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,M: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic1063845414844153500nteger @ A4 ) )
% 0.29/0.57 = ( ( member_Code_integer @ M @ A4 )
% 0.29/0.57 & ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Min_iff
% 0.29/0.57 thf(fact_2084_eq__Min__iff,axiom,
% 0.29/0.57 ! [A4: set_o,M: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic1973801136483472281_Min_o @ A4 ) )
% 0.29/0.57 = ( ( member_o @ M @ A4 )
% 0.29/0.57 & ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Min_iff
% 0.29/0.57 thf(fact_2085_eq__Min__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,M: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic8086005427650270231in_rat @ A4 ) )
% 0.29/0.57 = ( ( member_rat @ M @ A4 )
% 0.29/0.57 & ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Min_iff
% 0.29/0.57 thf(fact_2086_eq__Min__iff,axiom,
% 0.29/0.57 ! [A4: set_num,M: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic5278467273892544601in_num @ A4 ) )
% 0.29/0.57 = ( ( member_num @ M @ A4 )
% 0.29/0.57 & ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Min_iff
% 0.29/0.57 thf(fact_2087_eq__Min__iff,axiom,
% 0.29/0.57 ! [A4: set_int,M: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic8718645017227715691in_int @ A4 ) )
% 0.29/0.57 = ( ( member_int @ M @ A4 )
% 0.29/0.57 & ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Min_iff
% 0.29/0.57 thf(fact_2088_eq__Min__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,M: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic8721135487736765967in_nat @ A4 ) )
% 0.29/0.57 = ( ( member_nat @ M @ A4 )
% 0.29/0.57 & ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ M @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Min_iff
% 0.29/0.57 thf(fact_2089_Min_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_eq_real @ X @ ( lattic3629708407755379051n_real @ A4 ) )
% 0.29/0.57 => ! [A8: real] :
% 0.29/0.57 ( ( member_real @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ X @ A8 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedE
% 0.29/0.57 thf(fact_2090_Min_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) )
% 0.29/0.57 => ! [A8: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ A8 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X @ A8 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedE
% 0.29/0.57 thf(fact_2091_Min_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) )
% 0.29/0.57 => ! [A8: $o] :
% 0.29/0.57 ( ( member_o @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ X @ A8 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedE
% 0.29/0.57 thf(fact_2092_Min_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) )
% 0.29/0.57 => ! [A8: rat] :
% 0.29/0.57 ( ( member_rat @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X @ A8 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedE
% 0.29/0.57 thf(fact_2093_Min_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_eq_num @ X @ ( lattic5278467273892544601in_num @ A4 ) )
% 0.29/0.57 => ! [A8: num] :
% 0.29/0.57 ( ( member_num @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X @ A8 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedE
% 0.29/0.57 thf(fact_2094_Min_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A4 ) )
% 0.29/0.57 => ! [A8: int] :
% 0.29/0.57 ( ( member_int @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X @ A8 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedE
% 0.29/0.57 thf(fact_2095_Min_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) )
% 0.29/0.57 => ! [A8: nat] :
% 0.29/0.57 ( ( member_nat @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ A8 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedE
% 0.29/0.57 thf(fact_2096_Min_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ! [A3: real] :
% 0.29/0.57 ( ( member_real @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ X @ A3 ) )
% 0.29/0.57 => ( ord_less_eq_real @ X @ ( lattic3629708407755379051n_real @ A4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedI
% 0.29/0.57 thf(fact_2097_Min_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [A3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ A3 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X @ A3 ) )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedI
% 0.29/0.57 thf(fact_2098_Min_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ! [A3: $o] :
% 0.29/0.57 ( ( member_o @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ X @ A3 ) )
% 0.29/0.57 => ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedI
% 0.29/0.57 thf(fact_2099_Min_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ! [A3: rat] :
% 0.29/0.57 ( ( member_rat @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X @ A3 ) )
% 0.29/0.57 => ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedI
% 0.29/0.57 thf(fact_2100_Min_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ! [A3: num] :
% 0.29/0.57 ( ( member_num @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X @ A3 ) )
% 0.29/0.57 => ( ord_less_eq_num @ X @ ( lattic5278467273892544601in_num @ A4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedI
% 0.29/0.57 thf(fact_2101_Min_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ! [A3: int] :
% 0.29/0.57 ( ( member_int @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X @ A3 ) )
% 0.29/0.57 => ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedI
% 0.29/0.57 thf(fact_2102_Min_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ! [A3: nat] :
% 0.29/0.57 ( ( member_nat @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ A3 ) )
% 0.29/0.57 => ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min.boundedI
% 0.29/0.57 thf(fact_2103_Min__less__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le6747313008572928689nteger @ ( lattic1063845414844153500nteger @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 & ( ord_le6747313008572928689nteger @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_less_iff
% 0.29/0.57 thf(fact_2104_Min__less__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_o @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_less_iff
% 0.29/0.57 thf(fact_2105_Min__less__iff,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_real @ ( lattic3629708407755379051n_real @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_real @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_less_iff
% 0.29/0.57 thf(fact_2106_Min__less__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_rat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_less_iff
% 0.29/0.57 thf(fact_2107_Min__less__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_num @ ( lattic5278467273892544601in_num @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_num @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_less_iff
% 0.29/0.57 thf(fact_2108_Min__less__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_int @ ( lattic8718645017227715691in_int @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_int @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_less_iff
% 0.29/0.57 thf(fact_2109_Min__less__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ X )
% 0.29/0.57 = ( ? [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_nat @ X4 @ X ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_less_iff
% 0.29/0.57 thf(fact_2110_Min__insert2,axiom,
% 0.29/0.57 ! [A4: set_o,A: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ! [B3: $o] :
% 0.29/0.57 ( ( member_o @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ A @ B3 ) )
% 0.29/0.57 => ( ( lattic1973801136483472281_Min_o @ ( insert_o @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_insert2
% 0.29/0.57 thf(fact_2111_Min__insert2,axiom,
% 0.29/0.57 ! [A4: set_real,A: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ! [B3: real] :
% 0.29/0.57 ( ( member_real @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ A @ B3 ) )
% 0.29/0.57 => ( ( lattic3629708407755379051n_real @ ( insert_real @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_insert2
% 0.29/0.57 thf(fact_2112_Min__insert2,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,A: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ! [B3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ B3 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ A @ B3 ) )
% 0.29/0.57 => ( ( lattic1063845414844153500nteger @ ( insert_Code_integer @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_insert2
% 0.29/0.57 thf(fact_2113_Min__insert2,axiom,
% 0.29/0.57 ! [A4: set_rat,A: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ! [B3: rat] :
% 0.29/0.57 ( ( member_rat @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ A @ B3 ) )
% 0.29/0.57 => ( ( lattic8086005427650270231in_rat @ ( insert_rat @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_insert2
% 0.29/0.57 thf(fact_2114_Min__insert2,axiom,
% 0.29/0.57 ! [A4: set_num,A: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ! [B3: num] :
% 0.29/0.57 ( ( member_num @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ A @ B3 ) )
% 0.29/0.57 => ( ( lattic5278467273892544601in_num @ ( insert_num @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_insert2
% 0.29/0.57 thf(fact_2115_Min__insert2,axiom,
% 0.29/0.57 ! [A4: set_int,A: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ! [B3: int] :
% 0.29/0.57 ( ( member_int @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ A @ B3 ) )
% 0.29/0.57 => ( ( lattic8718645017227715691in_int @ ( insert_int @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_insert2
% 0.29/0.57 thf(fact_2116_Min__insert2,axiom,
% 0.29/0.57 ! [A4: set_nat,A: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ! [B3: nat] :
% 0.29/0.57 ( ( member_nat @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ A @ B3 ) )
% 0.29/0.57 => ( ( lattic8721135487736765967in_nat @ ( insert_nat @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_insert2
% 0.29/0.57 thf(fact_2117_Max__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_real,M: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ( lattic4275903605611617917x_real @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_real @ M @ A4 )
% 0.29/0.57 & ! [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_iff
% 0.29/0.57 thf(fact_2118_Max__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,M: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ( lattic4901227151466704046nteger @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_Code_integer @ M @ A4 )
% 0.29/0.57 & ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_iff
% 0.29/0.57 thf(fact_2119_Max__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_o,M: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ( lattic1921953407002678535_Max_o @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_o @ M @ A4 )
% 0.29/0.57 & ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_iff
% 0.29/0.57 thf(fact_2120_Max__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,M: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ( lattic7630753665789217321ax_rat @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_rat @ M @ A4 )
% 0.29/0.57 & ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_iff
% 0.29/0.57 thf(fact_2121_Max__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_num,M: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ( lattic4823215512031491691ax_num @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_num @ M @ A4 )
% 0.29/0.57 & ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_iff
% 0.29/0.57 thf(fact_2122_Max__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_int,M: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ( lattic8263393255366662781ax_int @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_int @ M @ A4 )
% 0.29/0.57 & ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_iff
% 0.29/0.57 thf(fact_2123_Max__eq__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,M: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ( lattic8265883725875713057ax_nat @ A4 )
% 0.29/0.57 = M )
% 0.29/0.57 = ( ( member_nat @ M @ A4 )
% 0.29/0.57 & ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_eq_iff
% 0.29/0.57 thf(fact_2124_Max__ge__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic4901227151466704046nteger @ A4 ) )
% 0.29/0.57 = ( ? [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 & ( ord_le3102999989581377725nteger @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge_iff
% 0.29/0.57 thf(fact_2125_Max__ge__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) )
% 0.29/0.57 = ( ? [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_o @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge_iff
% 0.29/0.57 thf(fact_2126_Max__ge__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_eq_rat @ X @ ( lattic7630753665789217321ax_rat @ A4 ) )
% 0.29/0.57 = ( ? [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_rat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge_iff
% 0.29/0.57 thf(fact_2127_Max__ge__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_eq_num @ X @ ( lattic4823215512031491691ax_num @ A4 ) )
% 0.29/0.57 = ( ? [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_num @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge_iff
% 0.29/0.57 thf(fact_2128_Max__ge__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) )
% 0.29/0.57 = ( ? [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_int @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge_iff
% 0.29/0.57 thf(fact_2129_Max__ge__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 0.29/0.57 = ( ? [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_eq_nat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_ge_iff
% 0.29/0.57 thf(fact_2130_eq__Max__iff,axiom,
% 0.29/0.57 ! [A4: set_real,M: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic4275903605611617917x_real @ A4 ) )
% 0.29/0.57 = ( ( member_real @ M @ A4 )
% 0.29/0.57 & ! [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Max_iff
% 0.29/0.57 thf(fact_2131_eq__Max__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,M: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic4901227151466704046nteger @ A4 ) )
% 0.29/0.57 = ( ( member_Code_integer @ M @ A4 )
% 0.29/0.57 & ! [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Max_iff
% 0.29/0.57 thf(fact_2132_eq__Max__iff,axiom,
% 0.29/0.57 ! [A4: set_o,M: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic1921953407002678535_Max_o @ A4 ) )
% 0.29/0.57 = ( ( member_o @ M @ A4 )
% 0.29/0.57 & ! [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Max_iff
% 0.29/0.57 thf(fact_2133_eq__Max__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,M: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic7630753665789217321ax_rat @ A4 ) )
% 0.29/0.57 = ( ( member_rat @ M @ A4 )
% 0.29/0.57 & ! [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Max_iff
% 0.29/0.57 thf(fact_2134_eq__Max__iff,axiom,
% 0.29/0.57 ! [A4: set_num,M: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic4823215512031491691ax_num @ A4 ) )
% 0.29/0.57 = ( ( member_num @ M @ A4 )
% 0.29/0.57 & ! [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Max_iff
% 0.29/0.57 thf(fact_2135_eq__Max__iff,axiom,
% 0.29/0.57 ! [A4: set_int,M: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic8263393255366662781ax_int @ A4 ) )
% 0.29/0.57 = ( ( member_int @ M @ A4 )
% 0.29/0.57 & ! [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Max_iff
% 0.29/0.57 thf(fact_2136_eq__Max__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,M: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( M
% 0.29/0.57 = ( lattic8265883725875713057ax_nat @ A4 ) )
% 0.29/0.57 = ( ( member_nat @ M @ A4 )
% 0.29/0.57 & ! [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ X4 @ M ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % eq_Max_iff
% 0.29/0.57 thf(fact_2137_Max_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_eq_real @ ( lattic4275903605611617917x_real @ A4 ) @ X )
% 0.29/0.57 => ! [A8: real] :
% 0.29/0.57 ( ( member_real @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ A8 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedE
% 0.29/0.57 thf(fact_2138_Max_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X )
% 0.29/0.57 => ! [A8: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ A8 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ A8 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedE
% 0.29/0.57 thf(fact_2139_Max_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X )
% 0.29/0.57 => ! [A8: $o] :
% 0.29/0.57 ( ( member_o @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ A8 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedE
% 0.29/0.57 thf(fact_2140_Max_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X )
% 0.29/0.57 => ! [A8: rat] :
% 0.29/0.57 ( ( member_rat @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ A8 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedE
% 0.29/0.57 thf(fact_2141_Max_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X )
% 0.29/0.57 => ! [A8: num] :
% 0.29/0.57 ( ( member_num @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ A8 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedE
% 0.29/0.57 thf(fact_2142_Max_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X )
% 0.29/0.57 => ! [A8: int] :
% 0.29/0.57 ( ( member_int @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ A8 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedE
% 0.29/0.57 thf(fact_2143_Max_OboundedE,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X )
% 0.29/0.57 => ! [A8: nat] :
% 0.29/0.57 ( ( member_nat @ A8 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ A8 @ X ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedE
% 0.29/0.57 thf(fact_2144_Max_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ! [A3: real] :
% 0.29/0.57 ( ( member_real @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ A3 @ X ) )
% 0.29/0.57 => ( ord_less_eq_real @ ( lattic4275903605611617917x_real @ A4 ) @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedI
% 0.29/0.57 thf(fact_2145_Max_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ! [A3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ A3 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ A3 @ X ) )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedI
% 0.29/0.57 thf(fact_2146_Max_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ! [A3: $o] :
% 0.29/0.57 ( ( member_o @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ A3 @ X ) )
% 0.29/0.57 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedI
% 0.29/0.57 thf(fact_2147_Max_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ! [A3: rat] :
% 0.29/0.57 ( ( member_rat @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ A3 @ X ) )
% 0.29/0.57 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedI
% 0.29/0.57 thf(fact_2148_Max_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ! [A3: num] :
% 0.29/0.57 ( ( member_num @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ A3 @ X ) )
% 0.29/0.57 => ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedI
% 0.29/0.57 thf(fact_2149_Max_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ! [A3: int] :
% 0.29/0.57 ( ( member_int @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ A3 @ X ) )
% 0.29/0.57 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedI
% 0.29/0.57 thf(fact_2150_Max_OboundedI,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ! [A3: nat] :
% 0.29/0.57 ( ( member_nat @ A3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ A3 @ X ) )
% 0.29/0.57 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max.boundedI
% 0.29/0.57 thf(fact_2151_Max__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,X: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( ord_le6747313008572928689nteger @ X @ ( lattic4901227151466704046nteger @ A4 ) )
% 0.29/0.57 = ( ? [X4: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ X4 @ A4 )
% 0.29/0.57 & ( ord_le6747313008572928689nteger @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_gr_iff
% 0.29/0.57 thf(fact_2152_Max__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_o,X: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_o )
% 0.29/0.57 => ( ( ord_less_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) )
% 0.29/0.57 = ( ? [X4: $o] :
% 0.29/0.57 ( ( member_o @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_o @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_gr_iff
% 0.29/0.57 thf(fact_2153_Max__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_real,X: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_real )
% 0.29/0.57 => ( ( ord_less_real @ X @ ( lattic4275903605611617917x_real @ A4 ) )
% 0.29/0.57 = ( ? [X4: real] :
% 0.29/0.57 ( ( member_real @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_real @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_gr_iff
% 0.29/0.57 thf(fact_2154_Max__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_rat,X: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.57 => ( ( ord_less_rat @ X @ ( lattic7630753665789217321ax_rat @ A4 ) )
% 0.29/0.57 = ( ? [X4: rat] :
% 0.29/0.57 ( ( member_rat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_rat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_gr_iff
% 0.29/0.57 thf(fact_2155_Max__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_num,X: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_num )
% 0.29/0.57 => ( ( ord_less_num @ X @ ( lattic4823215512031491691ax_num @ A4 ) )
% 0.29/0.57 = ( ? [X4: num] :
% 0.29/0.57 ( ( member_num @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_num @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_gr_iff
% 0.29/0.57 thf(fact_2156_Max__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_int,X: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_int )
% 0.29/0.57 => ( ( ord_less_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) )
% 0.29/0.57 = ( ? [X4: int] :
% 0.29/0.57 ( ( member_int @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_int @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_gr_iff
% 0.29/0.57 thf(fact_2157_Max__gr__iff,axiom,
% 0.29/0.57 ! [A4: set_nat,X: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.57 => ( ( ord_less_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 0.29/0.57 = ( ? [X4: nat] :
% 0.29/0.57 ( ( member_nat @ X4 @ A4 )
% 0.29/0.57 & ( ord_less_nat @ X @ X4 ) ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_gr_iff
% 0.29/0.57 thf(fact_2158_Max__insert2,axiom,
% 0.29/0.57 ! [A4: set_o,A: $o] :
% 0.29/0.57 ( ( finite_finite_o @ A4 )
% 0.29/0.57 => ( ! [B3: $o] :
% 0.29/0.57 ( ( member_o @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_o @ B3 @ A ) )
% 0.29/0.57 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_insert2
% 0.29/0.57 thf(fact_2159_Max__insert2,axiom,
% 0.29/0.57 ! [A4: set_real,A: real] :
% 0.29/0.57 ( ( finite_finite_real @ A4 )
% 0.29/0.57 => ( ! [B3: real] :
% 0.29/0.57 ( ( member_real @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_real @ B3 @ A ) )
% 0.29/0.57 => ( ( lattic4275903605611617917x_real @ ( insert_real @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_insert2
% 0.29/0.57 thf(fact_2160_Max__insert2,axiom,
% 0.29/0.57 ! [A4: set_Code_integer,A: code_integer] :
% 0.29/0.57 ( ( finite6017078050557962740nteger @ A4 )
% 0.29/0.57 => ( ! [B3: code_integer] :
% 0.29/0.57 ( ( member_Code_integer @ B3 @ A4 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ B3 @ A ) )
% 0.29/0.57 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_insert2
% 0.29/0.57 thf(fact_2161_Max__insert2,axiom,
% 0.29/0.57 ! [A4: set_rat,A: rat] :
% 0.29/0.57 ( ( finite_finite_rat @ A4 )
% 0.29/0.57 => ( ! [B3: rat] :
% 0.29/0.57 ( ( member_rat @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_rat @ B3 @ A ) )
% 0.29/0.57 => ( ( lattic7630753665789217321ax_rat @ ( insert_rat @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_insert2
% 0.29/0.57 thf(fact_2162_Max__insert2,axiom,
% 0.29/0.57 ! [A4: set_num,A: num] :
% 0.29/0.57 ( ( finite_finite_num @ A4 )
% 0.29/0.57 => ( ! [B3: num] :
% 0.29/0.57 ( ( member_num @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_num @ B3 @ A ) )
% 0.29/0.57 => ( ( lattic4823215512031491691ax_num @ ( insert_num @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_insert2
% 0.29/0.57 thf(fact_2163_Max__insert2,axiom,
% 0.29/0.57 ! [A4: set_int,A: int] :
% 0.29/0.57 ( ( finite_finite_int @ A4 )
% 0.29/0.57 => ( ! [B3: int] :
% 0.29/0.57 ( ( member_int @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_int @ B3 @ A ) )
% 0.29/0.57 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_insert2
% 0.29/0.57 thf(fact_2164_Max__insert2,axiom,
% 0.29/0.57 ! [A4: set_nat,A: nat] :
% 0.29/0.57 ( ( finite_finite_nat @ A4 )
% 0.29/0.57 => ( ! [B3: nat] :
% 0.29/0.57 ( ( member_nat @ B3 @ A4 )
% 0.29/0.57 => ( ord_less_eq_nat @ B3 @ A ) )
% 0.29/0.57 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ A @ A4 ) )
% 0.29/0.57 = A ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Max_insert2
% 0.29/0.57 thf(fact_2165_Min__antimono,axiom,
% 0.29/0.57 ! [M7: set_Code_integer,N8: set_Code_integer] :
% 0.29/0.57 ( ( ord_le7084787975880047091nteger @ M7 @ N8 )
% 0.29/0.57 => ( ( M7 != bot_bo3990330152332043303nteger )
% 0.29/0.57 => ( ( finite6017078050557962740nteger @ N8 )
% 0.29/0.57 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ N8 ) @ ( lattic1063845414844153500nteger @ M7 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_antimono
% 0.29/0.57 thf(fact_2166_Min__antimono,axiom,
% 0.29/0.57 ! [M7: set_o,N8: set_o] :
% 0.29/0.57 ( ( ord_less_eq_set_o @ M7 @ N8 )
% 0.29/0.57 => ( ( M7 != bot_bot_set_o )
% 0.29/0.57 => ( ( finite_finite_o @ N8 )
% 0.29/0.57 => ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ N8 ) @ ( lattic1973801136483472281_Min_o @ M7 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_antimono
% 0.29/0.57 thf(fact_2167_Min__antimono,axiom,
% 0.29/0.57 ! [M7: set_rat,N8: set_rat] :
% 0.29/0.57 ( ( ord_less_eq_set_rat @ M7 @ N8 )
% 0.29/0.57 => ( ( M7 != bot_bot_set_rat )
% 0.29/0.57 => ( ( finite_finite_rat @ N8 )
% 0.29/0.57 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ N8 ) @ ( lattic8086005427650270231in_rat @ M7 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_antimono
% 0.29/0.57 thf(fact_2168_Min__antimono,axiom,
% 0.29/0.57 ! [M7: set_num,N8: set_num] :
% 0.29/0.57 ( ( ord_less_eq_set_num @ M7 @ N8 )
% 0.29/0.57 => ( ( M7 != bot_bot_set_num )
% 0.29/0.57 => ( ( finite_finite_num @ N8 )
% 0.29/0.57 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ N8 ) @ ( lattic5278467273892544601in_num @ M7 ) ) ) ) ) ).
% 0.29/0.57
% 0.29/0.57 % Min_antimono
% 0.29/0.57 thf(fact_2169_Min__antimono,axiom,
% 0.29/0.57 ! [M7: set_int,N8: set_int] :
% 0.29/0.58 ( ( ord_less_eq_set_int @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bot_set_int )
% 0.29/0.58 => ( ( finite_finite_int @ N8 )
% 0.29/0.58 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ N8 ) @ ( lattic8718645017227715691in_int @ M7 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min_antimono
% 0.29/0.58 thf(fact_2170_Min__antimono,axiom,
% 0.29/0.58 ! [M7: set_nat,N8: set_nat] :
% 0.29/0.58 ( ( ord_less_eq_set_nat @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bot_set_nat )
% 0.29/0.58 => ( ( finite_finite_nat @ N8 )
% 0.29/0.58 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ N8 ) @ ( lattic8721135487736765967in_nat @ M7 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min_antimono
% 0.29/0.58 thf(fact_2171_Min_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.29/0.58 ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.58 => ( ( finite6017078050557962740nteger @ B4 )
% 0.29/0.58 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ B4 ) @ ( lattic1063845414844153500nteger @ A4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min.subset_imp
% 0.29/0.58 thf(fact_2172_Min_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_o,B4: set_o] :
% 0.29/0.58 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_o )
% 0.29/0.58 => ( ( finite_finite_o @ B4 )
% 0.29/0.58 => ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ B4 ) @ ( lattic1973801136483472281_Min_o @ A4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min.subset_imp
% 0.29/0.58 thf(fact_2173_Min_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_rat,B4: set_rat] :
% 0.29/0.58 ( ( ord_less_eq_set_rat @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.58 => ( ( finite_finite_rat @ B4 )
% 0.29/0.58 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ B4 ) @ ( lattic8086005427650270231in_rat @ A4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min.subset_imp
% 0.29/0.58 thf(fact_2174_Min_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_num,B4: set_num] :
% 0.29/0.58 ( ( ord_less_eq_set_num @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_num )
% 0.29/0.58 => ( ( finite_finite_num @ B4 )
% 0.29/0.58 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ B4 ) @ ( lattic5278467273892544601in_num @ A4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min.subset_imp
% 0.29/0.58 thf(fact_2175_Min_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_int,B4: set_int] :
% 0.29/0.58 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_int )
% 0.29/0.58 => ( ( finite_finite_int @ B4 )
% 0.29/0.58 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ B4 ) @ ( lattic8718645017227715691in_int @ A4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min.subset_imp
% 0.29/0.58 thf(fact_2176_Min_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.58 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.58 => ( ( finite_finite_nat @ B4 )
% 0.29/0.58 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ B4 ) @ ( lattic8721135487736765967in_nat @ A4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Min.subset_imp
% 0.29/0.58 thf(fact_2177_Max__mono,axiom,
% 0.29/0.58 ! [M7: set_Code_integer,N8: set_Code_integer] :
% 0.29/0.58 ( ( ord_le7084787975880047091nteger @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bo3990330152332043303nteger )
% 0.29/0.58 => ( ( finite6017078050557962740nteger @ N8 )
% 0.29/0.58 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ M7 ) @ ( lattic4901227151466704046nteger @ N8 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max_mono
% 0.29/0.58 thf(fact_2178_Max__mono,axiom,
% 0.29/0.58 ! [M7: set_o,N8: set_o] :
% 0.29/0.58 ( ( ord_less_eq_set_o @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bot_set_o )
% 0.29/0.58 => ( ( finite_finite_o @ N8 )
% 0.29/0.58 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ M7 ) @ ( lattic1921953407002678535_Max_o @ N8 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max_mono
% 0.29/0.58 thf(fact_2179_Max__mono,axiom,
% 0.29/0.58 ! [M7: set_rat,N8: set_rat] :
% 0.29/0.58 ( ( ord_less_eq_set_rat @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bot_set_rat )
% 0.29/0.58 => ( ( finite_finite_rat @ N8 )
% 0.29/0.58 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ M7 ) @ ( lattic7630753665789217321ax_rat @ N8 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max_mono
% 0.29/0.58 thf(fact_2180_Max__mono,axiom,
% 0.29/0.58 ! [M7: set_num,N8: set_num] :
% 0.29/0.58 ( ( ord_less_eq_set_num @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bot_set_num )
% 0.29/0.58 => ( ( finite_finite_num @ N8 )
% 0.29/0.58 => ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ M7 ) @ ( lattic4823215512031491691ax_num @ N8 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max_mono
% 0.29/0.58 thf(fact_2181_Max__mono,axiom,
% 0.29/0.58 ! [M7: set_int,N8: set_int] :
% 0.29/0.58 ( ( ord_less_eq_set_int @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bot_set_int )
% 0.29/0.58 => ( ( finite_finite_int @ N8 )
% 0.29/0.58 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ M7 ) @ ( lattic8263393255366662781ax_int @ N8 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max_mono
% 0.29/0.58 thf(fact_2182_Max__mono,axiom,
% 0.29/0.58 ! [M7: set_nat,N8: set_nat] :
% 0.29/0.58 ( ( ord_less_eq_set_nat @ M7 @ N8 )
% 0.29/0.58 => ( ( M7 != bot_bot_set_nat )
% 0.29/0.58 => ( ( finite_finite_nat @ N8 )
% 0.29/0.58 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ M7 ) @ ( lattic8265883725875713057ax_nat @ N8 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max_mono
% 0.29/0.58 thf(fact_2183_Max_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.29/0.58 ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.29/0.58 => ( ( finite6017078050557962740nteger @ B4 )
% 0.29/0.58 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ ( lattic4901227151466704046nteger @ B4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max.subset_imp
% 0.29/0.58 thf(fact_2184_Max_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_o,B4: set_o] :
% 0.29/0.58 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_o )
% 0.29/0.58 => ( ( finite_finite_o @ B4 )
% 0.29/0.58 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ ( lattic1921953407002678535_Max_o @ B4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max.subset_imp
% 0.29/0.58 thf(fact_2185_Max_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_rat,B4: set_rat] :
% 0.29/0.58 ( ( ord_less_eq_set_rat @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_rat )
% 0.29/0.58 => ( ( finite_finite_rat @ B4 )
% 0.29/0.58 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ ( lattic7630753665789217321ax_rat @ B4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max.subset_imp
% 0.29/0.58 thf(fact_2186_Max_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_num,B4: set_num] :
% 0.29/0.58 ( ( ord_less_eq_set_num @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_num )
% 0.29/0.58 => ( ( finite_finite_num @ B4 )
% 0.29/0.58 => ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ ( lattic4823215512031491691ax_num @ B4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max.subset_imp
% 0.29/0.58 thf(fact_2187_Max_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_int,B4: set_int] :
% 0.29/0.58 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_int )
% 0.29/0.58 => ( ( finite_finite_int @ B4 )
% 0.29/0.58 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ ( lattic8263393255366662781ax_int @ B4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max.subset_imp
% 0.29/0.58 thf(fact_2188_Max_Osubset__imp,axiom,
% 0.29/0.58 ! [A4: set_nat,B4: set_nat] :
% 0.29/0.58 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.29/0.58 => ( ( A4 != bot_bot_set_nat )
% 0.29/0.58 => ( ( finite_finite_nat @ B4 )
% 0.29/0.58 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ B4 ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % Max.subset_imp
% 0.29/0.58 thf(fact_2189_greater__shift,axiom,
% 0.29/0.58 ( ord_less_nat
% 0.29/0.58 = ( ^ [Y4: nat,X4: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % greater_shift
% 0.29/0.58 thf(fact_2190_less__shift,axiom,
% 0.29/0.58 ( ord_less_nat
% 0.29/0.58 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_less @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % less_shift
% 0.29/0.58 thf(fact_2191_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.29/0.58 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 0.29/0.58 thf(fact_2192_the__elem__eq,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT] :
% 0.29/0.58 ( ( the_elem_VEBT_VEBT @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 0.29/0.58 = X ) ).
% 0.29/0.58
% 0.29/0.58 % the_elem_eq
% 0.29/0.58 thf(fact_2193_the__elem__eq,axiom,
% 0.29/0.58 ! [X: nat] :
% 0.29/0.58 ( ( the_elem_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.29/0.58 = X ) ).
% 0.29/0.58
% 0.29/0.58 % the_elem_eq
% 0.29/0.58 thf(fact_2194_the__elem__eq,axiom,
% 0.29/0.58 ! [X: int] :
% 0.29/0.58 ( ( the_elem_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.29/0.58 = X ) ).
% 0.29/0.58
% 0.29/0.58 % the_elem_eq
% 0.29/0.58 thf(fact_2195_the__elem__eq,axiom,
% 0.29/0.58 ! [X: $o] :
% 0.29/0.58 ( ( the_elem_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.29/0.58 = X ) ).
% 0.29/0.58
% 0.29/0.58 % the_elem_eq
% 0.29/0.58 thf(fact_2196_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT,Y: nat] :
% 0.29/0.58 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 0.29/0.58 = Y )
% 0.29/0.58 => ( ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.58 => ( Y != one_one_nat ) )
% 0.29/0.58 => ( ( ? [Uv: $o] :
% 0.29/0.58 ( X
% 0.29/0.58 = ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.58 => ( Y != one_one_nat ) )
% 0.29/0.58 => ( ( ? [Uu: $o] :
% 0.29/0.58 ( X
% 0.29/0.58 = ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.58 => ( Y != one_one_nat ) )
% 0.29/0.58 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.58 ( X
% 0.29/0.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.29/0.58 => ( Y != one_one_nat ) )
% 0.29/0.58 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.58 ( X
% 0.29/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.29/0.58 => ( Y != one_one_nat ) ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.elims
% 0.29/0.58 thf(fact_2197_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(5)
% 0.29/0.58 thf(fact_2198_is__singletonI,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT] : ( is_sin24926331636114728T_VEBT @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI
% 0.29/0.58 thf(fact_2199_is__singletonI,axiom,
% 0.29/0.58 ! [X: nat] : ( is_singleton_nat @ ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI
% 0.29/0.58 thf(fact_2200_is__singletonI,axiom,
% 0.29/0.58 ! [X: int] : ( is_singleton_int @ ( insert_int @ X @ bot_bot_set_int ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI
% 0.29/0.58 thf(fact_2201_is__singletonI,axiom,
% 0.29/0.58 ! [X: $o] : ( is_singleton_o @ ( insert_o @ X @ bot_bot_set_o ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI
% 0.29/0.58 thf(fact_2202_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(5)
% 0.29/0.58 thf(fact_2203_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(6)
% 0.29/0.58 thf(fact_2204_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(6)
% 0.29/0.58 thf(fact_2205_is__singleton__the__elem,axiom,
% 0.29/0.58 ( is_sin24926331636114728T_VEBT
% 0.29/0.58 = ( ^ [A6: set_VEBT_VEBT] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_VEBT_VEBT @ ( the_elem_VEBT_VEBT @ A6 ) @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_the_elem
% 0.29/0.58 thf(fact_2206_is__singleton__the__elem,axiom,
% 0.29/0.58 ( is_singleton_nat
% 0.29/0.58 = ( ^ [A6: set_nat] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_nat @ ( the_elem_nat @ A6 ) @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_the_elem
% 0.29/0.58 thf(fact_2207_is__singleton__the__elem,axiom,
% 0.29/0.58 ( is_singleton_int
% 0.29/0.58 = ( ^ [A6: set_int] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_int @ ( the_elem_int @ A6 ) @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_the_elem
% 0.29/0.58 thf(fact_2208_is__singleton__the__elem,axiom,
% 0.29/0.58 ( is_singleton_o
% 0.29/0.58 = ( ^ [A6: set_o] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_o @ ( the_elem_o @ A6 ) @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_the_elem
% 0.29/0.58 thf(fact_2209_is__singletonI_H,axiom,
% 0.29/0.58 ! [A4: set_VEBT_VEBT] :
% 0.29/0.58 ( ( A4 != bot_bo8194388402131092736T_VEBT )
% 0.29/0.58 => ( ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 0.29/0.58 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.29/0.58 => ( ( member_VEBT_VEBT @ Y3 @ A4 )
% 0.29/0.58 => ( X3 = Y3 ) ) )
% 0.29/0.58 => ( is_sin24926331636114728T_VEBT @ A4 ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI'
% 0.29/0.58 thf(fact_2210_is__singletonI_H,axiom,
% 0.29/0.58 ! [A4: set_real] :
% 0.29/0.58 ( ( A4 != bot_bot_set_real )
% 0.29/0.58 => ( ! [X3: real,Y3: real] :
% 0.29/0.58 ( ( member_real @ X3 @ A4 )
% 0.29/0.58 => ( ( member_real @ Y3 @ A4 )
% 0.29/0.58 => ( X3 = Y3 ) ) )
% 0.29/0.58 => ( is_singleton_real @ A4 ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI'
% 0.29/0.58 thf(fact_2211_is__singletonI_H,axiom,
% 0.29/0.58 ! [A4: set_set_nat] :
% 0.29/0.58 ( ( A4 != bot_bot_set_set_nat )
% 0.29/0.58 => ( ! [X3: set_nat,Y3: set_nat] :
% 0.29/0.58 ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.58 => ( ( member_set_nat @ Y3 @ A4 )
% 0.29/0.58 => ( X3 = Y3 ) ) )
% 0.29/0.58 => ( is_singleton_set_nat @ A4 ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI'
% 0.29/0.58 thf(fact_2212_is__singletonI_H,axiom,
% 0.29/0.58 ! [A4: set_nat] :
% 0.29/0.58 ( ( A4 != bot_bot_set_nat )
% 0.29/0.58 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.58 ( ( member_nat @ X3 @ A4 )
% 0.29/0.58 => ( ( member_nat @ Y3 @ A4 )
% 0.29/0.58 => ( X3 = Y3 ) ) )
% 0.29/0.58 => ( is_singleton_nat @ A4 ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI'
% 0.29/0.58 thf(fact_2213_is__singletonI_H,axiom,
% 0.29/0.58 ! [A4: set_int] :
% 0.29/0.58 ( ( A4 != bot_bot_set_int )
% 0.29/0.58 => ( ! [X3: int,Y3: int] :
% 0.29/0.58 ( ( member_int @ X3 @ A4 )
% 0.29/0.58 => ( ( member_int @ Y3 @ A4 )
% 0.29/0.58 => ( X3 = Y3 ) ) )
% 0.29/0.58 => ( is_singleton_int @ A4 ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI'
% 0.29/0.58 thf(fact_2214_is__singletonI_H,axiom,
% 0.29/0.58 ! [A4: set_o] :
% 0.29/0.58 ( ( A4 != bot_bot_set_o )
% 0.29/0.58 => ( ! [X3: $o,Y3: $o] :
% 0.29/0.58 ( ( member_o @ X3 @ A4 )
% 0.29/0.58 => ( ( member_o @ Y3 @ A4 )
% 0.29/0.58 => ( X3 = Y3 ) ) )
% 0.29/0.58 => ( is_singleton_o @ A4 ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonI'
% 0.29/0.58 thf(fact_2215_minNull__bound,axiom,
% 0.29/0.58 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % minNull_bound
% 0.29/0.58 thf(fact_2216_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 0.29/0.58 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(1)
% 0.29/0.58 thf(fact_2217_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 0.29/0.58 ! [Uv2: $o] :
% 0.29/0.58 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(2)
% 0.29/0.58 thf(fact_2218_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 0.29/0.58 ! [Uu2: $o] :
% 0.29/0.58 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(3)
% 0.29/0.58 thf(fact_2219_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 0.29/0.58 ! [A: $o,B: $o,X: nat] :
% 0.29/0.58 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 0.29/0.58 thf(fact_2220_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 0.29/0.58 ! [Uu2: $o,Uv2: $o] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(1)
% 0.29/0.58 thf(fact_2221_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J,axiom,
% 0.29/0.58 ! [Uv2: $o,Uw2: $o,N: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(2)
% 0.29/0.58 thf(fact_2222_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I3_J,axiom,
% 0.29/0.58 ! [A: $o,B: $o,Va2: nat] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(3)
% 0.29/0.58 thf(fact_2223_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 0.29/0.58 ! [Uu2: $o,Uv2: $o] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(1)
% 0.29/0.58 thf(fact_2224_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J,axiom,
% 0.29/0.58 ! [Uy2: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz @ Va2 ) @ Vb )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(4)
% 0.29/0.58 thf(fact_2225_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J,axiom,
% 0.29/0.58 ! [Uv2: $o,Uw2: $o,N: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(2)
% 0.29/0.58 thf(fact_2226_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J,axiom,
% 0.29/0.58 ! [Uy2: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz @ Va2 ) @ Vb )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(4)
% 0.29/0.58 thf(fact_2227_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J,axiom,
% 0.29/0.58 ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz ) @ Va2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(3)
% 0.29/0.58 thf(fact_2228_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 0.29/0.58 ! [Uu2: $o,B: $o] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(1)
% 0.29/0.58 thf(fact_2229_is__singletonE,axiom,
% 0.29/0.58 ! [A4: set_VEBT_VEBT] :
% 0.29/0.58 ( ( is_sin24926331636114728T_VEBT @ A4 )
% 0.29/0.58 => ~ ! [X3: vEBT_VEBT] :
% 0.29/0.58 ( A4
% 0.29/0.58 != ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonE
% 0.29/0.58 thf(fact_2230_is__singletonE,axiom,
% 0.29/0.58 ! [A4: set_nat] :
% 0.29/0.58 ( ( is_singleton_nat @ A4 )
% 0.29/0.58 => ~ ! [X3: nat] :
% 0.29/0.58 ( A4
% 0.29/0.58 != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonE
% 0.29/0.58 thf(fact_2231_is__singletonE,axiom,
% 0.29/0.58 ! [A4: set_int] :
% 0.29/0.58 ( ( is_singleton_int @ A4 )
% 0.29/0.58 => ~ ! [X3: int] :
% 0.29/0.58 ( A4
% 0.29/0.58 != ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonE
% 0.29/0.58 thf(fact_2232_is__singletonE,axiom,
% 0.29/0.58 ! [A4: set_o] :
% 0.29/0.58 ( ( is_singleton_o @ A4 )
% 0.29/0.58 => ~ ! [X3: $o] :
% 0.29/0.58 ( A4
% 0.29/0.58 != ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singletonE
% 0.29/0.58 thf(fact_2233_is__singleton__def,axiom,
% 0.29/0.58 ( is_sin24926331636114728T_VEBT
% 0.29/0.58 = ( ^ [A6: set_VEBT_VEBT] :
% 0.29/0.58 ? [X4: vEBT_VEBT] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_def
% 0.29/0.58 thf(fact_2234_is__singleton__def,axiom,
% 0.29/0.58 ( is_singleton_nat
% 0.29/0.58 = ( ^ [A6: set_nat] :
% 0.29/0.58 ? [X4: nat] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_def
% 0.29/0.58 thf(fact_2235_is__singleton__def,axiom,
% 0.29/0.58 ( is_singleton_int
% 0.29/0.58 = ( ^ [A6: set_int] :
% 0.29/0.58 ? [X4: int] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_def
% 0.29/0.58 thf(fact_2236_is__singleton__def,axiom,
% 0.29/0.58 ( is_singleton_o
% 0.29/0.58 = ( ^ [A6: set_o] :
% 0.29/0.58 ? [X4: $o] :
% 0.29/0.58 ( A6
% 0.29/0.58 = ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % is_singleton_def
% 0.29/0.58 thf(fact_2237_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J,axiom,
% 0.29/0.58 ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz ) @ Va2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(3)
% 0.29/0.58 thf(fact_2238_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 0.29/0.58 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.29/0.58 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(5)
% 0.29/0.58 thf(fact_2239_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 0.29/0.58 ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 0.29/0.58 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.simps(4)
% 0.29/0.58 thf(fact_2240_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 0.29/0.58 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X: nat] :
% 0.29/0.58 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 0.29/0.58 thf(fact_2241_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(5)
% 0.29/0.58 thf(fact_2242_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 0.29/0.58 ! [A: $o,Uw2: $o] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(2)
% 0.29/0.58 thf(fact_2243_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(4)
% 0.29/0.58 thf(fact_2244_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 0.29/0.58 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(5)
% 0.29/0.58 thf(fact_2245_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 0.29/0.58 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(4)
% 0.29/0.58 thf(fact_2246_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 0.29/0.58 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.29/0.58 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 0.29/0.58 thf(fact_2247_set__removeAll,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.29/0.58 ( ( set_VEBT_VEBT2 @ ( removeAll_VEBT_VEBT @ X @ Xs ) )
% 0.29/0.58 = ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % set_removeAll
% 0.29/0.58 thf(fact_2248_set__removeAll,axiom,
% 0.29/0.58 ! [X: real,Xs: list_real] :
% 0.29/0.58 ( ( set_real2 @ ( removeAll_real @ X @ Xs ) )
% 0.29/0.58 = ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % set_removeAll
% 0.29/0.58 thf(fact_2249_set__removeAll,axiom,
% 0.29/0.58 ! [X: int,Xs: list_int] :
% 0.29/0.58 ( ( set_int2 @ ( removeAll_int @ X @ Xs ) )
% 0.29/0.58 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % set_removeAll
% 0.29/0.58 thf(fact_2250_set__removeAll,axiom,
% 0.29/0.58 ! [X: $o,Xs: list_o] :
% 0.29/0.58 ( ( set_o2 @ ( removeAll_o @ X @ Xs ) )
% 0.29/0.58 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % set_removeAll
% 0.29/0.58 thf(fact_2251_set__removeAll,axiom,
% 0.29/0.58 ! [X: nat,Xs: list_nat] :
% 0.29/0.58 ( ( set_nat2 @ ( removeAll_nat @ X @ Xs ) )
% 0.29/0.58 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % set_removeAll
% 0.29/0.58 thf(fact_2252_vebt__maxt_Opelims,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.29/0.58 ( ( ( vEBT_vebt_maxt @ X )
% 0.29/0.58 = Y )
% 0.29/0.58 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 0.29/0.58 => ( ! [A3: $o,B3: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.29/0.58 => ( ( ( B3
% 0.29/0.58 => ( Y
% 0.29/0.58 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.58 & ( ~ B3
% 0.29/0.58 => ( ( A3
% 0.29/0.58 => ( Y
% 0.29/0.58 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.58 & ( ~ A3
% 0.29/0.58 => ( Y = none_nat ) ) ) ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.29/0.58 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.58 => ( ( Y = none_nat )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.29/0.58 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.29/0.58 => ( ( Y
% 0.29/0.58 = ( some_nat @ Ma2 ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % vebt_maxt.pelims
% 0.29/0.58 thf(fact_2253_vebt__mint_Opelims,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.29/0.58 ( ( ( vEBT_vebt_mint @ X )
% 0.29/0.58 = Y )
% 0.29/0.58 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 0.29/0.58 => ( ! [A3: $o,B3: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.29/0.58 => ( ( ( A3
% 0.29/0.58 => ( Y
% 0.29/0.58 = ( some_nat @ zero_zero_nat ) ) )
% 0.29/0.58 & ( ~ A3
% 0.29/0.58 => ( ( B3
% 0.29/0.58 => ( Y
% 0.29/0.58 = ( some_nat @ one_one_nat ) ) )
% 0.29/0.58 & ( ~ B3
% 0.29/0.58 => ( Y = none_nat ) ) ) ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.29/0.58 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.29/0.58 => ( ( Y = none_nat )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.29/0.58 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.29/0.58 => ( ( Y
% 0.29/0.58 = ( some_nat @ Mi2 ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % vebt_mint.pelims
% 0.29/0.58 thf(fact_2254_height__node,axiom,
% 0.29/0.58 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.29/0.58 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.29/0.58 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % height_node
% 0.29/0.58 thf(fact_2255_insertsimp_H,axiom,
% 0.29/0.58 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 0.29/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.58 => ( ( vEBT_VEBT_minNull @ T )
% 0.29/0.58 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % insertsimp'
% 0.29/0.58 thf(fact_2256_insersimp_H,axiom,
% 0.29/0.58 ! [T: vEBT_VEBT,N: nat,Y: nat] :
% 0.29/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.58 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 0.29/0.58 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y ) @ one_one_nat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % insersimp'
% 0.29/0.58 thf(fact_2257_frac__unique__iff,axiom,
% 0.29/0.58 ! [X: real,A: real] :
% 0.29/0.58 ( ( ( archim2898591450579166408c_real @ X )
% 0.29/0.58 = A )
% 0.29/0.58 = ( ( member_real @ ( minus_minus_real @ X @ A ) @ ring_1_Ints_real )
% 0.29/0.58 & ( ord_less_eq_real @ zero_zero_real @ A )
% 0.29/0.58 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % frac_unique_iff
% 0.29/0.58 thf(fact_2258_frac__unique__iff,axiom,
% 0.29/0.58 ! [X: rat,A: rat] :
% 0.29/0.58 ( ( ( archimedean_frac_rat @ X )
% 0.29/0.58 = A )
% 0.29/0.58 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 0.29/0.58 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.58 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % frac_unique_iff
% 0.29/0.58 thf(fact_2259_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 0.29/0.58 ! [V2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.29/0.58 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(4)
% 0.29/0.58 thf(fact_2260_remove__def,axiom,
% 0.29/0.58 ( remove_VEBT_VEBT
% 0.29/0.58 = ( ^ [X4: vEBT_VEBT,A6: set_VEBT_VEBT] : ( minus_5127226145743854075T_VEBT @ A6 @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % remove_def
% 0.29/0.58 thf(fact_2261_remove__def,axiom,
% 0.29/0.58 ( remove_int
% 0.29/0.58 = ( ^ [X4: int,A6: set_int] : ( minus_minus_set_int @ A6 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % remove_def
% 0.29/0.58 thf(fact_2262_remove__def,axiom,
% 0.29/0.58 ( remove_o
% 0.29/0.58 = ( ^ [X4: $o,A6: set_o] : ( minus_minus_set_o @ A6 @ ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % remove_def
% 0.29/0.58 thf(fact_2263_remove__def,axiom,
% 0.29/0.58 ( remove_nat
% 0.29/0.58 = ( ^ [X4: nat,A6: set_nat] : ( minus_minus_set_nat @ A6 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % remove_def
% 0.29/0.58 thf(fact_2264_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 0.29/0.58 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.29/0.58 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(3)
% 0.29/0.58 thf(fact_2265_member__remove,axiom,
% 0.29/0.58 ! [X: nat,Y: nat,A4: set_nat] :
% 0.29/0.58 ( ( member_nat @ X @ ( remove_nat @ Y @ A4 ) )
% 0.29/0.58 = ( ( member_nat @ X @ A4 )
% 0.29/0.58 & ( X != Y ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % member_remove
% 0.29/0.58 thf(fact_2266_member__remove,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT,Y: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.58 ( ( member_VEBT_VEBT @ X @ ( remove_VEBT_VEBT @ Y @ A4 ) )
% 0.29/0.58 = ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.58 & ( X != Y ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % member_remove
% 0.29/0.58 thf(fact_2267_member__remove,axiom,
% 0.29/0.58 ! [X: real,Y: real,A4: set_real] :
% 0.29/0.58 ( ( member_real @ X @ ( remove_real @ Y @ A4 ) )
% 0.29/0.58 = ( ( member_real @ X @ A4 )
% 0.29/0.58 & ( X != Y ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % member_remove
% 0.29/0.58 thf(fact_2268_member__remove,axiom,
% 0.29/0.58 ! [X: int,Y: int,A4: set_int] :
% 0.29/0.58 ( ( member_int @ X @ ( remove_int @ Y @ A4 ) )
% 0.29/0.58 = ( ( member_int @ X @ A4 )
% 0.29/0.58 & ( X != Y ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % member_remove
% 0.29/0.58 thf(fact_2269_member__remove,axiom,
% 0.29/0.58 ! [X: set_nat,Y: set_nat,A4: set_set_nat] :
% 0.29/0.58 ( ( member_set_nat @ X @ ( remove_set_nat @ Y @ A4 ) )
% 0.29/0.58 = ( ( member_set_nat @ X @ A4 )
% 0.29/0.58 & ( X != Y ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % member_remove
% 0.29/0.58 thf(fact_2270_frac__eq__0__iff,axiom,
% 0.29/0.58 ! [X: real] :
% 0.29/0.58 ( ( ( archim2898591450579166408c_real @ X )
% 0.29/0.58 = zero_zero_real )
% 0.29/0.58 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 0.29/0.58
% 0.29/0.58 % frac_eq_0_iff
% 0.29/0.58 thf(fact_2271_frac__eq__0__iff,axiom,
% 0.29/0.58 ! [X: rat] :
% 0.29/0.58 ( ( ( archimedean_frac_rat @ X )
% 0.29/0.58 = zero_zero_rat )
% 0.29/0.58 = ( member_rat @ X @ ring_1_Ints_rat ) ) ).
% 0.29/0.58
% 0.29/0.58 % frac_eq_0_iff
% 0.29/0.58 thf(fact_2272_frac__gt__0__iff,axiom,
% 0.29/0.58 ! [X: real] :
% 0.29/0.58 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) )
% 0.29/0.58 = ( ~ ( member_real @ X @ ring_1_Ints_real ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % frac_gt_0_iff
% 0.29/0.58 thf(fact_2273_frac__gt__0__iff,axiom,
% 0.29/0.58 ! [X: rat] :
% 0.29/0.58 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) )
% 0.29/0.58 = ( ~ ( member_rat @ X @ ring_1_Ints_rat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % frac_gt_0_iff
% 0.29/0.58 thf(fact_2274_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 0.29/0.58 ! [A: $o,B: $o] :
% 0.29/0.58 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 0.29/0.58 = zero_zero_nat ) ).
% 0.29/0.58
% 0.29/0.58 % VEBT_internal.height.simps(1)
% 0.29/0.58 thf(fact_2275_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 0.29/0.58 ! [A: $o,B: $o,X: nat] :
% 0.29/0.58 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(1)
% 0.29/0.58 thf(fact_2276_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 0.29/0.58 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.29/0.58 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X )
% 0.29/0.58 = one_one_nat ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(2)
% 0.29/0.58 thf(fact_2277_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT,Y: nat] :
% 0.29/0.58 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 0.29/0.58 = Y )
% 0.29/0.58 => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X )
% 0.29/0.58 => ( ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.58 => ( ( Y = one_one_nat )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 0.29/0.58 => ( ! [Uv: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.58 => ( ( Y = one_one_nat )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv ) ) ) )
% 0.29/0.58 => ( ! [Uu: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.58 => ( ( Y = one_one_nat )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu @ $true ) ) ) )
% 0.29/0.58 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.29/0.58 => ( ( Y = one_one_nat )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) )
% 0.29/0.58 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.29/0.58 => ( ( Y = one_one_nat )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>N\<^sub>u\<^sub>l\<^sub>l.pelims
% 0.29/0.58 thf(fact_2278_delete__bound__height_H,axiom,
% 0.29/0.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.29/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.29/0.58 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % delete_bound_height'
% 0.29/0.58 thf(fact_2279_height__compose__child,axiom,
% 0.29/0.58 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 0.29/0.58 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.58 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % height_compose_child
% 0.29/0.58 thf(fact_2280_height__compose__list,axiom,
% 0.29/0.58 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.29/0.58 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.29/0.58 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % height_compose_list
% 0.29/0.58 thf(fact_2281_height__compose__summary,axiom,
% 0.29/0.58 ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % height_compose_summary
% 0.29/0.58 thf(fact_2282_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT,Y: $o] :
% 0.29/0.58 ( ( ( vEBT_VEBT_minNull @ X )
% 0.29/0.58 = Y )
% 0.29/0.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.29/0.58 => ( ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.58 => ( Y
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 0.29/0.58 => ( ! [Uv: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.58 => ( ~ Y
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) ) )
% 0.29/0.58 => ( ! [Uu: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.58 => ( ~ Y
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) ) )
% 0.29/0.58 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.29/0.58 => ( Y
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) )
% 0.29/0.58 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.29/0.58 => ( ~ Y
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % VEBT_internal.minNull.pelims(1)
% 0.29/0.58 thf(fact_2283_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT] :
% 0.29/0.58 ( ( vEBT_VEBT_minNull @ X )
% 0.29/0.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.29/0.58 => ( ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ $false @ $false ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 0.29/0.58 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % VEBT_internal.minNull.pelims(2)
% 0.29/0.58 thf(fact_2284_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 0.29/0.58 ! [X: vEBT_VEBT] :
% 0.29/0.58 ( ~ ( vEBT_VEBT_minNull @ X )
% 0.29/0.58 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.29/0.58 => ( ! [Uv: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ $true @ Uv ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) )
% 0.29/0.58 => ( ! [Uu: $o] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Leaf @ Uu @ $true ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) )
% 0.29/0.58 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.29/0.58 ( ( X
% 0.29/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 0.29/0.58 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % VEBT_internal.minNull.pelims(3)
% 0.29/0.58 thf(fact_2285_Ints__0,axiom,
% 0.29/0.58 member_uint32 @ zero_zero_uint32 @ ring_1_Ints_uint32 ).
% 0.29/0.58
% 0.29/0.58 % Ints_0
% 0.29/0.58 thf(fact_2286_Ints__0,axiom,
% 0.29/0.58 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 0.29/0.58
% 0.29/0.58 % Ints_0
% 0.29/0.58 thf(fact_2287_Ints__0,axiom,
% 0.29/0.58 member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 0.29/0.58
% 0.29/0.58 % Ints_0
% 0.29/0.58 thf(fact_2288_Ints__0,axiom,
% 0.29/0.58 member_int @ zero_zero_int @ ring_1_Ints_int ).
% 0.29/0.58
% 0.29/0.58 % Ints_0
% 0.29/0.58 thf(fact_2289_enumerate__Suc_H,axiom,
% 0.29/0.58 ! [S3: set_nat,N: nat] :
% 0.29/0.58 ( ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) )
% 0.29/0.58 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ ( infini8530281810654367211te_nat @ S3 @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N ) ) ).
% 0.29/0.58
% 0.29/0.58 % enumerate_Suc'
% 0.29/0.58 thf(fact_2290_even__odd__cases,axiom,
% 0.29/0.58 ! [X: nat] :
% 0.29/0.58 ( ! [N2: nat] :
% 0.29/0.58 ( X
% 0.29/0.58 != ( plus_plus_nat @ N2 @ N2 ) )
% 0.29/0.58 => ~ ! [N2: nat] :
% 0.29/0.58 ( X
% 0.29/0.58 != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % even_odd_cases
% 0.29/0.58 thf(fact_2291_add__right__cancel,axiom,
% 0.29/0.58 ! [B: real,A: real,C2: real] :
% 0.29/0.58 ( ( ( plus_plus_real @ B @ A )
% 0.29/0.58 = ( plus_plus_real @ C2 @ A ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_right_cancel
% 0.29/0.58 thf(fact_2292_add__right__cancel,axiom,
% 0.29/0.58 ! [B: rat,A: rat,C2: rat] :
% 0.29/0.58 ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.58 = ( plus_plus_rat @ C2 @ A ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_right_cancel
% 0.29/0.58 thf(fact_2293_add__right__cancel,axiom,
% 0.29/0.58 ! [B: nat,A: nat,C2: nat] :
% 0.29/0.58 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.58 = ( plus_plus_nat @ C2 @ A ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_right_cancel
% 0.29/0.58 thf(fact_2294_add__right__cancel,axiom,
% 0.29/0.58 ! [B: int,A: int,C2: int] :
% 0.29/0.58 ( ( ( plus_plus_int @ B @ A )
% 0.29/0.58 = ( plus_plus_int @ C2 @ A ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_right_cancel
% 0.29/0.58 thf(fact_2295_add__left__cancel,axiom,
% 0.29/0.58 ! [A: real,B: real,C2: real] :
% 0.29/0.58 ( ( ( plus_plus_real @ A @ B )
% 0.29/0.58 = ( plus_plus_real @ A @ C2 ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_left_cancel
% 0.29/0.58 thf(fact_2296_add__left__cancel,axiom,
% 0.29/0.58 ! [A: rat,B: rat,C2: rat] :
% 0.29/0.58 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.58 = ( plus_plus_rat @ A @ C2 ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_left_cancel
% 0.29/0.58 thf(fact_2297_add__left__cancel,axiom,
% 0.29/0.58 ! [A: nat,B: nat,C2: nat] :
% 0.29/0.58 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.58 = ( plus_plus_nat @ A @ C2 ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_left_cancel
% 0.29/0.58 thf(fact_2298_add__left__cancel,axiom,
% 0.29/0.58 ! [A: int,B: int,C2: int] :
% 0.29/0.58 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.58 = ( plus_plus_int @ A @ C2 ) )
% 0.29/0.58 = ( B = C2 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_left_cancel
% 0.29/0.58 thf(fact_2299_image__eqI,axiom,
% 0.29/0.58 ! [B: nat,F: nat > nat,X: nat,A4: set_nat] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_nat @ X @ A4 )
% 0.29/0.58 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2300_image__eqI,axiom,
% 0.29/0.58 ! [B: vEBT_VEBT,F: nat > vEBT_VEBT,X: nat,A4: set_nat] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_nat @ X @ A4 )
% 0.29/0.58 => ( member_VEBT_VEBT @ B @ ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2301_image__eqI,axiom,
% 0.29/0.58 ! [B: real,F: nat > real,X: nat,A4: set_nat] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_nat @ X @ A4 )
% 0.29/0.58 => ( member_real @ B @ ( image_nat_real @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2302_image__eqI,axiom,
% 0.29/0.58 ! [B: int,F: nat > int,X: nat,A4: set_nat] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_nat @ X @ A4 )
% 0.29/0.58 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2303_image__eqI,axiom,
% 0.29/0.58 ! [B: nat,F: vEBT_VEBT > nat,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.58 => ( member_nat @ B @ ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2304_image__eqI,axiom,
% 0.29/0.58 ! [B: vEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.58 => ( member_VEBT_VEBT @ B @ ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2305_image__eqI,axiom,
% 0.29/0.58 ! [B: real,F: vEBT_VEBT > real,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.58 => ( member_real @ B @ ( image_VEBT_VEBT_real @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2306_image__eqI,axiom,
% 0.29/0.58 ! [B: int,F: vEBT_VEBT > int,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.29/0.58 => ( member_int @ B @ ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2307_image__eqI,axiom,
% 0.29/0.58 ! [B: nat,F: real > nat,X: real,A4: set_real] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_real @ X @ A4 )
% 0.29/0.58 => ( member_nat @ B @ ( image_real_nat @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2308_image__eqI,axiom,
% 0.29/0.58 ! [B: vEBT_VEBT,F: real > vEBT_VEBT,X: real,A4: set_real] :
% 0.29/0.58 ( ( B
% 0.29/0.58 = ( F @ X ) )
% 0.29/0.58 => ( ( member_real @ X @ A4 )
% 0.29/0.58 => ( member_VEBT_VEBT @ B @ ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % image_eqI
% 0.29/0.58 thf(fact_2309_double__eq__0__iff,axiom,
% 0.29/0.58 ! [A: real] :
% 0.29/0.58 ( ( ( plus_plus_real @ A @ A )
% 0.29/0.58 = zero_zero_real )
% 0.29/0.58 = ( A = zero_zero_real ) ) ).
% 0.29/0.58
% 0.29/0.58 % double_eq_0_iff
% 0.29/0.58 thf(fact_2310_double__eq__0__iff,axiom,
% 0.29/0.58 ! [A: rat] :
% 0.29/0.58 ( ( ( plus_plus_rat @ A @ A )
% 0.29/0.58 = zero_zero_rat )
% 0.29/0.58 = ( A = zero_zero_rat ) ) ).
% 0.29/0.58
% 0.29/0.58 % double_eq_0_iff
% 0.29/0.58 thf(fact_2311_double__eq__0__iff,axiom,
% 0.29/0.58 ! [A: int] :
% 0.29/0.58 ( ( ( plus_plus_int @ A @ A )
% 0.29/0.58 = zero_zero_int )
% 0.29/0.58 = ( A = zero_zero_int ) ) ).
% 0.29/0.58
% 0.29/0.58 % double_eq_0_iff
% 0.29/0.58 thf(fact_2312_add_Oright__neutral,axiom,
% 0.29/0.58 ! [A: uint32] :
% 0.29/0.58 ( ( plus_plus_uint32 @ A @ zero_zero_uint32 )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add.right_neutral
% 0.29/0.58 thf(fact_2313_add_Oright__neutral,axiom,
% 0.29/0.58 ! [A: real] :
% 0.29/0.58 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add.right_neutral
% 0.29/0.58 thf(fact_2314_add_Oright__neutral,axiom,
% 0.29/0.58 ! [A: rat] :
% 0.29/0.58 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add.right_neutral
% 0.29/0.58 thf(fact_2315_add_Oright__neutral,axiom,
% 0.29/0.58 ! [A: nat] :
% 0.29/0.58 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add.right_neutral
% 0.29/0.58 thf(fact_2316_add_Oright__neutral,axiom,
% 0.29/0.58 ! [A: int] :
% 0.29/0.58 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add.right_neutral
% 0.29/0.58 thf(fact_2317_double__zero__sym,axiom,
% 0.29/0.58 ! [A: real] :
% 0.29/0.58 ( ( zero_zero_real
% 0.29/0.58 = ( plus_plus_real @ A @ A ) )
% 0.29/0.58 = ( A = zero_zero_real ) ) ).
% 0.29/0.58
% 0.29/0.58 % double_zero_sym
% 0.29/0.58 thf(fact_2318_double__zero__sym,axiom,
% 0.29/0.58 ! [A: rat] :
% 0.29/0.58 ( ( zero_zero_rat
% 0.29/0.58 = ( plus_plus_rat @ A @ A ) )
% 0.29/0.58 = ( A = zero_zero_rat ) ) ).
% 0.29/0.58
% 0.29/0.58 % double_zero_sym
% 0.29/0.58 thf(fact_2319_double__zero__sym,axiom,
% 0.29/0.58 ! [A: int] :
% 0.29/0.58 ( ( zero_zero_int
% 0.29/0.58 = ( plus_plus_int @ A @ A ) )
% 0.29/0.58 = ( A = zero_zero_int ) ) ).
% 0.29/0.58
% 0.29/0.58 % double_zero_sym
% 0.29/0.58 thf(fact_2320_add__cancel__left__left,axiom,
% 0.29/0.58 ! [B: uint32,A: uint32] :
% 0.29/0.58 ( ( ( plus_plus_uint32 @ B @ A )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_uint32 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_left
% 0.29/0.58 thf(fact_2321_add__cancel__left__left,axiom,
% 0.29/0.58 ! [B: real,A: real] :
% 0.29/0.58 ( ( ( plus_plus_real @ B @ A )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_real ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_left
% 0.29/0.58 thf(fact_2322_add__cancel__left__left,axiom,
% 0.29/0.58 ! [B: rat,A: rat] :
% 0.29/0.58 ( ( ( plus_plus_rat @ B @ A )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_rat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_left
% 0.29/0.58 thf(fact_2323_add__cancel__left__left,axiom,
% 0.29/0.58 ! [B: nat,A: nat] :
% 0.29/0.58 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_nat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_left
% 0.29/0.58 thf(fact_2324_add__cancel__left__left,axiom,
% 0.29/0.58 ! [B: int,A: int] :
% 0.29/0.58 ( ( ( plus_plus_int @ B @ A )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_int ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_left
% 0.29/0.58 thf(fact_2325_add__cancel__left__right,axiom,
% 0.29/0.58 ! [A: uint32,B: uint32] :
% 0.29/0.58 ( ( ( plus_plus_uint32 @ A @ B )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_uint32 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_right
% 0.29/0.58 thf(fact_2326_add__cancel__left__right,axiom,
% 0.29/0.58 ! [A: real,B: real] :
% 0.29/0.58 ( ( ( plus_plus_real @ A @ B )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_real ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_right
% 0.29/0.58 thf(fact_2327_add__cancel__left__right,axiom,
% 0.29/0.58 ! [A: rat,B: rat] :
% 0.29/0.58 ( ( ( plus_plus_rat @ A @ B )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_rat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_right
% 0.29/0.58 thf(fact_2328_add__cancel__left__right,axiom,
% 0.29/0.58 ! [A: nat,B: nat] :
% 0.29/0.58 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_nat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_right
% 0.29/0.58 thf(fact_2329_add__cancel__left__right,axiom,
% 0.29/0.58 ! [A: int,B: int] :
% 0.29/0.58 ( ( ( plus_plus_int @ A @ B )
% 0.29/0.58 = A )
% 0.29/0.58 = ( B = zero_zero_int ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_left_right
% 0.29/0.58 thf(fact_2330_add__cancel__right__left,axiom,
% 0.29/0.58 ! [A: uint32,B: uint32] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_uint32 @ B @ A ) )
% 0.29/0.58 = ( B = zero_zero_uint32 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_left
% 0.29/0.58 thf(fact_2331_add__cancel__right__left,axiom,
% 0.29/0.58 ! [A: real,B: real] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_real @ B @ A ) )
% 0.29/0.58 = ( B = zero_zero_real ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_left
% 0.29/0.58 thf(fact_2332_add__cancel__right__left,axiom,
% 0.29/0.58 ! [A: rat,B: rat] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_rat @ B @ A ) )
% 0.29/0.58 = ( B = zero_zero_rat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_left
% 0.29/0.58 thf(fact_2333_add__cancel__right__left,axiom,
% 0.29/0.58 ! [A: nat,B: nat] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_nat @ B @ A ) )
% 0.29/0.58 = ( B = zero_zero_nat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_left
% 0.29/0.58 thf(fact_2334_add__cancel__right__left,axiom,
% 0.29/0.58 ! [A: int,B: int] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_int @ B @ A ) )
% 0.29/0.58 = ( B = zero_zero_int ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_left
% 0.29/0.58 thf(fact_2335_add__cancel__right__right,axiom,
% 0.29/0.58 ! [A: uint32,B: uint32] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_uint32 @ A @ B ) )
% 0.29/0.58 = ( B = zero_zero_uint32 ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_right
% 0.29/0.58 thf(fact_2336_add__cancel__right__right,axiom,
% 0.29/0.58 ! [A: real,B: real] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_real @ A @ B ) )
% 0.29/0.58 = ( B = zero_zero_real ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_right
% 0.29/0.58 thf(fact_2337_add__cancel__right__right,axiom,
% 0.29/0.58 ! [A: rat,B: rat] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_rat @ A @ B ) )
% 0.29/0.58 = ( B = zero_zero_rat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_right
% 0.29/0.58 thf(fact_2338_add__cancel__right__right,axiom,
% 0.29/0.58 ! [A: nat,B: nat] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_nat @ A @ B ) )
% 0.29/0.58 = ( B = zero_zero_nat ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_right
% 0.29/0.58 thf(fact_2339_add__cancel__right__right,axiom,
% 0.29/0.58 ! [A: int,B: int] :
% 0.29/0.58 ( ( A
% 0.29/0.58 = ( plus_plus_int @ A @ B ) )
% 0.29/0.58 = ( B = zero_zero_int ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_cancel_right_right
% 0.29/0.58 thf(fact_2340_add__eq__0__iff__both__eq__0,axiom,
% 0.29/0.58 ! [X: nat,Y: nat] :
% 0.29/0.58 ( ( ( plus_plus_nat @ X @ Y )
% 0.29/0.58 = zero_zero_nat )
% 0.29/0.58 = ( ( X = zero_zero_nat )
% 0.29/0.58 & ( Y = zero_zero_nat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_eq_0_iff_both_eq_0
% 0.29/0.58 thf(fact_2341_zero__eq__add__iff__both__eq__0,axiom,
% 0.29/0.58 ! [X: nat,Y: nat] :
% 0.29/0.58 ( ( zero_zero_nat
% 0.29/0.58 = ( plus_plus_nat @ X @ Y ) )
% 0.29/0.58 = ( ( X = zero_zero_nat )
% 0.29/0.58 & ( Y = zero_zero_nat ) ) ) ).
% 0.29/0.58
% 0.29/0.58 % zero_eq_add_iff_both_eq_0
% 0.29/0.58 thf(fact_2342_add__0,axiom,
% 0.29/0.58 ! [A: uint32] :
% 0.29/0.58 ( ( plus_plus_uint32 @ zero_zero_uint32 @ A )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add_0
% 0.29/0.58 thf(fact_2343_add__0,axiom,
% 0.29/0.58 ! [A: real] :
% 0.29/0.58 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add_0
% 0.29/0.58 thf(fact_2344_add__0,axiom,
% 0.29/0.58 ! [A: rat] :
% 0.29/0.58 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add_0
% 0.29/0.58 thf(fact_2345_add__0,axiom,
% 0.29/0.58 ! [A: nat] :
% 0.29/0.58 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add_0
% 0.29/0.58 thf(fact_2346_add__0,axiom,
% 0.29/0.58 ! [A: int] :
% 0.29/0.58 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.29/0.58 = A ) ).
% 0.29/0.58
% 0.29/0.58 % add_0
% 0.29/0.58 thf(fact_2347_add__le__cancel__right,axiom,
% 0.29/0.58 ! [A: real,C2: real,B: real] :
% 0.29/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.29/0.58 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_le_cancel_right
% 0.29/0.58 thf(fact_2348_add__le__cancel__right,axiom,
% 0.29/0.58 ! [A: rat,C2: rat,B: rat] :
% 0.29/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.29/0.58 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.58
% 0.29/0.58 % add_le_cancel_right
% 0.29/0.58 thf(fact_2349_add__le__cancel__right,axiom,
% 0.37/0.58 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.37/0.58 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_cancel_right
% 0.37/0.58 thf(fact_2350_add__le__cancel__right,axiom,
% 0.37/0.58 ! [A: int,C2: int,B: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.37/0.58 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_cancel_right
% 0.37/0.58 thf(fact_2351_add__le__cancel__left,axiom,
% 0.37/0.58 ! [C2: real,A: real,B: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_cancel_left
% 0.37/0.58 thf(fact_2352_add__le__cancel__left,axiom,
% 0.37/0.58 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_cancel_left
% 0.37/0.58 thf(fact_2353_add__le__cancel__left,axiom,
% 0.37/0.58 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_cancel_left
% 0.37/0.58 thf(fact_2354_add__le__cancel__left,axiom,
% 0.37/0.58 ! [C2: int,A: int,B: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_cancel_left
% 0.37/0.58 thf(fact_2355_add__less__cancel__left,axiom,
% 0.37/0.58 ! [C2: real,A: real,B: real] :
% 0.37/0.58 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_real @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_left
% 0.37/0.58 thf(fact_2356_add__less__cancel__left,axiom,
% 0.37/0.58 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_rat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_left
% 0.37/0.58 thf(fact_2357_add__less__cancel__left,axiom,
% 0.37/0.58 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_left
% 0.37/0.58 thf(fact_2358_add__less__cancel__left,axiom,
% 0.37/0.58 ! [C2: int,A: int,B: int] :
% 0.37/0.58 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.37/0.58 = ( ord_less_int @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_left
% 0.37/0.58 thf(fact_2359_add__less__cancel__right,axiom,
% 0.37/0.58 ! [A: real,C2: real,B: real] :
% 0.37/0.58 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.37/0.58 = ( ord_less_real @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_right
% 0.37/0.58 thf(fact_2360_add__less__cancel__right,axiom,
% 0.37/0.58 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.37/0.58 = ( ord_less_rat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_right
% 0.37/0.58 thf(fact_2361_add__less__cancel__right,axiom,
% 0.37/0.58 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.37/0.58 = ( ord_less_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_right
% 0.37/0.58 thf(fact_2362_add__less__cancel__right,axiom,
% 0.37/0.58 ! [A: int,C2: int,B: int] :
% 0.37/0.58 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.37/0.58 = ( ord_less_int @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_cancel_right
% 0.37/0.58 thf(fact_2363_add__diff__cancel__right_H,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right'
% 0.37/0.58 thf(fact_2364_add__diff__cancel__right_H,axiom,
% 0.37/0.58 ! [A: uint32,B: uint32] :
% 0.37/0.58 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right'
% 0.37/0.58 thf(fact_2365_add__diff__cancel__right_H,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right'
% 0.37/0.58 thf(fact_2366_add__diff__cancel__right_H,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right'
% 0.37/0.58 thf(fact_2367_add__diff__cancel__right_H,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right'
% 0.37/0.58 thf(fact_2368_add__diff__cancel__right,axiom,
% 0.37/0.58 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.58 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.37/0.58 = ( minus_minus_rat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right
% 0.37/0.58 thf(fact_2369_add__diff__cancel__right,axiom,
% 0.37/0.58 ! [A: uint32,C2: uint32,B: uint32] :
% 0.37/0.58 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ C2 ) @ ( plus_plus_uint32 @ B @ C2 ) )
% 0.37/0.58 = ( minus_minus_uint32 @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right
% 0.37/0.58 thf(fact_2370_add__diff__cancel__right,axiom,
% 0.37/0.58 ! [A: real,C2: real,B: real] :
% 0.37/0.58 ( ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.37/0.58 = ( minus_minus_real @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right
% 0.37/0.58 thf(fact_2371_add__diff__cancel__right,axiom,
% 0.37/0.58 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.58 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.37/0.58 = ( minus_minus_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right
% 0.37/0.58 thf(fact_2372_add__diff__cancel__right,axiom,
% 0.37/0.58 ! [A: int,C2: int,B: int] :
% 0.37/0.58 ( ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.37/0.58 = ( minus_minus_int @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_right
% 0.37/0.58 thf(fact_2373_add__diff__cancel__left_H,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.37/0.58 = B ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left'
% 0.37/0.58 thf(fact_2374_add__diff__cancel__left_H,axiom,
% 0.37/0.58 ! [A: uint32,B: uint32] :
% 0.37/0.58 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ A )
% 0.37/0.58 = B ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left'
% 0.37/0.58 thf(fact_2375_add__diff__cancel__left_H,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.37/0.58 = B ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left'
% 0.37/0.58 thf(fact_2376_add__diff__cancel__left_H,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.37/0.58 = B ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left'
% 0.37/0.58 thf(fact_2377_add__diff__cancel__left_H,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.37/0.58 = B ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left'
% 0.37/0.58 thf(fact_2378_add__diff__cancel__left,axiom,
% 0.37/0.58 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.58 ( ( minus_minus_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.37/0.58 = ( minus_minus_rat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left
% 0.37/0.58 thf(fact_2379_add__diff__cancel__left,axiom,
% 0.37/0.58 ! [C2: uint32,A: uint32,B: uint32] :
% 0.37/0.58 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ C2 @ A ) @ ( plus_plus_uint32 @ C2 @ B ) )
% 0.37/0.58 = ( minus_minus_uint32 @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left
% 0.37/0.58 thf(fact_2380_add__diff__cancel__left,axiom,
% 0.37/0.58 ! [C2: real,A: real,B: real] :
% 0.37/0.58 ( ( minus_minus_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.37/0.58 = ( minus_minus_real @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left
% 0.37/0.58 thf(fact_2381_add__diff__cancel__left,axiom,
% 0.37/0.58 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.58 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.37/0.58 = ( minus_minus_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left
% 0.37/0.58 thf(fact_2382_add__diff__cancel__left,axiom,
% 0.37/0.58 ! [C2: int,A: int,B: int] :
% 0.37/0.58 ( ( minus_minus_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.37/0.58 = ( minus_minus_int @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel_left
% 0.37/0.58 thf(fact_2383_diff__add__cancel,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % diff_add_cancel
% 0.37/0.58 thf(fact_2384_diff__add__cancel,axiom,
% 0.37/0.58 ! [A: uint32,B: uint32] :
% 0.37/0.58 ( ( plus_plus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % diff_add_cancel
% 0.37/0.58 thf(fact_2385_diff__add__cancel,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % diff_add_cancel
% 0.37/0.58 thf(fact_2386_diff__add__cancel,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % diff_add_cancel
% 0.37/0.58 thf(fact_2387_add__diff__cancel,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel
% 0.37/0.58 thf(fact_2388_add__diff__cancel,axiom,
% 0.37/0.58 ! [A: uint32,B: uint32] :
% 0.37/0.58 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel
% 0.37/0.58 thf(fact_2389_add__diff__cancel,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel
% 0.37/0.58 thf(fact_2390_add__diff__cancel,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add_diff_cancel
% 0.37/0.58 thf(fact_2391_image__empty,axiom,
% 0.37/0.58 ! [F: nat > set_nat] :
% 0.37/0.58 ( ( image_nat_set_nat @ F @ bot_bot_set_nat )
% 0.37/0.58 = bot_bot_set_set_nat ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2392_image__empty,axiom,
% 0.37/0.58 ! [F: nat > nat] :
% 0.37/0.58 ( ( image_nat_nat @ F @ bot_bot_set_nat )
% 0.37/0.58 = bot_bot_set_nat ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2393_image__empty,axiom,
% 0.37/0.58 ! [F: nat > int] :
% 0.37/0.58 ( ( image_nat_int @ F @ bot_bot_set_nat )
% 0.37/0.58 = bot_bot_set_int ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2394_image__empty,axiom,
% 0.37/0.58 ! [F: nat > $o] :
% 0.37/0.58 ( ( image_nat_o @ F @ bot_bot_set_nat )
% 0.37/0.58 = bot_bot_set_o ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2395_image__empty,axiom,
% 0.37/0.58 ! [F: int > nat] :
% 0.37/0.58 ( ( image_int_nat @ F @ bot_bot_set_int )
% 0.37/0.58 = bot_bot_set_nat ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2396_image__empty,axiom,
% 0.37/0.58 ! [F: int > int] :
% 0.37/0.58 ( ( image_int_int @ F @ bot_bot_set_int )
% 0.37/0.58 = bot_bot_set_int ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2397_image__empty,axiom,
% 0.37/0.58 ! [F: int > $o] :
% 0.37/0.58 ( ( image_int_o @ F @ bot_bot_set_int )
% 0.37/0.58 = bot_bot_set_o ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2398_image__empty,axiom,
% 0.37/0.58 ! [F: $o > nat] :
% 0.37/0.58 ( ( image_o_nat @ F @ bot_bot_set_o )
% 0.37/0.58 = bot_bot_set_nat ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2399_image__empty,axiom,
% 0.37/0.58 ! [F: $o > int] :
% 0.37/0.58 ( ( image_o_int @ F @ bot_bot_set_o )
% 0.37/0.58 = bot_bot_set_int ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2400_image__empty,axiom,
% 0.37/0.58 ! [F: $o > $o] :
% 0.37/0.58 ( ( image_o_o @ F @ bot_bot_set_o )
% 0.37/0.58 = bot_bot_set_o ) ).
% 0.37/0.58
% 0.37/0.58 % image_empty
% 0.37/0.58 thf(fact_2401_empty__is__image,axiom,
% 0.37/0.58 ! [F: nat > set_nat,A4: set_nat] :
% 0.37/0.58 ( ( bot_bot_set_set_nat
% 0.37/0.58 = ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2402_empty__is__image,axiom,
% 0.37/0.58 ! [F: nat > nat,A4: set_nat] :
% 0.37/0.58 ( ( bot_bot_set_nat
% 0.37/0.58 = ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2403_empty__is__image,axiom,
% 0.37/0.58 ! [F: int > nat,A4: set_int] :
% 0.37/0.58 ( ( bot_bot_set_nat
% 0.37/0.58 = ( image_int_nat @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2404_empty__is__image,axiom,
% 0.37/0.58 ! [F: $o > nat,A4: set_o] :
% 0.37/0.58 ( ( bot_bot_set_nat
% 0.37/0.58 = ( image_o_nat @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_o ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2405_empty__is__image,axiom,
% 0.37/0.58 ! [F: nat > int,A4: set_nat] :
% 0.37/0.58 ( ( bot_bot_set_int
% 0.37/0.58 = ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2406_empty__is__image,axiom,
% 0.37/0.58 ! [F: int > int,A4: set_int] :
% 0.37/0.58 ( ( bot_bot_set_int
% 0.37/0.58 = ( image_int_int @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2407_empty__is__image,axiom,
% 0.37/0.58 ! [F: $o > int,A4: set_o] :
% 0.37/0.58 ( ( bot_bot_set_int
% 0.37/0.58 = ( image_o_int @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_o ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2408_empty__is__image,axiom,
% 0.37/0.58 ! [F: nat > $o,A4: set_nat] :
% 0.37/0.58 ( ( bot_bot_set_o
% 0.37/0.58 = ( image_nat_o @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2409_empty__is__image,axiom,
% 0.37/0.58 ! [F: int > $o,A4: set_int] :
% 0.37/0.58 ( ( bot_bot_set_o
% 0.37/0.58 = ( image_int_o @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2410_empty__is__image,axiom,
% 0.37/0.58 ! [F: $o > $o,A4: set_o] :
% 0.37/0.58 ( ( bot_bot_set_o
% 0.37/0.58 = ( image_o_o @ F @ A4 ) )
% 0.37/0.58 = ( A4 = bot_bot_set_o ) ) ).
% 0.37/0.58
% 0.37/0.58 % empty_is_image
% 0.37/0.58 thf(fact_2411_image__is__empty,axiom,
% 0.37/0.58 ! [F: nat > set_nat,A4: set_nat] :
% 0.37/0.58 ( ( ( image_nat_set_nat @ F @ A4 )
% 0.37/0.58 = bot_bot_set_set_nat )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2412_image__is__empty,axiom,
% 0.37/0.58 ! [F: nat > nat,A4: set_nat] :
% 0.37/0.58 ( ( ( image_nat_nat @ F @ A4 )
% 0.37/0.58 = bot_bot_set_nat )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2413_image__is__empty,axiom,
% 0.37/0.58 ! [F: int > nat,A4: set_int] :
% 0.37/0.58 ( ( ( image_int_nat @ F @ A4 )
% 0.37/0.58 = bot_bot_set_nat )
% 0.37/0.58 = ( A4 = bot_bot_set_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2414_image__is__empty,axiom,
% 0.37/0.58 ! [F: $o > nat,A4: set_o] :
% 0.37/0.58 ( ( ( image_o_nat @ F @ A4 )
% 0.37/0.58 = bot_bot_set_nat )
% 0.37/0.58 = ( A4 = bot_bot_set_o ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2415_image__is__empty,axiom,
% 0.37/0.58 ! [F: nat > int,A4: set_nat] :
% 0.37/0.58 ( ( ( image_nat_int @ F @ A4 )
% 0.37/0.58 = bot_bot_set_int )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2416_image__is__empty,axiom,
% 0.37/0.58 ! [F: int > int,A4: set_int] :
% 0.37/0.58 ( ( ( image_int_int @ F @ A4 )
% 0.37/0.58 = bot_bot_set_int )
% 0.37/0.58 = ( A4 = bot_bot_set_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2417_image__is__empty,axiom,
% 0.37/0.58 ! [F: $o > int,A4: set_o] :
% 0.37/0.58 ( ( ( image_o_int @ F @ A4 )
% 0.37/0.58 = bot_bot_set_int )
% 0.37/0.58 = ( A4 = bot_bot_set_o ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2418_image__is__empty,axiom,
% 0.37/0.58 ! [F: nat > $o,A4: set_nat] :
% 0.37/0.58 ( ( ( image_nat_o @ F @ A4 )
% 0.37/0.58 = bot_bot_set_o )
% 0.37/0.58 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2419_image__is__empty,axiom,
% 0.37/0.58 ! [F: int > $o,A4: set_int] :
% 0.37/0.58 ( ( ( image_int_o @ F @ A4 )
% 0.37/0.58 = bot_bot_set_o )
% 0.37/0.58 = ( A4 = bot_bot_set_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2420_image__is__empty,axiom,
% 0.37/0.58 ! [F: $o > $o,A4: set_o] :
% 0.37/0.58 ( ( ( image_o_o @ F @ A4 )
% 0.37/0.58 = bot_bot_set_o )
% 0.37/0.58 = ( A4 = bot_bot_set_o ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_is_empty
% 0.37/0.58 thf(fact_2421_add__Suc__right,axiom,
% 0.37/0.58 ! [M: nat,N: nat] :
% 0.37/0.58 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.37/0.58 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_Suc_right
% 0.37/0.58 thf(fact_2422_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_nat,H2: nat > nat] :
% 0.37/0.58 ( ( finite_finite_nat @ F2 )
% 0.37/0.58 => ( finite_finite_nat @ ( image_nat_nat @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2423_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_nat,H2: nat > int] :
% 0.37/0.58 ( ( finite_finite_nat @ F2 )
% 0.37/0.58 => ( finite_finite_int @ ( image_nat_int @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2424_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_nat,H2: nat > complex] :
% 0.37/0.58 ( ( finite_finite_nat @ F2 )
% 0.37/0.58 => ( finite3207457112153483333omplex @ ( image_nat_complex @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2425_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_nat,H2: nat > code_integer] :
% 0.37/0.58 ( ( finite_finite_nat @ F2 )
% 0.37/0.58 => ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2426_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_int,H2: int > nat] :
% 0.37/0.58 ( ( finite_finite_int @ F2 )
% 0.37/0.58 => ( finite_finite_nat @ ( image_int_nat @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2427_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_int,H2: int > int] :
% 0.37/0.58 ( ( finite_finite_int @ F2 )
% 0.37/0.58 => ( finite_finite_int @ ( image_int_int @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2428_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_int,H2: int > complex] :
% 0.37/0.58 ( ( finite_finite_int @ F2 )
% 0.37/0.58 => ( finite3207457112153483333omplex @ ( image_int_complex @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2429_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_int,H2: int > code_integer] :
% 0.37/0.58 ( ( finite_finite_int @ F2 )
% 0.37/0.58 => ( finite6017078050557962740nteger @ ( image_1587234942943678608nteger @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2430_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_complex,H2: complex > nat] :
% 0.37/0.58 ( ( finite3207457112153483333omplex @ F2 )
% 0.37/0.58 => ( finite_finite_nat @ ( image_complex_nat @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2431_finite__imageI,axiom,
% 0.37/0.58 ! [F2: set_complex,H2: complex > int] :
% 0.37/0.58 ( ( finite3207457112153483333omplex @ F2 )
% 0.37/0.58 => ( finite_finite_int @ ( image_complex_int @ H2 @ F2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % finite_imageI
% 0.37/0.58 thf(fact_2432_add__is__0,axiom,
% 0.37/0.58 ! [M: nat,N: nat] :
% 0.37/0.58 ( ( ( plus_plus_nat @ M @ N )
% 0.37/0.58 = zero_zero_nat )
% 0.37/0.58 = ( ( M = zero_zero_nat )
% 0.37/0.58 & ( N = zero_zero_nat ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_is_0
% 0.37/0.58 thf(fact_2433_Nat_Oadd__0__right,axiom,
% 0.37/0.58 ! [M: nat] :
% 0.37/0.58 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.37/0.58 = M ) ).
% 0.37/0.58
% 0.37/0.58 % Nat.add_0_right
% 0.37/0.58 thf(fact_2434_nat__add__left__cancel__less,axiom,
% 0.37/0.58 ! [K: nat,M: nat,N: nat] :
% 0.37/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.37/0.58 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.58
% 0.37/0.58 % nat_add_left_cancel_less
% 0.37/0.58 thf(fact_2435_insert__image,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > nat] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( insert_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 = ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2436_insert__image,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > vEBT_VEBT] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( insert_VEBT_VEBT @ ( F @ X ) @ ( image_nat_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.58 = ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2437_insert__image,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > int] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( insert_int @ ( F @ X ) @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 = ( image_nat_int @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2438_insert__image,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > $o] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( insert_o @ ( F @ X ) @ ( image_nat_o @ F @ A4 ) )
% 0.37/0.58 = ( image_nat_o @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2439_insert__image,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( insert_nat @ ( F @ X ) @ ( image_VEBT_VEBT_nat @ F @ A4 ) )
% 0.37/0.58 = ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2440_insert__image,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( insert_VEBT_VEBT @ ( F @ X ) @ ( image_3375948659692109573T_VEBT @ F @ A4 ) )
% 0.37/0.58 = ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2441_insert__image,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( insert_int @ ( F @ X ) @ ( image_VEBT_VEBT_int @ F @ A4 ) )
% 0.37/0.58 = ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2442_insert__image,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > $o] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( insert_o @ ( F @ X ) @ ( image_VEBT_VEBT_o @ F @ A4 ) )
% 0.37/0.58 = ( image_VEBT_VEBT_o @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2443_insert__image,axiom,
% 0.37/0.58 ! [X: real,A4: set_real,F: real > nat] :
% 0.37/0.58 ( ( member_real @ X @ A4 )
% 0.37/0.58 => ( ( insert_nat @ ( F @ X ) @ ( image_real_nat @ F @ A4 ) )
% 0.37/0.58 = ( image_real_nat @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2444_insert__image,axiom,
% 0.37/0.58 ! [X: real,A4: set_real,F: real > vEBT_VEBT] :
% 0.37/0.58 ( ( member_real @ X @ A4 )
% 0.37/0.58 => ( ( insert_VEBT_VEBT @ ( F @ X ) @ ( image_real_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.58 = ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % insert_image
% 0.37/0.58 thf(fact_2445_image__insert,axiom,
% 0.37/0.58 ! [F: nat > nat,A: nat,B4: set_nat] :
% 0.37/0.58 ( ( image_nat_nat @ F @ ( insert_nat @ A @ B4 ) )
% 0.37/0.58 = ( insert_nat @ ( F @ A ) @ ( image_nat_nat @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2446_image__insert,axiom,
% 0.37/0.58 ! [F: nat > vEBT_VEBT,A: nat,B4: set_nat] :
% 0.37/0.58 ( ( image_nat_VEBT_VEBT @ F @ ( insert_nat @ A @ B4 ) )
% 0.37/0.58 = ( insert_VEBT_VEBT @ ( F @ A ) @ ( image_nat_VEBT_VEBT @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2447_image__insert,axiom,
% 0.37/0.58 ! [F: nat > int,A: nat,B4: set_nat] :
% 0.37/0.58 ( ( image_nat_int @ F @ ( insert_nat @ A @ B4 ) )
% 0.37/0.58 = ( insert_int @ ( F @ A ) @ ( image_nat_int @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2448_image__insert,axiom,
% 0.37/0.58 ! [F: nat > $o,A: nat,B4: set_nat] :
% 0.37/0.58 ( ( image_nat_o @ F @ ( insert_nat @ A @ B4 ) )
% 0.37/0.58 = ( insert_o @ ( F @ A ) @ ( image_nat_o @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2449_image__insert,axiom,
% 0.37/0.58 ! [F: vEBT_VEBT > nat,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.58 ( ( image_VEBT_VEBT_nat @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 0.37/0.58 = ( insert_nat @ ( F @ A ) @ ( image_VEBT_VEBT_nat @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2450_image__insert,axiom,
% 0.37/0.58 ! [F: vEBT_VEBT > vEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.58 ( ( image_3375948659692109573T_VEBT @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 0.37/0.58 = ( insert_VEBT_VEBT @ ( F @ A ) @ ( image_3375948659692109573T_VEBT @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2451_image__insert,axiom,
% 0.37/0.58 ! [F: vEBT_VEBT > int,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.58 ( ( image_VEBT_VEBT_int @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 0.37/0.58 = ( insert_int @ ( F @ A ) @ ( image_VEBT_VEBT_int @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2452_image__insert,axiom,
% 0.37/0.58 ! [F: vEBT_VEBT > $o,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.58 ( ( image_VEBT_VEBT_o @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 0.37/0.58 = ( insert_o @ ( F @ A ) @ ( image_VEBT_VEBT_o @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2453_image__insert,axiom,
% 0.37/0.58 ! [F: int > nat,A: int,B4: set_int] :
% 0.37/0.58 ( ( image_int_nat @ F @ ( insert_int @ A @ B4 ) )
% 0.37/0.58 = ( insert_nat @ ( F @ A ) @ ( image_int_nat @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2454_image__insert,axiom,
% 0.37/0.58 ! [F: int > vEBT_VEBT,A: int,B4: set_int] :
% 0.37/0.58 ( ( image_int_VEBT_VEBT @ F @ ( insert_int @ A @ B4 ) )
% 0.37/0.58 = ( insert_VEBT_VEBT @ ( F @ A ) @ ( image_int_VEBT_VEBT @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_insert
% 0.37/0.58 thf(fact_2455_nat__add__left__cancel__le,axiom,
% 0.37/0.58 ! [K: nat,M: nat,N: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.37/0.58 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.58
% 0.37/0.58 % nat_add_left_cancel_le
% 0.37/0.58 thf(fact_2456_diff__diff__left,axiom,
% 0.37/0.58 ! [I: nat,J: nat,K: nat] :
% 0.37/0.58 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.37/0.58 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % diff_diff_left
% 0.37/0.58 thf(fact_2457_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.37/0.58 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.37/0.58
% 0.37/0.58 % zero_le_double_add_iff_zero_le_single_add
% 0.37/0.58 thf(fact_2458_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.37/0.58 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.37/0.58
% 0.37/0.58 % zero_le_double_add_iff_zero_le_single_add
% 0.37/0.58 thf(fact_2459_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.37/0.58 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.37/0.58
% 0.37/0.58 % zero_le_double_add_iff_zero_le_single_add
% 0.37/0.58 thf(fact_2460_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.37/0.58 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.37/0.58
% 0.37/0.58 % double_add_le_zero_iff_single_add_le_zero
% 0.37/0.58 thf(fact_2461_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.37/0.58 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.58
% 0.37/0.58 % double_add_le_zero_iff_single_add_le_zero
% 0.37/0.58 thf(fact_2462_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.37/0.58 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % double_add_le_zero_iff_single_add_le_zero
% 0.37/0.58 thf(fact_2463_le__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.37/0.58 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel2
% 0.37/0.58 thf(fact_2464_le__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.37/0.58 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel2
% 0.37/0.58 thf(fact_2465_le__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.37/0.58 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel2
% 0.37/0.58 thf(fact_2466_le__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.37/0.58 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel2
% 0.37/0.58 thf(fact_2467_le__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.37/0.58 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel1
% 0.37/0.58 thf(fact_2468_le__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.37/0.58 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel1
% 0.37/0.58 thf(fact_2469_le__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.37/0.58 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel1
% 0.37/0.58 thf(fact_2470_le__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.37/0.58 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_same_cancel1
% 0.37/0.58 thf(fact_2471_add__le__same__cancel2,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel2
% 0.37/0.58 thf(fact_2472_add__le__same__cancel2,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel2
% 0.37/0.58 thf(fact_2473_add__le__same__cancel2,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel2
% 0.37/0.58 thf(fact_2474_add__le__same__cancel2,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel2
% 0.37/0.58 thf(fact_2475_add__le__same__cancel1,axiom,
% 0.37/0.58 ! [B: real,A: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel1
% 0.37/0.58 thf(fact_2476_add__le__same__cancel1,axiom,
% 0.37/0.58 ! [B: rat,A: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel1
% 0.37/0.58 thf(fact_2477_add__le__same__cancel1,axiom,
% 0.37/0.58 ! [B: nat,A: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel1
% 0.37/0.58 thf(fact_2478_add__le__same__cancel1,axiom,
% 0.37/0.58 ! [B: int,A: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_same_cancel1
% 0.37/0.58 thf(fact_2479_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.37/0.58 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.37/0.58
% 0.37/0.58 % zero_less_double_add_iff_zero_less_single_add
% 0.37/0.58 thf(fact_2480_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.37/0.58 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.37/0.58
% 0.37/0.58 % zero_less_double_add_iff_zero_less_single_add
% 0.37/0.58 thf(fact_2481_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.37/0.58 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.37/0.58
% 0.37/0.58 % zero_less_double_add_iff_zero_less_single_add
% 0.37/0.58 thf(fact_2482_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.37/0.58 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.37/0.58
% 0.37/0.58 % double_add_less_zero_iff_single_add_less_zero
% 0.37/0.58 thf(fact_2483_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.37/0.58 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.58
% 0.37/0.58 % double_add_less_zero_iff_single_add_less_zero
% 0.37/0.58 thf(fact_2484_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.37/0.58 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % double_add_less_zero_iff_single_add_less_zero
% 0.37/0.58 thf(fact_2485_less__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.37/0.58 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel2
% 0.37/0.58 thf(fact_2486_less__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.37/0.58 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel2
% 0.37/0.58 thf(fact_2487_less__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.37/0.58 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel2
% 0.37/0.58 thf(fact_2488_less__add__same__cancel2,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.37/0.58 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel2
% 0.37/0.58 thf(fact_2489_less__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.37/0.58 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel1
% 0.37/0.58 thf(fact_2490_less__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.37/0.58 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel1
% 0.37/0.58 thf(fact_2491_less__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.37/0.58 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel1
% 0.37/0.58 thf(fact_2492_less__add__same__cancel1,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.37/0.58 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % less_add_same_cancel1
% 0.37/0.58 thf(fact_2493_add__less__same__cancel2,axiom,
% 0.37/0.58 ! [A: real,B: real] :
% 0.37/0.58 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel2
% 0.37/0.58 thf(fact_2494_add__less__same__cancel2,axiom,
% 0.37/0.58 ! [A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel2
% 0.37/0.58 thf(fact_2495_add__less__same__cancel2,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel2
% 0.37/0.58 thf(fact_2496_add__less__same__cancel2,axiom,
% 0.37/0.58 ! [A: int,B: int] :
% 0.37/0.58 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.37/0.58 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel2
% 0.37/0.58 thf(fact_2497_add__less__same__cancel1,axiom,
% 0.37/0.58 ! [B: real,A: real] :
% 0.37/0.58 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel1
% 0.37/0.58 thf(fact_2498_add__less__same__cancel1,axiom,
% 0.37/0.58 ! [B: rat,A: rat] :
% 0.37/0.58 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel1
% 0.37/0.58 thf(fact_2499_add__less__same__cancel1,axiom,
% 0.37/0.58 ! [B: nat,A: nat] :
% 0.37/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel1
% 0.37/0.58 thf(fact_2500_add__less__same__cancel1,axiom,
% 0.37/0.58 ! [B: int,A: int] :
% 0.37/0.58 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.37/0.58 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_less_same_cancel1
% 0.37/0.58 thf(fact_2501_diff__add__zero,axiom,
% 0.37/0.58 ! [A: nat,B: nat] :
% 0.37/0.58 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.37/0.58 = zero_zero_nat ) ).
% 0.37/0.58
% 0.37/0.58 % diff_add_zero
% 0.37/0.58 thf(fact_2502_le__add__diff__inverse2,axiom,
% 0.37/0.58 ! [B: real,A: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ B @ A )
% 0.37/0.58 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse2
% 0.37/0.58 thf(fact_2503_le__add__diff__inverse2,axiom,
% 0.37/0.58 ! [B: rat,A: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.58 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse2
% 0.37/0.58 thf(fact_2504_le__add__diff__inverse2,axiom,
% 0.37/0.58 ! [B: nat,A: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.58 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse2
% 0.37/0.58 thf(fact_2505_le__add__diff__inverse2,axiom,
% 0.37/0.58 ! [B: int,A: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.58 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse2
% 0.37/0.58 thf(fact_2506_le__add__diff__inverse,axiom,
% 0.37/0.58 ! [B: real,A: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ B @ A )
% 0.37/0.58 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse
% 0.37/0.58 thf(fact_2507_le__add__diff__inverse,axiom,
% 0.37/0.58 ! [B: rat,A: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.58 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse
% 0.37/0.58 thf(fact_2508_le__add__diff__inverse,axiom,
% 0.37/0.58 ! [B: nat,A: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.58 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse
% 0.37/0.58 thf(fact_2509_le__add__diff__inverse,axiom,
% 0.37/0.58 ! [B: int,A: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.58 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.37/0.58 = A ) ) ).
% 0.37/0.58
% 0.37/0.58 % le_add_diff_inverse
% 0.37/0.58 thf(fact_2510_image__add__0,axiom,
% 0.37/0.58 ! [S3: set_uint32] :
% 0.37/0.58 ( ( image_uint32_uint32 @ ( plus_plus_uint32 @ zero_zero_uint32 ) @ S3 )
% 0.37/0.58 = S3 ) ).
% 0.37/0.58
% 0.37/0.58 % image_add_0
% 0.37/0.58 thf(fact_2511_image__add__0,axiom,
% 0.37/0.58 ! [S3: set_real] :
% 0.37/0.58 ( ( image_real_real @ ( plus_plus_real @ zero_zero_real ) @ S3 )
% 0.37/0.58 = S3 ) ).
% 0.37/0.58
% 0.37/0.58 % image_add_0
% 0.37/0.58 thf(fact_2512_image__add__0,axiom,
% 0.37/0.58 ! [S3: set_rat] :
% 0.37/0.58 ( ( image_rat_rat @ ( plus_plus_rat @ zero_zero_rat ) @ S3 )
% 0.37/0.58 = S3 ) ).
% 0.37/0.58
% 0.37/0.58 % image_add_0
% 0.37/0.58 thf(fact_2513_image__add__0,axiom,
% 0.37/0.58 ! [S3: set_nat] :
% 0.37/0.58 ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S3 )
% 0.37/0.58 = S3 ) ).
% 0.37/0.58
% 0.37/0.58 % image_add_0
% 0.37/0.58 thf(fact_2514_image__add__0,axiom,
% 0.37/0.58 ! [S3: set_int] :
% 0.37/0.58 ( ( image_int_int @ ( plus_plus_int @ zero_zero_int ) @ S3 )
% 0.37/0.58 = S3 ) ).
% 0.37/0.58
% 0.37/0.58 % image_add_0
% 0.37/0.58 thf(fact_2515_add__gr__0,axiom,
% 0.37/0.58 ! [M: nat,N: nat] :
% 0.37/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.37/0.58 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.58 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_gr_0
% 0.37/0.58 thf(fact_2516_Nat_Odiff__diff__right,axiom,
% 0.37/0.58 ! [K: nat,J: nat,I: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.58 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.37/0.58 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % Nat.diff_diff_right
% 0.37/0.58 thf(fact_2517_Nat_Oadd__diff__assoc2,axiom,
% 0.37/0.58 ! [K: nat,J: nat,I: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.58 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.37/0.58 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % Nat.add_diff_assoc2
% 0.37/0.58 thf(fact_2518_Nat_Oadd__diff__assoc,axiom,
% 0.37/0.58 ! [K: nat,J: nat,I: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.58 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.37/0.58 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % Nat.add_diff_assoc
% 0.37/0.58 thf(fact_2519_diff__Suc__diff__eq1,axiom,
% 0.37/0.58 ! [K: nat,J: nat,I: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.58 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.37/0.58 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % diff_Suc_diff_eq1
% 0.37/0.58 thf(fact_2520_diff__Suc__diff__eq2,axiom,
% 0.37/0.58 ! [K: nat,J: nat,I: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.58 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 0.37/0.58 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % diff_Suc_diff_eq2
% 0.37/0.58 thf(fact_2521_enumerate__mono__iff,axiom,
% 0.37/0.58 ! [S3: set_nat,M: nat,N: nat] :
% 0.37/0.58 ( ~ ( finite_finite_nat @ S3 )
% 0.37/0.58 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) )
% 0.37/0.58 = ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % enumerate_mono_iff
% 0.37/0.58 thf(fact_2522_add__right__imp__eq,axiom,
% 0.37/0.58 ! [B: real,A: real,C2: real] :
% 0.37/0.58 ( ( ( plus_plus_real @ B @ A )
% 0.37/0.58 = ( plus_plus_real @ C2 @ A ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_right_imp_eq
% 0.37/0.58 thf(fact_2523_add__right__imp__eq,axiom,
% 0.37/0.58 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.58 ( ( ( plus_plus_rat @ B @ A )
% 0.37/0.58 = ( plus_plus_rat @ C2 @ A ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_right_imp_eq
% 0.37/0.58 thf(fact_2524_add__right__imp__eq,axiom,
% 0.37/0.58 ! [B: nat,A: nat,C2: nat] :
% 0.37/0.58 ( ( ( plus_plus_nat @ B @ A )
% 0.37/0.58 = ( plus_plus_nat @ C2 @ A ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_right_imp_eq
% 0.37/0.58 thf(fact_2525_add__right__imp__eq,axiom,
% 0.37/0.58 ! [B: int,A: int,C2: int] :
% 0.37/0.58 ( ( ( plus_plus_int @ B @ A )
% 0.37/0.58 = ( plus_plus_int @ C2 @ A ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_right_imp_eq
% 0.37/0.58 thf(fact_2526_add__left__imp__eq,axiom,
% 0.37/0.58 ! [A: real,B: real,C2: real] :
% 0.37/0.58 ( ( ( plus_plus_real @ A @ B )
% 0.37/0.58 = ( plus_plus_real @ A @ C2 ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_left_imp_eq
% 0.37/0.58 thf(fact_2527_add__left__imp__eq,axiom,
% 0.37/0.58 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.58 ( ( ( plus_plus_rat @ A @ B )
% 0.37/0.58 = ( plus_plus_rat @ A @ C2 ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_left_imp_eq
% 0.37/0.58 thf(fact_2528_add__left__imp__eq,axiom,
% 0.37/0.58 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.58 ( ( ( plus_plus_nat @ A @ B )
% 0.37/0.58 = ( plus_plus_nat @ A @ C2 ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_left_imp_eq
% 0.37/0.58 thf(fact_2529_add__left__imp__eq,axiom,
% 0.37/0.58 ! [A: int,B: int,C2: int] :
% 0.37/0.58 ( ( ( plus_plus_int @ A @ B )
% 0.37/0.58 = ( plus_plus_int @ A @ C2 ) )
% 0.37/0.58 => ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_left_imp_eq
% 0.37/0.58 thf(fact_2530_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.37/0.58 ! [B: real,A: real,C2: real] :
% 0.37/0.58 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C2 ) )
% 0.37/0.58 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.left_commute
% 0.37/0.58 thf(fact_2531_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.37/0.58 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.58 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C2 ) )
% 0.37/0.58 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.left_commute
% 0.37/0.58 thf(fact_2532_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.37/0.58 ! [B: nat,A: nat,C2: nat] :
% 0.37/0.58 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 0.37/0.58 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.left_commute
% 0.37/0.58 thf(fact_2533_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.37/0.58 ! [B: int,A: int,C2: int] :
% 0.37/0.58 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C2 ) )
% 0.37/0.58 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.left_commute
% 0.37/0.58 thf(fact_2534_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.37/0.58 ( plus_plus_real
% 0.37/0.58 = ( ^ [A7: real,B7: real] : ( plus_plus_real @ B7 @ A7 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.commute
% 0.37/0.58 thf(fact_2535_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.37/0.58 ( plus_plus_rat
% 0.37/0.58 = ( ^ [A7: rat,B7: rat] : ( plus_plus_rat @ B7 @ A7 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.commute
% 0.37/0.58 thf(fact_2536_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.37/0.58 ( plus_plus_nat
% 0.37/0.58 = ( ^ [A7: nat,B7: nat] : ( plus_plus_nat @ B7 @ A7 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.commute
% 0.37/0.58 thf(fact_2537_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.37/0.58 ( plus_plus_int
% 0.37/0.58 = ( ^ [A7: int,B7: int] : ( plus_plus_int @ B7 @ A7 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ab_semigroup_add_class.add.commute
% 0.37/0.58 thf(fact_2538_add_Oright__cancel,axiom,
% 0.37/0.58 ! [B: real,A: real,C2: real] :
% 0.37/0.58 ( ( ( plus_plus_real @ B @ A )
% 0.37/0.58 = ( plus_plus_real @ C2 @ A ) )
% 0.37/0.58 = ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.right_cancel
% 0.37/0.58 thf(fact_2539_add_Oright__cancel,axiom,
% 0.37/0.58 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.58 ( ( ( plus_plus_rat @ B @ A )
% 0.37/0.58 = ( plus_plus_rat @ C2 @ A ) )
% 0.37/0.58 = ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.right_cancel
% 0.37/0.58 thf(fact_2540_add_Oright__cancel,axiom,
% 0.37/0.58 ! [B: int,A: int,C2: int] :
% 0.37/0.58 ( ( ( plus_plus_int @ B @ A )
% 0.37/0.58 = ( plus_plus_int @ C2 @ A ) )
% 0.37/0.58 = ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.right_cancel
% 0.37/0.58 thf(fact_2541_add_Oleft__cancel,axiom,
% 0.37/0.58 ! [A: real,B: real,C2: real] :
% 0.37/0.58 ( ( ( plus_plus_real @ A @ B )
% 0.37/0.58 = ( plus_plus_real @ A @ C2 ) )
% 0.37/0.58 = ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.left_cancel
% 0.37/0.58 thf(fact_2542_add_Oleft__cancel,axiom,
% 0.37/0.58 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.58 ( ( ( plus_plus_rat @ A @ B )
% 0.37/0.58 = ( plus_plus_rat @ A @ C2 ) )
% 0.37/0.58 = ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.left_cancel
% 0.37/0.58 thf(fact_2543_add_Oleft__cancel,axiom,
% 0.37/0.58 ! [A: int,B: int,C2: int] :
% 0.37/0.58 ( ( ( plus_plus_int @ A @ B )
% 0.37/0.58 = ( plus_plus_int @ A @ C2 ) )
% 0.37/0.58 = ( B = C2 ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.left_cancel
% 0.37/0.58 thf(fact_2544_add_Oassoc,axiom,
% 0.37/0.58 ! [A: real,B: real,C2: real] :
% 0.37/0.58 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.37/0.58 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.assoc
% 0.37/0.58 thf(fact_2545_add_Oassoc,axiom,
% 0.37/0.58 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.58 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 0.37/0.58 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.assoc
% 0.37/0.58 thf(fact_2546_add_Oassoc,axiom,
% 0.37/0.58 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.58 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.37/0.58 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.assoc
% 0.37/0.58 thf(fact_2547_add_Oassoc,axiom,
% 0.37/0.58 ! [A: int,B: int,C2: int] :
% 0.37/0.58 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.37/0.58 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add.assoc
% 0.37/0.58 thf(fact_2548_group__cancel_Oadd2,axiom,
% 0.37/0.58 ! [B4: real,K: real,B: real,A: real] :
% 0.37/0.58 ( ( B4
% 0.37/0.58 = ( plus_plus_real @ K @ B ) )
% 0.37/0.58 => ( ( plus_plus_real @ A @ B4 )
% 0.37/0.58 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add2
% 0.37/0.58 thf(fact_2549_group__cancel_Oadd2,axiom,
% 0.37/0.58 ! [B4: rat,K: rat,B: rat,A: rat] :
% 0.37/0.58 ( ( B4
% 0.37/0.58 = ( plus_plus_rat @ K @ B ) )
% 0.37/0.58 => ( ( plus_plus_rat @ A @ B4 )
% 0.37/0.58 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add2
% 0.37/0.58 thf(fact_2550_group__cancel_Oadd2,axiom,
% 0.37/0.58 ! [B4: nat,K: nat,B: nat,A: nat] :
% 0.37/0.58 ( ( B4
% 0.37/0.58 = ( plus_plus_nat @ K @ B ) )
% 0.37/0.58 => ( ( plus_plus_nat @ A @ B4 )
% 0.37/0.58 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add2
% 0.37/0.58 thf(fact_2551_group__cancel_Oadd2,axiom,
% 0.37/0.58 ! [B4: int,K: int,B: int,A: int] :
% 0.37/0.58 ( ( B4
% 0.37/0.58 = ( plus_plus_int @ K @ B ) )
% 0.37/0.58 => ( ( plus_plus_int @ A @ B4 )
% 0.37/0.58 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add2
% 0.37/0.58 thf(fact_2552_group__cancel_Oadd1,axiom,
% 0.37/0.58 ! [A4: real,K: real,A: real,B: real] :
% 0.37/0.58 ( ( A4
% 0.37/0.58 = ( plus_plus_real @ K @ A ) )
% 0.37/0.58 => ( ( plus_plus_real @ A4 @ B )
% 0.37/0.58 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add1
% 0.37/0.58 thf(fact_2553_group__cancel_Oadd1,axiom,
% 0.37/0.58 ! [A4: rat,K: rat,A: rat,B: rat] :
% 0.37/0.58 ( ( A4
% 0.37/0.58 = ( plus_plus_rat @ K @ A ) )
% 0.37/0.58 => ( ( plus_plus_rat @ A4 @ B )
% 0.37/0.58 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add1
% 0.37/0.58 thf(fact_2554_group__cancel_Oadd1,axiom,
% 0.37/0.58 ! [A4: nat,K: nat,A: nat,B: nat] :
% 0.37/0.58 ( ( A4
% 0.37/0.58 = ( plus_plus_nat @ K @ A ) )
% 0.37/0.58 => ( ( plus_plus_nat @ A4 @ B )
% 0.37/0.58 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add1
% 0.37/0.58 thf(fact_2555_group__cancel_Oadd1,axiom,
% 0.37/0.58 ! [A4: int,K: int,A: int,B: int] :
% 0.37/0.58 ( ( A4
% 0.37/0.58 = ( plus_plus_int @ K @ A ) )
% 0.37/0.58 => ( ( plus_plus_int @ A4 @ B )
% 0.37/0.58 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % group_cancel.add1
% 0.37/0.58 thf(fact_2556_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.37/0.58 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.58 ( ( ( I = J )
% 0.37/0.58 & ( K = L ) )
% 0.37/0.58 => ( ( plus_plus_real @ I @ K )
% 0.37/0.58 = ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_mono_thms_linordered_semiring(4)
% 0.37/0.58 thf(fact_2557_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.37/0.58 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.58 ( ( ( I = J )
% 0.37/0.58 & ( K = L ) )
% 0.37/0.58 => ( ( plus_plus_rat @ I @ K )
% 0.37/0.58 = ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_mono_thms_linordered_semiring(4)
% 0.37/0.58 thf(fact_2558_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.37/0.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.58 ( ( ( I = J )
% 0.37/0.58 & ( K = L ) )
% 0.37/0.58 => ( ( plus_plus_nat @ I @ K )
% 0.37/0.58 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_mono_thms_linordered_semiring(4)
% 0.37/0.58 thf(fact_2559_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.37/0.58 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.58 ( ( ( I = J )
% 0.37/0.58 & ( K = L ) )
% 0.37/0.58 => ( ( plus_plus_int @ I @ K )
% 0.37/0.58 = ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_mono_thms_linordered_semiring(4)
% 0.37/0.58 thf(fact_2560_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,B: nat,F: nat > nat] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2561_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,B: vEBT_VEBT,F: nat > vEBT_VEBT] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_VEBT_VEBT @ B @ ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2562_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,B: real,F: nat > real] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_real @ B @ ( image_nat_real @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2563_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,B: int,F: nat > int] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2564_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: nat,F: vEBT_VEBT > nat] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_nat @ B @ ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2565_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_VEBT_VEBT @ B @ ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2566_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: real,F: vEBT_VEBT > real] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_real @ B @ ( image_VEBT_VEBT_real @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2567_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: int,F: vEBT_VEBT > int] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_int @ B @ ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2568_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: real,A4: set_real,B: nat,F: real > nat] :
% 0.37/0.58 ( ( member_real @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_nat @ B @ ( image_real_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2569_rev__image__eqI,axiom,
% 0.37/0.58 ! [X: real,A4: set_real,B: vEBT_VEBT,F: real > vEBT_VEBT] :
% 0.37/0.58 ( ( member_real @ X @ A4 )
% 0.37/0.58 => ( ( B
% 0.37/0.58 = ( F @ X ) )
% 0.37/0.58 => ( member_VEBT_VEBT @ B @ ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % rev_image_eqI
% 0.37/0.58 thf(fact_2570_ball__imageD,axiom,
% 0.37/0.58 ! [F: nat > set_nat,A4: set_nat,P2: set_nat > $o] :
% 0.37/0.58 ( ! [X3: set_nat] :
% 0.37/0.58 ( ( member_set_nat @ X3 @ ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ X3 ) )
% 0.37/0.58 => ! [X5: nat] :
% 0.37/0.58 ( ( member_nat @ X5 @ A4 )
% 0.37/0.58 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ball_imageD
% 0.37/0.58 thf(fact_2571_ball__imageD,axiom,
% 0.37/0.58 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 0.37/0.58 ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ X3 ) )
% 0.37/0.58 => ! [X5: nat] :
% 0.37/0.58 ( ( member_nat @ X5 @ A4 )
% 0.37/0.58 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ball_imageD
% 0.37/0.58 thf(fact_2572_ball__imageD,axiom,
% 0.37/0.58 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 0.37/0.58 ( ! [X3: int] :
% 0.37/0.58 ( ( member_int @ X3 @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ X3 ) )
% 0.37/0.58 => ! [X5: nat] :
% 0.37/0.58 ( ( member_nat @ X5 @ A4 )
% 0.37/0.58 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ball_imageD
% 0.37/0.58 thf(fact_2573_ball__imageD,axiom,
% 0.37/0.58 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 0.37/0.58 ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ X3 ) )
% 0.37/0.58 => ! [X5: int] :
% 0.37/0.58 ( ( member_int @ X5 @ A4 )
% 0.37/0.58 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ball_imageD
% 0.37/0.58 thf(fact_2574_ball__imageD,axiom,
% 0.37/0.58 ! [F: int > int,A4: set_int,P2: int > $o] :
% 0.37/0.58 ( ! [X3: int] :
% 0.37/0.58 ( ( member_int @ X3 @ ( image_int_int @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ X3 ) )
% 0.37/0.58 => ! [X5: int] :
% 0.37/0.58 ( ( member_int @ X5 @ A4 )
% 0.37/0.58 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % ball_imageD
% 0.37/0.58 thf(fact_2575_image__cong,axiom,
% 0.37/0.58 ! [M7: set_nat,N8: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 0.37/0.58 ( ( M7 = N8 )
% 0.37/0.58 => ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ N8 )
% 0.37/0.58 => ( ( F @ X3 )
% 0.37/0.58 = ( G @ X3 ) ) )
% 0.37/0.58 => ( ( image_nat_set_nat @ F @ M7 )
% 0.37/0.58 = ( image_nat_set_nat @ G @ N8 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_cong
% 0.37/0.58 thf(fact_2576_image__cong,axiom,
% 0.37/0.58 ! [M7: set_nat,N8: set_nat,F: nat > nat,G: nat > nat] :
% 0.37/0.58 ( ( M7 = N8 )
% 0.37/0.58 => ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ N8 )
% 0.37/0.58 => ( ( F @ X3 )
% 0.37/0.58 = ( G @ X3 ) ) )
% 0.37/0.58 => ( ( image_nat_nat @ F @ M7 )
% 0.37/0.58 = ( image_nat_nat @ G @ N8 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_cong
% 0.37/0.58 thf(fact_2577_image__cong,axiom,
% 0.37/0.58 ! [M7: set_nat,N8: set_nat,F: nat > int,G: nat > int] :
% 0.37/0.58 ( ( M7 = N8 )
% 0.37/0.58 => ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ N8 )
% 0.37/0.58 => ( ( F @ X3 )
% 0.37/0.58 = ( G @ X3 ) ) )
% 0.37/0.58 => ( ( image_nat_int @ F @ M7 )
% 0.37/0.58 = ( image_nat_int @ G @ N8 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_cong
% 0.37/0.58 thf(fact_2578_image__cong,axiom,
% 0.37/0.58 ! [M7: set_int,N8: set_int,F: int > nat,G: int > nat] :
% 0.37/0.58 ( ( M7 = N8 )
% 0.37/0.58 => ( ! [X3: int] :
% 0.37/0.58 ( ( member_int @ X3 @ N8 )
% 0.37/0.58 => ( ( F @ X3 )
% 0.37/0.58 = ( G @ X3 ) ) )
% 0.37/0.58 => ( ( image_int_nat @ F @ M7 )
% 0.37/0.58 = ( image_int_nat @ G @ N8 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_cong
% 0.37/0.58 thf(fact_2579_image__cong,axiom,
% 0.37/0.58 ! [M7: set_int,N8: set_int,F: int > int,G: int > int] :
% 0.37/0.58 ( ( M7 = N8 )
% 0.37/0.58 => ( ! [X3: int] :
% 0.37/0.58 ( ( member_int @ X3 @ N8 )
% 0.37/0.58 => ( ( F @ X3 )
% 0.37/0.58 = ( G @ X3 ) ) )
% 0.37/0.58 => ( ( image_int_int @ F @ M7 )
% 0.37/0.58 = ( image_int_int @ G @ N8 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_cong
% 0.37/0.58 thf(fact_2580_bex__imageD,axiom,
% 0.37/0.58 ! [F: nat > set_nat,A4: set_nat,P2: set_nat > $o] :
% 0.37/0.58 ( ? [X5: set_nat] :
% 0.37/0.58 ( ( member_set_nat @ X5 @ ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.58 & ( P2 @ X5 ) )
% 0.37/0.58 => ? [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ A4 )
% 0.37/0.58 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % bex_imageD
% 0.37/0.58 thf(fact_2581_bex__imageD,axiom,
% 0.37/0.58 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 0.37/0.58 ( ? [X5: nat] :
% 0.37/0.58 ( ( member_nat @ X5 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 & ( P2 @ X5 ) )
% 0.37/0.58 => ? [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ A4 )
% 0.37/0.58 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % bex_imageD
% 0.37/0.58 thf(fact_2582_bex__imageD,axiom,
% 0.37/0.58 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 0.37/0.58 ( ? [X5: int] :
% 0.37/0.58 ( ( member_int @ X5 @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 & ( P2 @ X5 ) )
% 0.37/0.58 => ? [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ A4 )
% 0.37/0.58 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % bex_imageD
% 0.37/0.58 thf(fact_2583_bex__imageD,axiom,
% 0.37/0.58 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 0.37/0.58 ( ? [X5: nat] :
% 0.37/0.58 ( ( member_nat @ X5 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.58 & ( P2 @ X5 ) )
% 0.37/0.58 => ? [X3: int] :
% 0.37/0.58 ( ( member_int @ X3 @ A4 )
% 0.37/0.58 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % bex_imageD
% 0.37/0.58 thf(fact_2584_bex__imageD,axiom,
% 0.37/0.58 ! [F: int > int,A4: set_int,P2: int > $o] :
% 0.37/0.58 ( ? [X5: int] :
% 0.37/0.58 ( ( member_int @ X5 @ ( image_int_int @ F @ A4 ) )
% 0.37/0.58 & ( P2 @ X5 ) )
% 0.37/0.58 => ? [X3: int] :
% 0.37/0.58 ( ( member_int @ X3 @ A4 )
% 0.37/0.58 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % bex_imageD
% 0.37/0.58 thf(fact_2585_image__iff,axiom,
% 0.37/0.58 ! [Z: nat,F: nat > nat,A4: set_nat] :
% 0.37/0.58 ( ( member_nat @ Z @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 = ( ? [X4: nat] :
% 0.37/0.58 ( ( member_nat @ X4 @ A4 )
% 0.37/0.58 & ( Z
% 0.37/0.58 = ( F @ X4 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_iff
% 0.37/0.58 thf(fact_2586_image__iff,axiom,
% 0.37/0.58 ! [Z: nat,F: int > nat,A4: set_int] :
% 0.37/0.58 ( ( member_nat @ Z @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.58 = ( ? [X4: int] :
% 0.37/0.58 ( ( member_int @ X4 @ A4 )
% 0.37/0.58 & ( Z
% 0.37/0.58 = ( F @ X4 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_iff
% 0.37/0.58 thf(fact_2587_image__iff,axiom,
% 0.37/0.58 ! [Z: int,F: nat > int,A4: set_nat] :
% 0.37/0.58 ( ( member_int @ Z @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 = ( ? [X4: nat] :
% 0.37/0.58 ( ( member_nat @ X4 @ A4 )
% 0.37/0.58 & ( Z
% 0.37/0.58 = ( F @ X4 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_iff
% 0.37/0.58 thf(fact_2588_image__iff,axiom,
% 0.37/0.58 ! [Z: int,F: int > int,A4: set_int] :
% 0.37/0.58 ( ( member_int @ Z @ ( image_int_int @ F @ A4 ) )
% 0.37/0.58 = ( ? [X4: int] :
% 0.37/0.58 ( ( member_int @ X4 @ A4 )
% 0.37/0.58 & ( Z
% 0.37/0.58 = ( F @ X4 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_iff
% 0.37/0.58 thf(fact_2589_image__iff,axiom,
% 0.37/0.58 ! [Z: set_nat,F: nat > set_nat,A4: set_nat] :
% 0.37/0.58 ( ( member_set_nat @ Z @ ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.58 = ( ? [X4: nat] :
% 0.37/0.58 ( ( member_nat @ X4 @ A4 )
% 0.37/0.58 & ( Z
% 0.37/0.58 = ( F @ X4 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_iff
% 0.37/0.58 thf(fact_2590_imageI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > nat] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2591_imageI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > vEBT_VEBT] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( member_VEBT_VEBT @ ( F @ X ) @ ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2592_imageI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > real] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( member_real @ ( F @ X ) @ ( image_nat_real @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2593_imageI,axiom,
% 0.37/0.58 ! [X: nat,A4: set_nat,F: nat > int] :
% 0.37/0.58 ( ( member_nat @ X @ A4 )
% 0.37/0.58 => ( member_int @ ( F @ X ) @ ( image_nat_int @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2594_imageI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X ) @ ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2595_imageI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( member_VEBT_VEBT @ ( F @ X ) @ ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2596_imageI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( member_real @ ( F @ X ) @ ( image_VEBT_VEBT_real @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2597_imageI,axiom,
% 0.37/0.58 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.58 => ( member_int @ ( F @ X ) @ ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2598_imageI,axiom,
% 0.37/0.58 ! [X: real,A4: set_real,F: real > nat] :
% 0.37/0.58 ( ( member_real @ X @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X ) @ ( image_real_nat @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2599_imageI,axiom,
% 0.37/0.58 ! [X: real,A4: set_real,F: real > vEBT_VEBT] :
% 0.37/0.58 ( ( member_real @ X @ A4 )
% 0.37/0.58 => ( member_VEBT_VEBT @ ( F @ X ) @ ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % imageI
% 0.37/0.58 thf(fact_2600_image__mono,axiom,
% 0.37/0.58 ! [A4: set_nat,B4: set_nat,F: nat > set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.58 => ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A4 ) @ ( image_nat_set_nat @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_mono
% 0.37/0.58 thf(fact_2601_image__mono,axiom,
% 0.37/0.58 ! [A4: set_nat,B4: set_nat,F: nat > nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.58 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_mono
% 0.37/0.58 thf(fact_2602_image__mono,axiom,
% 0.37/0.58 ! [A4: set_nat,B4: set_nat,F: nat > int] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.58 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_mono
% 0.37/0.58 thf(fact_2603_image__mono,axiom,
% 0.37/0.58 ! [A4: set_int,B4: set_int,F: int > nat] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.58 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_mono
% 0.37/0.58 thf(fact_2604_image__mono,axiom,
% 0.37/0.58 ! [A4: set_int,B4: set_int,F: int > int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.58 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B4 ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_mono
% 0.37/0.58 thf(fact_2605_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_nat,F: nat > nat,B4: set_nat] :
% 0.37/0.58 ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2606_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_nat,F: nat > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.58 ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ A4 )
% 0.37/0.58 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_le4337996190870823476T_VEBT @ ( image_nat_VEBT_VEBT @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2607_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_nat,F: nat > real,B4: set_real] :
% 0.37/0.58 ( ! [X3: nat] :
% 0.37/0.58 ( ( member_nat @ X3 @ A4 )
% 0.37/0.58 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_less_eq_set_real @ ( image_nat_real @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2608_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat,B4: set_nat] :
% 0.37/0.58 ( ! [X3: vEBT_VEBT] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_less_eq_set_nat @ ( image_VEBT_VEBT_nat @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2609_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.58 ( ! [X3: vEBT_VEBT] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.58 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_le4337996190870823476T_VEBT @ ( image_3375948659692109573T_VEBT @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2610_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real,B4: set_real] :
% 0.37/0.58 ( ! [X3: vEBT_VEBT] :
% 0.37/0.58 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.58 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_less_eq_set_real @ ( image_VEBT_VEBT_real @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2611_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_real,F: real > nat,B4: set_nat] :
% 0.37/0.58 ( ! [X3: real] :
% 0.37/0.58 ( ( member_real @ X3 @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_less_eq_set_nat @ ( image_real_nat @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2612_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_real,F: real > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.58 ( ! [X3: real] :
% 0.37/0.58 ( ( member_real @ X3 @ A4 )
% 0.37/0.58 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_le4337996190870823476T_VEBT @ ( image_real_VEBT_VEBT @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2613_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_real,F: real > real,B4: set_real] :
% 0.37/0.58 ( ! [X3: real] :
% 0.37/0.58 ( ( member_real @ X3 @ A4 )
% 0.37/0.58 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_less_eq_set_real @ ( image_real_real @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2614_image__subsetI,axiom,
% 0.37/0.58 ! [A4: set_int,F: int > nat,B4: set_nat] :
% 0.37/0.58 ( ! [X3: int] :
% 0.37/0.58 ( ( member_int @ X3 @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 0.37/0.58 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B4 ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subsetI
% 0.37/0.58 thf(fact_2615_subset__imageE,axiom,
% 0.37/0.58 ! [B4: set_set_nat,F: nat > set_nat,A4: set_nat] :
% 0.37/0.58 ( ( ord_le6893508408891458716et_nat @ B4 @ ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.58 => ~ ! [C5: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 0.37/0.58 => ( B4
% 0.37/0.58 != ( image_nat_set_nat @ F @ C5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_imageE
% 0.37/0.58 thf(fact_2616_subset__imageE,axiom,
% 0.37/0.58 ! [B4: set_nat,F: nat > nat,A4: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 => ~ ! [C5: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 0.37/0.58 => ( B4
% 0.37/0.58 != ( image_nat_nat @ F @ C5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_imageE
% 0.37/0.58 thf(fact_2617_subset__imageE,axiom,
% 0.37/0.58 ! [B4: set_nat,F: int > nat,A4: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.58 => ~ ! [C5: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ C5 @ A4 )
% 0.37/0.58 => ( B4
% 0.37/0.58 != ( image_int_nat @ F @ C5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_imageE
% 0.37/0.58 thf(fact_2618_subset__imageE,axiom,
% 0.37/0.58 ! [B4: set_int,F: nat > int,A4: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B4 @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 => ~ ! [C5: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 0.37/0.58 => ( B4
% 0.37/0.58 != ( image_nat_int @ F @ C5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_imageE
% 0.37/0.58 thf(fact_2619_subset__imageE,axiom,
% 0.37/0.58 ! [B4: set_int,F: int > int,A4: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B4 @ ( image_int_int @ F @ A4 ) )
% 0.37/0.58 => ~ ! [C5: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ C5 @ A4 )
% 0.37/0.58 => ( B4
% 0.37/0.58 != ( image_int_int @ F @ C5 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_imageE
% 0.37/0.58 thf(fact_2620_image__subset__iff,axiom,
% 0.37/0.58 ! [F: nat > nat,A4: set_nat,B4: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B4 )
% 0.37/0.58 = ( ! [X4: nat] :
% 0.37/0.58 ( ( member_nat @ X4 @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subset_iff
% 0.37/0.58 thf(fact_2621_image__subset__iff,axiom,
% 0.37/0.58 ! [F: int > nat,A4: set_int,B4: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B4 )
% 0.37/0.58 = ( ! [X4: int] :
% 0.37/0.58 ( ( member_int @ X4 @ A4 )
% 0.37/0.58 => ( member_nat @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subset_iff
% 0.37/0.58 thf(fact_2622_image__subset__iff,axiom,
% 0.37/0.58 ! [F: nat > set_nat,A4: set_nat,B4: set_set_nat] :
% 0.37/0.58 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A4 ) @ B4 )
% 0.37/0.58 = ( ! [X4: nat] :
% 0.37/0.58 ( ( member_nat @ X4 @ A4 )
% 0.37/0.58 => ( member_set_nat @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subset_iff
% 0.37/0.58 thf(fact_2623_image__subset__iff,axiom,
% 0.37/0.58 ! [F: nat > int,A4: set_nat,B4: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B4 )
% 0.37/0.58 = ( ! [X4: nat] :
% 0.37/0.58 ( ( member_nat @ X4 @ A4 )
% 0.37/0.58 => ( member_int @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subset_iff
% 0.37/0.58 thf(fact_2624_image__subset__iff,axiom,
% 0.37/0.58 ! [F: int > int,A4: set_int,B4: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B4 )
% 0.37/0.58 = ( ! [X4: int] :
% 0.37/0.58 ( ( member_int @ X4 @ A4 )
% 0.37/0.58 => ( member_int @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % image_subset_iff
% 0.37/0.58 thf(fact_2625_subset__image__iff,axiom,
% 0.37/0.58 ! [B4: set_set_nat,F: nat > set_nat,A4: set_nat] :
% 0.37/0.58 ( ( ord_le6893508408891458716et_nat @ B4 @ ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.58 = ( ? [AA: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 0.37/0.58 & ( B4
% 0.37/0.58 = ( image_nat_set_nat @ F @ AA ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_image_iff
% 0.37/0.58 thf(fact_2626_subset__image__iff,axiom,
% 0.37/0.58 ! [B4: set_nat,F: nat > nat,A4: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 = ( ? [AA: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 0.37/0.58 & ( B4
% 0.37/0.58 = ( image_nat_nat @ F @ AA ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_image_iff
% 0.37/0.58 thf(fact_2627_subset__image__iff,axiom,
% 0.37/0.58 ! [B4: set_nat,F: int > nat,A4: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.58 = ( ? [AA: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ AA @ A4 )
% 0.37/0.58 & ( B4
% 0.37/0.58 = ( image_int_nat @ F @ AA ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_image_iff
% 0.37/0.58 thf(fact_2628_subset__image__iff,axiom,
% 0.37/0.58 ! [B4: set_int,F: nat > int,A4: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B4 @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 = ( ? [AA: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 0.37/0.58 & ( B4
% 0.37/0.58 = ( image_nat_int @ F @ AA ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_image_iff
% 0.37/0.58 thf(fact_2629_subset__image__iff,axiom,
% 0.37/0.58 ! [B4: set_int,F: int > int,A4: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B4 @ ( image_int_int @ F @ A4 ) )
% 0.37/0.58 = ( ? [AA: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ AA @ A4 )
% 0.37/0.58 & ( B4
% 0.37/0.58 = ( image_int_int @ F @ AA ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % subset_image_iff
% 0.37/0.58 thf(fact_2630_all__subset__image,axiom,
% 0.37/0.58 ! [F: nat > set_nat,A4: set_nat,P2: set_set_nat > $o] :
% 0.37/0.58 ( ( ! [B6: set_set_nat] :
% 0.37/0.58 ( ( ord_le6893508408891458716et_nat @ B6 @ ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ B6 ) ) )
% 0.37/0.58 = ( ! [B6: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.37/0.58 => ( P2 @ ( image_nat_set_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % all_subset_image
% 0.37/0.58 thf(fact_2631_all__subset__image,axiom,
% 0.37/0.58 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 0.37/0.58 ( ( ! [B6: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ B6 ) ) )
% 0.37/0.58 = ( ! [B6: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.37/0.58 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % all_subset_image
% 0.37/0.58 thf(fact_2632_all__subset__image,axiom,
% 0.37/0.58 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 0.37/0.58 ( ( ! [B6: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ B6 ) ) )
% 0.37/0.58 = ( ! [B6: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 0.37/0.58 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % all_subset_image
% 0.37/0.58 thf(fact_2633_all__subset__image,axiom,
% 0.37/0.58 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 0.37/0.58 ( ( ! [B6: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ B6 ) ) )
% 0.37/0.58 = ( ! [B6: set_nat] :
% 0.37/0.58 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.37/0.58 => ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % all_subset_image
% 0.37/0.58 thf(fact_2634_all__subset__image,axiom,
% 0.37/0.58 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 0.37/0.58 ( ( ! [B6: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) )
% 0.37/0.58 => ( P2 @ B6 ) ) )
% 0.37/0.58 = ( ! [B6: set_int] :
% 0.37/0.58 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 0.37/0.58 => ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 0.37/0.58
% 0.37/0.58 % all_subset_image
% 0.37/0.58 thf(fact_2635_verit__sum__simplify,axiom,
% 0.37/0.58 ! [A: uint32] :
% 0.37/0.58 ( ( plus_plus_uint32 @ A @ zero_zero_uint32 )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % verit_sum_simplify
% 0.37/0.58 thf(fact_2636_verit__sum__simplify,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % verit_sum_simplify
% 0.37/0.58 thf(fact_2637_verit__sum__simplify,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % verit_sum_simplify
% 0.37/0.58 thf(fact_2638_verit__sum__simplify,axiom,
% 0.37/0.58 ! [A: nat] :
% 0.37/0.58 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % verit_sum_simplify
% 0.37/0.58 thf(fact_2639_verit__sum__simplify,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % verit_sum_simplify
% 0.37/0.58 thf(fact_2640_comm__monoid__add__class_Oadd__0,axiom,
% 0.37/0.58 ! [A: uint32] :
% 0.37/0.58 ( ( plus_plus_uint32 @ zero_zero_uint32 @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % comm_monoid_add_class.add_0
% 0.37/0.58 thf(fact_2641_comm__monoid__add__class_Oadd__0,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % comm_monoid_add_class.add_0
% 0.37/0.58 thf(fact_2642_comm__monoid__add__class_Oadd__0,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % comm_monoid_add_class.add_0
% 0.37/0.58 thf(fact_2643_comm__monoid__add__class_Oadd__0,axiom,
% 0.37/0.58 ! [A: nat] :
% 0.37/0.58 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % comm_monoid_add_class.add_0
% 0.37/0.58 thf(fact_2644_comm__monoid__add__class_Oadd__0,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % comm_monoid_add_class.add_0
% 0.37/0.58 thf(fact_2645_add_Ocomm__neutral,axiom,
% 0.37/0.58 ! [A: uint32] :
% 0.37/0.58 ( ( plus_plus_uint32 @ A @ zero_zero_uint32 )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.comm_neutral
% 0.37/0.58 thf(fact_2646_add_Ocomm__neutral,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.comm_neutral
% 0.37/0.58 thf(fact_2647_add_Ocomm__neutral,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.comm_neutral
% 0.37/0.58 thf(fact_2648_add_Ocomm__neutral,axiom,
% 0.37/0.58 ! [A: nat] :
% 0.37/0.58 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.comm_neutral
% 0.37/0.58 thf(fact_2649_add_Ocomm__neutral,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.comm_neutral
% 0.37/0.58 thf(fact_2650_add_Ogroup__left__neutral,axiom,
% 0.37/0.58 ! [A: uint32] :
% 0.37/0.58 ( ( plus_plus_uint32 @ zero_zero_uint32 @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.group_left_neutral
% 0.37/0.58 thf(fact_2651_add_Ogroup__left__neutral,axiom,
% 0.37/0.58 ! [A: real] :
% 0.37/0.58 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.group_left_neutral
% 0.37/0.58 thf(fact_2652_add_Ogroup__left__neutral,axiom,
% 0.37/0.58 ! [A: rat] :
% 0.37/0.58 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.group_left_neutral
% 0.37/0.58 thf(fact_2653_add_Ogroup__left__neutral,axiom,
% 0.37/0.58 ! [A: int] :
% 0.37/0.58 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.37/0.58 = A ) ).
% 0.37/0.58
% 0.37/0.58 % add.group_left_neutral
% 0.37/0.58 thf(fact_2654_add__le__imp__le__right,axiom,
% 0.37/0.58 ! [A: real,C2: real,B: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.37/0.58 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_imp_le_right
% 0.37/0.58 thf(fact_2655_add__le__imp__le__right,axiom,
% 0.37/0.58 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.37/0.58 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_imp_le_right
% 0.37/0.58 thf(fact_2656_add__le__imp__le__right,axiom,
% 0.37/0.58 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.37/0.58 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_imp_le_right
% 0.37/0.58 thf(fact_2657_add__le__imp__le__right,axiom,
% 0.37/0.58 ! [A: int,C2: int,B: int] :
% 0.37/0.58 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.37/0.58 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_imp_le_right
% 0.37/0.58 thf(fact_2658_add__le__imp__le__left,axiom,
% 0.37/0.58 ! [C2: real,A: real,B: real] :
% 0.37/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.37/0.58 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_imp_le_left
% 0.37/0.58 thf(fact_2659_add__le__imp__le__left,axiom,
% 0.37/0.58 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.37/0.58 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_imp_le_left
% 0.37/0.58 thf(fact_2660_add__le__imp__le__left,axiom,
% 0.37/0.58 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.58 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.37/0.58 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.37/0.58
% 0.37/0.58 % add_le_imp_le_left
% 0.37/0.59 thf(fact_2661_add__le__imp__le__left,axiom,
% 0.37/0.59 ! [C2: int,A: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.37/0.59 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_imp_le_left
% 0.37/0.59 thf(fact_2662_le__iff__add,axiom,
% 0.37/0.59 ( ord_less_eq_nat
% 0.37/0.59 = ( ^ [A7: nat,B7: nat] :
% 0.37/0.59 ? [C6: nat] :
% 0.37/0.59 ( B7
% 0.37/0.59 = ( plus_plus_nat @ A7 @ C6 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_iff_add
% 0.37/0.59 thf(fact_2663_add__right__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_right_mono
% 0.37/0.59 thf(fact_2664_add__right__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_right_mono
% 0.37/0.59 thf(fact_2665_add__right__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_right_mono
% 0.37/0.59 thf(fact_2666_add__right__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_right_mono
% 0.37/0.59 thf(fact_2667_less__eqE,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ~ ! [C: nat] :
% 0.37/0.59 ( B
% 0.37/0.59 != ( plus_plus_nat @ A @ C ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_eqE
% 0.37/0.59 thf(fact_2668_add__left__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_left_mono
% 0.37/0.59 thf(fact_2669_add__left__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_left_mono
% 0.37/0.59 thf(fact_2670_add__left__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_left_mono
% 0.37/0.59 thf(fact_2671_add__left__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_left_mono
% 0.37/0.59 thf(fact_2672_add__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_real @ C2 @ D )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono
% 0.37/0.59 thf(fact_2673_add__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono
% 0.37/0.59 thf(fact_2674_add__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono
% 0.37/0.59 thf(fact_2675_add__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_int @ C2 @ D )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono
% 0.37/0.59 thf(fact_2676_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( ord_less_eq_real @ I @ J )
% 0.37/0.59 & ( ord_less_eq_real @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(1)
% 0.37/0.59 thf(fact_2677_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( ord_less_eq_rat @ I @ J )
% 0.37/0.59 & ( ord_less_eq_rat @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(1)
% 0.37/0.59 thf(fact_2678_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 & ( ord_less_eq_nat @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(1)
% 0.37/0.59 thf(fact_2679_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( ord_less_eq_int @ I @ J )
% 0.37/0.59 & ( ord_less_eq_int @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(1)
% 0.37/0.59 thf(fact_2680_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_eq_real @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(2)
% 0.37/0.59 thf(fact_2681_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_eq_rat @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(2)
% 0.37/0.59 thf(fact_2682_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_eq_nat @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(2)
% 0.37/0.59 thf(fact_2683_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_eq_int @ K @ L ) )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(2)
% 0.37/0.59 thf(fact_2684_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( ord_less_eq_real @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(3)
% 0.37/0.59 thf(fact_2685_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( ord_less_eq_rat @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(3)
% 0.37/0.59 thf(fact_2686_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(3)
% 0.37/0.59 thf(fact_2687_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( ord_less_eq_int @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_semiring(3)
% 0.37/0.59 thf(fact_2688_add__mono__thms__linordered__field_I5_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( ord_less_real @ I @ J )
% 0.37/0.59 & ( ord_less_real @ K @ L ) )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(5)
% 0.37/0.59 thf(fact_2689_add__mono__thms__linordered__field_I5_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( ord_less_rat @ I @ J )
% 0.37/0.59 & ( ord_less_rat @ K @ L ) )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(5)
% 0.37/0.59 thf(fact_2690_add__mono__thms__linordered__field_I5_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( ord_less_nat @ I @ J )
% 0.37/0.59 & ( ord_less_nat @ K @ L ) )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(5)
% 0.37/0.59 thf(fact_2691_add__mono__thms__linordered__field_I5_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( ord_less_int @ I @ J )
% 0.37/0.59 & ( ord_less_int @ K @ L ) )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(5)
% 0.37/0.59 thf(fact_2692_add__mono__thms__linordered__field_I2_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_real @ K @ L ) )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(2)
% 0.37/0.59 thf(fact_2693_add__mono__thms__linordered__field_I2_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_rat @ K @ L ) )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(2)
% 0.37/0.59 thf(fact_2694_add__mono__thms__linordered__field_I2_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_nat @ K @ L ) )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(2)
% 0.37/0.59 thf(fact_2695_add__mono__thms__linordered__field_I2_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( I = J )
% 0.37/0.59 & ( ord_less_int @ K @ L ) )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(2)
% 0.37/0.59 thf(fact_2696_add__mono__thms__linordered__field_I1_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( ord_less_real @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(1)
% 0.37/0.59 thf(fact_2697_add__mono__thms__linordered__field_I1_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( ord_less_rat @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(1)
% 0.37/0.59 thf(fact_2698_add__mono__thms__linordered__field_I1_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( ord_less_nat @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(1)
% 0.37/0.59 thf(fact_2699_add__mono__thms__linordered__field_I1_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( ord_less_int @ I @ J )
% 0.37/0.59 & ( K = L ) )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(1)
% 0.37/0.59 thf(fact_2700_add__strict__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ B )
% 0.37/0.59 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_mono
% 0.37/0.59 thf(fact_2701_add__strict__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ B )
% 0.37/0.59 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_mono
% 0.37/0.59 thf(fact_2702_add__strict__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ B )
% 0.37/0.59 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_mono
% 0.37/0.59 thf(fact_2703_add__strict__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ B )
% 0.37/0.59 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_mono
% 0.37/0.59 thf(fact_2704_add__strict__left__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ B )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_left_mono
% 0.37/0.59 thf(fact_2705_add__strict__left__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ B )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_left_mono
% 0.37/0.59 thf(fact_2706_add__strict__left__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ B )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_left_mono
% 0.37/0.59 thf(fact_2707_add__strict__left__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ B )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_left_mono
% 0.37/0.59 thf(fact_2708_add__strict__right__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ B )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_right_mono
% 0.37/0.59 thf(fact_2709_add__strict__right__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ B )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_right_mono
% 0.37/0.59 thf(fact_2710_add__strict__right__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ B )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_right_mono
% 0.37/0.59 thf(fact_2711_add__strict__right__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ B )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_right_mono
% 0.37/0.59 thf(fact_2712_add__less__imp__less__left,axiom,
% 0.37/0.59 ! [C2: real,A: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.37/0.59 => ( ord_less_real @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_left
% 0.37/0.59 thf(fact_2713_add__less__imp__less__left,axiom,
% 0.37/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.37/0.59 => ( ord_less_rat @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_left
% 0.37/0.59 thf(fact_2714_add__less__imp__less__left,axiom,
% 0.37/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.37/0.59 => ( ord_less_nat @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_left
% 0.37/0.59 thf(fact_2715_add__less__imp__less__left,axiom,
% 0.37/0.59 ! [C2: int,A: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.37/0.59 => ( ord_less_int @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_left
% 0.37/0.59 thf(fact_2716_add__less__imp__less__right,axiom,
% 0.37/0.59 ! [A: real,C2: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.37/0.59 => ( ord_less_real @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_right
% 0.37/0.59 thf(fact_2717_add__less__imp__less__right,axiom,
% 0.37/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.37/0.59 => ( ord_less_rat @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_right
% 0.37/0.59 thf(fact_2718_add__less__imp__less__right,axiom,
% 0.37/0.59 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.37/0.59 => ( ord_less_nat @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_right
% 0.37/0.59 thf(fact_2719_add__less__imp__less__right,axiom,
% 0.37/0.59 ! [A: int,C2: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.37/0.59 => ( ord_less_int @ A @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_imp_less_right
% 0.37/0.59 thf(fact_2720_diff__diff__eq,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq
% 0.37/0.59 thf(fact_2721_diff__diff__eq,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32,C2: uint32] :
% 0.37/0.59 ( ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_uint32 @ A @ ( plus_plus_uint32 @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq
% 0.37/0.59 thf(fact_2722_diff__diff__eq,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq
% 0.37/0.59 thf(fact_2723_diff__diff__eq,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq
% 0.37/0.59 thf(fact_2724_diff__diff__eq,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq
% 0.37/0.59 thf(fact_2725_add__implies__diff,axiom,
% 0.37/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.37/0.59 ( ( ( plus_plus_rat @ C2 @ B )
% 0.37/0.59 = A )
% 0.37/0.59 => ( C2
% 0.37/0.59 = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_implies_diff
% 0.37/0.59 thf(fact_2726_add__implies__diff,axiom,
% 0.37/0.59 ! [C2: uint32,B: uint32,A: uint32] :
% 0.37/0.59 ( ( ( plus_plus_uint32 @ C2 @ B )
% 0.37/0.59 = A )
% 0.37/0.59 => ( C2
% 0.37/0.59 = ( minus_minus_uint32 @ A @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_implies_diff
% 0.37/0.59 thf(fact_2727_add__implies__diff,axiom,
% 0.37/0.59 ! [C2: real,B: real,A: real] :
% 0.37/0.59 ( ( ( plus_plus_real @ C2 @ B )
% 0.37/0.59 = A )
% 0.37/0.59 => ( C2
% 0.37/0.59 = ( minus_minus_real @ A @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_implies_diff
% 0.37/0.59 thf(fact_2728_add__implies__diff,axiom,
% 0.37/0.59 ! [C2: nat,B: nat,A: nat] :
% 0.37/0.59 ( ( ( plus_plus_nat @ C2 @ B )
% 0.37/0.59 = A )
% 0.37/0.59 => ( C2
% 0.37/0.59 = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_implies_diff
% 0.37/0.59 thf(fact_2729_add__implies__diff,axiom,
% 0.37/0.59 ! [C2: int,B: int,A: int] :
% 0.37/0.59 ( ( ( plus_plus_int @ C2 @ B )
% 0.37/0.59 = A )
% 0.37/0.59 => ( C2
% 0.37/0.59 = ( minus_minus_int @ A @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_implies_diff
% 0.37/0.59 thf(fact_2730_diff__add__eq__diff__diff__swap,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq_diff_diff_swap
% 0.37/0.59 thf(fact_2731_diff__add__eq__diff__diff__swap,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32,C2: uint32] :
% 0.37/0.59 ( ( minus_minus_uint32 @ A @ ( plus_plus_uint32 @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq_diff_diff_swap
% 0.37/0.59 thf(fact_2732_diff__add__eq__diff__diff__swap,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_real @ ( minus_minus_real @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq_diff_diff_swap
% 0.37/0.59 thf(fact_2733_diff__add__eq__diff__diff__swap,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq_diff_diff_swap
% 0.37/0.59 thf(fact_2734_diff__add__eq,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq
% 0.37/0.59 thf(fact_2735_diff__add__eq,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32,C2: uint32] :
% 0.37/0.59 ( ( plus_plus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq
% 0.37/0.59 thf(fact_2736_diff__add__eq,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq
% 0.37/0.59 thf(fact_2737_diff__add__eq,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.37/0.59 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_eq
% 0.37/0.59 thf(fact_2738_diff__diff__eq2,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq2
% 0.37/0.59 thf(fact_2739_diff__diff__eq2,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32,C2: uint32] :
% 0.37/0.59 ( ( minus_minus_uint32 @ A @ ( minus_minus_uint32 @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq2
% 0.37/0.59 thf(fact_2740_diff__diff__eq2,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq2
% 0.37/0.59 thf(fact_2741_diff__diff__eq2,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_diff_eq2
% 0.37/0.59 thf(fact_2742_add__diff__eq,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_diff_eq
% 0.37/0.59 thf(fact_2743_add__diff__eq,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32,C2: uint32] :
% 0.37/0.59 ( ( plus_plus_uint32 @ A @ ( minus_minus_uint32 @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_diff_eq
% 0.37/0.59 thf(fact_2744_add__diff__eq,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_diff_eq
% 0.37/0.59 thf(fact_2745_add__diff__eq,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 0.37/0.59 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_diff_eq
% 0.37/0.59 thf(fact_2746_eq__diff__eq,axiom,
% 0.37/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.59 ( ( A
% 0.37/0.59 = ( minus_minus_rat @ C2 @ B ) )
% 0.37/0.59 = ( ( plus_plus_rat @ A @ B )
% 0.37/0.59 = C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % eq_diff_eq
% 0.37/0.59 thf(fact_2747_eq__diff__eq,axiom,
% 0.37/0.59 ! [A: uint32,C2: uint32,B: uint32] :
% 0.37/0.59 ( ( A
% 0.37/0.59 = ( minus_minus_uint32 @ C2 @ B ) )
% 0.37/0.59 = ( ( plus_plus_uint32 @ A @ B )
% 0.37/0.59 = C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % eq_diff_eq
% 0.37/0.59 thf(fact_2748_eq__diff__eq,axiom,
% 0.37/0.59 ! [A: real,C2: real,B: real] :
% 0.37/0.59 ( ( A
% 0.37/0.59 = ( minus_minus_real @ C2 @ B ) )
% 0.37/0.59 = ( ( plus_plus_real @ A @ B )
% 0.37/0.59 = C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % eq_diff_eq
% 0.37/0.59 thf(fact_2749_eq__diff__eq,axiom,
% 0.37/0.59 ! [A: int,C2: int,B: int] :
% 0.37/0.59 ( ( A
% 0.37/0.59 = ( minus_minus_int @ C2 @ B ) )
% 0.37/0.59 = ( ( plus_plus_int @ A @ B )
% 0.37/0.59 = C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % eq_diff_eq
% 0.37/0.59 thf(fact_2750_diff__eq__eq,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ( minus_minus_rat @ A @ B )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( A
% 0.37/0.59 = ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_eq_eq
% 0.37/0.59 thf(fact_2751_diff__eq__eq,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32,C2: uint32] :
% 0.37/0.59 ( ( ( minus_minus_uint32 @ A @ B )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( A
% 0.37/0.59 = ( plus_plus_uint32 @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_eq_eq
% 0.37/0.59 thf(fact_2752_diff__eq__eq,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ( minus_minus_real @ A @ B )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( A
% 0.37/0.59 = ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_eq_eq
% 0.37/0.59 thf(fact_2753_diff__eq__eq,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ( minus_minus_int @ A @ B )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( A
% 0.37/0.59 = ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_eq_eq
% 0.37/0.59 thf(fact_2754_group__cancel_Osub1,axiom,
% 0.37/0.59 ! [A4: rat,K: rat,A: rat,B: rat] :
% 0.37/0.59 ( ( A4
% 0.37/0.59 = ( plus_plus_rat @ K @ A ) )
% 0.37/0.59 => ( ( minus_minus_rat @ A4 @ B )
% 0.37/0.59 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % group_cancel.sub1
% 0.37/0.59 thf(fact_2755_group__cancel_Osub1,axiom,
% 0.37/0.59 ! [A4: uint32,K: uint32,A: uint32,B: uint32] :
% 0.37/0.59 ( ( A4
% 0.37/0.59 = ( plus_plus_uint32 @ K @ A ) )
% 0.37/0.59 => ( ( minus_minus_uint32 @ A4 @ B )
% 0.37/0.59 = ( plus_plus_uint32 @ K @ ( minus_minus_uint32 @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % group_cancel.sub1
% 0.37/0.59 thf(fact_2756_group__cancel_Osub1,axiom,
% 0.37/0.59 ! [A4: real,K: real,A: real,B: real] :
% 0.37/0.59 ( ( A4
% 0.37/0.59 = ( plus_plus_real @ K @ A ) )
% 0.37/0.59 => ( ( minus_minus_real @ A4 @ B )
% 0.37/0.59 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % group_cancel.sub1
% 0.37/0.59 thf(fact_2757_group__cancel_Osub1,axiom,
% 0.37/0.59 ! [A4: int,K: int,A: int,B: int] :
% 0.37/0.59 ( ( A4
% 0.37/0.59 = ( plus_plus_int @ K @ A ) )
% 0.37/0.59 => ( ( minus_minus_int @ A4 @ B )
% 0.37/0.59 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % group_cancel.sub1
% 0.37/0.59 thf(fact_2758_nat__arith_Osuc1,axiom,
% 0.37/0.59 ! [A4: nat,K: nat,A: nat] :
% 0.37/0.59 ( ( A4
% 0.37/0.59 = ( plus_plus_nat @ K @ A ) )
% 0.37/0.59 => ( ( suc @ A4 )
% 0.37/0.59 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % nat_arith.suc1
% 0.37/0.59 thf(fact_2759_add__Suc,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.37/0.59 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_Suc
% 0.37/0.59 thf(fact_2760_add__Suc__shift,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.37/0.59 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_Suc_shift
% 0.37/0.59 thf(fact_2761_plus__nat_Oadd__0,axiom,
% 0.37/0.59 ! [N: nat] :
% 0.37/0.59 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.37/0.59 = N ) ).
% 0.37/0.59
% 0.37/0.59 % plus_nat.add_0
% 0.37/0.59 thf(fact_2762_add__eq__self__zero,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ( plus_plus_nat @ M @ N )
% 0.37/0.59 = M )
% 0.37/0.59 => ( N = zero_zero_nat ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_eq_self_zero
% 0.37/0.59 thf(fact_2763_add__lessD1,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat] :
% 0.37/0.59 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.37/0.59 => ( ord_less_nat @ I @ K ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_lessD1
% 0.37/0.59 thf(fact_2764_add__less__mono,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ord_less_nat @ I @ J )
% 0.37/0.59 => ( ( ord_less_nat @ K @ L )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_mono
% 0.37/0.59 thf(fact_2765_not__add__less1,axiom,
% 0.37/0.59 ! [I: nat,J: nat] :
% 0.37/0.59 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.37/0.59
% 0.37/0.59 % not_add_less1
% 0.37/0.59 thf(fact_2766_not__add__less2,axiom,
% 0.37/0.59 ! [J: nat,I: nat] :
% 0.37/0.59 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.37/0.59
% 0.37/0.59 % not_add_less2
% 0.37/0.59 thf(fact_2767_add__less__mono1,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat] :
% 0.37/0.59 ( ( ord_less_nat @ I @ J )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_mono1
% 0.37/0.59 thf(fact_2768_trans__less__add1,axiom,
% 0.37/0.59 ! [I: nat,J: nat,M: nat] :
% 0.37/0.59 ( ( ord_less_nat @ I @ J )
% 0.37/0.59 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % trans_less_add1
% 0.37/0.59 thf(fact_2769_trans__less__add2,axiom,
% 0.37/0.59 ! [I: nat,J: nat,M: nat] :
% 0.37/0.59 ( ( ord_less_nat @ I @ J )
% 0.37/0.59 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % trans_less_add2
% 0.37/0.59 thf(fact_2770_less__add__eq__less,axiom,
% 0.37/0.59 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_nat @ K @ L )
% 0.37/0.59 => ( ( ( plus_plus_nat @ M @ L )
% 0.37/0.59 = ( plus_plus_nat @ K @ N ) )
% 0.37/0.59 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_add_eq_less
% 0.37/0.59 thf(fact_2771_nat__le__iff__add,axiom,
% 0.37/0.59 ( ord_less_eq_nat
% 0.37/0.59 = ( ^ [M5: nat,N6: nat] :
% 0.37/0.59 ? [K3: nat] :
% 0.37/0.59 ( N6
% 0.37/0.59 = ( plus_plus_nat @ M5 @ K3 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % nat_le_iff_add
% 0.37/0.59 thf(fact_2772_trans__le__add2,axiom,
% 0.37/0.59 ! [I: nat,J: nat,M: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % trans_le_add2
% 0.37/0.59 thf(fact_2773_trans__le__add1,axiom,
% 0.37/0.59 ! [I: nat,J: nat,M: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % trans_le_add1
% 0.37/0.59 thf(fact_2774_add__le__mono1,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_mono1
% 0.37/0.59 thf(fact_2775_add__le__mono,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 => ( ( ord_less_eq_nat @ K @ L )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_mono
% 0.37/0.59 thf(fact_2776_le__Suc__ex,axiom,
% 0.37/0.59 ! [K: nat,L: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ K @ L )
% 0.37/0.59 => ? [N2: nat] :
% 0.37/0.59 ( L
% 0.37/0.59 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_Suc_ex
% 0.37/0.59 thf(fact_2777_add__leD2,axiom,
% 0.37/0.59 ! [M: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.37/0.59 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_leD2
% 0.37/0.59 thf(fact_2778_add__leD1,axiom,
% 0.37/0.59 ! [M: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.37/0.59 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_leD1
% 0.37/0.59 thf(fact_2779_le__add2,axiom,
% 0.37/0.59 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_add2
% 0.37/0.59 thf(fact_2780_le__add1,axiom,
% 0.37/0.59 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_add1
% 0.37/0.59 thf(fact_2781_add__leE,axiom,
% 0.37/0.59 ! [M: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.37/0.59 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.59 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_leE
% 0.37/0.59 thf(fact_2782_diff__add__inverse2,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.37/0.59 = M ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_inverse2
% 0.37/0.59 thf(fact_2783_diff__add__inverse,axiom,
% 0.37/0.59 ! [N: nat,M: nat] :
% 0.37/0.59 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.37/0.59 = M ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_inverse
% 0.37/0.59 thf(fact_2784_diff__cancel2,axiom,
% 0.37/0.59 ! [M: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.37/0.59 = ( minus_minus_nat @ M @ N ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_cancel2
% 0.37/0.59 thf(fact_2785_Nat_Odiff__cancel,axiom,
% 0.37/0.59 ! [K: nat,M: nat,N: nat] :
% 0.37/0.59 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.37/0.59 = ( minus_minus_nat @ M @ N ) ) ).
% 0.37/0.59
% 0.37/0.59 % Nat.diff_cancel
% 0.37/0.59 thf(fact_2786_enumerate__in__set,axiom,
% 0.37/0.59 ! [S3: set_nat,N: nat] :
% 0.37/0.59 ( ~ ( finite_finite_nat @ S3 )
% 0.37/0.59 => ( member_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ S3 ) ) ).
% 0.37/0.59
% 0.37/0.59 % enumerate_in_set
% 0.37/0.59 thf(fact_2787_Ints__double__eq__0__iff,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( member_real @ A @ ring_1_Ints_real )
% 0.37/0.59 => ( ( ( plus_plus_real @ A @ A )
% 0.37/0.59 = zero_zero_real )
% 0.37/0.59 = ( A = zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_double_eq_0_iff
% 0.37/0.59 thf(fact_2788_Ints__double__eq__0__iff,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.37/0.59 => ( ( ( plus_plus_rat @ A @ A )
% 0.37/0.59 = zero_zero_rat )
% 0.37/0.59 = ( A = zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_double_eq_0_iff
% 0.37/0.59 thf(fact_2789_Ints__double__eq__0__iff,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( member_int @ A @ ring_1_Ints_int )
% 0.37/0.59 => ( ( ( plus_plus_int @ A @ A )
% 0.37/0.59 = zero_zero_int )
% 0.37/0.59 = ( A = zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_double_eq_0_iff
% 0.37/0.59 thf(fact_2790_enumerate__Ex,axiom,
% 0.37/0.59 ! [S3: set_nat,S: nat] :
% 0.37/0.59 ( ~ ( finite_finite_nat @ S3 )
% 0.37/0.59 => ( ( member_nat @ S @ S3 )
% 0.37/0.59 => ? [N2: nat] :
% 0.37/0.59 ( ( infini8530281810654367211te_nat @ S3 @ N2 )
% 0.37/0.59 = S ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % enumerate_Ex
% 0.37/0.59 thf(fact_2791_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 0.37/0.59 ( ( ! [B6: set_nat] :
% 0.37/0.59 ( ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_nat] :
% 0.37/0.59 ( ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2792_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: complex > nat,A4: set_complex,P2: set_nat > $o] :
% 0.37/0.59 ( ( ! [B6: set_nat] :
% 0.37/0.59 ( ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_complex_nat @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_complex] :
% 0.37/0.59 ( ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_complex_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2793_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: code_integer > nat,A4: set_Code_integer,P2: set_nat > $o] :
% 0.37/0.59 ( ( ! [B6: set_nat] :
% 0.37/0.59 ( ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_951025933927791156er_nat @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_Code_integer] :
% 0.37/0.59 ( ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_951025933927791156er_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2794_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: nat > complex,A4: set_nat,P2: set_complex > $o] :
% 0.37/0.59 ( ( ! [B6: set_complex] :
% 0.37/0.59 ( ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ ( image_nat_complex @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_nat] :
% 0.37/0.59 ( ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_nat_complex @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2795_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: complex > complex,A4: set_complex,P2: set_complex > $o] :
% 0.37/0.59 ( ( ! [B6: set_complex] :
% 0.37/0.59 ( ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ ( image_1468599708987790691omplex @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_complex] :
% 0.37/0.59 ( ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_1468599708987790691omplex @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2796_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: code_integer > complex,A4: set_Code_integer,P2: set_complex > $o] :
% 0.37/0.59 ( ( ! [B6: set_complex] :
% 0.37/0.59 ( ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ ( image_3397630267976458002omplex @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_Code_integer] :
% 0.37/0.59 ( ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_3397630267976458002omplex @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2797_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: nat > code_integer,A4: set_nat,P2: set_Code_integer > $o] :
% 0.37/0.59 ( ( ! [B6: set_Code_integer] :
% 0.37/0.59 ( ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1215581382706833972nteger @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_nat] :
% 0.37/0.59 ( ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_1215581382706833972nteger @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2798_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: complex > code_integer,A4: set_complex,P2: set_Code_integer > $o] :
% 0.37/0.59 ( ( ! [B6: set_Code_integer] :
% 0.37/0.59 ( ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1994230757181692690nteger @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_complex] :
% 0.37/0.59 ( ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_1994230757181692690nteger @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2799_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: code_integer > code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.37/0.59 ( ( ! [B6: set_Code_integer] :
% 0.37/0.59 ( ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ ( image_4470545334726330049nteger @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_Code_integer] :
% 0.37/0.59 ( ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_4470545334726330049nteger @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2800_all__finite__subset__image,axiom,
% 0.37/0.59 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 0.37/0.59 ( ( ! [B6: set_nat] :
% 0.37/0.59 ( ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) ) )
% 0.37/0.59 => ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ! [B6: set_int] :
% 0.37/0.59 ( ( ( finite_finite_int @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_int @ B6 @ A4 ) )
% 0.37/0.59 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % all_finite_subset_image
% 0.37/0.59 thf(fact_2801_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 0.37/0.59 ( ( ? [B6: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2802_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: complex > nat,A4: set_complex,P2: set_nat > $o] :
% 0.37/0.59 ( ( ? [B6: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_complex_nat @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_complex_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2803_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: code_integer > nat,A4: set_Code_integer,P2: set_nat > $o] :
% 0.37/0.59 ( ( ? [B6: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_951025933927791156er_nat @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_Code_integer] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_951025933927791156er_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2804_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: nat > complex,A4: set_nat,P2: set_complex > $o] :
% 0.37/0.59 ( ( ? [B6: set_complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ ( image_nat_complex @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_nat_complex @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2805_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: complex > complex,A4: set_complex,P2: set_complex > $o] :
% 0.37/0.59 ( ( ? [B6: set_complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_1468599708987790691omplex @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2806_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: code_integer > complex,A4: set_Code_integer,P2: set_complex > $o] :
% 0.37/0.59 ( ( ? [B6: set_complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ ( image_3397630267976458002omplex @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_Code_integer] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_3397630267976458002omplex @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2807_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: nat > code_integer,A4: set_nat,P2: set_Code_integer > $o] :
% 0.37/0.59 ( ( ? [B6: set_Code_integer] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1215581382706833972nteger @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_1215581382706833972nteger @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2808_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: complex > code_integer,A4: set_complex,P2: set_Code_integer > $o] :
% 0.37/0.59 ( ( ? [B6: set_Code_integer] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1994230757181692690nteger @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B6 )
% 0.37/0.59 & ( ord_le211207098394363844omplex @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_1994230757181692690nteger @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2809_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: code_integer > code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 0.37/0.59 ( ( ? [B6: set_Code_integer] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ ( image_4470545334726330049nteger @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_Code_integer] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B6 )
% 0.37/0.59 & ( ord_le7084787975880047091nteger @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_4470545334726330049nteger @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2810_ex__finite__subset__image,axiom,
% 0.37/0.59 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 0.37/0.59 ( ( ? [B6: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.59 & ( P2 @ B6 ) ) )
% 0.37/0.59 = ( ? [B6: set_int] :
% 0.37/0.59 ( ( finite_finite_int @ B6 )
% 0.37/0.59 & ( ord_less_eq_set_int @ B6 @ A4 )
% 0.37/0.59 & ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ex_finite_subset_image
% 0.37/0.59 thf(fact_2811_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_nat,F: nat > nat,A4: set_nat] :
% 0.37/0.59 ( ( finite_finite_nat @ B4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_nat] :
% 0.37/0.59 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 0.37/0.59 & ( finite_finite_nat @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_nat_nat @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2812_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_nat,F: complex > nat,A4: set_complex] :
% 0.37/0.59 ( ( finite_finite_nat @ B4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_complex_nat @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_complex] :
% 0.37/0.59 ( ( ord_le211207098394363844omplex @ C5 @ A4 )
% 0.37/0.59 & ( finite3207457112153483333omplex @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_complex_nat @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2813_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_nat,F: code_integer > nat,A4: set_Code_integer] :
% 0.37/0.59 ( ( finite_finite_nat @ B4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_951025933927791156er_nat @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_Code_integer] :
% 0.37/0.59 ( ( ord_le7084787975880047091nteger @ C5 @ A4 )
% 0.37/0.59 & ( finite6017078050557962740nteger @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_951025933927791156er_nat @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2814_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_complex,F: nat > complex,A4: set_nat] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.59 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_nat_complex @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_nat] :
% 0.37/0.59 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 0.37/0.59 & ( finite_finite_nat @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_nat_complex @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2815_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_complex,F: complex > complex,A4: set_complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.59 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_complex] :
% 0.37/0.59 ( ( ord_le211207098394363844omplex @ C5 @ A4 )
% 0.37/0.59 & ( finite3207457112153483333omplex @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_1468599708987790691omplex @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2816_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_complex,F: code_integer > complex,A4: set_Code_integer] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.59 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_3397630267976458002omplex @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_Code_integer] :
% 0.37/0.59 ( ( ord_le7084787975880047091nteger @ C5 @ A4 )
% 0.37/0.59 & ( finite6017078050557962740nteger @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_3397630267976458002omplex @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2817_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_Code_integer,F: nat > code_integer,A4: set_nat] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.59 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1215581382706833972nteger @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_nat] :
% 0.37/0.59 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 0.37/0.59 & ( finite_finite_nat @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_1215581382706833972nteger @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2818_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_Code_integer,F: complex > code_integer,A4: set_complex] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.59 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1994230757181692690nteger @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_complex] :
% 0.37/0.59 ( ( ord_le211207098394363844omplex @ C5 @ A4 )
% 0.37/0.59 & ( finite3207457112153483333omplex @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_1994230757181692690nteger @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2819_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_Code_integer,F: code_integer > code_integer,A4: set_Code_integer] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.59 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_4470545334726330049nteger @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_Code_integer] :
% 0.37/0.59 ( ( ord_le7084787975880047091nteger @ C5 @ A4 )
% 0.37/0.59 & ( finite6017078050557962740nteger @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_4470545334726330049nteger @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2820_finite__subset__image,axiom,
% 0.37/0.59 ! [B4: set_nat,F: int > nat,A4: set_int] :
% 0.37/0.59 ( ( finite_finite_nat @ B4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.59 => ? [C5: set_int] :
% 0.37/0.59 ( ( ord_less_eq_set_int @ C5 @ A4 )
% 0.37/0.59 & ( finite_finite_int @ C5 )
% 0.37/0.59 & ( B4
% 0.37/0.59 = ( image_int_nat @ F @ C5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_subset_image
% 0.37/0.59 thf(fact_2821_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_nat,B4: set_nat,F: nat > nat] :
% 0.37/0.59 ( ( finite_finite_nat @ A4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.59 => ( finite_finite_nat @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2822_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_nat,B4: set_complex,F: nat > complex] :
% 0.37/0.59 ( ( finite_finite_nat @ A4 )
% 0.37/0.59 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_nat_complex @ F @ A4 ) )
% 0.37/0.59 => ( finite3207457112153483333omplex @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2823_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_nat,B4: set_Code_integer,F: nat > code_integer] :
% 0.37/0.59 ( ( finite_finite_nat @ A4 )
% 0.37/0.59 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1215581382706833972nteger @ F @ A4 ) )
% 0.37/0.59 => ( finite6017078050557962740nteger @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2824_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_int,B4: set_nat,F: int > nat] :
% 0.37/0.59 ( ( finite_finite_int @ A4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.59 => ( finite_finite_nat @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2825_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_int,B4: set_complex,F: int > complex] :
% 0.37/0.59 ( ( finite_finite_int @ A4 )
% 0.37/0.59 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_int_complex @ F @ A4 ) )
% 0.37/0.59 => ( finite3207457112153483333omplex @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2826_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_int,B4: set_Code_integer,F: int > code_integer] :
% 0.37/0.59 ( ( finite_finite_int @ A4 )
% 0.37/0.59 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1587234942943678608nteger @ F @ A4 ) )
% 0.37/0.59 => ( finite6017078050557962740nteger @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2827_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_complex,B4: set_nat,F: complex > nat] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_complex_nat @ F @ A4 ) )
% 0.37/0.59 => ( finite_finite_nat @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2828_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_complex,B4: set_complex,F: complex > complex] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.59 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 0.37/0.59 => ( finite3207457112153483333omplex @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2829_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_complex,B4: set_Code_integer,F: complex > code_integer] :
% 0.37/0.59 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.59 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1994230757181692690nteger @ F @ A4 ) )
% 0.37/0.59 => ( finite6017078050557962740nteger @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2830_finite__surj,axiom,
% 0.37/0.59 ! [A4: set_Code_integer,B4: set_nat,F: code_integer > nat] :
% 0.37/0.59 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.59 => ( ( ord_less_eq_set_nat @ B4 @ ( image_951025933927791156er_nat @ F @ A4 ) )
% 0.37/0.59 => ( finite_finite_nat @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % finite_surj
% 0.37/0.59 thf(fact_2831_image__diff__subset,axiom,
% 0.37/0.59 ! [F: nat > set_nat,A4: set_nat,B4: set_nat] : ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ ( image_nat_set_nat @ F @ A4 ) @ ( image_nat_set_nat @ F @ B4 ) ) @ ( image_nat_set_nat @ F @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % image_diff_subset
% 0.37/0.59 thf(fact_2832_image__diff__subset,axiom,
% 0.37/0.59 ! [F: int > nat,A4: set_int,B4: set_int] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B4 ) ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % image_diff_subset
% 0.37/0.59 thf(fact_2833_image__diff__subset,axiom,
% 0.37/0.59 ! [F: nat > nat,A4: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B4 ) ) @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % image_diff_subset
% 0.37/0.59 thf(fact_2834_image__diff__subset,axiom,
% 0.37/0.59 ! [F: int > int,A4: set_int,B4: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B4 ) ) @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % image_diff_subset
% 0.37/0.59 thf(fact_2835_image__diff__subset,axiom,
% 0.37/0.59 ! [F: nat > int,A4: set_nat,B4: set_nat] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B4 ) ) @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % image_diff_subset
% 0.37/0.59 thf(fact_2836_add__nonpos__eq__0__iff,axiom,
% 0.37/0.59 ! [X: real,Y: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.37/0.59 => ( ( ( plus_plus_real @ X @ Y )
% 0.37/0.59 = zero_zero_real )
% 0.37/0.59 = ( ( X = zero_zero_real )
% 0.37/0.59 & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_eq_0_iff
% 0.37/0.59 thf(fact_2837_add__nonpos__eq__0__iff,axiom,
% 0.37/0.59 ! [X: rat,Y: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.37/0.59 => ( ( ( plus_plus_rat @ X @ Y )
% 0.37/0.59 = zero_zero_rat )
% 0.37/0.59 = ( ( X = zero_zero_rat )
% 0.37/0.59 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_eq_0_iff
% 0.37/0.59 thf(fact_2838_add__nonpos__eq__0__iff,axiom,
% 0.37/0.59 ! [X: nat,Y: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 0.37/0.59 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.37/0.59 => ( ( ( plus_plus_nat @ X @ Y )
% 0.37/0.59 = zero_zero_nat )
% 0.37/0.59 = ( ( X = zero_zero_nat )
% 0.37/0.59 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_eq_0_iff
% 0.37/0.59 thf(fact_2839_add__nonpos__eq__0__iff,axiom,
% 0.37/0.59 ! [X: int,Y: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.37/0.59 => ( ( ( plus_plus_int @ X @ Y )
% 0.37/0.59 = zero_zero_int )
% 0.37/0.59 = ( ( X = zero_zero_int )
% 0.37/0.59 & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_eq_0_iff
% 0.37/0.59 thf(fact_2840_add__nonneg__eq__0__iff,axiom,
% 0.37/0.59 ! [X: real,Y: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.59 => ( ( ( plus_plus_real @ X @ Y )
% 0.37/0.59 = zero_zero_real )
% 0.37/0.59 = ( ( X = zero_zero_real )
% 0.37/0.59 & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_eq_0_iff
% 0.37/0.59 thf(fact_2841_add__nonneg__eq__0__iff,axiom,
% 0.37/0.59 ! [X: rat,Y: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.37/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.37/0.59 => ( ( ( plus_plus_rat @ X @ Y )
% 0.37/0.59 = zero_zero_rat )
% 0.37/0.59 = ( ( X = zero_zero_rat )
% 0.37/0.59 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_eq_0_iff
% 0.37/0.59 thf(fact_2842_add__nonneg__eq__0__iff,axiom,
% 0.37/0.59 ! [X: nat,Y: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.37/0.59 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.37/0.59 => ( ( ( plus_plus_nat @ X @ Y )
% 0.37/0.59 = zero_zero_nat )
% 0.37/0.59 = ( ( X = zero_zero_nat )
% 0.37/0.59 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_eq_0_iff
% 0.37/0.59 thf(fact_2843_add__nonneg__eq__0__iff,axiom,
% 0.37/0.59 ! [X: int,Y: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.59 => ( ( ( plus_plus_int @ X @ Y )
% 0.37/0.59 = zero_zero_int )
% 0.37/0.59 = ( ( X = zero_zero_int )
% 0.37/0.59 & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_eq_0_iff
% 0.37/0.59 thf(fact_2844_add__nonpos__nonpos,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_nonpos
% 0.37/0.59 thf(fact_2845_add__nonpos__nonpos,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_nonpos
% 0.37/0.59 thf(fact_2846_add__nonpos__nonpos,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.37/0.59 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_nonpos
% 0.37/0.59 thf(fact_2847_add__nonpos__nonpos,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_nonpos
% 0.37/0.59 thf(fact_2848_add__nonneg__nonneg,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.59 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_nonneg
% 0.37/0.59 thf(fact_2849_add__nonneg__nonneg,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_nonneg
% 0.37/0.59 thf(fact_2850_add__nonneg__nonneg,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.59 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_nonneg
% 0.37/0.59 thf(fact_2851_add__nonneg__nonneg,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.59 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_nonneg
% 0.37/0.59 thf(fact_2852_add__increasing2,axiom,
% 0.37/0.59 ! [C2: real,B: real,A: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.59 => ( ( ord_less_eq_real @ B @ A )
% 0.37/0.59 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing2
% 0.37/0.59 thf(fact_2853_add__increasing2,axiom,
% 0.37/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.59 => ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.59 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing2
% 0.37/0.59 thf(fact_2854_add__increasing2,axiom,
% 0.37/0.59 ! [C2: nat,B: nat,A: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.59 => ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.59 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing2
% 0.37/0.59 thf(fact_2855_add__increasing2,axiom,
% 0.37/0.59 ! [C2: int,B: int,A: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.59 => ( ( ord_less_eq_int @ B @ A )
% 0.37/0.59 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing2
% 0.37/0.59 thf(fact_2856_add__decreasing2,axiom,
% 0.37/0.59 ! [C2: real,A: real,B: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_eq_real @ A @ B )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing2
% 0.37/0.59 thf(fact_2857_add__decreasing2,axiom,
% 0.37/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing2
% 0.37/0.59 thf(fact_2858_add__decreasing2,axiom,
% 0.37/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ C2 @ zero_zero_nat )
% 0.37/0.59 => ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing2
% 0.37/0.59 thf(fact_2859_add__decreasing2,axiom,
% 0.37/0.59 ! [C2: int,A: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_eq_int @ A @ B )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing2
% 0.37/0.59 thf(fact_2860_add__increasing,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_eq_real @ B @ C2 )
% 0.37/0.59 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing
% 0.37/0.59 thf(fact_2861_add__increasing,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.37/0.59 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing
% 0.37/0.59 thf(fact_2862_add__increasing,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.37/0.59 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing
% 0.37/0.59 thf(fact_2863_add__increasing,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_eq_int @ B @ C2 )
% 0.37/0.59 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_increasing
% 0.37/0.59 thf(fact_2864_add__decreasing,axiom,
% 0.37/0.59 ! [A: real,C2: real,B: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_eq_real @ C2 @ B )
% 0.37/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing
% 0.37/0.59 thf(fact_2865_add__decreasing,axiom,
% 0.37/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_eq_rat @ C2 @ B )
% 0.37/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing
% 0.37/0.59 thf(fact_2866_add__decreasing,axiom,
% 0.37/0.59 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.37/0.59 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing
% 0.37/0.59 thf(fact_2867_add__decreasing,axiom,
% 0.37/0.59 ! [A: int,C2: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_eq_int @ C2 @ B )
% 0.37/0.59 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_decreasing
% 0.37/0.59 thf(fact_2868_pos__add__strict,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_real @ B @ C2 )
% 0.37/0.59 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % pos_add_strict
% 0.37/0.59 thf(fact_2869_pos__add__strict,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_rat @ B @ C2 )
% 0.37/0.59 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % pos_add_strict
% 0.37/0.59 thf(fact_2870_pos__add__strict,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_nat @ B @ C2 )
% 0.37/0.59 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % pos_add_strict
% 0.37/0.59 thf(fact_2871_pos__add__strict,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_int @ B @ C2 )
% 0.37/0.59 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % pos_add_strict
% 0.37/0.59 thf(fact_2872_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ B )
% 0.37/0.59 => ~ ! [C: nat] :
% 0.37/0.59 ( ( B
% 0.37/0.59 = ( plus_plus_nat @ A @ C ) )
% 0.37/0.59 => ( C = zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % canonically_ordered_monoid_add_class.lessE
% 0.37/0.59 thf(fact_2873_add__pos__pos,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.59 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_pos
% 0.37/0.59 thf(fact_2874_add__pos__pos,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.37/0.59 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_pos
% 0.37/0.59 thf(fact_2875_add__pos__pos,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.59 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_pos
% 0.37/0.59 thf(fact_2876_add__pos__pos,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.59 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_pos
% 0.37/0.59 thf(fact_2877_add__neg__neg,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_neg
% 0.37/0.59 thf(fact_2878_add__neg__neg,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_neg
% 0.37/0.59 thf(fact_2879_add__neg__neg,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.37/0.59 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_neg
% 0.37/0.59 thf(fact_2880_add__neg__neg,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_neg
% 0.37/0.59 thf(fact_2881_add__less__zeroD,axiom,
% 0.37/0.59 ! [X: real,Y: real] :
% 0.37/0.59 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.59 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_zeroD
% 0.37/0.59 thf(fact_2882_add__less__zeroD,axiom,
% 0.37/0.59 ! [X: rat,Y: rat] :
% 0.37/0.59 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.37/0.59 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_zeroD
% 0.37/0.59 thf(fact_2883_add__less__zeroD,axiom,
% 0.37/0.59 ! [X: int,Y: int] :
% 0.37/0.59 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_int @ X @ zero_zero_int )
% 0.37/0.59 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_zeroD
% 0.37/0.59 thf(fact_2884_add__mono__thms__linordered__field_I4_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( ord_less_eq_real @ I @ J )
% 0.37/0.59 & ( ord_less_real @ K @ L ) )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(4)
% 0.37/0.59 thf(fact_2885_add__mono__thms__linordered__field_I4_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( ord_less_eq_rat @ I @ J )
% 0.37/0.59 & ( ord_less_rat @ K @ L ) )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(4)
% 0.37/0.59 thf(fact_2886_add__mono__thms__linordered__field_I4_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 & ( ord_less_nat @ K @ L ) )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(4)
% 0.37/0.59 thf(fact_2887_add__mono__thms__linordered__field_I4_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( ord_less_eq_int @ I @ J )
% 0.37/0.59 & ( ord_less_int @ K @ L ) )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(4)
% 0.37/0.59 thf(fact_2888_add__mono__thms__linordered__field_I3_J,axiom,
% 0.37/0.59 ! [I: real,J: real,K: real,L: real] :
% 0.37/0.59 ( ( ( ord_less_real @ I @ J )
% 0.37/0.59 & ( ord_less_eq_real @ K @ L ) )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(3)
% 0.37/0.59 thf(fact_2889_add__mono__thms__linordered__field_I3_J,axiom,
% 0.37/0.59 ! [I: rat,J: rat,K: rat,L: rat] :
% 0.37/0.59 ( ( ( ord_less_rat @ I @ J )
% 0.37/0.59 & ( ord_less_eq_rat @ K @ L ) )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(3)
% 0.37/0.59 thf(fact_2890_add__mono__thms__linordered__field_I3_J,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.59 ( ( ( ord_less_nat @ I @ J )
% 0.37/0.59 & ( ord_less_eq_nat @ K @ L ) )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(3)
% 0.37/0.59 thf(fact_2891_add__mono__thms__linordered__field_I3_J,axiom,
% 0.37/0.59 ! [I: int,J: int,K: int,L: int] :
% 0.37/0.59 ( ( ( ord_less_int @ I @ J )
% 0.37/0.59 & ( ord_less_eq_int @ K @ L ) )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono_thms_linordered_field(3)
% 0.37/0.59 thf(fact_2892_add__le__less__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.59 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_less_mono
% 0.37/0.59 thf(fact_2893_add__le__less__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.59 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_less_mono
% 0.37/0.59 thf(fact_2894_add__le__less__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_less_mono
% 0.37/0.59 thf(fact_2895_add__le__less__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.59 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_less_mono
% 0.37/0.59 thf(fact_2896_add__less__le__mono,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_real @ C2 @ D )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_le_mono
% 0.37/0.59 thf(fact_2897_add__less__le__mono,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_le_mono
% 0.37/0.59 thf(fact_2898_add__less__le__mono,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_le_mono
% 0.37/0.59 thf(fact_2899_add__less__le__mono,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_int @ C2 @ D )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_less_le_mono
% 0.37/0.59 thf(fact_2900_add__mono1,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ B )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono1
% 0.37/0.59 thf(fact_2901_add__mono1,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ B )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono1
% 0.37/0.59 thf(fact_2902_add__mono1,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ B )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono1
% 0.37/0.59 thf(fact_2903_add__mono1,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ B )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_mono1
% 0.37/0.59 thf(fact_2904_less__add__one,axiom,
% 0.37/0.59 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_add_one
% 0.37/0.59 thf(fact_2905_less__add__one,axiom,
% 0.37/0.59 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_add_one
% 0.37/0.59 thf(fact_2906_less__add__one,axiom,
% 0.37/0.59 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_add_one
% 0.37/0.59 thf(fact_2907_less__add__one,axiom,
% 0.37/0.59 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_add_one
% 0.37/0.59 thf(fact_2908_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( ( minus_minus_nat @ B @ A )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( B
% 0.37/0.59 = ( plus_plus_nat @ C2 @ A ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.37/0.59 thf(fact_2909_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.37/0.59 = B ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.37/0.59 thf(fact_2910_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( minus_minus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 0.37/0.59 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.37/0.59 thf(fact_2911_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A )
% 0.37/0.59 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.37/0.59 thf(fact_2912_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 )
% 0.37/0.59 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.37/0.59 thf(fact_2913_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A )
% 0.37/0.59 = ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.37/0.59 thf(fact_2914_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 0.37/0.59 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.37/0.59 thf(fact_2915_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 0.37/0.59 = ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.37/0.59 thf(fact_2916_le__add__diff,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_add_diff
% 0.37/0.59 thf(fact_2917_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.59 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.37/0.59 = B ) ) ).
% 0.37/0.59
% 0.37/0.59 % ordered_cancel_comm_monoid_diff_class.diff_add
% 0.37/0.59 thf(fact_2918_le__diff__eq,axiom,
% 0.37/0.59 ! [A: real,C2: real,B: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 0.37/0.59 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_diff_eq
% 0.37/0.59 thf(fact_2919_le__diff__eq,axiom,
% 0.37/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 0.37/0.59 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_diff_eq
% 0.37/0.59 thf(fact_2920_le__diff__eq,axiom,
% 0.37/0.59 ! [A: int,C2: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 0.37/0.59 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_diff_eq
% 0.37/0.59 thf(fact_2921_diff__le__eq,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.37/0.59 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_le_eq
% 0.37/0.59 thf(fact_2922_diff__le__eq,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.37/0.59 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_le_eq
% 0.37/0.59 thf(fact_2923_diff__le__eq,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.37/0.59 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_le_eq
% 0.37/0.59 thf(fact_2924_add__le__add__imp__diff__le,axiom,
% 0.37/0.59 ! [I: real,K: real,N: real,J: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.37/0.59 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.37/0.59 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_add_imp_diff_le
% 0.37/0.59 thf(fact_2925_add__le__add__imp__diff__le,axiom,
% 0.37/0.59 ! [I: rat,K: rat,N: rat,J: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.37/0.59 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 0.37/0.59 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_add_imp_diff_le
% 0.37/0.59 thf(fact_2926_add__le__add__imp__diff__le,axiom,
% 0.37/0.59 ! [I: nat,K: nat,N: nat,J: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.37/0.59 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.37/0.59 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_add_imp_diff_le
% 0.37/0.59 thf(fact_2927_add__le__add__imp__diff__le,axiom,
% 0.37/0.59 ! [I: int,K: int,N: int,J: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.37/0.59 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.37/0.59 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 0.37/0.59 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_add_imp_diff_le
% 0.37/0.59 thf(fact_2928_add__le__imp__le__diff,axiom,
% 0.37/0.59 ! [I: real,K: real,N: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.37/0.59 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_imp_le_diff
% 0.37/0.59 thf(fact_2929_add__le__imp__le__diff,axiom,
% 0.37/0.59 ! [I: rat,K: rat,N: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 0.37/0.59 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_imp_le_diff
% 0.37/0.59 thf(fact_2930_add__le__imp__le__diff,axiom,
% 0.37/0.59 ! [I: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.37/0.59 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_imp_le_diff
% 0.37/0.59 thf(fact_2931_add__le__imp__le__diff,axiom,
% 0.37/0.59 ! [I: int,K: int,N: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 0.37/0.59 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_le_imp_le_diff
% 0.37/0.59 thf(fact_2932_diff__less__eq,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.37/0.59 = ( ord_less_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_less_eq
% 0.37/0.59 thf(fact_2933_diff__less__eq,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.37/0.59 = ( ord_less_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_less_eq
% 0.37/0.59 thf(fact_2934_diff__less__eq,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.37/0.59 = ( ord_less_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % diff_less_eq
% 0.37/0.59 thf(fact_2935_less__diff__eq,axiom,
% 0.37/0.59 ! [A: real,C2: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 0.37/0.59 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_diff_eq
% 0.37/0.59 thf(fact_2936_less__diff__eq,axiom,
% 0.37/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 0.37/0.59 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_diff_eq
% 0.37/0.59 thf(fact_2937_less__diff__eq,axiom,
% 0.37/0.59 ! [A: int,C2: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 0.37/0.59 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_diff_eq
% 0.37/0.59 thf(fact_2938_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ~ ( ord_less_real @ A @ B )
% 0.37/0.59 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.37/0.59 = A ) ) ).
% 0.37/0.59
% 0.37/0.59 % linordered_semidom_class.add_diff_inverse
% 0.37/0.59 thf(fact_2939_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ~ ( ord_less_rat @ A @ B )
% 0.37/0.59 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.37/0.59 = A ) ) ).
% 0.37/0.59
% 0.37/0.59 % linordered_semidom_class.add_diff_inverse
% 0.37/0.59 thf(fact_2940_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ~ ( ord_less_nat @ A @ B )
% 0.37/0.59 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.37/0.59 = A ) ) ).
% 0.37/0.59
% 0.37/0.59 % linordered_semidom_class.add_diff_inverse
% 0.37/0.59 thf(fact_2941_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ~ ( ord_less_int @ A @ B )
% 0.37/0.59 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.37/0.59 = A ) ) ).
% 0.37/0.59
% 0.37/0.59 % linordered_semidom_class.add_diff_inverse
% 0.37/0.59 thf(fact_2942_Ints__odd__nonzero,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( member_real @ A @ ring_1_Ints_real )
% 0.37/0.59 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 0.37/0.59 != zero_zero_real ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_odd_nonzero
% 0.37/0.59 thf(fact_2943_Ints__odd__nonzero,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.37/0.59 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 0.37/0.59 != zero_zero_rat ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_odd_nonzero
% 0.37/0.59 thf(fact_2944_Ints__odd__nonzero,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( member_int @ A @ ring_1_Ints_int )
% 0.37/0.59 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 0.37/0.59 != zero_zero_int ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_odd_nonzero
% 0.37/0.59 thf(fact_2945_one__is__add,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ( suc @ zero_zero_nat )
% 0.37/0.59 = ( plus_plus_nat @ M @ N ) )
% 0.37/0.59 = ( ( ( M
% 0.37/0.59 = ( suc @ zero_zero_nat ) )
% 0.37/0.59 & ( N = zero_zero_nat ) )
% 0.37/0.59 | ( ( M = zero_zero_nat )
% 0.37/0.59 & ( N
% 0.37/0.59 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % one_is_add
% 0.37/0.59 thf(fact_2946_add__is__1,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ( plus_plus_nat @ M @ N )
% 0.37/0.59 = ( suc @ zero_zero_nat ) )
% 0.37/0.59 = ( ( ( M
% 0.37/0.59 = ( suc @ zero_zero_nat ) )
% 0.37/0.59 & ( N = zero_zero_nat ) )
% 0.37/0.59 | ( ( M = zero_zero_nat )
% 0.37/0.59 & ( N
% 0.37/0.59 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_is_1
% 0.37/0.59 thf(fact_2947_less__natE,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_nat @ M @ N )
% 0.37/0.59 => ~ ! [Q5: nat] :
% 0.37/0.59 ( N
% 0.37/0.59 != ( suc @ ( plus_plus_nat @ M @ Q5 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_natE
% 0.37/0.59 thf(fact_2948_less__add__Suc1,axiom,
% 0.37/0.59 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_add_Suc1
% 0.37/0.59 thf(fact_2949_less__add__Suc2,axiom,
% 0.37/0.59 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_add_Suc2
% 0.37/0.59 thf(fact_2950_less__iff__Suc__add,axiom,
% 0.37/0.59 ( ord_less_nat
% 0.37/0.59 = ( ^ [M5: nat,N6: nat] :
% 0.37/0.59 ? [K3: nat] :
% 0.37/0.59 ( N6
% 0.37/0.59 = ( suc @ ( plus_plus_nat @ M5 @ K3 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_iff_Suc_add
% 0.37/0.59 thf(fact_2951_less__imp__Suc__add,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_nat @ M @ N )
% 0.37/0.59 => ? [K2: nat] :
% 0.37/0.59 ( N
% 0.37/0.59 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_imp_Suc_add
% 0.37/0.59 thf(fact_2952_less__imp__add__positive,axiom,
% 0.37/0.59 ! [I: nat,J: nat] :
% 0.37/0.59 ( ( ord_less_nat @ I @ J )
% 0.37/0.59 => ? [K2: nat] :
% 0.37/0.59 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.37/0.59 & ( ( plus_plus_nat @ I @ K2 )
% 0.37/0.59 = J ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_imp_add_positive
% 0.37/0.59 thf(fact_2953_Suc__eq__plus1__left,axiom,
% 0.37/0.59 ( suc
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.37/0.59
% 0.37/0.59 % Suc_eq_plus1_left
% 0.37/0.59 thf(fact_2954_plus__1__eq__Suc,axiom,
% 0.37/0.59 ( ( plus_plus_nat @ one_one_nat )
% 0.37/0.59 = suc ) ).
% 0.37/0.59
% 0.37/0.59 % plus_1_eq_Suc
% 0.37/0.59 thf(fact_2955_Suc__eq__plus1,axiom,
% 0.37/0.59 ( suc
% 0.37/0.59 = ( ^ [N6: nat] : ( plus_plus_nat @ N6 @ one_one_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Suc_eq_plus1
% 0.37/0.59 thf(fact_2956_mono__nat__linear__lb,axiom,
% 0.37/0.59 ! [F: nat > nat,M: nat,K: nat] :
% 0.37/0.59 ( ! [M3: nat,N2: nat] :
% 0.37/0.59 ( ( ord_less_nat @ M3 @ N2 )
% 0.37/0.59 => ( ord_less_nat @ ( F @ M3 ) @ ( F @ N2 ) ) )
% 0.37/0.59 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mono_nat_linear_lb
% 0.37/0.59 thf(fact_2957_diff__add__0,axiom,
% 0.37/0.59 ! [N: nat,M: nat] :
% 0.37/0.59 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.37/0.59 = zero_zero_nat ) ).
% 0.37/0.59
% 0.37/0.59 % diff_add_0
% 0.37/0.59 thf(fact_2958_add__diff__inverse__nat,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ~ ( ord_less_nat @ M @ N )
% 0.37/0.59 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.59 = M ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_diff_inverse_nat
% 0.37/0.59 thf(fact_2959_less__diff__conv,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat] :
% 0.37/0.59 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.37/0.59 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_diff_conv
% 0.37/0.59 thf(fact_2960_Nat_Ole__imp__diff__is__add,axiom,
% 0.37/0.59 ! [I: nat,J: nat,K: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.59 => ( ( ( minus_minus_nat @ J @ I )
% 0.37/0.59 = K )
% 0.37/0.59 = ( J
% 0.37/0.59 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Nat.le_imp_diff_is_add
% 0.37/0.59 thf(fact_2961_Nat_Odiff__add__assoc2,axiom,
% 0.37/0.59 ! [K: nat,J: nat,I: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.59 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 0.37/0.59 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Nat.diff_add_assoc2
% 0.37/0.59 thf(fact_2962_Nat_Odiff__add__assoc,axiom,
% 0.37/0.59 ! [K: nat,J: nat,I: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.59 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.37/0.59 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Nat.diff_add_assoc
% 0.37/0.59 thf(fact_2963_Nat_Ole__diff__conv2,axiom,
% 0.37/0.59 ! [K: nat,J: nat,I: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.59 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.37/0.59 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Nat.le_diff_conv2
% 0.37/0.59 thf(fact_2964_le__diff__conv,axiom,
% 0.37/0.59 ! [J: nat,K: nat,I: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.37/0.59 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_diff_conv
% 0.37/0.59 thf(fact_2965_le__enumerate,axiom,
% 0.37/0.59 ! [S3: set_nat,N: nat] :
% 0.37/0.59 ( ~ ( finite_finite_nat @ S3 )
% 0.37/0.59 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % le_enumerate
% 0.37/0.59 thf(fact_2966_the__elem__image__unique,axiom,
% 0.37/0.59 ! [A4: set_nat,F: nat > set_nat,X: nat] :
% 0.37/0.59 ( ( A4 != bot_bot_set_nat )
% 0.37/0.59 => ( ! [Y3: nat] :
% 0.37/0.59 ( ( member_nat @ Y3 @ A4 )
% 0.37/0.59 => ( ( F @ Y3 )
% 0.37/0.59 = ( F @ X ) ) )
% 0.37/0.59 => ( ( the_elem_set_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 0.37/0.59 = ( F @ X ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % the_elem_image_unique
% 0.37/0.59 thf(fact_2967_the__elem__image__unique,axiom,
% 0.37/0.59 ! [A4: set_nat,F: nat > nat,X: nat] :
% 0.37/0.59 ( ( A4 != bot_bot_set_nat )
% 0.37/0.59 => ( ! [Y3: nat] :
% 0.37/0.59 ( ( member_nat @ Y3 @ A4 )
% 0.37/0.59 => ( ( F @ Y3 )
% 0.37/0.59 = ( F @ X ) ) )
% 0.37/0.59 => ( ( the_elem_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.59 = ( F @ X ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % the_elem_image_unique
% 0.37/0.59 thf(fact_2968_the__elem__image__unique,axiom,
% 0.37/0.59 ! [A4: set_nat,F: nat > int,X: nat] :
% 0.37/0.59 ( ( A4 != bot_bot_set_nat )
% 0.37/0.59 => ( ! [Y3: nat] :
% 0.37/0.59 ( ( member_nat @ Y3 @ A4 )
% 0.37/0.59 => ( ( F @ Y3 )
% 0.37/0.59 = ( F @ X ) ) )
% 0.37/0.59 => ( ( the_elem_int @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.59 = ( F @ X ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % the_elem_image_unique
% 0.37/0.59 thf(fact_2969_the__elem__image__unique,axiom,
% 0.37/0.59 ! [A4: set_int,F: int > nat,X: int] :
% 0.37/0.59 ( ( A4 != bot_bot_set_int )
% 0.37/0.59 => ( ! [Y3: int] :
% 0.37/0.59 ( ( member_int @ Y3 @ A4 )
% 0.37/0.59 => ( ( F @ Y3 )
% 0.37/0.59 = ( F @ X ) ) )
% 0.37/0.59 => ( ( the_elem_nat @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.59 = ( F @ X ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % the_elem_image_unique
% 0.37/0.59 thf(fact_2970_the__elem__image__unique,axiom,
% 0.37/0.59 ! [A4: set_int,F: int > int,X: int] :
% 0.37/0.59 ( ( A4 != bot_bot_set_int )
% 0.37/0.59 => ( ! [Y3: int] :
% 0.37/0.59 ( ( member_int @ Y3 @ A4 )
% 0.37/0.59 => ( ( F @ Y3 )
% 0.37/0.59 = ( F @ X ) ) )
% 0.37/0.59 => ( ( the_elem_int @ ( image_int_int @ F @ A4 ) )
% 0.37/0.59 = ( F @ X ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % the_elem_image_unique
% 0.37/0.59 thf(fact_2971_Ints__odd__less__0,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( member_real @ A @ ring_1_Ints_real )
% 0.37/0.59 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 0.37/0.59 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_odd_less_0
% 0.37/0.59 thf(fact_2972_Ints__odd__less__0,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( member_rat @ A @ ring_1_Ints_rat )
% 0.37/0.59 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 0.37/0.59 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_odd_less_0
% 0.37/0.59 thf(fact_2973_Ints__odd__less__0,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( member_int @ A @ ring_1_Ints_int )
% 0.37/0.59 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 0.37/0.59 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Ints_odd_less_0
% 0.37/0.59 thf(fact_2974_add__strict__increasing2,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_real @ B @ C2 )
% 0.37/0.59 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing2
% 0.37/0.59 thf(fact_2975_add__strict__increasing2,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_rat @ B @ C2 )
% 0.37/0.59 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing2
% 0.37/0.59 thf(fact_2976_add__strict__increasing2,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_nat @ B @ C2 )
% 0.37/0.59 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing2
% 0.37/0.59 thf(fact_2977_add__strict__increasing2,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_int @ B @ C2 )
% 0.37/0.59 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing2
% 0.37/0.59 thf(fact_2978_add__strict__increasing,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_eq_real @ B @ C2 )
% 0.37/0.59 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing
% 0.37/0.59 thf(fact_2979_add__strict__increasing,axiom,
% 0.37/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.37/0.59 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing
% 0.37/0.59 thf(fact_2980_add__strict__increasing,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.37/0.59 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing
% 0.37/0.59 thf(fact_2981_add__strict__increasing,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_eq_int @ B @ C2 )
% 0.37/0.59 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_strict_increasing
% 0.37/0.59 thf(fact_2982_add__pos__nonneg,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.59 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_nonneg
% 0.37/0.59 thf(fact_2983_add__pos__nonneg,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.59 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_nonneg
% 0.37/0.59 thf(fact_2984_add__pos__nonneg,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.59 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_nonneg
% 0.37/0.59 thf(fact_2985_add__pos__nonneg,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.59 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_pos_nonneg
% 0.37/0.59 thf(fact_2986_add__nonpos__neg,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_neg
% 0.37/0.59 thf(fact_2987_add__nonpos__neg,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_neg
% 0.37/0.59 thf(fact_2988_add__nonpos__neg,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.37/0.59 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_neg
% 0.37/0.59 thf(fact_2989_add__nonpos__neg,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonpos_neg
% 0.37/0.59 thf(fact_2990_add__nonneg__pos,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.59 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.59 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_pos
% 0.37/0.59 thf(fact_2991_add__nonneg__pos,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.59 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.37/0.59 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_pos
% 0.37/0.59 thf(fact_2992_add__nonneg__pos,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.59 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.59 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_pos
% 0.37/0.59 thf(fact_2993_add__nonneg__pos,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.59 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_nonneg_pos
% 0.37/0.59 thf(fact_2994_add__neg__nonpos,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ord_less_real @ A @ zero_zero_real )
% 0.37/0.59 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.37/0.59 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_nonpos
% 0.37/0.59 thf(fact_2995_add__neg__nonpos,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.37/0.59 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.37/0.59 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_nonpos
% 0.37/0.59 thf(fact_2996_add__neg__nonpos,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.37/0.59 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.37/0.59 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_nonpos
% 0.37/0.59 thf(fact_2997_add__neg__nonpos,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.59 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.37/0.59 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_neg_nonpos
% 0.37/0.59 thf(fact_2998_zero__less__two,axiom,
% 0.37/0.59 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.37/0.59
% 0.37/0.59 % zero_less_two
% 0.37/0.59 thf(fact_2999_zero__less__two,axiom,
% 0.37/0.59 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.37/0.59
% 0.37/0.59 % zero_less_two
% 0.37/0.59 thf(fact_3000_zero__less__two,axiom,
% 0.37/0.59 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.37/0.59
% 0.37/0.59 % zero_less_two
% 0.37/0.59 thf(fact_3001_zero__less__two,axiom,
% 0.37/0.59 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.37/0.59
% 0.37/0.59 % zero_less_two
% 0.37/0.59 thf(fact_3002_discrete,axiom,
% 0.37/0.59 ( ord_less_nat
% 0.37/0.59 = ( ^ [A7: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A7 @ one_one_nat ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % discrete
% 0.37/0.59 thf(fact_3003_discrete,axiom,
% 0.37/0.59 ( ord_less_int
% 0.37/0.59 = ( ^ [A7: int] : ( ord_less_eq_int @ ( plus_plus_int @ A7 @ one_one_int ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % discrete
% 0.37/0.59 thf(fact_3004_nat__diff__split__asm,axiom,
% 0.37/0.59 ! [P2: nat > $o,A: nat,B: nat] :
% 0.37/0.59 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 0.37/0.59 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.37/0.59 & ~ ( P2 @ zero_zero_nat ) )
% 0.37/0.59 | ? [D5: nat] :
% 0.37/0.59 ( ( A
% 0.37/0.59 = ( plus_plus_nat @ B @ D5 ) )
% 0.37/0.59 & ~ ( P2 @ D5 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % nat_diff_split_asm
% 0.37/0.59 thf(fact_3005_nat__diff__split,axiom,
% 0.37/0.59 ! [P2: nat > $o,A: nat,B: nat] :
% 0.37/0.59 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 0.37/0.59 = ( ( ( ord_less_nat @ A @ B )
% 0.37/0.59 => ( P2 @ zero_zero_nat ) )
% 0.37/0.59 & ! [D5: nat] :
% 0.37/0.59 ( ( A
% 0.37/0.59 = ( plus_plus_nat @ B @ D5 ) )
% 0.37/0.59 => ( P2 @ D5 ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % nat_diff_split
% 0.37/0.59 thf(fact_3006_less__diff__conv2,axiom,
% 0.37/0.59 ! [K: nat,J: nat,I: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ K @ J )
% 0.37/0.59 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.37/0.59 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % less_diff_conv2
% 0.37/0.59 thf(fact_3007_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 0.37/0.59 ! [Uu2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.59 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu2 @ Deg @ TreeList @ Summary ) )
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % VEBT_internal.height.simps(2)
% 0.37/0.59 thf(fact_3008_enumerate__step,axiom,
% 0.37/0.59 ! [S3: set_nat,N: nat] :
% 0.37/0.59 ( ~ ( finite_finite_nat @ S3 )
% 0.37/0.59 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % enumerate_step
% 0.37/0.59 thf(fact_3009_enumerate__mono,axiom,
% 0.37/0.59 ! [M: nat,N: nat,S3: set_nat] :
% 0.37/0.59 ( ( ord_less_nat @ M @ N )
% 0.37/0.59 => ( ~ ( finite_finite_nat @ S3 )
% 0.37/0.59 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % enumerate_mono
% 0.37/0.59 thf(fact_3010_add__eq__if,axiom,
% 0.37/0.59 ( plus_plus_nat
% 0.37/0.59 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N6 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N6 ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % add_eq_if
% 0.37/0.59 thf(fact_3011_frac__add,axiom,
% 0.37/0.59 ! [X: real,Y: real] :
% 0.37/0.59 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 0.37/0.59 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 0.37/0.59 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 0.37/0.59 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 0.37/0.59 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 0.37/0.59 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % frac_add
% 0.37/0.59 thf(fact_3012_frac__add,axiom,
% 0.37/0.59 ! [X: rat,Y: rat] :
% 0.37/0.59 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.37/0.59 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.37/0.59 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 0.37/0.59 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.37/0.59 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.37/0.59 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % frac_add
% 0.37/0.59 thf(fact_3013_VEBT__internal_Oheight_Oelims,axiom,
% 0.37/0.59 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.59 ( ( ( vEBT_VEBT_height @ X )
% 0.37/0.59 = Y )
% 0.37/0.59 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.59 ( X
% 0.37/0.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.59 => ( Y != zero_zero_nat ) )
% 0.37/0.59 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.59 => ( Y
% 0.37/0.59 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % VEBT_internal.height.elims
% 0.37/0.59 thf(fact_3014_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I3_J,axiom,
% 0.37/0.59 ! [A: $o,B: $o,Va2: nat] :
% 0.37/0.59 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(3)
% 0.37/0.59 thf(fact_3015_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 0.37/0.59 ! [Uu2: $o,B: $o] :
% 0.37/0.59 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 0.37/0.59
% 0.37/0.59 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(1)
% 0.37/0.59 thf(fact_3016_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 0.37/0.59 ! [A: $o,Uw2: $o] :
% 0.37/0.59 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 0.37/0.59
% 0.37/0.59 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(2)
% 0.37/0.59 thf(fact_3017_pred__bound__height_H,axiom,
% 0.37/0.59 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.59 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % pred_bound_height'
% 0.37/0.59 thf(fact_3018_succ_H__bound__height,axiom,
% 0.37/0.59 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.59 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % succ'_bound_height
% 0.37/0.59 thf(fact_3019_insert_H__bound__height,axiom,
% 0.37/0.59 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.59 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % insert'_bound_height
% 0.37/0.59 thf(fact_3020_member__bound__height_H,axiom,
% 0.37/0.59 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.59 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % member_bound_height'
% 0.37/0.59 thf(fact_3021_VEBT__internal_Oheight_Opelims,axiom,
% 0.37/0.59 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.59 ( ( ( vEBT_VEBT_height @ X )
% 0.37/0.59 = Y )
% 0.37/0.59 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X )
% 0.37/0.59 => ( ! [A3: $o,B3: $o] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.59 => ( ( Y = zero_zero_nat )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.59 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.59 => ( ( Y
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % VEBT_internal.height.pelims
% 0.37/0.59 thf(fact_3022_max__ins__scaled,axiom,
% 0.37/0.59 ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % max_ins_scaled
% 0.37/0.59 thf(fact_3023_field__le__epsilon,axiom,
% 0.37/0.59 ! [X: real,Y: real] :
% 0.37/0.59 ( ! [E: real] :
% 0.37/0.59 ( ( ord_less_real @ zero_zero_real @ E )
% 0.37/0.59 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E ) ) )
% 0.37/0.59 => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.59
% 0.37/0.59 % field_le_epsilon
% 0.37/0.59 thf(fact_3024_field__le__epsilon,axiom,
% 0.37/0.59 ! [X: rat,Y: rat] :
% 0.37/0.59 ( ! [E: rat] :
% 0.37/0.59 ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.37/0.59 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E ) ) )
% 0.37/0.59 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.37/0.59
% 0.37/0.59 % field_le_epsilon
% 0.37/0.59 thf(fact_3025_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 0.37/0.59 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.59 ( ( ( vEBT_T_m_i_n_t @ X )
% 0.37/0.59 = Y )
% 0.37/0.59 => ( ! [A3: $o] :
% 0.37/0.59 ( ? [B3: $o] :
% 0.37/0.59 ( X
% 0.37/0.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.59 => ( Y
% 0.37/0.59 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.37/0.59 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.59 ( X
% 0.37/0.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.59 => ( Y != one_one_nat ) )
% 0.37/0.59 => ~ ( ? [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.59 ( X
% 0.37/0.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.59 => ( Y != one_one_nat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.elims
% 0.37/0.59 thf(fact_3026_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 0.37/0.59 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.59 ( ( ( vEBT_T_m_a_x_t @ X )
% 0.37/0.59 = Y )
% 0.37/0.59 => ( ! [A3: $o,B3: $o] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.59 => ( Y
% 0.37/0.59 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.37/0.59 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.59 ( X
% 0.37/0.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.59 => ( Y != one_one_nat ) )
% 0.37/0.59 => ~ ( ? [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.59 ( X
% 0.37/0.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.59 => ( Y != one_one_nat ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.elims
% 0.37/0.59 thf(fact_3027_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 0.37/0.59 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.59 ( ( ( vEBT_T_m_i_n_t @ X )
% 0.37/0.59 = Y )
% 0.37/0.59 => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X )
% 0.37/0.59 => ( ! [A3: $o,B3: $o] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.59 => ( ( Y
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.59 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.59 => ( ( Y = one_one_nat )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.37/0.59 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.59 => ( ( Y = one_one_nat )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.pelims
% 0.37/0.59 thf(fact_3028_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 0.37/0.59 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.59 ( ( ( vEBT_T_m_a_x_t @ X )
% 0.37/0.59 = Y )
% 0.37/0.59 => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X )
% 0.37/0.59 => ( ! [A3: $o,B3: $o] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.59 => ( ( Y
% 0.37/0.59 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.59 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.59 => ( ( Y = one_one_nat )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.37/0.59 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.59 ( ( X
% 0.37/0.59 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.59 => ( ( Y = one_one_nat )
% 0.37/0.59 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.pelims
% 0.37/0.59 thf(fact_3029_Euclid__induct,axiom,
% 0.37/0.59 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 0.37/0.59 ( ! [A3: nat,B3: nat] :
% 0.37/0.59 ( ( P2 @ A3 @ B3 )
% 0.37/0.59 = ( P2 @ B3 @ A3 ) )
% 0.37/0.59 => ( ! [A3: nat] : ( P2 @ A3 @ zero_zero_nat )
% 0.37/0.59 => ( ! [A3: nat,B3: nat] :
% 0.37/0.59 ( ( P2 @ A3 @ B3 )
% 0.37/0.59 => ( P2 @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 0.37/0.59 => ( P2 @ A @ B ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % Euclid_induct
% 0.37/0.59 thf(fact_3030_triangle__Suc,axiom,
% 0.37/0.59 ! [N: nat] :
% 0.37/0.59 ( ( nat_triangle @ ( suc @ N ) )
% 0.37/0.59 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % triangle_Suc
% 0.37/0.59 thf(fact_3031_mult__cancel__right,axiom,
% 0.37/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.59 ( ( ( times_times_rat @ A @ C2 )
% 0.37/0.59 = ( times_times_rat @ B @ C2 ) )
% 0.37/0.59 = ( ( C2 = zero_zero_rat )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right
% 0.37/0.59 thf(fact_3032_mult__cancel__right,axiom,
% 0.37/0.59 ! [A: real,C2: real,B: real] :
% 0.37/0.59 ( ( ( times_times_real @ A @ C2 )
% 0.37/0.59 = ( times_times_real @ B @ C2 ) )
% 0.37/0.59 = ( ( C2 = zero_zero_real )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right
% 0.37/0.59 thf(fact_3033_mult__cancel__right,axiom,
% 0.37/0.59 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ A @ C2 )
% 0.37/0.59 = ( times_times_nat @ B @ C2 ) )
% 0.37/0.59 = ( ( C2 = zero_zero_nat )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right
% 0.37/0.59 thf(fact_3034_mult__cancel__right,axiom,
% 0.37/0.59 ! [A: int,C2: int,B: int] :
% 0.37/0.59 ( ( ( times_times_int @ A @ C2 )
% 0.37/0.59 = ( times_times_int @ B @ C2 ) )
% 0.37/0.59 = ( ( C2 = zero_zero_int )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right
% 0.37/0.59 thf(fact_3035_mult__cancel__left,axiom,
% 0.37/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.59 ( ( ( times_times_rat @ C2 @ A )
% 0.37/0.59 = ( times_times_rat @ C2 @ B ) )
% 0.37/0.59 = ( ( C2 = zero_zero_rat )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left
% 0.37/0.59 thf(fact_3036_mult__cancel__left,axiom,
% 0.37/0.59 ! [C2: real,A: real,B: real] :
% 0.37/0.59 ( ( ( times_times_real @ C2 @ A )
% 0.37/0.59 = ( times_times_real @ C2 @ B ) )
% 0.37/0.59 = ( ( C2 = zero_zero_real )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left
% 0.37/0.59 thf(fact_3037_mult__cancel__left,axiom,
% 0.37/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ C2 @ A )
% 0.37/0.59 = ( times_times_nat @ C2 @ B ) )
% 0.37/0.59 = ( ( C2 = zero_zero_nat )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left
% 0.37/0.59 thf(fact_3038_mult__cancel__left,axiom,
% 0.37/0.59 ! [C2: int,A: int,B: int] :
% 0.37/0.59 ( ( ( times_times_int @ C2 @ A )
% 0.37/0.59 = ( times_times_int @ C2 @ B ) )
% 0.37/0.59 = ( ( C2 = zero_zero_int )
% 0.37/0.59 | ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left
% 0.37/0.59 thf(fact_3039_mult__eq__0__iff,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ( times_times_rat @ A @ B )
% 0.37/0.59 = zero_zero_rat )
% 0.37/0.59 = ( ( A = zero_zero_rat )
% 0.37/0.59 | ( B = zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_eq_0_iff
% 0.37/0.59 thf(fact_3040_mult__eq__0__iff,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ( times_times_real @ A @ B )
% 0.37/0.59 = zero_zero_real )
% 0.37/0.59 = ( ( A = zero_zero_real )
% 0.37/0.59 | ( B = zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_eq_0_iff
% 0.37/0.59 thf(fact_3041_mult__eq__0__iff,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ A @ B )
% 0.37/0.59 = zero_zero_nat )
% 0.37/0.59 = ( ( A = zero_zero_nat )
% 0.37/0.59 | ( B = zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_eq_0_iff
% 0.37/0.59 thf(fact_3042_mult__eq__0__iff,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ( times_times_int @ A @ B )
% 0.37/0.59 = zero_zero_int )
% 0.37/0.59 = ( ( A = zero_zero_int )
% 0.37/0.59 | ( B = zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_eq_0_iff
% 0.37/0.59 thf(fact_3043_mult__zero__right,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( times_times_rat @ A @ zero_zero_rat )
% 0.37/0.59 = zero_zero_rat ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_right
% 0.37/0.59 thf(fact_3044_mult__zero__right,axiom,
% 0.37/0.59 ! [A: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ A @ zero_zero_uint32 )
% 0.37/0.59 = zero_zero_uint32 ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_right
% 0.37/0.59 thf(fact_3045_mult__zero__right,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( times_times_real @ A @ zero_zero_real )
% 0.37/0.59 = zero_zero_real ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_right
% 0.37/0.59 thf(fact_3046_mult__zero__right,axiom,
% 0.37/0.59 ! [A: nat] :
% 0.37/0.59 ( ( times_times_nat @ A @ zero_zero_nat )
% 0.37/0.59 = zero_zero_nat ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_right
% 0.37/0.59 thf(fact_3047_mult__zero__right,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( times_times_int @ A @ zero_zero_int )
% 0.37/0.59 = zero_zero_int ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_right
% 0.37/0.59 thf(fact_3048_mult__zero__left,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( times_times_rat @ zero_zero_rat @ A )
% 0.37/0.59 = zero_zero_rat ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_left
% 0.37/0.59 thf(fact_3049_mult__zero__left,axiom,
% 0.37/0.59 ! [A: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ zero_zero_uint32 @ A )
% 0.37/0.59 = zero_zero_uint32 ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_left
% 0.37/0.59 thf(fact_3050_mult__zero__left,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( times_times_real @ zero_zero_real @ A )
% 0.37/0.59 = zero_zero_real ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_left
% 0.37/0.59 thf(fact_3051_mult__zero__left,axiom,
% 0.37/0.59 ! [A: nat] :
% 0.37/0.59 ( ( times_times_nat @ zero_zero_nat @ A )
% 0.37/0.59 = zero_zero_nat ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_left
% 0.37/0.59 thf(fact_3052_mult__zero__left,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( times_times_int @ zero_zero_int @ A )
% 0.37/0.59 = zero_zero_int ) ).
% 0.37/0.59
% 0.37/0.59 % mult_zero_left
% 0.37/0.59 thf(fact_3053_mult_Oright__neutral,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( times_times_rat @ A @ one_one_rat )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.right_neutral
% 0.37/0.59 thf(fact_3054_mult_Oright__neutral,axiom,
% 0.37/0.59 ! [A: assn] :
% 0.37/0.59 ( ( times_times_assn @ A @ one_one_assn )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.right_neutral
% 0.37/0.59 thf(fact_3055_mult_Oright__neutral,axiom,
% 0.37/0.59 ! [A: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ A @ one_one_uint32 )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.right_neutral
% 0.37/0.59 thf(fact_3056_mult_Oright__neutral,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( times_times_real @ A @ one_one_real )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.right_neutral
% 0.37/0.59 thf(fact_3057_mult_Oright__neutral,axiom,
% 0.37/0.59 ! [A: nat] :
% 0.37/0.59 ( ( times_times_nat @ A @ one_one_nat )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.right_neutral
% 0.37/0.59 thf(fact_3058_mult_Oright__neutral,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( times_times_int @ A @ one_one_int )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.right_neutral
% 0.37/0.59 thf(fact_3059_mult__1,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( times_times_rat @ one_one_rat @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult_1
% 0.37/0.59 thf(fact_3060_mult__1,axiom,
% 0.37/0.59 ! [A: assn] :
% 0.37/0.59 ( ( times_times_assn @ one_one_assn @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult_1
% 0.37/0.59 thf(fact_3061_mult__1,axiom,
% 0.37/0.59 ! [A: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ one_one_uint32 @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult_1
% 0.37/0.59 thf(fact_3062_mult__1,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( times_times_real @ one_one_real @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult_1
% 0.37/0.59 thf(fact_3063_mult__1,axiom,
% 0.37/0.59 ! [A: nat] :
% 0.37/0.59 ( ( times_times_nat @ one_one_nat @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult_1
% 0.37/0.59 thf(fact_3064_mult__1,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( times_times_int @ one_one_int @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult_1
% 0.37/0.59 thf(fact_3065_mult__cancel2,axiom,
% 0.37/0.59 ! [M: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ M @ K )
% 0.37/0.59 = ( times_times_nat @ N @ K ) )
% 0.37/0.59 = ( ( M = N )
% 0.37/0.59 | ( K = zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel2
% 0.37/0.59 thf(fact_3066_mult__cancel1,axiom,
% 0.37/0.59 ! [K: nat,M: nat,N: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ K @ M )
% 0.37/0.59 = ( times_times_nat @ K @ N ) )
% 0.37/0.59 = ( ( M = N )
% 0.37/0.59 | ( K = zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel1
% 0.37/0.59 thf(fact_3067_mult__0__right,axiom,
% 0.37/0.59 ! [M: nat] :
% 0.37/0.59 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.37/0.59 = zero_zero_nat ) ).
% 0.37/0.59
% 0.37/0.59 % mult_0_right
% 0.37/0.59 thf(fact_3068_mult__is__0,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ M @ N )
% 0.37/0.59 = zero_zero_nat )
% 0.37/0.59 = ( ( M = zero_zero_nat )
% 0.37/0.59 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_is_0
% 0.37/0.59 thf(fact_3069_nat__1__eq__mult__iff,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( one_one_nat
% 0.37/0.59 = ( times_times_nat @ M @ N ) )
% 0.37/0.59 = ( ( M = one_one_nat )
% 0.37/0.59 & ( N = one_one_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % nat_1_eq_mult_iff
% 0.37/0.59 thf(fact_3070_nat__mult__eq__1__iff,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ M @ N )
% 0.37/0.59 = one_one_nat )
% 0.37/0.59 = ( ( M = one_one_nat )
% 0.37/0.59 & ( N = one_one_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % nat_mult_eq_1_iff
% 0.37/0.59 thf(fact_3071_triangle__0,axiom,
% 0.37/0.59 ( ( nat_triangle @ zero_zero_nat )
% 0.37/0.59 = zero_zero_nat ) ).
% 0.37/0.59
% 0.37/0.59 % triangle_0
% 0.37/0.59 thf(fact_3072_mult__cancel__right2,axiom,
% 0.37/0.59 ! [A: rat,C2: rat] :
% 0.37/0.59 ( ( ( times_times_rat @ A @ C2 )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( ( C2 = zero_zero_rat )
% 0.37/0.59 | ( A = one_one_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right2
% 0.37/0.59 thf(fact_3073_mult__cancel__right2,axiom,
% 0.37/0.59 ! [A: real,C2: real] :
% 0.37/0.59 ( ( ( times_times_real @ A @ C2 )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( ( C2 = zero_zero_real )
% 0.37/0.59 | ( A = one_one_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right2
% 0.37/0.59 thf(fact_3074_mult__cancel__right2,axiom,
% 0.37/0.59 ! [A: int,C2: int] :
% 0.37/0.59 ( ( ( times_times_int @ A @ C2 )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( ( C2 = zero_zero_int )
% 0.37/0.59 | ( A = one_one_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right2
% 0.37/0.59 thf(fact_3075_mult__cancel__right1,axiom,
% 0.37/0.59 ! [C2: rat,B: rat] :
% 0.37/0.59 ( ( C2
% 0.37/0.59 = ( times_times_rat @ B @ C2 ) )
% 0.37/0.59 = ( ( C2 = zero_zero_rat )
% 0.37/0.59 | ( B = one_one_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right1
% 0.37/0.59 thf(fact_3076_mult__cancel__right1,axiom,
% 0.37/0.59 ! [C2: real,B: real] :
% 0.37/0.59 ( ( C2
% 0.37/0.59 = ( times_times_real @ B @ C2 ) )
% 0.37/0.59 = ( ( C2 = zero_zero_real )
% 0.37/0.59 | ( B = one_one_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right1
% 0.37/0.59 thf(fact_3077_mult__cancel__right1,axiom,
% 0.37/0.59 ! [C2: int,B: int] :
% 0.37/0.59 ( ( C2
% 0.37/0.59 = ( times_times_int @ B @ C2 ) )
% 0.37/0.59 = ( ( C2 = zero_zero_int )
% 0.37/0.59 | ( B = one_one_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_right1
% 0.37/0.59 thf(fact_3078_mult__cancel__left2,axiom,
% 0.37/0.59 ! [C2: rat,A: rat] :
% 0.37/0.59 ( ( ( times_times_rat @ C2 @ A )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( ( C2 = zero_zero_rat )
% 0.37/0.59 | ( A = one_one_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left2
% 0.37/0.59 thf(fact_3079_mult__cancel__left2,axiom,
% 0.37/0.59 ! [C2: real,A: real] :
% 0.37/0.59 ( ( ( times_times_real @ C2 @ A )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( ( C2 = zero_zero_real )
% 0.37/0.59 | ( A = one_one_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left2
% 0.37/0.59 thf(fact_3080_mult__cancel__left2,axiom,
% 0.37/0.59 ! [C2: int,A: int] :
% 0.37/0.59 ( ( ( times_times_int @ C2 @ A )
% 0.37/0.59 = C2 )
% 0.37/0.59 = ( ( C2 = zero_zero_int )
% 0.37/0.59 | ( A = one_one_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left2
% 0.37/0.59 thf(fact_3081_mult__cancel__left1,axiom,
% 0.37/0.59 ! [C2: rat,B: rat] :
% 0.37/0.59 ( ( C2
% 0.37/0.59 = ( times_times_rat @ C2 @ B ) )
% 0.37/0.59 = ( ( C2 = zero_zero_rat )
% 0.37/0.59 | ( B = one_one_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left1
% 0.37/0.59 thf(fact_3082_mult__cancel__left1,axiom,
% 0.37/0.59 ! [C2: real,B: real] :
% 0.37/0.59 ( ( C2
% 0.37/0.59 = ( times_times_real @ C2 @ B ) )
% 0.37/0.59 = ( ( C2 = zero_zero_real )
% 0.37/0.59 | ( B = one_one_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left1
% 0.37/0.59 thf(fact_3083_mult__cancel__left1,axiom,
% 0.37/0.59 ! [C2: int,B: int] :
% 0.37/0.59 ( ( C2
% 0.37/0.59 = ( times_times_int @ C2 @ B ) )
% 0.37/0.59 = ( ( C2 = zero_zero_int )
% 0.37/0.59 | ( B = one_one_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_cancel_left1
% 0.37/0.59 thf(fact_3084_mult__eq__1__iff,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ M @ N )
% 0.37/0.59 = ( suc @ zero_zero_nat ) )
% 0.37/0.59 = ( ( M
% 0.37/0.59 = ( suc @ zero_zero_nat ) )
% 0.37/0.59 & ( N
% 0.37/0.59 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_eq_1_iff
% 0.37/0.59 thf(fact_3085_one__eq__mult__iff,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ( suc @ zero_zero_nat )
% 0.37/0.59 = ( times_times_nat @ M @ N ) )
% 0.37/0.59 = ( ( M
% 0.37/0.59 = ( suc @ zero_zero_nat ) )
% 0.37/0.59 & ( N
% 0.37/0.59 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % one_eq_mult_iff
% 0.37/0.59 thf(fact_3086_mult__less__cancel2,axiom,
% 0.37/0.59 ! [M: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.37/0.59 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.59 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_less_cancel2
% 0.37/0.59 thf(fact_3087_nat__0__less__mult__iff,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.37/0.59 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.59 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % nat_0_less_mult_iff
% 0.37/0.59 thf(fact_3088_mult__Suc__right,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( times_times_nat @ M @ ( suc @ N ) )
% 0.37/0.59 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_Suc_right
% 0.37/0.59 thf(fact_3089_one__le__mult__iff,axiom,
% 0.37/0.59 ! [M: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 0.37/0.59 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.37/0.59 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % one_le_mult_iff
% 0.37/0.59 thf(fact_3090_mult__le__cancel2,axiom,
% 0.37/0.59 ! [M: nat,K: nat,N: nat] :
% 0.37/0.59 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.37/0.59 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.59 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_le_cancel2
% 0.37/0.59 thf(fact_3091_mult_Oassoc,axiom,
% 0.37/0.59 ! [A: assn,B: assn,C2: assn] :
% 0.37/0.59 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C2 )
% 0.37/0.59 = ( times_times_assn @ A @ ( times_times_assn @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult.assoc
% 0.37/0.59 thf(fact_3092_mult_Oassoc,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32,C2: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ ( times_times_uint32 @ A @ B ) @ C2 )
% 0.37/0.59 = ( times_times_uint32 @ A @ ( times_times_uint32 @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult.assoc
% 0.37/0.59 thf(fact_3093_mult_Oassoc,axiom,
% 0.37/0.59 ! [A: real,B: real,C2: real] :
% 0.37/0.59 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 0.37/0.59 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult.assoc
% 0.37/0.59 thf(fact_3094_mult_Oassoc,axiom,
% 0.37/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.59 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.37/0.59 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult.assoc
% 0.37/0.59 thf(fact_3095_mult_Oassoc,axiom,
% 0.37/0.59 ! [A: int,B: int,C2: int] :
% 0.37/0.59 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.37/0.59 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult.assoc
% 0.37/0.59 thf(fact_3096_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.37/0.59 ( times_times_assn
% 0.37/0.59 = ( ^ [A7: assn,B7: assn] : ( times_times_assn @ B7 @ A7 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.commute
% 0.37/0.59 thf(fact_3097_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.37/0.59 ( times_times_uint32
% 0.37/0.59 = ( ^ [A7: uint32,B7: uint32] : ( times_times_uint32 @ B7 @ A7 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.commute
% 0.37/0.59 thf(fact_3098_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.37/0.59 ( times_times_real
% 0.37/0.59 = ( ^ [A7: real,B7: real] : ( times_times_real @ B7 @ A7 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.commute
% 0.37/0.59 thf(fact_3099_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.37/0.59 ( times_times_nat
% 0.37/0.59 = ( ^ [A7: nat,B7: nat] : ( times_times_nat @ B7 @ A7 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.commute
% 0.37/0.59 thf(fact_3100_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.37/0.59 ( times_times_int
% 0.37/0.59 = ( ^ [A7: int,B7: int] : ( times_times_int @ B7 @ A7 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.commute
% 0.37/0.59 thf(fact_3101_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.37/0.59 ! [B: assn,A: assn,C2: assn] :
% 0.37/0.59 ( ( times_times_assn @ B @ ( times_times_assn @ A @ C2 ) )
% 0.37/0.59 = ( times_times_assn @ A @ ( times_times_assn @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.left_commute
% 0.37/0.59 thf(fact_3102_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.37/0.59 ! [B: uint32,A: uint32,C2: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ B @ ( times_times_uint32 @ A @ C2 ) )
% 0.37/0.59 = ( times_times_uint32 @ A @ ( times_times_uint32 @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.left_commute
% 0.37/0.59 thf(fact_3103_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.37/0.59 ! [B: real,A: real,C2: real] :
% 0.37/0.59 ( ( times_times_real @ B @ ( times_times_real @ A @ C2 ) )
% 0.37/0.59 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.left_commute
% 0.37/0.59 thf(fact_3104_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.37/0.59 ! [B: nat,A: nat,C2: nat] :
% 0.37/0.59 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C2 ) )
% 0.37/0.59 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.left_commute
% 0.37/0.59 thf(fact_3105_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.37/0.59 ! [B: int,A: int,C2: int] :
% 0.37/0.59 ( ( times_times_int @ B @ ( times_times_int @ A @ C2 ) )
% 0.37/0.59 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % ab_semigroup_mult_class.mult.left_commute
% 0.37/0.59 thf(fact_3106_mult__right__cancel,axiom,
% 0.37/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.59 ( ( C2 != zero_zero_rat )
% 0.37/0.59 => ( ( ( times_times_rat @ A @ C2 )
% 0.37/0.59 = ( times_times_rat @ B @ C2 ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_right_cancel
% 0.37/0.59 thf(fact_3107_mult__right__cancel,axiom,
% 0.37/0.59 ! [C2: real,A: real,B: real] :
% 0.37/0.59 ( ( C2 != zero_zero_real )
% 0.37/0.59 => ( ( ( times_times_real @ A @ C2 )
% 0.37/0.59 = ( times_times_real @ B @ C2 ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_right_cancel
% 0.37/0.59 thf(fact_3108_mult__right__cancel,axiom,
% 0.37/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.59 ( ( C2 != zero_zero_nat )
% 0.37/0.59 => ( ( ( times_times_nat @ A @ C2 )
% 0.37/0.59 = ( times_times_nat @ B @ C2 ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_right_cancel
% 0.37/0.59 thf(fact_3109_mult__right__cancel,axiom,
% 0.37/0.59 ! [C2: int,A: int,B: int] :
% 0.37/0.59 ( ( C2 != zero_zero_int )
% 0.37/0.59 => ( ( ( times_times_int @ A @ C2 )
% 0.37/0.59 = ( times_times_int @ B @ C2 ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_right_cancel
% 0.37/0.59 thf(fact_3110_mult__left__cancel,axiom,
% 0.37/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.59 ( ( C2 != zero_zero_rat )
% 0.37/0.59 => ( ( ( times_times_rat @ C2 @ A )
% 0.37/0.59 = ( times_times_rat @ C2 @ B ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_left_cancel
% 0.37/0.59 thf(fact_3111_mult__left__cancel,axiom,
% 0.37/0.59 ! [C2: real,A: real,B: real] :
% 0.37/0.59 ( ( C2 != zero_zero_real )
% 0.37/0.59 => ( ( ( times_times_real @ C2 @ A )
% 0.37/0.59 = ( times_times_real @ C2 @ B ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_left_cancel
% 0.37/0.59 thf(fact_3112_mult__left__cancel,axiom,
% 0.37/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.59 ( ( C2 != zero_zero_nat )
% 0.37/0.59 => ( ( ( times_times_nat @ C2 @ A )
% 0.37/0.59 = ( times_times_nat @ C2 @ B ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_left_cancel
% 0.37/0.59 thf(fact_3113_mult__left__cancel,axiom,
% 0.37/0.59 ! [C2: int,A: int,B: int] :
% 0.37/0.59 ( ( C2 != zero_zero_int )
% 0.37/0.59 => ( ( ( times_times_int @ C2 @ A )
% 0.37/0.59 = ( times_times_int @ C2 @ B ) )
% 0.37/0.59 = ( A = B ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_left_cancel
% 0.37/0.59 thf(fact_3114_no__zero__divisors,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( A != zero_zero_rat )
% 0.37/0.59 => ( ( B != zero_zero_rat )
% 0.37/0.59 => ( ( times_times_rat @ A @ B )
% 0.37/0.59 != zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % no_zero_divisors
% 0.37/0.59 thf(fact_3115_no__zero__divisors,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( A != zero_zero_real )
% 0.37/0.59 => ( ( B != zero_zero_real )
% 0.37/0.59 => ( ( times_times_real @ A @ B )
% 0.37/0.59 != zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % no_zero_divisors
% 0.37/0.59 thf(fact_3116_no__zero__divisors,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( A != zero_zero_nat )
% 0.37/0.59 => ( ( B != zero_zero_nat )
% 0.37/0.59 => ( ( times_times_nat @ A @ B )
% 0.37/0.59 != zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % no_zero_divisors
% 0.37/0.59 thf(fact_3117_no__zero__divisors,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( A != zero_zero_int )
% 0.37/0.59 => ( ( B != zero_zero_int )
% 0.37/0.59 => ( ( times_times_int @ A @ B )
% 0.37/0.59 != zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % no_zero_divisors
% 0.37/0.59 thf(fact_3118_divisors__zero,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ( times_times_rat @ A @ B )
% 0.37/0.59 = zero_zero_rat )
% 0.37/0.59 => ( ( A = zero_zero_rat )
% 0.37/0.59 | ( B = zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % divisors_zero
% 0.37/0.59 thf(fact_3119_divisors__zero,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ( times_times_real @ A @ B )
% 0.37/0.59 = zero_zero_real )
% 0.37/0.59 => ( ( A = zero_zero_real )
% 0.37/0.59 | ( B = zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % divisors_zero
% 0.37/0.59 thf(fact_3120_divisors__zero,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ A @ B )
% 0.37/0.59 = zero_zero_nat )
% 0.37/0.59 => ( ( A = zero_zero_nat )
% 0.37/0.59 | ( B = zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % divisors_zero
% 0.37/0.59 thf(fact_3121_divisors__zero,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ( times_times_int @ A @ B )
% 0.37/0.59 = zero_zero_int )
% 0.37/0.59 => ( ( A = zero_zero_int )
% 0.37/0.59 | ( B = zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % divisors_zero
% 0.37/0.59 thf(fact_3122_mult__not__zero,axiom,
% 0.37/0.59 ! [A: rat,B: rat] :
% 0.37/0.59 ( ( ( times_times_rat @ A @ B )
% 0.37/0.59 != zero_zero_rat )
% 0.37/0.59 => ( ( A != zero_zero_rat )
% 0.37/0.59 & ( B != zero_zero_rat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_not_zero
% 0.37/0.59 thf(fact_3123_mult__not__zero,axiom,
% 0.37/0.59 ! [A: uint32,B: uint32] :
% 0.37/0.59 ( ( ( times_times_uint32 @ A @ B )
% 0.37/0.59 != zero_zero_uint32 )
% 0.37/0.59 => ( ( A != zero_zero_uint32 )
% 0.37/0.59 & ( B != zero_zero_uint32 ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_not_zero
% 0.37/0.59 thf(fact_3124_mult__not__zero,axiom,
% 0.37/0.59 ! [A: real,B: real] :
% 0.37/0.59 ( ( ( times_times_real @ A @ B )
% 0.37/0.59 != zero_zero_real )
% 0.37/0.59 => ( ( A != zero_zero_real )
% 0.37/0.59 & ( B != zero_zero_real ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_not_zero
% 0.37/0.59 thf(fact_3125_mult__not__zero,axiom,
% 0.37/0.59 ! [A: nat,B: nat] :
% 0.37/0.59 ( ( ( times_times_nat @ A @ B )
% 0.37/0.59 != zero_zero_nat )
% 0.37/0.59 => ( ( A != zero_zero_nat )
% 0.37/0.59 & ( B != zero_zero_nat ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_not_zero
% 0.37/0.59 thf(fact_3126_mult__not__zero,axiom,
% 0.37/0.59 ! [A: int,B: int] :
% 0.37/0.59 ( ( ( times_times_int @ A @ B )
% 0.37/0.59 != zero_zero_int )
% 0.37/0.59 => ( ( A != zero_zero_int )
% 0.37/0.59 & ( B != zero_zero_int ) ) ) ).
% 0.37/0.59
% 0.37/0.59 % mult_not_zero
% 0.37/0.59 thf(fact_3127_comm__monoid__mult__class_Omult__1,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( times_times_rat @ one_one_rat @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % comm_monoid_mult_class.mult_1
% 0.37/0.59 thf(fact_3128_comm__monoid__mult__class_Omult__1,axiom,
% 0.37/0.59 ! [A: assn] :
% 0.37/0.59 ( ( times_times_assn @ one_one_assn @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % comm_monoid_mult_class.mult_1
% 0.37/0.59 thf(fact_3129_comm__monoid__mult__class_Omult__1,axiom,
% 0.37/0.59 ! [A: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ one_one_uint32 @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % comm_monoid_mult_class.mult_1
% 0.37/0.59 thf(fact_3130_comm__monoid__mult__class_Omult__1,axiom,
% 0.37/0.59 ! [A: real] :
% 0.37/0.59 ( ( times_times_real @ one_one_real @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % comm_monoid_mult_class.mult_1
% 0.37/0.59 thf(fact_3131_comm__monoid__mult__class_Omult__1,axiom,
% 0.37/0.59 ! [A: nat] :
% 0.37/0.59 ( ( times_times_nat @ one_one_nat @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % comm_monoid_mult_class.mult_1
% 0.37/0.59 thf(fact_3132_comm__monoid__mult__class_Omult__1,axiom,
% 0.37/0.59 ! [A: int] :
% 0.37/0.59 ( ( times_times_int @ one_one_int @ A )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % comm_monoid_mult_class.mult_1
% 0.37/0.59 thf(fact_3133_mult_Ocomm__neutral,axiom,
% 0.37/0.59 ! [A: rat] :
% 0.37/0.59 ( ( times_times_rat @ A @ one_one_rat )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.comm_neutral
% 0.37/0.59 thf(fact_3134_mult_Ocomm__neutral,axiom,
% 0.37/0.59 ! [A: assn] :
% 0.37/0.59 ( ( times_times_assn @ A @ one_one_assn )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.comm_neutral
% 0.37/0.59 thf(fact_3135_mult_Ocomm__neutral,axiom,
% 0.37/0.59 ! [A: uint32] :
% 0.37/0.59 ( ( times_times_uint32 @ A @ one_one_uint32 )
% 0.37/0.59 = A ) ).
% 0.37/0.59
% 0.37/0.59 % mult.comm_neutral
% 0.37/0.59 thf(fact_3136_mult_Ocomm__neutral,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( times_times_real @ A @ one_one_real )
% 0.37/0.60 = A ) ).
% 0.37/0.60
% 0.37/0.60 % mult.comm_neutral
% 0.37/0.60 thf(fact_3137_mult_Ocomm__neutral,axiom,
% 0.37/0.60 ! [A: nat] :
% 0.37/0.60 ( ( times_times_nat @ A @ one_one_nat )
% 0.37/0.60 = A ) ).
% 0.37/0.60
% 0.37/0.60 % mult.comm_neutral
% 0.37/0.60 thf(fact_3138_mult_Ocomm__neutral,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( times_times_int @ A @ one_one_int )
% 0.37/0.60 = A ) ).
% 0.37/0.60
% 0.37/0.60 % mult.comm_neutral
% 0.37/0.60 thf(fact_3139_Suc__mult__cancel1,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.37/0.60 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.37/0.60 = ( M = N ) ) ).
% 0.37/0.60
% 0.37/0.60 % Suc_mult_cancel1
% 0.37/0.60 thf(fact_3140_mult__0,axiom,
% 0.37/0.60 ! [N: nat] :
% 0.37/0.60 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.37/0.60 = zero_zero_nat ) ).
% 0.37/0.60
% 0.37/0.60 % mult_0
% 0.37/0.60 thf(fact_3141_add__mult__distrib,axiom,
% 0.37/0.60 ! [M: nat,N: nat,K: nat] :
% 0.37/0.60 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.37/0.60 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_mult_distrib
% 0.37/0.60 thf(fact_3142_add__mult__distrib2,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.37/0.60 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_mult_distrib2
% 0.37/0.60 thf(fact_3143_le__cube,axiom,
% 0.37/0.60 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_cube
% 0.37/0.60 thf(fact_3144_le__square,axiom,
% 0.37/0.60 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_square
% 0.37/0.60 thf(fact_3145_mult__le__mono,axiom,
% 0.37/0.60 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.60 => ( ( ord_less_eq_nat @ K @ L )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_mono
% 0.37/0.60 thf(fact_3146_mult__le__mono1,axiom,
% 0.37/0.60 ! [I: nat,J: nat,K: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_mono1
% 0.37/0.60 thf(fact_3147_mult__le__mono2,axiom,
% 0.37/0.60 ! [I: nat,J: nat,K: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_mono2
% 0.37/0.60 thf(fact_3148_nat__mult__1,axiom,
% 0.37/0.60 ! [N: nat] :
% 0.37/0.60 ( ( times_times_nat @ one_one_nat @ N )
% 0.37/0.60 = N ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_1
% 0.37/0.60 thf(fact_3149_nat__mult__1__right,axiom,
% 0.37/0.60 ! [N: nat] :
% 0.37/0.60 ( ( times_times_nat @ N @ one_one_nat )
% 0.37/0.60 = N ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_1_right
% 0.37/0.60 thf(fact_3150_diff__mult__distrib,axiom,
% 0.37/0.60 ! [M: nat,N: nat,K: nat] :
% 0.37/0.60 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.37/0.60 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_mult_distrib
% 0.37/0.60 thf(fact_3151_diff__mult__distrib2,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.60 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_mult_distrib2
% 0.37/0.60 thf(fact_3152_zero__notin__Suc__image,axiom,
% 0.37/0.60 ! [A4: set_nat] :
% 0.37/0.60 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_notin_Suc_image
% 0.37/0.60 thf(fact_3153_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.37/0.60 thf(fact_3154_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.37/0.60 thf(fact_3155_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.37/0.60 thf(fact_3156_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.37/0.60 thf(fact_3157_zero__le__mult__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.37/0.60 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.60 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_le_mult_iff
% 0.37/0.60 thf(fact_3158_zero__le__mult__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.37/0.60 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_le_mult_iff
% 0.37/0.60 thf(fact_3159_zero__le__mult__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.37/0.60 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.60 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_le_mult_iff
% 0.37/0.60 thf(fact_3160_mult__nonneg__nonpos2,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos2
% 0.37/0.60 thf(fact_3161_mult__nonneg__nonpos2,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos2
% 0.37/0.60 thf(fact_3162_mult__nonneg__nonpos2,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos2
% 0.37/0.60 thf(fact_3163_mult__nonneg__nonpos2,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos2
% 0.37/0.60 thf(fact_3164_mult__nonpos__nonneg,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonpos_nonneg
% 0.37/0.60 thf(fact_3165_mult__nonpos__nonneg,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonpos_nonneg
% 0.37/0.60 thf(fact_3166_mult__nonpos__nonneg,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonpos_nonneg
% 0.37/0.60 thf(fact_3167_mult__nonpos__nonneg,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonpos_nonneg
% 0.37/0.60 thf(fact_3168_mult__nonneg__nonpos,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos
% 0.37/0.60 thf(fact_3169_mult__nonneg__nonpos,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos
% 0.37/0.60 thf(fact_3170_mult__nonneg__nonpos,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos
% 0.37/0.60 thf(fact_3171_mult__nonneg__nonpos,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonpos
% 0.37/0.60 thf(fact_3172_mult__nonneg__nonneg,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.60 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonneg
% 0.37/0.60 thf(fact_3173_mult__nonneg__nonneg,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonneg
% 0.37/0.60 thf(fact_3174_mult__nonneg__nonneg,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.60 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonneg
% 0.37/0.60 thf(fact_3175_mult__nonneg__nonneg,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.60 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonneg_nonneg
% 0.37/0.60 thf(fact_3176_split__mult__neg__le,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.37/0.60 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.60 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % split_mult_neg_le
% 0.37/0.60 thf(fact_3177_split__mult__neg__le,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.37/0.60 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % split_mult_neg_le
% 0.37/0.60 thf(fact_3178_split__mult__neg__le,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.37/0.60 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.37/0.60 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.37/0.60
% 0.37/0.60 % split_mult_neg_le
% 0.37/0.60 thf(fact_3179_split__mult__neg__le,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.37/0.60 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.60 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % split_mult_neg_le
% 0.37/0.60 thf(fact_3180_mult__le__0__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.37/0.60 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.60 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_0_iff
% 0.37/0.60 thf(fact_3181_mult__le__0__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.37/0.60 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_0_iff
% 0.37/0.60 thf(fact_3182_mult__le__0__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.37/0.60 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.60 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_0_iff
% 0.37/0.60 thf(fact_3183_mult__right__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_mono
% 0.37/0.60 thf(fact_3184_mult__right__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_mono
% 0.37/0.60 thf(fact_3185_mult__right__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_mono
% 0.37/0.60 thf(fact_3186_mult__right__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_mono
% 0.37/0.60 thf(fact_3187_mult__right__mono__neg,axiom,
% 0.37/0.60 ! [B: real,A: real,C2: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ B @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_mono_neg
% 0.37/0.60 thf(fact_3188_mult__right__mono__neg,axiom,
% 0.37/0.60 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_mono_neg
% 0.37/0.60 thf(fact_3189_mult__right__mono__neg,axiom,
% 0.37/0.60 ! [B: int,A: int,C2: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_mono_neg
% 0.37/0.60 thf(fact_3190_mult__left__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_mono
% 0.37/0.60 thf(fact_3191_mult__left__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_mono
% 0.37/0.60 thf(fact_3192_mult__left__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_mono
% 0.37/0.60 thf(fact_3193_mult__left__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_mono
% 0.37/0.60 thf(fact_3194_mult__nonpos__nonpos,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.60 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonpos_nonpos
% 0.37/0.60 thf(fact_3195_mult__nonpos__nonpos,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.60 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonpos_nonpos
% 0.37/0.60 thf(fact_3196_mult__nonpos__nonpos,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.60 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_nonpos_nonpos
% 0.37/0.60 thf(fact_3197_mult__left__mono__neg,axiom,
% 0.37/0.60 ! [B: real,A: real,C2: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ B @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_mono_neg
% 0.37/0.60 thf(fact_3198_mult__left__mono__neg,axiom,
% 0.37/0.60 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_mono_neg
% 0.37/0.60 thf(fact_3199_mult__left__mono__neg,axiom,
% 0.37/0.60 ! [B: int,A: int,C2: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_mono_neg
% 0.37/0.60 thf(fact_3200_split__mult__pos__le,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.37/0.60 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.60 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.37/0.60 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % split_mult_pos_le
% 0.37/0.60 thf(fact_3201_split__mult__pos__le,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.37/0.60 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.37/0.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % split_mult_pos_le
% 0.37/0.60 thf(fact_3202_split__mult__pos__le,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.37/0.60 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.60 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.37/0.60 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % split_mult_pos_le
% 0.37/0.60 thf(fact_3203_zero__le__square,axiom,
% 0.37/0.60 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_le_square
% 0.37/0.60 thf(fact_3204_zero__le__square,axiom,
% 0.37/0.60 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_le_square
% 0.37/0.60 thf(fact_3205_zero__le__square,axiom,
% 0.37/0.60 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_le_square
% 0.37/0.60 thf(fact_3206_mult__mono_H,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono'
% 0.37/0.60 thf(fact_3207_mult__mono_H,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono'
% 0.37/0.60 thf(fact_3208_mult__mono_H,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono'
% 0.37/0.60 thf(fact_3209_mult__mono_H,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono'
% 0.37/0.60 thf(fact_3210_mult__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono
% 0.37/0.60 thf(fact_3211_mult__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono
% 0.37/0.60 thf(fact_3212_mult__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono
% 0.37/0.60 thf(fact_3213_mult__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_mono
% 0.37/0.60 thf(fact_3214_mult__neg__neg,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ zero_zero_real )
% 0.37/0.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_neg_neg
% 0.37/0.60 thf(fact_3215_mult__neg__neg,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.37/0.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_neg_neg
% 0.37/0.60 thf(fact_3216_mult__neg__neg,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.60 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_neg_neg
% 0.37/0.60 thf(fact_3217_not__square__less__zero,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % not_square_less_zero
% 0.37/0.60 thf(fact_3218_not__square__less__zero,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % not_square_less_zero
% 0.37/0.60 thf(fact_3219_not__square__less__zero,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % not_square_less_zero
% 0.37/0.60 thf(fact_3220_mult__less__0__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 & ( ord_less_real @ B @ zero_zero_real ) )
% 0.37/0.60 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.37/0.60 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_0_iff
% 0.37/0.60 thf(fact_3221_mult__less__0__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.37/0.60 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_0_iff
% 0.37/0.60 thf(fact_3222_mult__less__0__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 & ( ord_less_int @ B @ zero_zero_int ) )
% 0.37/0.60 | ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.60 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_0_iff
% 0.37/0.60 thf(fact_3223_mult__neg__pos,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ zero_zero_real )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_neg_pos
% 0.37/0.60 thf(fact_3224_mult__neg__pos,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_neg_pos
% 0.37/0.60 thf(fact_3225_mult__neg__pos,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_neg_pos
% 0.37/0.60 thf(fact_3226_mult__neg__pos,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_neg_pos
% 0.37/0.60 thf(fact_3227_mult__pos__neg,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg
% 0.37/0.60 thf(fact_3228_mult__pos__neg,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg
% 0.37/0.60 thf(fact_3229_mult__pos__neg,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg
% 0.37/0.60 thf(fact_3230_mult__pos__neg,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg
% 0.37/0.60 thf(fact_3231_mult__pos__pos,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.60 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_pos
% 0.37/0.60 thf(fact_3232_mult__pos__pos,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.37/0.60 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_pos
% 0.37/0.60 thf(fact_3233_mult__pos__pos,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.60 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_pos
% 0.37/0.60 thf(fact_3234_mult__pos__pos,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.60 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_pos
% 0.37/0.60 thf(fact_3235_mult__pos__neg2,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg2
% 0.37/0.60 thf(fact_3236_mult__pos__neg2,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg2
% 0.37/0.60 thf(fact_3237_mult__pos__neg2,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg2
% 0.37/0.60 thf(fact_3238_mult__pos__neg2,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_pos_neg2
% 0.37/0.60 thf(fact_3239_zero__less__mult__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 & ( ord_less_real @ zero_zero_real @ B ) )
% 0.37/0.60 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.37/0.60 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_iff
% 0.37/0.60 thf(fact_3240_zero__less__mult__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.37/0.60 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_iff
% 0.37/0.60 thf(fact_3241_zero__less__mult__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 & ( ord_less_int @ zero_zero_int @ B ) )
% 0.37/0.60 | ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.60 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_iff
% 0.37/0.60 thf(fact_3242_zero__less__mult__pos,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos
% 0.37/0.60 thf(fact_3243_zero__less__mult__pos,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos
% 0.37/0.60 thf(fact_3244_zero__less__mult__pos,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos
% 0.37/0.60 thf(fact_3245_zero__less__mult__pos,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos
% 0.37/0.60 thf(fact_3246_zero__less__mult__pos2,axiom,
% 0.37/0.60 ! [B: real,A: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos2
% 0.37/0.60 thf(fact_3247_zero__less__mult__pos2,axiom,
% 0.37/0.60 ! [B: rat,A: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos2
% 0.37/0.60 thf(fact_3248_zero__less__mult__pos2,axiom,
% 0.37/0.60 ! [B: nat,A: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos2
% 0.37/0.60 thf(fact_3249_zero__less__mult__pos2,axiom,
% 0.37/0.60 ! [B: int,A: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % zero_less_mult_pos2
% 0.37/0.60 thf(fact_3250_mult__less__cancel__left__neg,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_real @ B @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_neg
% 0.37/0.60 thf(fact_3251_mult__less__cancel__left__neg,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_rat @ B @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_neg
% 0.37/0.60 thf(fact_3252_mult__less__cancel__left__neg,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_int @ B @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_neg
% 0.37/0.60 thf(fact_3253_mult__less__cancel__left__pos,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_pos
% 0.37/0.60 thf(fact_3254_mult__less__cancel__left__pos,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_rat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_pos
% 0.37/0.60 thf(fact_3255_mult__less__cancel__left__pos,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_int @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_pos
% 0.37/0.60 thf(fact_3256_mult__strict__left__mono__neg,axiom,
% 0.37/0.60 ! [B: real,A: real,C2: real] :
% 0.37/0.60 ( ( ord_less_real @ B @ A )
% 0.37/0.60 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_left_mono_neg
% 0.37/0.60 thf(fact_3257_mult__strict__left__mono__neg,axiom,
% 0.37/0.60 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_rat @ B @ A )
% 0.37/0.60 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_left_mono_neg
% 0.37/0.60 thf(fact_3258_mult__strict__left__mono__neg,axiom,
% 0.37/0.60 ! [B: int,A: int,C2: int] :
% 0.37/0.60 ( ( ord_less_int @ B @ A )
% 0.37/0.60 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_left_mono_neg
% 0.37/0.60 thf(fact_3259_mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_left_mono
% 0.37/0.60 thf(fact_3260_mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_left_mono
% 0.37/0.60 thf(fact_3261_mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_left_mono
% 0.37/0.60 thf(fact_3262_mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_left_mono
% 0.37/0.60 thf(fact_3263_mult__less__cancel__left__disj,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 & ( ord_less_real @ A @ B ) )
% 0.37/0.60 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_disj
% 0.37/0.60 thf(fact_3264_mult__less__cancel__left__disj,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 & ( ord_less_rat @ A @ B ) )
% 0.37/0.60 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_disj
% 0.37/0.60 thf(fact_3265_mult__less__cancel__left__disj,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 & ( ord_less_int @ A @ B ) )
% 0.37/0.60 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left_disj
% 0.37/0.60 thf(fact_3266_mult__strict__right__mono__neg,axiom,
% 0.37/0.60 ! [B: real,A: real,C2: real] :
% 0.37/0.60 ( ( ord_less_real @ B @ A )
% 0.37/0.60 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_right_mono_neg
% 0.37/0.60 thf(fact_3267_mult__strict__right__mono__neg,axiom,
% 0.37/0.60 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_rat @ B @ A )
% 0.37/0.60 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_right_mono_neg
% 0.37/0.60 thf(fact_3268_mult__strict__right__mono__neg,axiom,
% 0.37/0.60 ! [B: int,A: int,C2: int] :
% 0.37/0.60 ( ( ord_less_int @ B @ A )
% 0.37/0.60 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_right_mono_neg
% 0.37/0.60 thf(fact_3269_mult__strict__right__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_right_mono
% 0.37/0.60 thf(fact_3270_mult__strict__right__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_right_mono
% 0.37/0.60 thf(fact_3271_mult__strict__right__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_right_mono
% 0.37/0.60 thf(fact_3272_mult__strict__right__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_right_mono
% 0.37/0.60 thf(fact_3273_mult__less__cancel__right__disj,axiom,
% 0.37/0.60 ! [A: real,C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 & ( ord_less_real @ A @ B ) )
% 0.37/0.60 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right_disj
% 0.37/0.60 thf(fact_3274_mult__less__cancel__right__disj,axiom,
% 0.37/0.60 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 & ( ord_less_rat @ A @ B ) )
% 0.37/0.60 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right_disj
% 0.37/0.60 thf(fact_3275_mult__less__cancel__right__disj,axiom,
% 0.37/0.60 ! [A: int,C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 & ( ord_less_int @ A @ B ) )
% 0.37/0.60 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right_disj
% 0.37/0.60 thf(fact_3276_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.37/0.60 thf(fact_3277_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.37/0.60 thf(fact_3278_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.37/0.60 thf(fact_3279_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.37/0.60 thf(fact_3280_less__1__mult,axiom,
% 0.37/0.60 ! [M: real,N: real] :
% 0.37/0.60 ( ( ord_less_real @ one_one_real @ M )
% 0.37/0.60 => ( ( ord_less_real @ one_one_real @ N )
% 0.37/0.60 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_1_mult
% 0.37/0.60 thf(fact_3281_less__1__mult,axiom,
% 0.37/0.60 ! [M: rat,N: rat] :
% 0.37/0.60 ( ( ord_less_rat @ one_one_rat @ M )
% 0.37/0.60 => ( ( ord_less_rat @ one_one_rat @ N )
% 0.37/0.60 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_1_mult
% 0.37/0.60 thf(fact_3282_less__1__mult,axiom,
% 0.37/0.60 ! [M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_nat @ one_one_nat @ M )
% 0.37/0.60 => ( ( ord_less_nat @ one_one_nat @ N )
% 0.37/0.60 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_1_mult
% 0.37/0.60 thf(fact_3283_less__1__mult,axiom,
% 0.37/0.60 ! [M: int,N: int] :
% 0.37/0.60 ( ( ord_less_int @ one_one_int @ M )
% 0.37/0.60 => ( ( ord_less_int @ one_one_int @ N )
% 0.37/0.60 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_1_mult
% 0.37/0.60 thf(fact_3284_Suc__mult__less__cancel1,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.37/0.60 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.60
% 0.37/0.60 % Suc_mult_less_cancel1
% 0.37/0.60 thf(fact_3285_mult__less__mono1,axiom,
% 0.37/0.60 ! [I: nat,J: nat,K: nat] :
% 0.37/0.60 ( ( ord_less_nat @ I @ J )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_mono1
% 0.37/0.60 thf(fact_3286_mult__less__mono2,axiom,
% 0.37/0.60 ! [I: nat,J: nat,K: nat] :
% 0.37/0.60 ( ( ord_less_nat @ I @ J )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_mono2
% 0.37/0.60 thf(fact_3287_mult__Suc,axiom,
% 0.37/0.60 ! [M: nat,N: nat] :
% 0.37/0.60 ( ( times_times_nat @ ( suc @ M ) @ N )
% 0.37/0.60 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_Suc
% 0.37/0.60 thf(fact_3288_Suc__mult__le__cancel1,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.37/0.60 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.60
% 0.37/0.60 % Suc_mult_le_cancel1
% 0.37/0.60 thf(fact_3289_mult__eq__self__implies__10,axiom,
% 0.37/0.60 ! [M: nat,N: nat] :
% 0.37/0.60 ( ( M
% 0.37/0.60 = ( times_times_nat @ M @ N ) )
% 0.37/0.60 => ( ( N = one_one_nat )
% 0.37/0.60 | ( M = zero_zero_nat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_eq_self_implies_10
% 0.37/0.60 thf(fact_3290_mlex__snd__decrI,axiom,
% 0.37/0.60 ! [A: nat,A2: nat,B: nat,B2: nat,N8: nat] :
% 0.37/0.60 ( ( A = A2 )
% 0.37/0.60 => ( ( ord_less_nat @ B @ B2 )
% 0.37/0.60 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N8 ) @ B2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mlex_snd_decrI
% 0.37/0.60 thf(fact_3291_mlex__fst__decrI,axiom,
% 0.37/0.60 ! [A: nat,A2: nat,B: nat,N8: nat,B2: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ A2 )
% 0.37/0.60 => ( ( ord_less_nat @ B @ N8 )
% 0.37/0.60 => ( ( ord_less_nat @ B2 @ N8 )
% 0.37/0.60 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N8 ) @ B2 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mlex_fst_decrI
% 0.37/0.60 thf(fact_3292_mlex__bound,axiom,
% 0.37/0.60 ! [A: nat,A4: nat,B: nat,N8: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ A4 )
% 0.37/0.60 => ( ( ord_less_nat @ B @ N8 )
% 0.37/0.60 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( times_times_nat @ A4 @ N8 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mlex_bound
% 0.37/0.60 thf(fact_3293_mlex__leI,axiom,
% 0.37/0.60 ! [A: nat,A2: nat,B: nat,B2: nat,N8: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ A2 )
% 0.37/0.60 => ( ( ord_less_eq_nat @ B @ B2 )
% 0.37/0.60 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N8 ) @ B2 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mlex_leI
% 0.37/0.60 thf(fact_3294_field__le__mult__one__interval,axiom,
% 0.37/0.60 ! [X: real,Y: real] :
% 0.37/0.60 ( ! [Z3: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.37/0.60 => ( ( ord_less_real @ Z3 @ one_one_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ Y ) ) )
% 0.37/0.60 => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.60
% 0.37/0.60 % field_le_mult_one_interval
% 0.37/0.60 thf(fact_3295_field__le__mult__one__interval,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] :
% 0.37/0.60 ( ! [Z3: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.37/0.60 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y ) ) )
% 0.37/0.60 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.37/0.60
% 0.37/0.60 % field_le_mult_one_interval
% 0.37/0.60 thf(fact_3296_in__image__insert__iff,axiom,
% 0.37/0.60 ! [B4: set_set_VEBT_VEBT,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.60 ( ! [C5: set_VEBT_VEBT] :
% 0.37/0.60 ( ( member_set_VEBT_VEBT @ C5 @ B4 )
% 0.37/0.60 => ~ ( member_VEBT_VEBT @ X @ C5 ) )
% 0.37/0.60 => ( ( member_set_VEBT_VEBT @ A4 @ ( image_1661326939266726661T_VEBT @ ( insert_VEBT_VEBT @ X ) @ B4 ) )
% 0.37/0.60 = ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.60 & ( member_set_VEBT_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % in_image_insert_iff
% 0.37/0.60 thf(fact_3297_in__image__insert__iff,axiom,
% 0.37/0.60 ! [B4: set_set_real,X: real,A4: set_real] :
% 0.37/0.60 ( ! [C5: set_real] :
% 0.37/0.60 ( ( member_set_real @ C5 @ B4 )
% 0.37/0.60 => ~ ( member_real @ X @ C5 ) )
% 0.37/0.60 => ( ( member_set_real @ A4 @ ( image_2436557299294012491t_real @ ( insert_real @ X ) @ B4 ) )
% 0.37/0.60 = ( ( member_real @ X @ A4 )
% 0.37/0.60 & ( member_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B4 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % in_image_insert_iff
% 0.37/0.60 thf(fact_3298_in__image__insert__iff,axiom,
% 0.37/0.60 ! [B4: set_set_set_nat,X: set_nat,A4: set_set_nat] :
% 0.37/0.60 ( ! [C5: set_set_nat] :
% 0.37/0.60 ( ( member_set_set_nat @ C5 @ B4 )
% 0.37/0.60 => ~ ( member_set_nat @ X @ C5 ) )
% 0.37/0.60 => ( ( member_set_set_nat @ A4 @ ( image_7884819252390400639et_nat @ ( insert_set_nat @ X ) @ B4 ) )
% 0.37/0.60 = ( ( member_set_nat @ X @ A4 )
% 0.37/0.60 & ( member_set_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B4 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % in_image_insert_iff
% 0.37/0.60 thf(fact_3299_in__image__insert__iff,axiom,
% 0.37/0.60 ! [B4: set_set_int,X: int,A4: set_int] :
% 0.37/0.60 ( ! [C5: set_int] :
% 0.37/0.60 ( ( member_set_int @ C5 @ B4 )
% 0.37/0.60 => ~ ( member_int @ X @ C5 ) )
% 0.37/0.60 => ( ( member_set_int @ A4 @ ( image_524474410958335435et_int @ ( insert_int @ X ) @ B4 ) )
% 0.37/0.60 = ( ( member_int @ X @ A4 )
% 0.37/0.60 & ( member_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % in_image_insert_iff
% 0.37/0.60 thf(fact_3300_in__image__insert__iff,axiom,
% 0.37/0.60 ! [B4: set_set_o,X: $o,A4: set_o] :
% 0.37/0.60 ( ! [C5: set_o] :
% 0.37/0.60 ( ( member_set_o @ C5 @ B4 )
% 0.37/0.60 => ~ ( member_o @ X @ C5 ) )
% 0.37/0.60 => ( ( member_set_o @ A4 @ ( image_set_o_set_o @ ( insert_o @ X ) @ B4 ) )
% 0.37/0.60 = ( ( member_o @ X @ A4 )
% 0.37/0.60 & ( member_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % in_image_insert_iff
% 0.37/0.60 thf(fact_3301_in__image__insert__iff,axiom,
% 0.37/0.60 ! [B4: set_set_nat,X: nat,A4: set_nat] :
% 0.37/0.60 ( ! [C5: set_nat] :
% 0.37/0.60 ( ( member_set_nat @ C5 @ B4 )
% 0.37/0.60 => ~ ( member_nat @ X @ C5 ) )
% 0.37/0.60 => ( ( member_set_nat @ A4 @ ( image_7916887816326733075et_nat @ ( insert_nat @ X ) @ B4 ) )
% 0.37/0.60 = ( ( member_nat @ X @ A4 )
% 0.37/0.60 & ( member_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % in_image_insert_iff
% 0.37/0.60 thf(fact_3302_mult__le__cancel__left,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left
% 0.37/0.60 thf(fact_3303_mult__le__cancel__left,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left
% 0.37/0.60 thf(fact_3304_mult__le__cancel__left,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left
% 0.37/0.60 thf(fact_3305_mult__le__cancel__right,axiom,
% 0.37/0.60 ! [A: real,C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right
% 0.37/0.60 thf(fact_3306_mult__le__cancel__right,axiom,
% 0.37/0.60 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right
% 0.37/0.60 thf(fact_3307_mult__le__cancel__right,axiom,
% 0.37/0.60 ! [A: int,C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right
% 0.37/0.60 thf(fact_3308_mult__left__less__imp__less,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_less_imp_less
% 0.37/0.60 thf(fact_3309_mult__left__less__imp__less,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_less_imp_less
% 0.37/0.60 thf(fact_3310_mult__left__less__imp__less,axiom,
% 0.37/0.60 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_less_imp_less
% 0.37/0.60 thf(fact_3311_mult__left__less__imp__less,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_less_imp_less
% 0.37/0.60 thf(fact_3312_mult__strict__mono,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono
% 0.37/0.60 thf(fact_3313_mult__strict__mono,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono
% 0.37/0.60 thf(fact_3314_mult__strict__mono,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono
% 0.37/0.60 thf(fact_3315_mult__strict__mono,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono
% 0.37/0.60 thf(fact_3316_mult__less__cancel__left,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left
% 0.37/0.60 thf(fact_3317_mult__less__cancel__left,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left
% 0.37/0.60 thf(fact_3318_mult__less__cancel__left,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left
% 0.37/0.60 thf(fact_3319_mult__right__less__imp__less,axiom,
% 0.37/0.60 ! [A: real,C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_less_imp_less
% 0.37/0.60 thf(fact_3320_mult__right__less__imp__less,axiom,
% 0.37/0.60 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_less_imp_less
% 0.37/0.60 thf(fact_3321_mult__right__less__imp__less,axiom,
% 0.37/0.60 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_less_imp_less
% 0.37/0.60 thf(fact_3322_mult__right__less__imp__less,axiom,
% 0.37/0.60 ! [A: int,C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_less_imp_less
% 0.37/0.60 thf(fact_3323_mult__strict__mono_H,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono'
% 0.37/0.60 thf(fact_3324_mult__strict__mono_H,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono'
% 0.37/0.60 thf(fact_3325_mult__strict__mono_H,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono'
% 0.37/0.60 thf(fact_3326_mult__strict__mono_H,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_strict_mono'
% 0.37/0.60 thf(fact_3327_mult__less__cancel__right,axiom,
% 0.37/0.60 ! [A: real,C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right
% 0.37/0.60 thf(fact_3328_mult__less__cancel__right,axiom,
% 0.37/0.60 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right
% 0.37/0.60 thf(fact_3329_mult__less__cancel__right,axiom,
% 0.37/0.60 ! [A: int,C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ A @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right
% 0.37/0.60 thf(fact_3330_mult__le__cancel__left__neg,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left_neg
% 0.37/0.60 thf(fact_3331_mult__le__cancel__left__neg,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left_neg
% 0.37/0.60 thf(fact_3332_mult__le__cancel__left__neg,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left_neg
% 0.37/0.60 thf(fact_3333_mult__le__cancel__left__pos,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left_pos
% 0.37/0.60 thf(fact_3334_mult__le__cancel__left__pos,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left_pos
% 0.37/0.60 thf(fact_3335_mult__le__cancel__left__pos,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left_pos
% 0.37/0.60 thf(fact_3336_mult__left__le__imp__le,axiom,
% 0.37/0.60 ! [C2: real,A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le_imp_le
% 0.37/0.60 thf(fact_3337_mult__left__le__imp__le,axiom,
% 0.37/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le_imp_le
% 0.37/0.60 thf(fact_3338_mult__left__le__imp__le,axiom,
% 0.37/0.60 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le_imp_le
% 0.37/0.60 thf(fact_3339_mult__left__le__imp__le,axiom,
% 0.37/0.60 ! [C2: int,A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le_imp_le
% 0.37/0.60 thf(fact_3340_mult__right__le__imp__le,axiom,
% 0.37/0.60 ! [A: real,C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_le_imp_le
% 0.37/0.60 thf(fact_3341_mult__right__le__imp__le,axiom,
% 0.37/0.60 ! [A: rat,C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_le_imp_le
% 0.37/0.60 thf(fact_3342_mult__right__le__imp__le,axiom,
% 0.37/0.60 ! [A: nat,C2: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_le_imp_le
% 0.37/0.60 thf(fact_3343_mult__right__le__imp__le,axiom,
% 0.37/0.60 ! [A: int,C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_le_imp_le
% 0.37/0.60 thf(fact_3344_mult__le__less__imp__less,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_less_imp_less
% 0.37/0.60 thf(fact_3345_mult__le__less__imp__less,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_less_imp_less
% 0.37/0.60 thf(fact_3346_mult__le__less__imp__less,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_less_imp_less
% 0.37/0.60 thf(fact_3347_mult__le__less__imp__less,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_less_imp_less
% 0.37/0.60 thf(fact_3348_mult__less__le__imp__less,axiom,
% 0.37/0.60 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_le_imp_less
% 0.37/0.60 thf(fact_3349_mult__less__le__imp__less,axiom,
% 0.37/0.60 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_le_imp_less
% 0.37/0.60 thf(fact_3350_mult__less__le__imp__less,axiom,
% 0.37/0.60 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.60 ( ( ord_less_nat @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.60 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_le_imp_less
% 0.37/0.60 thf(fact_3351_mult__less__le__imp__less,axiom,
% 0.37/0.60 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ C2 @ D )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_le_imp_less
% 0.37/0.60 thf(fact_3352_sum__squares__ge__zero,axiom,
% 0.37/0.60 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_ge_zero
% 0.37/0.60 thf(fact_3353_sum__squares__ge__zero,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_ge_zero
% 0.37/0.60 thf(fact_3354_sum__squares__ge__zero,axiom,
% 0.37/0.60 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_ge_zero
% 0.37/0.60 thf(fact_3355_mult__left__le,axiom,
% 0.37/0.60 ! [C2: real,A: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ C2 @ one_one_real )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le
% 0.37/0.60 thf(fact_3356_mult__left__le,axiom,
% 0.37/0.60 ! [C2: rat,A: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ C2 @ one_one_rat )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le
% 0.37/0.60 thf(fact_3357_mult__left__le,axiom,
% 0.37/0.60 ! [C2: nat,A: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ C2 @ one_one_nat )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le
% 0.37/0.60 thf(fact_3358_mult__left__le,axiom,
% 0.37/0.60 ! [C2: int,A: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ C2 @ one_one_int )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le
% 0.37/0.60 thf(fact_3359_mult__le__one,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ one_one_real )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.60 => ( ( ord_less_eq_real @ B @ one_one_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_one
% 0.37/0.60 thf(fact_3360_mult__le__one,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.60 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_one
% 0.37/0.60 thf(fact_3361_mult__le__one,axiom,
% 0.37/0.60 ! [A: nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.37/0.60 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.60 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.37/0.60 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_one
% 0.37/0.60 thf(fact_3362_mult__le__one,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ one_one_int )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.60 => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_one
% 0.37/0.60 thf(fact_3363_mult__right__le__one__le,axiom,
% 0.37/0.60 ! [X: real,Y: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.60 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_le_one_le
% 0.37/0.60 thf(fact_3364_mult__right__le__one__le,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.37/0.60 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_le_one_le
% 0.37/0.60 thf(fact_3365_mult__right__le__one__le,axiom,
% 0.37/0.60 ! [X: int,Y: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.60 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_right_le_one_le
% 0.37/0.60 thf(fact_3366_mult__left__le__one__le,axiom,
% 0.37/0.60 ! [X: real,Y: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.60 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le_one_le
% 0.37/0.60 thf(fact_3367_mult__left__le__one__le,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.37/0.60 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le_one_le
% 0.37/0.60 thf(fact_3368_mult__left__le__one__le,axiom,
% 0.37/0.60 ! [X: int,Y: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.60 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_left_le_one_le
% 0.37/0.60 thf(fact_3369_not__sum__squares__lt__zero,axiom,
% 0.37/0.60 ! [X: real,Y: real] :
% 0.37/0.60 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % not_sum_squares_lt_zero
% 0.37/0.60 thf(fact_3370_not__sum__squares__lt__zero,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] :
% 0.37/0.60 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % not_sum_squares_lt_zero
% 0.37/0.60 thf(fact_3371_not__sum__squares__lt__zero,axiom,
% 0.37/0.60 ! [X: int,Y: int] :
% 0.37/0.60 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % not_sum_squares_lt_zero
% 0.37/0.60 thf(fact_3372_ordered__ring__class_Ole__add__iff1,axiom,
% 0.37/0.60 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_ring_class.le_add_iff1
% 0.37/0.60 thf(fact_3373_ordered__ring__class_Ole__add__iff1,axiom,
% 0.37/0.60 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_ring_class.le_add_iff1
% 0.37/0.60 thf(fact_3374_ordered__ring__class_Ole__add__iff1,axiom,
% 0.37/0.60 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_ring_class.le_add_iff1
% 0.37/0.60 thf(fact_3375_ordered__ring__class_Ole__add__iff2,axiom,
% 0.37/0.60 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_eq_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_ring_class.le_add_iff2
% 0.37/0.60 thf(fact_3376_ordered__ring__class_Ole__add__iff2,axiom,
% 0.37/0.60 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_eq_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_ring_class.le_add_iff2
% 0.37/0.60 thf(fact_3377_ordered__ring__class_Ole__add__iff2,axiom,
% 0.37/0.60 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_eq_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % ordered_ring_class.le_add_iff2
% 0.37/0.60 thf(fact_3378_less__add__iff2,axiom,
% 0.37/0.60 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 0.37/0.60 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_add_iff2
% 0.37/0.60 thf(fact_3379_less__add__iff2,axiom,
% 0.37/0.60 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_add_iff2
% 0.37/0.60 thf(fact_3380_less__add__iff2,axiom,
% 0.37/0.60 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 0.37/0.60 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_add_iff2
% 0.37/0.60 thf(fact_3381_less__add__iff1,axiom,
% 0.37/0.60 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 0.37/0.60 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_add_iff1
% 0.37/0.60 thf(fact_3382_less__add__iff1,axiom,
% 0.37/0.60 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_add_iff1
% 0.37/0.60 thf(fact_3383_less__add__iff1,axiom,
% 0.37/0.60 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 0.37/0.60 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 0.37/0.60 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_add_iff1
% 0.37/0.60 thf(fact_3384_one__less__mult,axiom,
% 0.37/0.60 ! [N: nat,M: nat] :
% 0.37/0.60 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.60 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.37/0.60 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % one_less_mult
% 0.37/0.60 thf(fact_3385_n__less__m__mult__n,axiom,
% 0.37/0.60 ! [N: nat,M: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.60 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.37/0.60 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % n_less_m_mult_n
% 0.37/0.60 thf(fact_3386_n__less__n__mult__m,axiom,
% 0.37/0.60 ! [N: nat,M: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.60 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.37/0.60 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % n_less_n_mult_m
% 0.37/0.60 thf(fact_3387_linordered__field__no__ub,axiom,
% 0.37/0.60 ! [X5: real] :
% 0.37/0.60 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_field_no_ub
% 0.37/0.60 thf(fact_3388_linordered__field__no__ub,axiom,
% 0.37/0.60 ! [X5: rat] :
% 0.37/0.60 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_field_no_ub
% 0.37/0.60 thf(fact_3389_linordered__field__no__lb,axiom,
% 0.37/0.60 ! [X5: real] :
% 0.37/0.60 ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_field_no_lb
% 0.37/0.60 thf(fact_3390_linordered__field__no__lb,axiom,
% 0.37/0.60 ! [X5: rat] :
% 0.37/0.60 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 0.37/0.60
% 0.37/0.60 % linordered_field_no_lb
% 0.37/0.60 thf(fact_3391_mult__le__cancel__left1,axiom,
% 0.37/0.60 ! [C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.37/0.60 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left1
% 0.37/0.60 thf(fact_3392_mult__le__cancel__left1,axiom,
% 0.37/0.60 ! [C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.37/0.60 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left1
% 0.37/0.60 thf(fact_3393_mult__le__cancel__left1,axiom,
% 0.37/0.60 ! [C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.37/0.60 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left1
% 0.37/0.60 thf(fact_3394_mult__le__cancel__left2,axiom,
% 0.37/0.60 ! [C2: real,A: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.37/0.60 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left2
% 0.37/0.60 thf(fact_3395_mult__le__cancel__left2,axiom,
% 0.37/0.60 ! [C2: rat,A: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.37/0.60 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left2
% 0.37/0.60 thf(fact_3396_mult__le__cancel__left2,axiom,
% 0.37/0.60 ! [C2: int,A: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.37/0.60 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_left2
% 0.37/0.60 thf(fact_3397_mult__le__cancel__right1,axiom,
% 0.37/0.60 ! [C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.37/0.60 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right1
% 0.37/0.60 thf(fact_3398_mult__le__cancel__right1,axiom,
% 0.37/0.60 ! [C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.37/0.60 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right1
% 0.37/0.60 thf(fact_3399_mult__le__cancel__right1,axiom,
% 0.37/0.60 ! [C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.37/0.60 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right1
% 0.37/0.60 thf(fact_3400_mult__le__cancel__right2,axiom,
% 0.37/0.60 ! [A: real,C2: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.37/0.60 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right2
% 0.37/0.60 thf(fact_3401_mult__le__cancel__right2,axiom,
% 0.37/0.60 ! [A: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.37/0.60 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right2
% 0.37/0.60 thf(fact_3402_mult__le__cancel__right2,axiom,
% 0.37/0.60 ! [A: int,C2: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.37/0.60 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_right2
% 0.37/0.60 thf(fact_3403_mult__less__cancel__left1,axiom,
% 0.37/0.60 ! [C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ one_one_real @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left1
% 0.37/0.60 thf(fact_3404_mult__less__cancel__left1,axiom,
% 0.37/0.60 ! [C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ one_one_rat @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left1
% 0.37/0.60 thf(fact_3405_mult__less__cancel__left1,axiom,
% 0.37/0.60 ! [C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ one_one_int @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left1
% 0.37/0.60 thf(fact_3406_mult__less__cancel__left2,axiom,
% 0.37/0.60 ! [C2: real,A: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ A @ one_one_real ) )
% 0.37/0.60 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left2
% 0.37/0.60 thf(fact_3407_mult__less__cancel__left2,axiom,
% 0.37/0.60 ! [C2: rat,A: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ A @ one_one_rat ) )
% 0.37/0.60 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left2
% 0.37/0.60 thf(fact_3408_mult__less__cancel__left2,axiom,
% 0.37/0.60 ! [C2: int,A: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ A @ one_one_int ) )
% 0.37/0.60 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_left2
% 0.37/0.60 thf(fact_3409_mult__less__cancel__right1,axiom,
% 0.37/0.60 ! [C2: real,B: real] :
% 0.37/0.60 ( ( ord_less_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ one_one_real @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right1
% 0.37/0.60 thf(fact_3410_mult__less__cancel__right1,axiom,
% 0.37/0.60 ! [C2: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ one_one_rat @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right1
% 0.37/0.60 thf(fact_3411_mult__less__cancel__right1,axiom,
% 0.37/0.60 ! [C2: int,B: int] :
% 0.37/0.60 ( ( ord_less_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ one_one_int @ B ) )
% 0.37/0.60 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right1
% 0.37/0.60 thf(fact_3412_mult__less__cancel__right2,axiom,
% 0.37/0.60 ! [A: real,C2: real] :
% 0.37/0.60 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.60 => ( ord_less_real @ A @ one_one_real ) )
% 0.37/0.60 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.37/0.60 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right2
% 0.37/0.60 thf(fact_3413_mult__less__cancel__right2,axiom,
% 0.37/0.60 ! [A: rat,C2: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.37/0.60 => ( ord_less_rat @ A @ one_one_rat ) )
% 0.37/0.60 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.37/0.60 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right2
% 0.37/0.60 thf(fact_3414_mult__less__cancel__right2,axiom,
% 0.37/0.60 ! [A: int,C2: int] :
% 0.37/0.60 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 0.37/0.60 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.60 => ( ord_less_int @ A @ one_one_int ) )
% 0.37/0.60 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.37/0.60 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_cancel_right2
% 0.37/0.60 thf(fact_3415_convex__bound__le,axiom,
% 0.37/0.60 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ X @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ Y @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 0.37/0.60 => ( ( ( plus_plus_real @ U @ V2 )
% 0.37/0.60 = one_one_real )
% 0.37/0.60 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % convex_bound_le
% 0.37/0.60 thf(fact_3416_convex__bound__le,axiom,
% 0.37/0.60 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ X @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ Y @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 0.37/0.60 => ( ( ( plus_plus_rat @ U @ V2 )
% 0.37/0.60 = one_one_rat )
% 0.37/0.60 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % convex_bound_le
% 0.37/0.60 thf(fact_3417_convex__bound__le,axiom,
% 0.37/0.60 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ X @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ Y @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 0.37/0.60 => ( ( ( plus_plus_int @ U @ V2 )
% 0.37/0.60 = one_one_int )
% 0.37/0.60 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % convex_bound_le
% 0.37/0.60 thf(fact_3418_mult__eq__if,axiom,
% 0.37/0.60 ( times_times_nat
% 0.37/0.60 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N6 @ ( times_times_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N6 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_eq_if
% 0.37/0.60 thf(fact_3419_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.37/0.60 ! [A: $o,B: $o] :
% 0.37/0.60 ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 0.37/0.60 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(1)
% 0.37/0.60 thf(fact_3420_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.37/0.60 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.37/0.60 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.37/0.60 = one_one_nat ) ).
% 0.37/0.60
% 0.37/0.60 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(2)
% 0.37/0.60 thf(fact_3421_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.37/0.60 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 0.37/0.60 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.37/0.60 = one_one_nat ) ).
% 0.37/0.60
% 0.37/0.60 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(2)
% 0.37/0.60 thf(fact_3422_convex__bound__lt,axiom,
% 0.37/0.60 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 0.37/0.60 ( ( ord_less_real @ X @ A )
% 0.37/0.60 => ( ( ord_less_real @ Y @ A )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.37/0.60 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 0.37/0.60 => ( ( ( plus_plus_real @ U @ V2 )
% 0.37/0.60 = one_one_real )
% 0.37/0.60 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % convex_bound_lt
% 0.37/0.60 thf(fact_3423_convex__bound__lt,axiom,
% 0.37/0.60 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 0.37/0.60 ( ( ord_less_rat @ X @ A )
% 0.37/0.60 => ( ( ord_less_rat @ Y @ A )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.37/0.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 0.37/0.60 => ( ( ( plus_plus_rat @ U @ V2 )
% 0.37/0.60 = one_one_rat )
% 0.37/0.60 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % convex_bound_lt
% 0.37/0.60 thf(fact_3424_convex__bound__lt,axiom,
% 0.37/0.60 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 0.37/0.60 ( ( ord_less_int @ X @ A )
% 0.37/0.60 => ( ( ord_less_int @ Y @ A )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.37/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 0.37/0.60 => ( ( ( plus_plus_int @ U @ V2 )
% 0.37/0.60 = one_one_int )
% 0.37/0.60 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % convex_bound_lt
% 0.37/0.60 thf(fact_3425_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.37/0.60 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.37/0.60 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.37/0.60 = one_one_nat ) ).
% 0.37/0.60
% 0.37/0.60 % T\<^sub>m\<^sub>a\<^sub>x\<^sub>t.simps(3)
% 0.37/0.60 thf(fact_3426_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.37/0.60 ! [A: $o,B: $o] :
% 0.37/0.60 ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 0.37/0.60 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(1)
% 0.37/0.60 thf(fact_3427_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.37/0.60 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.37/0.60 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.37/0.60 = one_one_nat ) ).
% 0.37/0.60
% 0.37/0.60 % T\<^sub>m\<^sub>i\<^sub>n\<^sub>t.simps(3)
% 0.37/0.60 thf(fact_3428_nat__mult__le__cancel__disj,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.60 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.60 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_le_cancel_disj
% 0.37/0.60 thf(fact_3429_nat__mult__less__cancel__disj,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.60 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.60 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_less_cancel_disj
% 0.37/0.60 thf(fact_3430_sum__squares__eq__zero__iff,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] :
% 0.37/0.60 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.37/0.60 = zero_zero_rat )
% 0.37/0.60 = ( ( X = zero_zero_rat )
% 0.37/0.60 & ( Y = zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_eq_zero_iff
% 0.37/0.60 thf(fact_3431_sum__squares__eq__zero__iff,axiom,
% 0.37/0.60 ! [X: real,Y: real] :
% 0.37/0.60 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 0.37/0.60 = zero_zero_real )
% 0.37/0.60 = ( ( X = zero_zero_real )
% 0.37/0.60 & ( Y = zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_eq_zero_iff
% 0.37/0.60 thf(fact_3432_sum__squares__eq__zero__iff,axiom,
% 0.37/0.60 ! [X: int,Y: int] :
% 0.37/0.60 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.37/0.60 = zero_zero_int )
% 0.37/0.60 = ( ( X = zero_zero_int )
% 0.37/0.60 & ( Y = zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_eq_zero_iff
% 0.37/0.60 thf(fact_3433_nat__less__add__iff2,axiom,
% 0.37/0.60 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.60 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_less_add_iff2
% 0.37/0.60 thf(fact_3434_nat__less__add__iff1,axiom,
% 0.37/0.60 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ J @ I )
% 0.37/0.60 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_less_add_iff1
% 0.37/0.60 thf(fact_3435_nat__diff__add__eq2,axiom,
% 0.37/0.60 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.60 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_diff_add_eq2
% 0.37/0.60 thf(fact_3436_nat__diff__add__eq1,axiom,
% 0.37/0.60 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ J @ I )
% 0.37/0.60 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_diff_add_eq1
% 0.37/0.60 thf(fact_3437_nat__le__add__iff2,axiom,
% 0.37/0.60 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.60 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_le_add_iff2
% 0.37/0.60 thf(fact_3438_nat__le__add__iff1,axiom,
% 0.37/0.60 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ J @ I )
% 0.37/0.60 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_le_add_iff1
% 0.37/0.60 thf(fact_3439_star__false__left,axiom,
% 0.37/0.60 ! [P2: assn] :
% 0.37/0.60 ( ( times_times_assn @ bot_bot_assn @ P2 )
% 0.37/0.60 = bot_bot_assn ) ).
% 0.37/0.60
% 0.37/0.60 % star_false_left
% 0.37/0.60 thf(fact_3440_star__false__right,axiom,
% 0.37/0.60 ! [P2: assn] :
% 0.37/0.60 ( ( times_times_assn @ P2 @ bot_bot_assn )
% 0.37/0.60 = bot_bot_assn ) ).
% 0.37/0.60
% 0.37/0.60 % star_false_right
% 0.37/0.60 thf(fact_3441_snga__same__false,axiom,
% 0.37/0.60 ! [P3: array_VEBT_VEBTi,X: list_VEBT_VEBTi,Y: list_VEBT_VEBTi] :
% 0.37/0.60 ( ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ P3 @ X ) @ ( snga_assn_VEBT_VEBTi @ P3 @ Y ) )
% 0.37/0.60 = bot_bot_assn ) ).
% 0.37/0.60
% 0.37/0.60 % snga_same_false
% 0.37/0.60 thf(fact_3442_mod__h__bot__iff_I5_J,axiom,
% 0.37/0.60 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 0.37/0.60 ( ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.37/0.60 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.37/0.60 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mod_h_bot_iff(5)
% 0.37/0.60 thf(fact_3443_mod__starE,axiom,
% 0.37/0.60 ! [A: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.60 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H2 )
% 0.37/0.60 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 0.37/0.60 => ! [H_2: produc3658429121746597890et_nat] :
% 0.37/0.60 ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mod_starE
% 0.37/0.60 thf(fact_3444_mod__starD,axiom,
% 0.37/0.60 ! [A4: assn,B4: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.60 ( ( rep_assn @ ( times_times_assn @ A4 @ B4 ) @ H2 )
% 0.37/0.60 => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 0.37/0.60 ( ( rep_assn @ A4 @ H1 )
% 0.37/0.60 & ( rep_assn @ B4 @ H22 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mod_starD
% 0.37/0.60 thf(fact_3445_assn__one__left,axiom,
% 0.37/0.60 ! [P2: assn] :
% 0.37/0.60 ( ( times_times_assn @ one_one_assn @ P2 )
% 0.37/0.60 = P2 ) ).
% 0.37/0.60
% 0.37/0.60 % assn_one_left
% 0.37/0.60 thf(fact_3446_nat__mult__eq__cancel__disj,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ( times_times_nat @ K @ M )
% 0.37/0.60 = ( times_times_nat @ K @ N ) )
% 0.37/0.60 = ( ( K = zero_zero_nat )
% 0.37/0.60 | ( M = N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_eq_cancel_disj
% 0.37/0.60 thf(fact_3447_nat__mult__less__cancel1,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.60 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.60 = ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_less_cancel1
% 0.37/0.60 thf(fact_3448_nat__mult__eq__cancel1,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.60 => ( ( ( times_times_nat @ K @ M )
% 0.37/0.60 = ( times_times_nat @ K @ N ) )
% 0.37/0.60 = ( M = N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_eq_cancel1
% 0.37/0.60 thf(fact_3449_sum__squares__le__zero__iff,axiom,
% 0.37/0.60 ! [X: real,Y: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 0.37/0.60 = ( ( X = zero_zero_real )
% 0.37/0.60 & ( Y = zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_le_zero_iff
% 0.37/0.60 thf(fact_3450_sum__squares__le__zero__iff,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.37/0.60 = ( ( X = zero_zero_rat )
% 0.37/0.60 & ( Y = zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_le_zero_iff
% 0.37/0.60 thf(fact_3451_sum__squares__le__zero__iff,axiom,
% 0.37/0.60 ! [X: int,Y: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.37/0.60 = ( ( X = zero_zero_int )
% 0.37/0.60 & ( Y = zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_le_zero_iff
% 0.37/0.60 thf(fact_3452_sum__squares__gt__zero__iff,axiom,
% 0.37/0.60 ! [X: real,Y: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 0.37/0.60 = ( ( X != zero_zero_real )
% 0.37/0.60 | ( Y != zero_zero_real ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_gt_zero_iff
% 0.37/0.60 thf(fact_3453_sum__squares__gt__zero__iff,axiom,
% 0.37/0.60 ! [X: rat,Y: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.37/0.60 = ( ( X != zero_zero_rat )
% 0.37/0.60 | ( Y != zero_zero_rat ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_gt_zero_iff
% 0.37/0.60 thf(fact_3454_sum__squares__gt__zero__iff,axiom,
% 0.37/0.60 ! [X: int,Y: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 0.37/0.60 = ( ( X != zero_zero_int )
% 0.37/0.60 | ( Y != zero_zero_int ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % sum_squares_gt_zero_iff
% 0.37/0.60 thf(fact_3455_nat__mult__le__cancel1,axiom,
% 0.37/0.60 ! [K: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.60 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.60 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_mult_le_cancel1
% 0.37/0.60 thf(fact_3456_nat__eq__add__iff1,axiom,
% 0.37/0.60 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ J @ I )
% 0.37/0.60 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.37/0.60 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 0.37/0.60 = N ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_eq_add_iff1
% 0.37/0.60 thf(fact_3457_nat__eq__add__iff2,axiom,
% 0.37/0.60 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.37/0.60 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.60 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.37/0.60 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.37/0.60 = ( M
% 0.37/0.60 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % nat_eq_add_iff2
% 0.37/0.60 thf(fact_3458_mult__le__cancel__iff2,axiom,
% 0.37/0.60 ! [Z: real,X: real,Y: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.37/0.60 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 0.37/0.60 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_iff2
% 0.37/0.60 thf(fact_3459_mult__le__cancel__iff2,axiom,
% 0.37/0.60 ! [Z: rat,X: rat,Y: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.37/0.60 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 0.37/0.60 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_iff2
% 0.37/0.60 thf(fact_3460_mult__le__cancel__iff2,axiom,
% 0.37/0.60 ! [Z: int,X: int,Y: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ Z )
% 0.37/0.60 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 0.37/0.60 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_iff2
% 0.37/0.60 thf(fact_3461_mult__le__cancel__iff1,axiom,
% 0.37/0.60 ! [Z: real,X: real,Y: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.37/0.60 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.37/0.60 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_iff1
% 0.37/0.60 thf(fact_3462_mult__le__cancel__iff1,axiom,
% 0.37/0.60 ! [Z: rat,X: rat,Y: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.37/0.60 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.37/0.60 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_iff1
% 0.37/0.60 thf(fact_3463_mult__le__cancel__iff1,axiom,
% 0.37/0.60 ! [Z: int,X: int,Y: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ Z )
% 0.37/0.60 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.37/0.60 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_le_cancel_iff1
% 0.37/0.60 thf(fact_3464_add__scale__eq__noteq,axiom,
% 0.37/0.60 ! [R: rat,A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.60 ( ( R != zero_zero_rat )
% 0.37/0.60 => ( ( ( A = B )
% 0.37/0.60 & ( C2 != D ) )
% 0.37/0.60 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C2 ) )
% 0.37/0.60 != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_scale_eq_noteq
% 0.37/0.60 thf(fact_3465_add__scale__eq__noteq,axiom,
% 0.37/0.60 ! [R: real,A: real,B: real,C2: real,D: real] :
% 0.37/0.60 ( ( R != zero_zero_real )
% 0.37/0.60 => ( ( ( A = B )
% 0.37/0.60 & ( C2 != D ) )
% 0.37/0.60 => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C2 ) )
% 0.37/0.60 != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_scale_eq_noteq
% 0.37/0.60 thf(fact_3466_add__scale__eq__noteq,axiom,
% 0.37/0.60 ! [R: nat,A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.60 ( ( R != zero_zero_nat )
% 0.37/0.60 => ( ( ( A = B )
% 0.37/0.60 & ( C2 != D ) )
% 0.37/0.60 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C2 ) )
% 0.37/0.60 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_scale_eq_noteq
% 0.37/0.60 thf(fact_3467_add__scale__eq__noteq,axiom,
% 0.37/0.60 ! [R: int,A: int,B: int,C2: int,D: int] :
% 0.37/0.60 ( ( R != zero_zero_int )
% 0.37/0.60 => ( ( ( A = B )
% 0.37/0.60 & ( C2 != D ) )
% 0.37/0.60 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C2 ) )
% 0.37/0.60 != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_scale_eq_noteq
% 0.37/0.60 thf(fact_3468_mult__less__iff1,axiom,
% 0.37/0.60 ! [Z: real,X: real,Y: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.37/0.60 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.37/0.60 = ( ord_less_real @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_iff1
% 0.37/0.60 thf(fact_3469_mult__less__iff1,axiom,
% 0.37/0.60 ! [Z: rat,X: rat,Y: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.37/0.60 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.37/0.60 = ( ord_less_rat @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_iff1
% 0.37/0.60 thf(fact_3470_mult__less__iff1,axiom,
% 0.37/0.60 ! [Z: int,X: int,Y: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ Z )
% 0.37/0.60 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.37/0.60 = ( ord_less_int @ X @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mult_less_iff1
% 0.37/0.60 thf(fact_3471_add__0__iff,axiom,
% 0.37/0.60 ! [B: real,A: real] :
% 0.37/0.60 ( ( B
% 0.37/0.60 = ( plus_plus_real @ B @ A ) )
% 0.37/0.60 = ( A = zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_0_iff
% 0.37/0.60 thf(fact_3472_add__0__iff,axiom,
% 0.37/0.60 ! [B: rat,A: rat] :
% 0.37/0.60 ( ( B
% 0.37/0.60 = ( plus_plus_rat @ B @ A ) )
% 0.37/0.60 = ( A = zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_0_iff
% 0.37/0.60 thf(fact_3473_add__0__iff,axiom,
% 0.37/0.60 ! [B: nat,A: nat] :
% 0.37/0.60 ( ( B
% 0.37/0.60 = ( plus_plus_nat @ B @ A ) )
% 0.37/0.60 = ( A = zero_zero_nat ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_0_iff
% 0.37/0.60 thf(fact_3474_add__0__iff,axiom,
% 0.37/0.60 ! [B: int,A: int] :
% 0.37/0.60 ( ( B
% 0.37/0.60 = ( plus_plus_int @ B @ A ) )
% 0.37/0.60 = ( A = zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_0_iff
% 0.37/0.60 thf(fact_3475_mul__shift,axiom,
% 0.37/0.60 ! [X: nat,Y: nat,Z: nat] :
% 0.37/0.60 ( ( ( times_times_nat @ X @ Y )
% 0.37/0.60 = Z )
% 0.37/0.60 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.37/0.60 = ( some_nat @ Z ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % mul_shift
% 0.37/0.60 thf(fact_3476_minus__Max__eq__Min,axiom,
% 0.37/0.60 ! [S3: set_Code_integer] :
% 0.37/0.60 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.60 => ( ( uminus1351360451143612070nteger @ ( lattic4901227151466704046nteger @ S3 ) )
% 0.37/0.60 = ( lattic1063845414844153500nteger @ ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Max_eq_Min
% 0.37/0.60 thf(fact_3477_minus__Max__eq__Min,axiom,
% 0.37/0.60 ! [S3: set_real] :
% 0.37/0.60 ( ( finite_finite_real @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bot_set_real )
% 0.37/0.60 => ( ( uminus_uminus_real @ ( lattic4275903605611617917x_real @ S3 ) )
% 0.37/0.60 = ( lattic3629708407755379051n_real @ ( image_real_real @ uminus_uminus_real @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Max_eq_Min
% 0.37/0.60 thf(fact_3478_minus__Max__eq__Min,axiom,
% 0.37/0.60 ! [S3: set_rat] :
% 0.37/0.60 ( ( finite_finite_rat @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bot_set_rat )
% 0.37/0.60 => ( ( uminus_uminus_rat @ ( lattic7630753665789217321ax_rat @ S3 ) )
% 0.37/0.60 = ( lattic8086005427650270231in_rat @ ( image_rat_rat @ uminus_uminus_rat @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Max_eq_Min
% 0.37/0.60 thf(fact_3479_minus__Max__eq__Min,axiom,
% 0.37/0.60 ! [S3: set_int] :
% 0.37/0.60 ( ( finite_finite_int @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bot_set_int )
% 0.37/0.60 => ( ( uminus_uminus_int @ ( lattic8263393255366662781ax_int @ S3 ) )
% 0.37/0.60 = ( lattic8718645017227715691in_int @ ( image_int_int @ uminus_uminus_int @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Max_eq_Min
% 0.37/0.60 thf(fact_3480_minus__Min__eq__Max,axiom,
% 0.37/0.60 ! [S3: set_Code_integer] :
% 0.37/0.60 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.60 => ( ( uminus1351360451143612070nteger @ ( lattic1063845414844153500nteger @ S3 ) )
% 0.37/0.60 = ( lattic4901227151466704046nteger @ ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Min_eq_Max
% 0.37/0.60 thf(fact_3481_minus__Min__eq__Max,axiom,
% 0.37/0.60 ! [S3: set_real] :
% 0.37/0.60 ( ( finite_finite_real @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bot_set_real )
% 0.37/0.60 => ( ( uminus_uminus_real @ ( lattic3629708407755379051n_real @ S3 ) )
% 0.37/0.60 = ( lattic4275903605611617917x_real @ ( image_real_real @ uminus_uminus_real @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Min_eq_Max
% 0.37/0.60 thf(fact_3482_minus__Min__eq__Max,axiom,
% 0.37/0.60 ! [S3: set_rat] :
% 0.37/0.60 ( ( finite_finite_rat @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bot_set_rat )
% 0.37/0.60 => ( ( uminus_uminus_rat @ ( lattic8086005427650270231in_rat @ S3 ) )
% 0.37/0.60 = ( lattic7630753665789217321ax_rat @ ( image_rat_rat @ uminus_uminus_rat @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Min_eq_Max
% 0.37/0.60 thf(fact_3483_minus__Min__eq__Max,axiom,
% 0.37/0.60 ! [S3: set_int] :
% 0.37/0.60 ( ( finite_finite_int @ S3 )
% 0.37/0.60 => ( ( S3 != bot_bot_set_int )
% 0.37/0.60 => ( ( uminus_uminus_int @ ( lattic8718645017227715691in_int @ S3 ) )
% 0.37/0.60 = ( lattic8263393255366662781ax_int @ ( image_int_int @ uminus_uminus_int @ S3 ) ) ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_Min_eq_Max
% 0.37/0.60 thf(fact_3484_add__shift,axiom,
% 0.37/0.60 ! [X: nat,Y: nat,Z: nat] :
% 0.37/0.60 ( ( ( plus_plus_nat @ X @ Y )
% 0.37/0.60 = Z )
% 0.37/0.60 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.37/0.60 = ( some_nat @ Z ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_shift
% 0.37/0.60 thf(fact_3485_add_Oinverse__inverse,axiom,
% 0.37/0.60 ! [A: uint32] :
% 0.37/0.60 ( ( uminus_uminus_uint32 @ ( uminus_uminus_uint32 @ A ) )
% 0.37/0.60 = A ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_inverse
% 0.37/0.60 thf(fact_3486_add_Oinverse__inverse,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = A ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_inverse
% 0.37/0.60 thf(fact_3487_add_Oinverse__inverse,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = A ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_inverse
% 0.37/0.60 thf(fact_3488_add_Oinverse__inverse,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = A ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_inverse
% 0.37/0.60 thf(fact_3489_neg__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( ( uminus_uminus_uint32 @ A )
% 0.37/0.60 = ( uminus_uminus_uint32 @ B ) )
% 0.37/0.60 = ( A = B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_iff_equal
% 0.37/0.60 thf(fact_3490_neg__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ( uminus_uminus_real @ A )
% 0.37/0.60 = ( uminus_uminus_real @ B ) )
% 0.37/0.60 = ( A = B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_iff_equal
% 0.37/0.60 thf(fact_3491_neg__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ( uminus_uminus_rat @ A )
% 0.37/0.60 = ( uminus_uminus_rat @ B ) )
% 0.37/0.60 = ( A = B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_iff_equal
% 0.37/0.60 thf(fact_3492_neg__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ( uminus_uminus_int @ A )
% 0.37/0.60 = ( uminus_uminus_int @ B ) )
% 0.37/0.60 = ( A = B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_iff_equal
% 0.37/0.60 thf(fact_3493_Compl__subset__Compl__iff,axiom,
% 0.37/0.60 ! [A4: set_int,B4: set_int] :
% 0.37/0.60 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A4 ) @ ( uminus1532241313380277803et_int @ B4 ) )
% 0.37/0.60 = ( ord_less_eq_set_int @ B4 @ A4 ) ) ).
% 0.37/0.60
% 0.37/0.60 % Compl_subset_Compl_iff
% 0.37/0.60 thf(fact_3494_Compl__anti__mono,axiom,
% 0.37/0.60 ! [A4: set_int,B4: set_int] :
% 0.37/0.60 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.60 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B4 ) @ ( uminus1532241313380277803et_int @ A4 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % Compl_anti_mono
% 0.37/0.60 thf(fact_3495_neg__equal__zero,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ( uminus_uminus_real @ A )
% 0.37/0.60 = A )
% 0.37/0.60 = ( A = zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_zero
% 0.37/0.60 thf(fact_3496_neg__equal__zero,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ( uminus_uminus_rat @ A )
% 0.37/0.60 = A )
% 0.37/0.60 = ( A = zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_zero
% 0.37/0.60 thf(fact_3497_neg__equal__zero,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ( uminus_uminus_int @ A )
% 0.37/0.60 = A )
% 0.37/0.60 = ( A = zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_zero
% 0.37/0.60 thf(fact_3498_equal__neg__zero,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( A
% 0.37/0.60 = ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( A = zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % equal_neg_zero
% 0.37/0.60 thf(fact_3499_equal__neg__zero,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( A
% 0.37/0.60 = ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( A = zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % equal_neg_zero
% 0.37/0.60 thf(fact_3500_equal__neg__zero,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( A
% 0.37/0.60 = ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( A = zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % equal_neg_zero
% 0.37/0.60 thf(fact_3501_neg__equal__0__iff__equal,axiom,
% 0.37/0.60 ! [A: uint32] :
% 0.37/0.60 ( ( ( uminus_uminus_uint32 @ A )
% 0.37/0.60 = zero_zero_uint32 )
% 0.37/0.60 = ( A = zero_zero_uint32 ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_0_iff_equal
% 0.37/0.60 thf(fact_3502_neg__equal__0__iff__equal,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ( uminus_uminus_real @ A )
% 0.37/0.60 = zero_zero_real )
% 0.37/0.60 = ( A = zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_0_iff_equal
% 0.37/0.60 thf(fact_3503_neg__equal__0__iff__equal,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ( uminus_uminus_rat @ A )
% 0.37/0.60 = zero_zero_rat )
% 0.37/0.60 = ( A = zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_0_iff_equal
% 0.37/0.60 thf(fact_3504_neg__equal__0__iff__equal,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ( uminus_uminus_int @ A )
% 0.37/0.60 = zero_zero_int )
% 0.37/0.60 = ( A = zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_equal_0_iff_equal
% 0.37/0.60 thf(fact_3505_neg__0__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: uint32] :
% 0.37/0.60 ( ( zero_zero_uint32
% 0.37/0.60 = ( uminus_uminus_uint32 @ A ) )
% 0.37/0.60 = ( zero_zero_uint32 = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_equal_iff_equal
% 0.37/0.60 thf(fact_3506_neg__0__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( zero_zero_real
% 0.37/0.60 = ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( zero_zero_real = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_equal_iff_equal
% 0.37/0.60 thf(fact_3507_neg__0__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( zero_zero_rat
% 0.37/0.60 = ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( zero_zero_rat = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_equal_iff_equal
% 0.37/0.60 thf(fact_3508_neg__0__equal__iff__equal,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( zero_zero_int
% 0.37/0.60 = ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( zero_zero_int = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_equal_iff_equal
% 0.37/0.60 thf(fact_3509_add_Oinverse__neutral,axiom,
% 0.37/0.60 ( ( uminus_uminus_uint32 @ zero_zero_uint32 )
% 0.37/0.60 = zero_zero_uint32 ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_neutral
% 0.37/0.60 thf(fact_3510_add_Oinverse__neutral,axiom,
% 0.37/0.60 ( ( uminus_uminus_real @ zero_zero_real )
% 0.37/0.60 = zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_neutral
% 0.37/0.60 thf(fact_3511_add_Oinverse__neutral,axiom,
% 0.37/0.60 ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.37/0.60 = zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_neutral
% 0.37/0.60 thf(fact_3512_add_Oinverse__neutral,axiom,
% 0.37/0.60 ( ( uminus_uminus_int @ zero_zero_int )
% 0.37/0.60 = zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % add.inverse_neutral
% 0.37/0.60 thf(fact_3513_neg__le__iff__le,axiom,
% 0.37/0.60 ! [B: real,A: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_le_iff_le
% 0.37/0.60 thf(fact_3514_neg__le__iff__le,axiom,
% 0.37/0.60 ! [B: rat,A: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_le_iff_le
% 0.37/0.60 thf(fact_3515_neg__le__iff__le,axiom,
% 0.37/0.60 ! [B: int,A: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_le_iff_le
% 0.37/0.60 thf(fact_3516_compl__le__compl__iff,axiom,
% 0.37/0.60 ! [X: assn,Y: assn] :
% 0.37/0.60 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 0.37/0.60 = ( ord_less_eq_assn @ Y @ X ) ) ).
% 0.37/0.60
% 0.37/0.60 % compl_le_compl_iff
% 0.37/0.60 thf(fact_3517_compl__le__compl__iff,axiom,
% 0.37/0.60 ! [X: set_int,Y: set_int] :
% 0.37/0.60 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 0.37/0.60 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 0.37/0.60
% 0.37/0.60 % compl_le_compl_iff
% 0.37/0.60 thf(fact_3518_neg__less__iff__less,axiom,
% 0.37/0.60 ! [B: real,A: real] :
% 0.37/0.60 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( ord_less_real @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_iff_less
% 0.37/0.60 thf(fact_3519_neg__less__iff__less,axiom,
% 0.37/0.60 ! [B: rat,A: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( ord_less_rat @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_iff_less
% 0.37/0.60 thf(fact_3520_neg__less__iff__less,axiom,
% 0.37/0.60 ! [B: int,A: int] :
% 0.37/0.60 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( ord_less_int @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_iff_less
% 0.37/0.60 thf(fact_3521_compl__less__compl__iff,axiom,
% 0.37/0.60 ! [X: assn,Y: assn] :
% 0.37/0.60 ( ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 0.37/0.60 = ( ord_less_assn @ Y @ X ) ) ).
% 0.37/0.60
% 0.37/0.60 % compl_less_compl_iff
% 0.37/0.60 thf(fact_3522_add__minus__cancel,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( plus_plus_uint32 @ A @ ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % add_minus_cancel
% 0.37/0.60 thf(fact_3523_add__minus__cancel,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % add_minus_cancel
% 0.37/0.60 thf(fact_3524_add__minus__cancel,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % add_minus_cancel
% 0.37/0.60 thf(fact_3525_add__minus__cancel,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % add_minus_cancel
% 0.37/0.60 thf(fact_3526_minus__add__cancel,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ ( plus_plus_uint32 @ A @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_cancel
% 0.37/0.60 thf(fact_3527_minus__add__cancel,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_cancel
% 0.37/0.60 thf(fact_3528_minus__add__cancel,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_cancel
% 0.37/0.60 thf(fact_3529_minus__add__cancel,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.37/0.60 = B ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_cancel
% 0.37/0.60 thf(fact_3530_minus__add__distrib,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( uminus_uminus_uint32 @ ( plus_plus_uint32 @ A @ B ) )
% 0.37/0.60 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ ( uminus_uminus_uint32 @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_distrib
% 0.37/0.60 thf(fact_3531_minus__add__distrib,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.37/0.60 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_distrib
% 0.37/0.60 thf(fact_3532_minus__add__distrib,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.37/0.60 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_distrib
% 0.37/0.60 thf(fact_3533_minus__add__distrib,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.37/0.60 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_add_distrib
% 0.37/0.60 thf(fact_3534_minus__diff__eq,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( uminus_uminus_uint32 @ ( minus_minus_uint32 @ A @ B ) )
% 0.37/0.60 = ( minus_minus_uint32 @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_diff_eq
% 0.37/0.60 thf(fact_3535_minus__diff__eq,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.37/0.60 = ( minus_minus_real @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_diff_eq
% 0.37/0.60 thf(fact_3536_minus__diff__eq,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.37/0.60 = ( minus_minus_rat @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_diff_eq
% 0.37/0.60 thf(fact_3537_minus__diff__eq,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.37/0.60 = ( minus_minus_int @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_diff_eq
% 0.37/0.60 thf(fact_3538_neg__0__le__iff__le,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_le_iff_le
% 0.37/0.60 thf(fact_3539_neg__0__le__iff__le,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_le_iff_le
% 0.37/0.60 thf(fact_3540_neg__0__le__iff__le,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_le_iff_le
% 0.37/0.60 thf(fact_3541_neg__le__0__iff__le,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.37/0.60 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_le_0_iff_le
% 0.37/0.60 thf(fact_3542_neg__le__0__iff__le,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.37/0.60 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_le_0_iff_le
% 0.37/0.60 thf(fact_3543_neg__le__0__iff__le,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.37/0.60 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_le_0_iff_le
% 0.37/0.60 thf(fact_3544_less__eq__neg__nonpos,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_eq_neg_nonpos
% 0.37/0.60 thf(fact_3545_less__eq__neg__nonpos,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_eq_neg_nonpos
% 0.37/0.60 thf(fact_3546_less__eq__neg__nonpos,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_eq_neg_nonpos
% 0.37/0.60 thf(fact_3547_neg__less__eq__nonneg,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.37/0.60 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_eq_nonneg
% 0.37/0.60 thf(fact_3548_neg__less__eq__nonneg,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.37/0.60 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_eq_nonneg
% 0.37/0.60 thf(fact_3549_neg__less__eq__nonneg,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.37/0.60 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_eq_nonneg
% 0.37/0.60 thf(fact_3550_less__neg__neg,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_neg_neg
% 0.37/0.60 thf(fact_3551_less__neg__neg,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_neg_neg
% 0.37/0.60 thf(fact_3552_less__neg__neg,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % less_neg_neg
% 0.37/0.60 thf(fact_3553_neg__less__pos,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.37/0.60 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_pos
% 0.37/0.60 thf(fact_3554_neg__less__pos,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.37/0.60 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_pos
% 0.37/0.60 thf(fact_3555_neg__less__pos,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.37/0.60 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_pos
% 0.37/0.60 thf(fact_3556_neg__0__less__iff__less,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_less_iff_less
% 0.37/0.60 thf(fact_3557_neg__0__less__iff__less,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_less_iff_less
% 0.37/0.60 thf(fact_3558_neg__0__less__iff__less,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_0_less_iff_less
% 0.37/0.60 thf(fact_3559_neg__less__0__iff__less,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.37/0.60 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_0_iff_less
% 0.37/0.60 thf(fact_3560_neg__less__0__iff__less,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.37/0.60 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_0_iff_less
% 0.37/0.60 thf(fact_3561_neg__less__0__iff__less,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.37/0.60 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % neg_less_0_iff_less
% 0.37/0.60 thf(fact_3562_ab__left__minus,axiom,
% 0.37/0.60 ! [A: uint32] :
% 0.37/0.60 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ A )
% 0.37/0.60 = zero_zero_uint32 ) ).
% 0.37/0.60
% 0.37/0.60 % ab_left_minus
% 0.37/0.60 thf(fact_3563_ab__left__minus,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.37/0.60 = zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % ab_left_minus
% 0.37/0.60 thf(fact_3564_ab__left__minus,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.37/0.60 = zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % ab_left_minus
% 0.37/0.60 thf(fact_3565_ab__left__minus,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.37/0.60 = zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % ab_left_minus
% 0.37/0.60 thf(fact_3566_add_Oright__inverse,axiom,
% 0.37/0.60 ! [A: uint32] :
% 0.37/0.60 ( ( plus_plus_uint32 @ A @ ( uminus_uminus_uint32 @ A ) )
% 0.37/0.60 = zero_zero_uint32 ) ).
% 0.37/0.60
% 0.37/0.60 % add.right_inverse
% 0.37/0.60 thf(fact_3567_add_Oright__inverse,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.37/0.60 = zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % add.right_inverse
% 0.37/0.60 thf(fact_3568_add_Oright__inverse,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.37/0.60 = zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % add.right_inverse
% 0.37/0.60 thf(fact_3569_add_Oright__inverse,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.37/0.60 = zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % add.right_inverse
% 0.37/0.60 thf(fact_3570_diff__0,axiom,
% 0.37/0.60 ! [A: uint32] :
% 0.37/0.60 ( ( minus_minus_uint32 @ zero_zero_uint32 @ A )
% 0.37/0.60 = ( uminus_uminus_uint32 @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_0
% 0.37/0.60 thf(fact_3571_diff__0,axiom,
% 0.37/0.60 ! [A: real] :
% 0.37/0.60 ( ( minus_minus_real @ zero_zero_real @ A )
% 0.37/0.60 = ( uminus_uminus_real @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_0
% 0.37/0.60 thf(fact_3572_diff__0,axiom,
% 0.37/0.60 ! [A: rat] :
% 0.37/0.60 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.37/0.60 = ( uminus_uminus_rat @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_0
% 0.37/0.60 thf(fact_3573_diff__0,axiom,
% 0.37/0.60 ! [A: int] :
% 0.37/0.60 ( ( minus_minus_int @ zero_zero_int @ A )
% 0.37/0.60 = ( uminus_uminus_int @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_0
% 0.37/0.60 thf(fact_3574_verit__minus__simplify_I3_J,axiom,
% 0.37/0.60 ! [B: uint32] :
% 0.37/0.60 ( ( minus_minus_uint32 @ zero_zero_uint32 @ B )
% 0.37/0.60 = ( uminus_uminus_uint32 @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % verit_minus_simplify(3)
% 0.37/0.60 thf(fact_3575_verit__minus__simplify_I3_J,axiom,
% 0.37/0.60 ! [B: real] :
% 0.37/0.60 ( ( minus_minus_real @ zero_zero_real @ B )
% 0.37/0.60 = ( uminus_uminus_real @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % verit_minus_simplify(3)
% 0.37/0.60 thf(fact_3576_verit__minus__simplify_I3_J,axiom,
% 0.37/0.60 ! [B: rat] :
% 0.37/0.60 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.37/0.60 = ( uminus_uminus_rat @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % verit_minus_simplify(3)
% 0.37/0.60 thf(fact_3577_verit__minus__simplify_I3_J,axiom,
% 0.37/0.60 ! [B: int] :
% 0.37/0.60 ( ( minus_minus_int @ zero_zero_int @ B )
% 0.37/0.60 = ( uminus_uminus_int @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % verit_minus_simplify(3)
% 0.37/0.60 thf(fact_3578_uminus__add__conv__diff,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ B )
% 0.37/0.60 = ( minus_minus_uint32 @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % uminus_add_conv_diff
% 0.37/0.60 thf(fact_3579_uminus__add__conv__diff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.37/0.60 = ( minus_minus_real @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % uminus_add_conv_diff
% 0.37/0.60 thf(fact_3580_uminus__add__conv__diff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.37/0.60 = ( minus_minus_rat @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % uminus_add_conv_diff
% 0.37/0.60 thf(fact_3581_uminus__add__conv__diff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.37/0.60 = ( minus_minus_int @ B @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % uminus_add_conv_diff
% 0.37/0.60 thf(fact_3582_diff__minus__eq__add,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( minus_minus_uint32 @ A @ ( uminus_uminus_uint32 @ B ) )
% 0.37/0.60 = ( plus_plus_uint32 @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_minus_eq_add
% 0.37/0.60 thf(fact_3583_diff__minus__eq__add,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.37/0.60 = ( plus_plus_real @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_minus_eq_add
% 0.37/0.60 thf(fact_3584_diff__minus__eq__add,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.37/0.60 = ( plus_plus_rat @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_minus_eq_add
% 0.37/0.60 thf(fact_3585_diff__minus__eq__add,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.37/0.60 = ( plus_plus_int @ A @ B ) ) ).
% 0.37/0.60
% 0.37/0.60 % diff_minus_eq_add
% 0.37/0.60 thf(fact_3586_subset__Compl__singleton,axiom,
% 0.37/0.60 ! [A4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 0.37/0.60 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.60 = ( ~ ( member_VEBT_VEBT @ B @ A4 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % subset_Compl_singleton
% 0.37/0.60 thf(fact_3587_subset__Compl__singleton,axiom,
% 0.37/0.60 ! [A4: set_real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_set_real @ A4 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 0.37/0.60 = ( ~ ( member_real @ B @ A4 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % subset_Compl_singleton
% 0.37/0.60 thf(fact_3588_subset__Compl__singleton,axiom,
% 0.37/0.60 ! [A4: set_set_nat,B: set_nat] :
% 0.37/0.60 ( ( ord_le6893508408891458716et_nat @ A4 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 0.37/0.60 = ( ~ ( member_set_nat @ B @ A4 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % subset_Compl_singleton
% 0.37/0.60 thf(fact_3589_subset__Compl__singleton,axiom,
% 0.37/0.60 ! [A4: set_nat,B: nat] :
% 0.37/0.60 ( ( ord_less_eq_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.37/0.60 = ( ~ ( member_nat @ B @ A4 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % subset_Compl_singleton
% 0.37/0.60 thf(fact_3590_subset__Compl__singleton,axiom,
% 0.37/0.60 ! [A4: set_o,B: $o] :
% 0.37/0.60 ( ( ord_less_eq_set_o @ A4 @ ( uminus_uminus_set_o @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.37/0.60 = ( ~ ( member_o @ B @ A4 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % subset_Compl_singleton
% 0.37/0.60 thf(fact_3591_subset__Compl__singleton,axiom,
% 0.37/0.60 ! [A4: set_int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.37/0.60 = ( ~ ( member_int @ B @ A4 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % subset_Compl_singleton
% 0.37/0.60 thf(fact_3592_add__neg__numeral__special_I7_J,axiom,
% 0.37/0.60 ( ( plus_plus_uint32 @ one_one_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) )
% 0.37/0.60 = zero_zero_uint32 ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(7)
% 0.37/0.60 thf(fact_3593_add__neg__numeral__special_I7_J,axiom,
% 0.37/0.60 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.37/0.60 = zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(7)
% 0.37/0.60 thf(fact_3594_add__neg__numeral__special_I7_J,axiom,
% 0.37/0.60 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.37/0.60 = zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(7)
% 0.37/0.60 thf(fact_3595_add__neg__numeral__special_I7_J,axiom,
% 0.37/0.60 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.37/0.60 = zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(7)
% 0.37/0.60 thf(fact_3596_add__neg__numeral__special_I8_J,axiom,
% 0.37/0.60 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ one_one_uint32 )
% 0.37/0.60 = zero_zero_uint32 ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(8)
% 0.37/0.60 thf(fact_3597_add__neg__numeral__special_I8_J,axiom,
% 0.37/0.60 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.37/0.60 = zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(8)
% 0.37/0.60 thf(fact_3598_add__neg__numeral__special_I8_J,axiom,
% 0.37/0.60 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.37/0.60 = zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(8)
% 0.37/0.60 thf(fact_3599_add__neg__numeral__special_I8_J,axiom,
% 0.37/0.60 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.37/0.60 = zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % add_neg_numeral_special(8)
% 0.37/0.60 thf(fact_3600_diff__numeral__special_I12_J,axiom,
% 0.37/0.60 ( ( minus_minus_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ ( uminus_uminus_uint32 @ one_one_uint32 ) )
% 0.37/0.60 = zero_zero_uint32 ) ).
% 0.37/0.60
% 0.37/0.60 % diff_numeral_special(12)
% 0.37/0.60 thf(fact_3601_diff__numeral__special_I12_J,axiom,
% 0.37/0.60 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.37/0.60 = zero_zero_real ) ).
% 0.37/0.60
% 0.37/0.60 % diff_numeral_special(12)
% 0.37/0.60 thf(fact_3602_diff__numeral__special_I12_J,axiom,
% 0.37/0.60 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.37/0.60 = zero_zero_rat ) ).
% 0.37/0.60
% 0.37/0.60 % diff_numeral_special(12)
% 0.37/0.60 thf(fact_3603_diff__numeral__special_I12_J,axiom,
% 0.37/0.60 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.37/0.60 = zero_zero_int ) ).
% 0.37/0.60
% 0.37/0.60 % diff_numeral_special(12)
% 0.37/0.60 thf(fact_3604_add__def,axiom,
% 0.37/0.60 ( vEBT_VEBT_add
% 0.37/0.60 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 0.37/0.60
% 0.37/0.60 % add_def
% 0.37/0.60 thf(fact_3605_mul__def,axiom,
% 0.37/0.60 ( vEBT_VEBT_mul
% 0.37/0.60 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 0.37/0.60
% 0.37/0.60 % mul_def
% 0.37/0.60 thf(fact_3606_assn__times__comm,axiom,
% 0.37/0.60 ( times_times_assn
% 0.37/0.60 = ( ^ [P5: assn,Q6: assn] : ( times_times_assn @ Q6 @ P5 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % assn_times_comm
% 0.37/0.60 thf(fact_3607_assn__times__assoc,axiom,
% 0.37/0.60 ! [P2: assn,Q2: assn,R2: assn] :
% 0.37/0.60 ( ( times_times_assn @ ( times_times_assn @ P2 @ Q2 ) @ R2 )
% 0.37/0.60 = ( times_times_assn @ P2 @ ( times_times_assn @ Q2 @ R2 ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % assn_times_assoc
% 0.37/0.60 thf(fact_3608_equation__minus__iff,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( A
% 0.37/0.60 = ( uminus_uminus_uint32 @ B ) )
% 0.37/0.60 = ( B
% 0.37/0.60 = ( uminus_uminus_uint32 @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % equation_minus_iff
% 0.37/0.60 thf(fact_3609_equation__minus__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( A
% 0.37/0.60 = ( uminus_uminus_real @ B ) )
% 0.37/0.60 = ( B
% 0.37/0.60 = ( uminus_uminus_real @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % equation_minus_iff
% 0.37/0.60 thf(fact_3610_equation__minus__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( A
% 0.37/0.60 = ( uminus_uminus_rat @ B ) )
% 0.37/0.60 = ( B
% 0.37/0.60 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % equation_minus_iff
% 0.37/0.60 thf(fact_3611_equation__minus__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( A
% 0.37/0.60 = ( uminus_uminus_int @ B ) )
% 0.37/0.60 = ( B
% 0.37/0.60 = ( uminus_uminus_int @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % equation_minus_iff
% 0.37/0.60 thf(fact_3612_minus__equation__iff,axiom,
% 0.37/0.60 ! [A: uint32,B: uint32] :
% 0.37/0.60 ( ( ( uminus_uminus_uint32 @ A )
% 0.37/0.60 = B )
% 0.37/0.60 = ( ( uminus_uminus_uint32 @ B )
% 0.37/0.60 = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_equation_iff
% 0.37/0.60 thf(fact_3613_minus__equation__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ( uminus_uminus_real @ A )
% 0.37/0.60 = B )
% 0.37/0.60 = ( ( uminus_uminus_real @ B )
% 0.37/0.60 = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_equation_iff
% 0.37/0.60 thf(fact_3614_minus__equation__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ( uminus_uminus_rat @ A )
% 0.37/0.60 = B )
% 0.37/0.60 = ( ( uminus_uminus_rat @ B )
% 0.37/0.60 = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_equation_iff
% 0.37/0.60 thf(fact_3615_minus__equation__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ( uminus_uminus_int @ A )
% 0.37/0.60 = B )
% 0.37/0.60 = ( ( uminus_uminus_int @ B )
% 0.37/0.60 = A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_equation_iff
% 0.37/0.60 thf(fact_3616_le__minus__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.37/0.60 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_minus_iff
% 0.37/0.60 thf(fact_3617_le__minus__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.37/0.60 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_minus_iff
% 0.37/0.60 thf(fact_3618_le__minus__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.37/0.60 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_minus_iff
% 0.37/0.60 thf(fact_3619_minus__le__iff,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.37/0.60 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_le_iff
% 0.37/0.60 thf(fact_3620_minus__le__iff,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.37/0.60 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_le_iff
% 0.37/0.60 thf(fact_3621_minus__le__iff,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.37/0.60 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.37/0.60
% 0.37/0.60 % minus_le_iff
% 0.37/0.60 thf(fact_3622_le__imp__neg__le,axiom,
% 0.37/0.60 ! [A: real,B: real] :
% 0.37/0.60 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.60 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_imp_neg_le
% 0.37/0.60 thf(fact_3623_le__imp__neg__le,axiom,
% 0.37/0.60 ! [A: rat,B: rat] :
% 0.37/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.60 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_imp_neg_le
% 0.37/0.60 thf(fact_3624_le__imp__neg__le,axiom,
% 0.37/0.60 ! [A: int,B: int] :
% 0.37/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.60 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % le_imp_neg_le
% 0.37/0.60 thf(fact_3625_compl__le__swap2,axiom,
% 0.37/0.60 ! [Y: assn,X: assn] :
% 0.37/0.60 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 0.37/0.60 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 0.37/0.60
% 0.37/0.60 % compl_le_swap2
% 0.37/0.60 thf(fact_3626_compl__le__swap2,axiom,
% 0.37/0.60 ! [Y: set_int,X: set_int] :
% 0.37/0.60 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 0.37/0.60 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 0.37/0.60
% 0.37/0.60 % compl_le_swap2
% 0.37/0.60 thf(fact_3627_compl__le__swap1,axiom,
% 0.37/0.60 ! [Y: assn,X: assn] :
% 0.37/0.60 ( ( ord_less_eq_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 0.37/0.60 => ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 0.37/0.60
% 0.37/0.60 % compl_le_swap1
% 0.37/0.60 thf(fact_3628_compl__le__swap1,axiom,
% 0.37/0.60 ! [Y: set_int,X: set_int] :
% 0.37/0.60 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 0.37/0.60 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % compl_le_swap1
% 0.37/0.61 thf(fact_3629_compl__mono,axiom,
% 0.37/0.61 ! [X: assn,Y: assn] :
% 0.37/0.61 ( ( ord_less_eq_assn @ X @ Y )
% 0.37/0.61 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ ( uminus_uminus_assn @ X ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % compl_mono
% 0.37/0.61 thf(fact_3630_compl__mono,axiom,
% 0.37/0.61 ! [X: set_int,Y: set_int] :
% 0.37/0.61 ( ( ord_less_eq_set_int @ X @ Y )
% 0.37/0.61 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % compl_mono
% 0.37/0.61 thf(fact_3631_minus__less__iff,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.37/0.61 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % minus_less_iff
% 0.37/0.61 thf(fact_3632_minus__less__iff,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.37/0.61 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % minus_less_iff
% 0.37/0.61 thf(fact_3633_minus__less__iff,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.37/0.61 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % minus_less_iff
% 0.37/0.61 thf(fact_3634_less__minus__iff,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.37/0.61 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_iff
% 0.37/0.61 thf(fact_3635_less__minus__iff,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.37/0.61 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_iff
% 0.37/0.61 thf(fact_3636_less__minus__iff,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.37/0.61 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_iff
% 0.37/0.61 thf(fact_3637_verit__negate__coefficient_I2_J,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( ord_less_real @ A @ B )
% 0.37/0.61 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % verit_negate_coefficient(2)
% 0.37/0.61 thf(fact_3638_verit__negate__coefficient_I2_J,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( ord_less_rat @ A @ B )
% 0.37/0.61 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % verit_negate_coefficient(2)
% 0.37/0.61 thf(fact_3639_verit__negate__coefficient_I2_J,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( ord_less_int @ A @ B )
% 0.37/0.61 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % verit_negate_coefficient(2)
% 0.37/0.61 thf(fact_3640_compl__less__swap2,axiom,
% 0.37/0.61 ! [Y: assn,X: assn] :
% 0.37/0.61 ( ( ord_less_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 0.37/0.61 => ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 0.37/0.61
% 0.37/0.61 % compl_less_swap2
% 0.37/0.61 thf(fact_3641_compl__less__swap1,axiom,
% 0.37/0.61 ! [Y: assn,X: assn] :
% 0.37/0.61 ( ( ord_less_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 0.37/0.61 => ( ord_less_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % compl_less_swap1
% 0.37/0.61 thf(fact_3642_group__cancel_Oneg1,axiom,
% 0.37/0.61 ! [A4: uint32,K: uint32,A: uint32] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( plus_plus_uint32 @ K @ A ) )
% 0.37/0.61 => ( ( uminus_uminus_uint32 @ A4 )
% 0.37/0.61 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ K ) @ ( uminus_uminus_uint32 @ A ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.neg1
% 0.37/0.61 thf(fact_3643_group__cancel_Oneg1,axiom,
% 0.37/0.61 ! [A4: real,K: real,A: real] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( plus_plus_real @ K @ A ) )
% 0.37/0.61 => ( ( uminus_uminus_real @ A4 )
% 0.37/0.61 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.neg1
% 0.37/0.61 thf(fact_3644_group__cancel_Oneg1,axiom,
% 0.37/0.61 ! [A4: rat,K: rat,A: rat] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( plus_plus_rat @ K @ A ) )
% 0.37/0.61 => ( ( uminus_uminus_rat @ A4 )
% 0.37/0.61 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.neg1
% 0.37/0.61 thf(fact_3645_group__cancel_Oneg1,axiom,
% 0.37/0.61 ! [A4: int,K: int,A: int] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( plus_plus_int @ K @ A ) )
% 0.37/0.61 => ( ( uminus_uminus_int @ A4 )
% 0.37/0.61 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.neg1
% 0.37/0.61 thf(fact_3646_add_Oinverse__distrib__swap,axiom,
% 0.37/0.61 ! [A: uint32,B: uint32] :
% 0.37/0.61 ( ( uminus_uminus_uint32 @ ( plus_plus_uint32 @ A @ B ) )
% 0.37/0.61 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ B ) @ ( uminus_uminus_uint32 @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_distrib_swap
% 0.37/0.61 thf(fact_3647_add_Oinverse__distrib__swap,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.37/0.61 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_distrib_swap
% 0.37/0.61 thf(fact_3648_add_Oinverse__distrib__swap,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.37/0.61 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_distrib_swap
% 0.37/0.61 thf(fact_3649_add_Oinverse__distrib__swap,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.37/0.61 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_distrib_swap
% 0.37/0.61 thf(fact_3650_minus__diff__commute,axiom,
% 0.37/0.61 ! [B: uint32,A: uint32] :
% 0.37/0.61 ( ( minus_minus_uint32 @ ( uminus_uminus_uint32 @ B ) @ A )
% 0.37/0.61 = ( minus_minus_uint32 @ ( uminus_uminus_uint32 @ A ) @ B ) ) ).
% 0.37/0.61
% 0.37/0.61 % minus_diff_commute
% 0.37/0.61 thf(fact_3651_minus__diff__commute,axiom,
% 0.37/0.61 ! [B: real,A: real] :
% 0.37/0.61 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.37/0.61 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.37/0.61
% 0.37/0.61 % minus_diff_commute
% 0.37/0.61 thf(fact_3652_minus__diff__commute,axiom,
% 0.37/0.61 ! [B: rat,A: rat] :
% 0.37/0.61 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.37/0.61 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.37/0.61
% 0.37/0.61 % minus_diff_commute
% 0.37/0.61 thf(fact_3653_minus__diff__commute,axiom,
% 0.37/0.61 ! [B: int,A: int] :
% 0.37/0.61 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.37/0.61 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.37/0.61
% 0.37/0.61 % minus_diff_commute
% 0.37/0.61 thf(fact_3654_neg__eq__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: uint32,B: uint32] :
% 0.37/0.61 ( ( ( uminus_uminus_uint32 @ A )
% 0.37/0.61 = B )
% 0.37/0.61 = ( ( plus_plus_uint32 @ A @ B )
% 0.37/0.61 = zero_zero_uint32 ) ) ).
% 0.37/0.61
% 0.37/0.61 % neg_eq_iff_add_eq_0
% 0.37/0.61 thf(fact_3655_neg__eq__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( ( uminus_uminus_real @ A )
% 0.37/0.61 = B )
% 0.37/0.61 = ( ( plus_plus_real @ A @ B )
% 0.37/0.61 = zero_zero_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % neg_eq_iff_add_eq_0
% 0.37/0.61 thf(fact_3656_neg__eq__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( ( uminus_uminus_rat @ A )
% 0.37/0.61 = B )
% 0.37/0.61 = ( ( plus_plus_rat @ A @ B )
% 0.37/0.61 = zero_zero_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % neg_eq_iff_add_eq_0
% 0.37/0.61 thf(fact_3657_neg__eq__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( ( uminus_uminus_int @ A )
% 0.37/0.61 = B )
% 0.37/0.61 = ( ( plus_plus_int @ A @ B )
% 0.37/0.61 = zero_zero_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % neg_eq_iff_add_eq_0
% 0.37/0.61 thf(fact_3658_eq__neg__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: uint32,B: uint32] :
% 0.37/0.61 ( ( A
% 0.37/0.61 = ( uminus_uminus_uint32 @ B ) )
% 0.37/0.61 = ( ( plus_plus_uint32 @ A @ B )
% 0.37/0.61 = zero_zero_uint32 ) ) ).
% 0.37/0.61
% 0.37/0.61 % eq_neg_iff_add_eq_0
% 0.37/0.61 thf(fact_3659_eq__neg__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( A
% 0.37/0.61 = ( uminus_uminus_real @ B ) )
% 0.37/0.61 = ( ( plus_plus_real @ A @ B )
% 0.37/0.61 = zero_zero_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % eq_neg_iff_add_eq_0
% 0.37/0.61 thf(fact_3660_eq__neg__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( A
% 0.37/0.61 = ( uminus_uminus_rat @ B ) )
% 0.37/0.61 = ( ( plus_plus_rat @ A @ B )
% 0.37/0.61 = zero_zero_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % eq_neg_iff_add_eq_0
% 0.37/0.61 thf(fact_3661_eq__neg__iff__add__eq__0,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( A
% 0.37/0.61 = ( uminus_uminus_int @ B ) )
% 0.37/0.61 = ( ( plus_plus_int @ A @ B )
% 0.37/0.61 = zero_zero_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % eq_neg_iff_add_eq_0
% 0.37/0.61 thf(fact_3662_add_Oinverse__unique,axiom,
% 0.37/0.61 ! [A: uint32,B: uint32] :
% 0.37/0.61 ( ( ( plus_plus_uint32 @ A @ B )
% 0.37/0.61 = zero_zero_uint32 )
% 0.37/0.61 => ( ( uminus_uminus_uint32 @ A )
% 0.37/0.61 = B ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_unique
% 0.37/0.61 thf(fact_3663_add_Oinverse__unique,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( ( plus_plus_real @ A @ B )
% 0.37/0.61 = zero_zero_real )
% 0.37/0.61 => ( ( uminus_uminus_real @ A )
% 0.37/0.61 = B ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_unique
% 0.37/0.61 thf(fact_3664_add_Oinverse__unique,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( ( plus_plus_rat @ A @ B )
% 0.37/0.61 = zero_zero_rat )
% 0.37/0.61 => ( ( uminus_uminus_rat @ A )
% 0.37/0.61 = B ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_unique
% 0.37/0.61 thf(fact_3665_add_Oinverse__unique,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( ( plus_plus_int @ A @ B )
% 0.37/0.61 = zero_zero_int )
% 0.37/0.61 => ( ( uminus_uminus_int @ A )
% 0.37/0.61 = B ) ) ).
% 0.37/0.61
% 0.37/0.61 % add.inverse_unique
% 0.37/0.61 thf(fact_3666_ab__group__add__class_Oab__left__minus,axiom,
% 0.37/0.61 ! [A: uint32] :
% 0.37/0.61 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ A )
% 0.37/0.61 = zero_zero_uint32 ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_left_minus
% 0.37/0.61 thf(fact_3667_ab__group__add__class_Oab__left__minus,axiom,
% 0.37/0.61 ! [A: real] :
% 0.37/0.61 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.37/0.61 = zero_zero_real ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_left_minus
% 0.37/0.61 thf(fact_3668_ab__group__add__class_Oab__left__minus,axiom,
% 0.37/0.61 ! [A: rat] :
% 0.37/0.61 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.37/0.61 = zero_zero_rat ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_left_minus
% 0.37/0.61 thf(fact_3669_ab__group__add__class_Oab__left__minus,axiom,
% 0.37/0.61 ! [A: int] :
% 0.37/0.61 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.37/0.61 = zero_zero_int ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_left_minus
% 0.37/0.61 thf(fact_3670_add__eq__0__iff,axiom,
% 0.37/0.61 ! [A: uint32,B: uint32] :
% 0.37/0.61 ( ( ( plus_plus_uint32 @ A @ B )
% 0.37/0.61 = zero_zero_uint32 )
% 0.37/0.61 = ( B
% 0.37/0.61 = ( uminus_uminus_uint32 @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add_eq_0_iff
% 0.37/0.61 thf(fact_3671_add__eq__0__iff,axiom,
% 0.37/0.61 ! [A: real,B: real] :
% 0.37/0.61 ( ( ( plus_plus_real @ A @ B )
% 0.37/0.61 = zero_zero_real )
% 0.37/0.61 = ( B
% 0.37/0.61 = ( uminus_uminus_real @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add_eq_0_iff
% 0.37/0.61 thf(fact_3672_add__eq__0__iff,axiom,
% 0.37/0.61 ! [A: rat,B: rat] :
% 0.37/0.61 ( ( ( plus_plus_rat @ A @ B )
% 0.37/0.61 = zero_zero_rat )
% 0.37/0.61 = ( B
% 0.37/0.61 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add_eq_0_iff
% 0.37/0.61 thf(fact_3673_add__eq__0__iff,axiom,
% 0.37/0.61 ! [A: int,B: int] :
% 0.37/0.61 ( ( ( plus_plus_int @ A @ B )
% 0.37/0.61 = zero_zero_int )
% 0.37/0.61 = ( B
% 0.37/0.61 = ( uminus_uminus_int @ A ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % add_eq_0_iff
% 0.37/0.61 thf(fact_3674_zero__neq__neg__one,axiom,
% 0.37/0.61 ( zero_zero_real
% 0.37/0.61 != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_neq_neg_one
% 0.37/0.61 thf(fact_3675_zero__neq__neg__one,axiom,
% 0.37/0.61 ( zero_zero_rat
% 0.37/0.61 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_neq_neg_one
% 0.37/0.61 thf(fact_3676_zero__neq__neg__one,axiom,
% 0.37/0.61 ( zero_zero_int
% 0.37/0.61 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_neq_neg_one
% 0.37/0.61 thf(fact_3677_le__minus__one__simps_I2_J,axiom,
% 0.37/0.61 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(2)
% 0.37/0.61 thf(fact_3678_le__minus__one__simps_I2_J,axiom,
% 0.37/0.61 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(2)
% 0.37/0.61 thf(fact_3679_le__minus__one__simps_I2_J,axiom,
% 0.37/0.61 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(2)
% 0.37/0.61 thf(fact_3680_le__minus__one__simps_I4_J,axiom,
% 0.37/0.61 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(4)
% 0.37/0.61 thf(fact_3681_le__minus__one__simps_I4_J,axiom,
% 0.37/0.61 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(4)
% 0.37/0.61 thf(fact_3682_le__minus__one__simps_I4_J,axiom,
% 0.37/0.61 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(4)
% 0.37/0.61 thf(fact_3683_less__minus__one__simps_I4_J,axiom,
% 0.37/0.61 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(4)
% 0.37/0.61 thf(fact_3684_less__minus__one__simps_I4_J,axiom,
% 0.37/0.61 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(4)
% 0.37/0.61 thf(fact_3685_less__minus__one__simps_I4_J,axiom,
% 0.37/0.61 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(4)
% 0.37/0.61 thf(fact_3686_less__minus__one__simps_I2_J,axiom,
% 0.37/0.61 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(2)
% 0.37/0.61 thf(fact_3687_less__minus__one__simps_I2_J,axiom,
% 0.37/0.61 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(2)
% 0.37/0.61 thf(fact_3688_less__minus__one__simps_I2_J,axiom,
% 0.37/0.61 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(2)
% 0.37/0.61 thf(fact_3689_group__cancel_Osub2,axiom,
% 0.37/0.61 ! [B4: uint32,K: uint32,B: uint32,A: uint32] :
% 0.37/0.61 ( ( B4
% 0.37/0.61 = ( plus_plus_uint32 @ K @ B ) )
% 0.37/0.61 => ( ( minus_minus_uint32 @ A @ B4 )
% 0.37/0.61 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ K ) @ ( minus_minus_uint32 @ A @ B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.sub2
% 0.37/0.61 thf(fact_3690_group__cancel_Osub2,axiom,
% 0.37/0.61 ! [B4: real,K: real,B: real,A: real] :
% 0.37/0.61 ( ( B4
% 0.37/0.61 = ( plus_plus_real @ K @ B ) )
% 0.37/0.61 => ( ( minus_minus_real @ A @ B4 )
% 0.37/0.61 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.sub2
% 0.37/0.61 thf(fact_3691_group__cancel_Osub2,axiom,
% 0.37/0.61 ! [B4: rat,K: rat,B: rat,A: rat] :
% 0.37/0.61 ( ( B4
% 0.37/0.61 = ( plus_plus_rat @ K @ B ) )
% 0.37/0.61 => ( ( minus_minus_rat @ A @ B4 )
% 0.37/0.61 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.sub2
% 0.37/0.61 thf(fact_3692_group__cancel_Osub2,axiom,
% 0.37/0.61 ! [B4: int,K: int,B: int,A: int] :
% 0.37/0.61 ( ( B4
% 0.37/0.61 = ( plus_plus_int @ K @ B ) )
% 0.37/0.61 => ( ( minus_minus_int @ A @ B4 )
% 0.37/0.61 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % group_cancel.sub2
% 0.37/0.61 thf(fact_3693_diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_uint32
% 0.37/0.61 = ( ^ [A7: uint32,B7: uint32] : ( plus_plus_uint32 @ A7 @ ( uminus_uminus_uint32 @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % diff_conv_add_uminus
% 0.37/0.61 thf(fact_3694_diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_real
% 0.37/0.61 = ( ^ [A7: real,B7: real] : ( plus_plus_real @ A7 @ ( uminus_uminus_real @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % diff_conv_add_uminus
% 0.37/0.61 thf(fact_3695_diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_rat
% 0.37/0.61 = ( ^ [A7: rat,B7: rat] : ( plus_plus_rat @ A7 @ ( uminus_uminus_rat @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % diff_conv_add_uminus
% 0.37/0.61 thf(fact_3696_diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_int
% 0.37/0.61 = ( ^ [A7: int,B7: int] : ( plus_plus_int @ A7 @ ( uminus_uminus_int @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % diff_conv_add_uminus
% 0.37/0.61 thf(fact_3697_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_uint32
% 0.37/0.61 = ( ^ [A7: uint32,B7: uint32] : ( plus_plus_uint32 @ A7 @ ( uminus_uminus_uint32 @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.37/0.61 thf(fact_3698_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_real
% 0.37/0.61 = ( ^ [A7: real,B7: real] : ( plus_plus_real @ A7 @ ( uminus_uminus_real @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.37/0.61 thf(fact_3699_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_rat
% 0.37/0.61 = ( ^ [A7: rat,B7: rat] : ( plus_plus_rat @ A7 @ ( uminus_uminus_rat @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.37/0.61 thf(fact_3700_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.37/0.61 ( minus_minus_int
% 0.37/0.61 = ( ^ [A7: int,B7: int] : ( plus_plus_int @ A7 @ ( uminus_uminus_int @ B7 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.37/0.61 thf(fact_3701_subset__Compl__self__eq,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( ord_less_eq_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 0.37/0.61 = ( A4 = bot_bot_set_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % subset_Compl_self_eq
% 0.37/0.61 thf(fact_3702_subset__Compl__self__eq,axiom,
% 0.37/0.61 ! [A4: set_o] :
% 0.37/0.61 ( ( ord_less_eq_set_o @ A4 @ ( uminus_uminus_set_o @ A4 ) )
% 0.37/0.61 = ( A4 = bot_bot_set_o ) ) ).
% 0.37/0.61
% 0.37/0.61 % subset_Compl_self_eq
% 0.37/0.61 thf(fact_3703_subset__Compl__self__eq,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( ord_less_eq_set_int @ A4 @ ( uminus1532241313380277803et_int @ A4 ) )
% 0.37/0.61 = ( A4 = bot_bot_set_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % subset_Compl_self_eq
% 0.37/0.61 thf(fact_3704_le__minus__one__simps_I1_J,axiom,
% 0.37/0.61 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(1)
% 0.37/0.61 thf(fact_3705_le__minus__one__simps_I1_J,axiom,
% 0.37/0.61 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(1)
% 0.37/0.61 thf(fact_3706_le__minus__one__simps_I1_J,axiom,
% 0.37/0.61 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(1)
% 0.37/0.61 thf(fact_3707_le__minus__one__simps_I3_J,axiom,
% 0.37/0.61 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(3)
% 0.37/0.61 thf(fact_3708_le__minus__one__simps_I3_J,axiom,
% 0.37/0.61 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(3)
% 0.37/0.61 thf(fact_3709_le__minus__one__simps_I3_J,axiom,
% 0.37/0.61 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % le_minus_one_simps(3)
% 0.37/0.61 thf(fact_3710_less__minus__one__simps_I3_J,axiom,
% 0.37/0.61 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(3)
% 0.37/0.61 thf(fact_3711_less__minus__one__simps_I3_J,axiom,
% 0.37/0.61 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(3)
% 0.37/0.61 thf(fact_3712_less__minus__one__simps_I3_J,axiom,
% 0.37/0.61 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(3)
% 0.37/0.61 thf(fact_3713_less__minus__one__simps_I1_J,axiom,
% 0.37/0.61 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(1)
% 0.37/0.61 thf(fact_3714_less__minus__one__simps_I1_J,axiom,
% 0.37/0.61 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(1)
% 0.37/0.61 thf(fact_3715_less__minus__one__simps_I1_J,axiom,
% 0.37/0.61 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.37/0.61
% 0.37/0.61 % less_minus_one_simps(1)
% 0.37/0.61 thf(fact_3716_Compl__insert,axiom,
% 0.37/0.61 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.61 ( ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.61 = ( minus_5127226145743854075T_VEBT @ ( uminus8041839845116263051T_VEBT @ A4 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_insert
% 0.37/0.61 thf(fact_3717_Compl__insert,axiom,
% 0.37/0.61 ! [X: int,A4: set_int] :
% 0.37/0.61 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.61 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A4 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_insert
% 0.37/0.61 thf(fact_3718_Compl__insert,axiom,
% 0.37/0.61 ! [X: $o,A4: set_o] :
% 0.37/0.61 ( ( uminus_uminus_set_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.61 = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A4 ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_insert
% 0.37/0.61 thf(fact_3719_Compl__insert,axiom,
% 0.37/0.61 ! [X: nat,A4: set_nat] :
% 0.37/0.61 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.61 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A4 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_insert
% 0.37/0.61 thf(fact_3720_frac__neg,axiom,
% 0.37/0.61 ! [X: real] :
% 0.37/0.61 ( ( ( member_real @ X @ ring_1_Ints_real )
% 0.37/0.61 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 0.37/0.61 = zero_zero_real ) )
% 0.37/0.61 & ( ~ ( member_real @ X @ ring_1_Ints_real )
% 0.37/0.61 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 0.37/0.61 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % frac_neg
% 0.37/0.61 thf(fact_3721_frac__neg,axiom,
% 0.37/0.61 ! [X: rat] :
% 0.37/0.61 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 0.37/0.61 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 0.37/0.61 = zero_zero_rat ) )
% 0.37/0.61 & ( ~ ( member_rat @ X @ ring_1_Ints_rat )
% 0.37/0.61 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 0.37/0.61 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % frac_neg
% 0.37/0.61 thf(fact_3722_dbl__dec__simps_I2_J,axiom,
% 0.37/0.61 ( ( neg_nu965353292909893953uint32 @ zero_zero_uint32 )
% 0.37/0.61 = ( uminus_uminus_uint32 @ one_one_uint32 ) ) ).
% 0.37/0.61
% 0.37/0.61 % dbl_dec_simps(2)
% 0.37/0.61 thf(fact_3723_dbl__dec__simps_I2_J,axiom,
% 0.37/0.61 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 0.37/0.61 = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % dbl_dec_simps(2)
% 0.37/0.61 thf(fact_3724_dbl__dec__simps_I2_J,axiom,
% 0.37/0.61 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.37/0.61 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % dbl_dec_simps(2)
% 0.37/0.61 thf(fact_3725_dbl__dec__simps_I2_J,axiom,
% 0.37/0.61 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.37/0.61 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % dbl_dec_simps(2)
% 0.37/0.61 thf(fact_3726_foldr__one,axiom,
% 0.37/0.61 ! [D: nat,Ys: list_nat] : ( ord_less_eq_nat @ D @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D ) ) ).
% 0.37/0.61
% 0.37/0.61 % foldr_one
% 0.37/0.61 thf(fact_3727_Gcd__remove0__nat,axiom,
% 0.37/0.61 ! [M7: set_nat] :
% 0.37/0.61 ( ( finite_finite_nat @ M7 )
% 0.37/0.61 => ( ( gcd_Gcd_nat @ M7 )
% 0.37/0.61 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_remove0_nat
% 0.37/0.61 thf(fact_3728_Gcd__0__iff,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( ( gcd_Gcd_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_0_iff
% 0.37/0.61 thf(fact_3729_Gcd__0__iff,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( ( gcd_Gcd_int @ A4 )
% 0.37/0.61 = zero_zero_int )
% 0.37/0.61 = ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_0_iff
% 0.37/0.61 thf(fact_3730_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 0.37/0.61 ! [A: $o,B: $o,X: nat] :
% 0.37/0.61 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.37/0.61 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(1)
% 0.37/0.61 thf(fact_3731_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 0.37/0.61 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.37/0.61 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X )
% 0.37/0.61 = one_one_nat ) ).
% 0.37/0.61
% 0.37/0.61 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(3)
% 0.37/0.61 thf(fact_3732_the__dflt__None__empty,axiom,
% 0.37/0.61 ( ( dflt_None_set_nat @ bot_bot_set_nat )
% 0.37/0.61 = none_set_nat ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_empty
% 0.37/0.61 thf(fact_3733_the__dflt__None__empty,axiom,
% 0.37/0.61 ( ( dflt_None_set_int @ bot_bot_set_int )
% 0.37/0.61 = none_set_int ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_empty
% 0.37/0.61 thf(fact_3734_the__dflt__None__empty,axiom,
% 0.37/0.61 ( ( dflt_None_set_o @ bot_bot_set_o )
% 0.37/0.61 = none_set_o ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_empty
% 0.37/0.61 thf(fact_3735_ComplI,axiom,
% 0.37/0.61 ! [C2: nat,A4: set_nat] :
% 0.37/0.61 ( ~ ( member_nat @ C2 @ A4 )
% 0.37/0.61 => ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplI
% 0.37/0.61 thf(fact_3736_ComplI,axiom,
% 0.37/0.61 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.61 ( ~ ( member_VEBT_VEBT @ C2 @ A4 )
% 0.37/0.61 => ( member_VEBT_VEBT @ C2 @ ( uminus8041839845116263051T_VEBT @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplI
% 0.37/0.61 thf(fact_3737_ComplI,axiom,
% 0.37/0.61 ! [C2: real,A4: set_real] :
% 0.37/0.61 ( ~ ( member_real @ C2 @ A4 )
% 0.37/0.61 => ( member_real @ C2 @ ( uminus612125837232591019t_real @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplI
% 0.37/0.61 thf(fact_3738_ComplI,axiom,
% 0.37/0.61 ! [C2: int,A4: set_int] :
% 0.37/0.61 ( ~ ( member_int @ C2 @ A4 )
% 0.37/0.61 => ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplI
% 0.37/0.61 thf(fact_3739_ComplI,axiom,
% 0.37/0.61 ! [C2: set_nat,A4: set_set_nat] :
% 0.37/0.61 ( ~ ( member_set_nat @ C2 @ A4 )
% 0.37/0.61 => ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplI
% 0.37/0.61 thf(fact_3740_Compl__iff,axiom,
% 0.37/0.61 ! [C2: nat,A4: set_nat] :
% 0.37/0.61 ( ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 0.37/0.61 = ( ~ ( member_nat @ C2 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_iff
% 0.37/0.61 thf(fact_3741_Compl__iff,axiom,
% 0.37/0.61 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ C2 @ ( uminus8041839845116263051T_VEBT @ A4 ) )
% 0.37/0.61 = ( ~ ( member_VEBT_VEBT @ C2 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_iff
% 0.37/0.61 thf(fact_3742_Compl__iff,axiom,
% 0.37/0.61 ! [C2: real,A4: set_real] :
% 0.37/0.61 ( ( member_real @ C2 @ ( uminus612125837232591019t_real @ A4 ) )
% 0.37/0.61 = ( ~ ( member_real @ C2 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_iff
% 0.37/0.61 thf(fact_3743_Compl__iff,axiom,
% 0.37/0.61 ! [C2: int,A4: set_int] :
% 0.37/0.61 ( ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) )
% 0.37/0.61 = ( ~ ( member_int @ C2 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_iff
% 0.37/0.61 thf(fact_3744_Compl__iff,axiom,
% 0.37/0.61 ! [C2: set_nat,A4: set_set_nat] :
% 0.37/0.61 ( ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) )
% 0.37/0.61 = ( ~ ( member_set_nat @ C2 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Compl_iff
% 0.37/0.61 thf(fact_3745_the__dflt__None__nonempty,axiom,
% 0.37/0.61 ! [S3: set_nat] :
% 0.37/0.61 ( ( S3 != bot_bot_set_nat )
% 0.37/0.61 => ( ( dflt_None_set_nat @ S3 )
% 0.37/0.61 = ( some_set_nat @ S3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_nonempty
% 0.37/0.61 thf(fact_3746_the__dflt__None__nonempty,axiom,
% 0.37/0.61 ! [S3: set_int] :
% 0.37/0.61 ( ( S3 != bot_bot_set_int )
% 0.37/0.61 => ( ( dflt_None_set_int @ S3 )
% 0.37/0.61 = ( some_set_int @ S3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_nonempty
% 0.37/0.61 thf(fact_3747_the__dflt__None__nonempty,axiom,
% 0.37/0.61 ! [S3: set_o] :
% 0.37/0.61 ( ( S3 != bot_bot_set_o )
% 0.37/0.61 => ( ( dflt_None_set_o @ S3 )
% 0.37/0.61 = ( some_set_o @ S3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_nonempty
% 0.37/0.61 thf(fact_3748_Gcd__empty,axiom,
% 0.37/0.61 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_empty
% 0.37/0.61 thf(fact_3749_Gcd__empty,axiom,
% 0.37/0.61 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 0.37/0.61 = zero_zero_int ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_empty
% 0.37/0.61 thf(fact_3750_ComplD,axiom,
% 0.37/0.61 ! [C2: nat,A4: set_nat] :
% 0.37/0.61 ( ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 0.37/0.61 => ~ ( member_nat @ C2 @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplD
% 0.37/0.61 thf(fact_3751_ComplD,axiom,
% 0.37/0.61 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ C2 @ ( uminus8041839845116263051T_VEBT @ A4 ) )
% 0.37/0.61 => ~ ( member_VEBT_VEBT @ C2 @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplD
% 0.37/0.61 thf(fact_3752_ComplD,axiom,
% 0.37/0.61 ! [C2: real,A4: set_real] :
% 0.37/0.61 ( ( member_real @ C2 @ ( uminus612125837232591019t_real @ A4 ) )
% 0.37/0.61 => ~ ( member_real @ C2 @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplD
% 0.37/0.61 thf(fact_3753_ComplD,axiom,
% 0.37/0.61 ! [C2: int,A4: set_int] :
% 0.37/0.61 ( ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) )
% 0.37/0.61 => ~ ( member_int @ C2 @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplD
% 0.37/0.61 thf(fact_3754_ComplD,axiom,
% 0.37/0.61 ! [C2: set_nat,A4: set_set_nat] :
% 0.37/0.61 ( ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) )
% 0.37/0.61 => ~ ( member_set_nat @ C2 @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % ComplD
% 0.37/0.61 thf(fact_3755_dflt__None__set__def,axiom,
% 0.37/0.61 ( dflt_None_set_nat
% 0.37/0.61 = ( ^ [S6: set_nat] : ( if_option_set_nat @ ( S6 = bot_bot_set_nat ) @ none_set_nat @ ( some_set_nat @ S6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % dflt_None_set_def
% 0.37/0.61 thf(fact_3756_dflt__None__set__def,axiom,
% 0.37/0.61 ( dflt_None_set_int
% 0.37/0.61 = ( ^ [S6: set_int] : ( if_option_set_int @ ( S6 = bot_bot_set_int ) @ none_set_int @ ( some_set_int @ S6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % dflt_None_set_def
% 0.37/0.61 thf(fact_3757_dflt__None__set__def,axiom,
% 0.37/0.61 ( dflt_None_set_o
% 0.37/0.61 = ( ^ [S6: set_o] : ( if_option_set_o @ ( S6 = bot_bot_set_o ) @ none_set_o @ ( some_set_o @ S6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % dflt_None_set_def
% 0.37/0.61 thf(fact_3758_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 0.37/0.61 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.37/0.61 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X )
% 0.37/0.61 = one_one_nat ) ).
% 0.37/0.61
% 0.37/0.61 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(2)
% 0.37/0.61 thf(fact_3759_the__dflt__None__set,axiom,
% 0.37/0.61 ! [X: set_nat] :
% 0.37/0.61 ( ( the_default_set_nat @ bot_bot_set_nat @ ( dflt_None_set_nat @ X ) )
% 0.37/0.61 = X ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_set
% 0.37/0.61 thf(fact_3760_the__dflt__None__set,axiom,
% 0.37/0.61 ! [X: set_int] :
% 0.37/0.61 ( ( the_default_set_int @ bot_bot_set_int @ ( dflt_None_set_int @ X ) )
% 0.37/0.61 = X ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_set
% 0.37/0.61 thf(fact_3761_the__dflt__None__set,axiom,
% 0.37/0.61 ! [X: set_o] :
% 0.37/0.61 ( ( the_default_set_o @ bot_bot_set_o @ ( dflt_None_set_o @ X ) )
% 0.37/0.61 = X ) ).
% 0.37/0.61
% 0.37/0.61 % the_dflt_None_set
% 0.37/0.61 thf(fact_3762_foldr__same__int,axiom,
% 0.37/0.61 ! [Xs: list_nat,Y: nat] :
% 0.37/0.61 ( ! [X3: nat,Y3: nat] :
% 0.37/0.61 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.37/0.61 => ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 0.37/0.61 => ( X3 = Y3 ) ) )
% 0.37/0.61 => ( ! [X3: nat] :
% 0.37/0.61 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.37/0.61 => ( X3 = Y ) )
% 0.37/0.61 => ( ( foldr_nat_nat @ plus_plus_nat @ Xs @ zero_zero_nat )
% 0.37/0.61 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ Y ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % foldr_same_int
% 0.37/0.61 thf(fact_3763_Gcd__fin__0__iff,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( ( semiri4258706085729940814in_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 0.37/0.61 & ( finite_finite_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin_0_iff
% 0.37/0.61 thf(fact_3764_Gcd__fin__0__iff,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( ( semiri4256215615220890538in_int @ A4 )
% 0.37/0.61 = zero_zero_int )
% 0.37/0.61 = ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) )
% 0.37/0.61 & ( finite_finite_int @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin_0_iff
% 0.37/0.61 thf(fact_3765_power__decreasing__iff,axiom,
% 0.37/0.61 ! [B: real,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.61 => ( ( ord_less_real @ B @ one_one_real )
% 0.37/0.61 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_decreasing_iff
% 0.37/0.61 thf(fact_3766_power__decreasing__iff,axiom,
% 0.37/0.61 ! [B: rat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.37/0.61 => ( ( ord_less_rat @ B @ one_one_rat )
% 0.37/0.61 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_decreasing_iff
% 0.37/0.61 thf(fact_3767_power__decreasing__iff,axiom,
% 0.37/0.61 ! [B: nat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.61 => ( ( ord_less_nat @ B @ one_one_nat )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_decreasing_iff
% 0.37/0.61 thf(fact_3768_power__decreasing__iff,axiom,
% 0.37/0.61 ! [B: int,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.61 => ( ( ord_less_int @ B @ one_one_int )
% 0.37/0.61 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_decreasing_iff
% 0.37/0.61 thf(fact_3769_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3770_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_int,X: int] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3771_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_o,X: $o] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_o @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_o @ ( insert_o @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3772_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_complex,X: complex] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_complex @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_complex @ ( insert_complex @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3773_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_literal,X: literal] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_literal @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_literal @ ( insert_literal @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3774_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_list_nat,X: list_nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3775_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_set_nat,X: set_nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3776_card__insert__le__m1,axiom,
% 0.37/0.61 ! [N: nat,Y: set_nat,X: nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le_m1
% 0.37/0.61 thf(fact_3777_count__notin,axiom,
% 0.37/0.61 ! [X: int,Xs: list_int] :
% 0.37/0.61 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.61 => ( ( count_list_int @ Xs @ X )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_notin
% 0.37/0.61 thf(fact_3778_count__notin,axiom,
% 0.37/0.61 ! [X: set_nat,Xs: list_set_nat] :
% 0.37/0.61 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.37/0.61 => ( ( count_list_set_nat @ Xs @ X )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_notin
% 0.37/0.61 thf(fact_3779_count__notin,axiom,
% 0.37/0.61 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.61 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.61 => ( ( count_list_VEBT_VEBT @ Xs @ X )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_notin
% 0.37/0.61 thf(fact_3780_count__notin,axiom,
% 0.37/0.61 ! [X: nat,Xs: list_nat] :
% 0.37/0.61 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.61 => ( ( count_list_nat @ Xs @ X )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_notin
% 0.37/0.61 thf(fact_3781_count__notin,axiom,
% 0.37/0.61 ! [X: real,Xs: list_real] :
% 0.37/0.61 ( ~ ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.37/0.61 => ( ( count_list_real @ Xs @ X )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_notin
% 0.37/0.61 thf(fact_3782_count__notin,axiom,
% 0.37/0.61 ! [X: $o,Xs: list_o] :
% 0.37/0.61 ( ~ ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.37/0.61 => ( ( count_list_o @ Xs @ X )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_notin
% 0.37/0.61 thf(fact_3783_image__Fpow__mono,axiom,
% 0.37/0.61 ! [F: nat > set_nat,A4: set_nat,B4: set_set_nat] :
% 0.37/0.61 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A4 ) @ B4 )
% 0.37/0.61 => ( ord_le9131159989063066194et_nat @ ( image_6725021117256019401et_nat @ ( image_nat_set_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_set_nat @ B4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % image_Fpow_mono
% 0.37/0.61 thf(fact_3784_image__Fpow__mono,axiom,
% 0.37/0.61 ! [F: nat > nat,A4: set_nat,B4: set_nat] :
% 0.37/0.61 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B4 )
% 0.37/0.61 => ( ord_le6893508408891458716et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_nat @ B4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % image_Fpow_mono
% 0.37/0.61 thf(fact_3785_image__Fpow__mono,axiom,
% 0.37/0.61 ! [F: int > nat,A4: set_int,B4: set_nat] :
% 0.37/0.61 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B4 )
% 0.37/0.61 => ( ord_le6893508408891458716et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_nat @ B4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % image_Fpow_mono
% 0.37/0.61 thf(fact_3786_image__Fpow__mono,axiom,
% 0.37/0.61 ! [F: nat > int,A4: set_nat,B4: set_int] :
% 0.37/0.61 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B4 )
% 0.37/0.61 => ( ord_le4403425263959731960et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_int @ B4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % image_Fpow_mono
% 0.37/0.61 thf(fact_3787_image__Fpow__mono,axiom,
% 0.37/0.61 ! [F: int > int,A4: set_int,B4: set_int] :
% 0.37/0.61 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B4 )
% 0.37/0.61 => ( ord_le4403425263959731960et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_int @ B4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % image_Fpow_mono
% 0.37/0.61 thf(fact_3788_power__shift,axiom,
% 0.37/0.61 ! [X: nat,Y: nat,Z: nat] :
% 0.37/0.61 ( ( ( power_power_nat @ X @ Y )
% 0.37/0.61 = Z )
% 0.37/0.61 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.37/0.61 = ( some_nat @ Z ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_shift
% 0.37/0.61 thf(fact_3789_local_Opower__def,axiom,
% 0.37/0.61 ( vEBT_VEBT_power
% 0.37/0.61 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % local.power_def
% 0.37/0.61 thf(fact_3790_power__Suc__0,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.61 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc_0
% 0.37/0.61 thf(fact_3791_nat__power__eq__Suc__0__iff,axiom,
% 0.37/0.61 ! [X: nat,M: nat] :
% 0.37/0.61 ( ( ( power_power_nat @ X @ M )
% 0.37/0.61 = ( suc @ zero_zero_nat ) )
% 0.37/0.61 = ( ( M = zero_zero_nat )
% 0.37/0.61 | ( X
% 0.37/0.61 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % nat_power_eq_Suc_0_iff
% 0.37/0.61 thf(fact_3792_nat__zero__less__power__iff,axiom,
% 0.37/0.61 ! [X: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 0.37/0.61 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.37/0.61 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % nat_zero_less_power_iff
% 0.37/0.61 thf(fact_3793_power__inject__exp,axiom,
% 0.37/0.61 ! [A: real,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.61 => ( ( ( power_power_real @ A @ M )
% 0.37/0.61 = ( power_power_real @ A @ N ) )
% 0.37/0.61 = ( M = N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_exp
% 0.37/0.61 thf(fact_3794_power__inject__exp,axiom,
% 0.37/0.61 ! [A: rat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.61 => ( ( ( power_power_rat @ A @ M )
% 0.37/0.61 = ( power_power_rat @ A @ N ) )
% 0.37/0.61 = ( M = N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_exp
% 0.37/0.61 thf(fact_3795_power__inject__exp,axiom,
% 0.37/0.61 ! [A: nat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.61 => ( ( ( power_power_nat @ A @ M )
% 0.37/0.61 = ( power_power_nat @ A @ N ) )
% 0.37/0.61 = ( M = N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_exp
% 0.37/0.61 thf(fact_3796_power__inject__exp,axiom,
% 0.37/0.61 ! [A: int,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.61 => ( ( ( power_power_int @ A @ M )
% 0.37/0.61 = ( power_power_int @ A @ N ) )
% 0.37/0.61 = ( M = N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_exp
% 0.37/0.61 thf(fact_3797_power__0__Suc,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( power_power_uint32 @ zero_zero_uint32 @ ( suc @ N ) )
% 0.37/0.61 = zero_zero_uint32 ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_Suc
% 0.37/0.61 thf(fact_3798_power__0__Suc,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 0.37/0.61 = zero_zero_rat ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_Suc
% 0.37/0.61 thf(fact_3799_power__0__Suc,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_Suc
% 0.37/0.61 thf(fact_3800_power__0__Suc,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 0.37/0.61 = zero_zero_real ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_Suc
% 0.37/0.61 thf(fact_3801_power__0__Suc,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 0.37/0.61 = zero_zero_complex ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_Suc
% 0.37/0.61 thf(fact_3802_power__0__Suc,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 0.37/0.61 = zero_zero_int ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_Suc
% 0.37/0.61 thf(fact_3803_power__Suc0__right,axiom,
% 0.37/0.61 ! [A: nat] :
% 0.37/0.61 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.37/0.61 = A ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc0_right
% 0.37/0.61 thf(fact_3804_power__Suc0__right,axiom,
% 0.37/0.61 ! [A: real] :
% 0.37/0.61 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 0.37/0.61 = A ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc0_right
% 0.37/0.61 thf(fact_3805_power__Suc0__right,axiom,
% 0.37/0.61 ! [A: complex] :
% 0.37/0.61 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 0.37/0.61 = A ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc0_right
% 0.37/0.61 thf(fact_3806_power__Suc0__right,axiom,
% 0.37/0.61 ! [A: int] :
% 0.37/0.61 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.37/0.61 = A ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc0_right
% 0.37/0.61 thf(fact_3807_card_Oempty,axiom,
% 0.37/0.61 ( ( finite_card_complex @ bot_bot_set_complex )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % card.empty
% 0.37/0.61 thf(fact_3808_card_Oempty,axiom,
% 0.37/0.61 ( ( finite_card_literal @ bot_bot_set_literal )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % card.empty
% 0.37/0.61 thf(fact_3809_card_Oempty,axiom,
% 0.37/0.61 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % card.empty
% 0.37/0.61 thf(fact_3810_card_Oempty,axiom,
% 0.37/0.61 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % card.empty
% 0.37/0.61 thf(fact_3811_card_Oempty,axiom,
% 0.37/0.61 ( ( finite_card_nat @ bot_bot_set_nat )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % card.empty
% 0.37/0.61 thf(fact_3812_card_Oempty,axiom,
% 0.37/0.61 ( ( finite_card_int @ bot_bot_set_int )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % card.empty
% 0.37/0.61 thf(fact_3813_card_Oempty,axiom,
% 0.37/0.61 ( ( finite_card_o @ bot_bot_set_o )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % card.empty
% 0.37/0.61 thf(fact_3814_card_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_literal] :
% 0.37/0.61 ( ~ ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ( finite_card_literal @ A4 )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % card.infinite
% 0.37/0.61 thf(fact_3815_card_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_list_nat] :
% 0.37/0.61 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.61 => ( ( finite_card_list_nat @ A4 )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % card.infinite
% 0.37/0.61 thf(fact_3816_card_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_set_nat] :
% 0.37/0.61 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.61 => ( ( finite_card_set_nat @ A4 )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % card.infinite
% 0.37/0.61 thf(fact_3817_card_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ( finite_card_nat @ A4 )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % card.infinite
% 0.37/0.61 thf(fact_3818_card_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ~ ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ( finite_card_int @ A4 )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % card.infinite
% 0.37/0.61 thf(fact_3819_card_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_complex] :
% 0.37/0.61 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.37/0.61 => ( ( finite_card_complex @ A4 )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % card.infinite
% 0.37/0.61 thf(fact_3820_card_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_Code_integer] :
% 0.37/0.61 ( ~ ( finite6017078050557962740nteger @ A4 )
% 0.37/0.61 => ( ( finite4902975817058060853nteger @ A4 )
% 0.37/0.61 = zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % card.infinite
% 0.37/0.61 thf(fact_3821_Gcd__fin_Oempty,axiom,
% 0.37/0.61 ( ( semiri4258706085729940814in_nat @ bot_bot_set_nat )
% 0.37/0.61 = zero_zero_nat ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin.empty
% 0.37/0.61 thf(fact_3822_Gcd__fin_Oempty,axiom,
% 0.37/0.61 ( ( semiri4256215615220890538in_int @ bot_bot_set_int )
% 0.37/0.61 = zero_zero_int ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin.empty
% 0.37/0.61 thf(fact_3823_Gcd__fin_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ( semiri4258706085729940814in_nat @ A4 )
% 0.37/0.61 = one_one_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin.infinite
% 0.37/0.61 thf(fact_3824_Gcd__fin_Oinfinite,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ~ ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ( semiri4256215615220890538in_int @ A4 )
% 0.37/0.61 = one_one_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin.infinite
% 0.37/0.61 thf(fact_3825_Gcd__fin__eq__Gcd,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ( semiri4258706085729940814in_nat @ A4 )
% 0.37/0.61 = ( gcd_Gcd_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin_eq_Gcd
% 0.37/0.61 thf(fact_3826_Gcd__fin__eq__Gcd,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ( semiri4256215615220890538in_int @ A4 )
% 0.37/0.61 = ( gcd_Gcd_int @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Gcd_fin_eq_Gcd
% 0.37/0.61 thf(fact_3827_power__strict__increasing__iff,axiom,
% 0.37/0.61 ! [B: real,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.61 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 0.37/0.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing_iff
% 0.37/0.61 thf(fact_3828_power__strict__increasing__iff,axiom,
% 0.37/0.61 ! [B: rat,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_rat @ one_one_rat @ B )
% 0.37/0.61 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.37/0.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing_iff
% 0.37/0.61 thf(fact_3829_power__strict__increasing__iff,axiom,
% 0.37/0.61 ! [B: nat,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_nat @ one_one_nat @ B )
% 0.37/0.61 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.37/0.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing_iff
% 0.37/0.61 thf(fact_3830_power__strict__increasing__iff,axiom,
% 0.37/0.61 ! [B: int,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_int @ one_one_int @ B )
% 0.37/0.61 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.37/0.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing_iff
% 0.37/0.61 thf(fact_3831_power__eq__0__iff,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ( power_power_rat @ A @ N )
% 0.37/0.61 = zero_zero_rat )
% 0.37/0.61 = ( ( A = zero_zero_rat )
% 0.37/0.61 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_eq_0_iff
% 0.37/0.61 thf(fact_3832_power__eq__0__iff,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ( power_power_nat @ A @ N )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A = zero_zero_nat )
% 0.37/0.61 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_eq_0_iff
% 0.37/0.61 thf(fact_3833_power__eq__0__iff,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ( power_power_real @ A @ N )
% 0.37/0.61 = zero_zero_real )
% 0.37/0.61 = ( ( A = zero_zero_real )
% 0.37/0.61 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_eq_0_iff
% 0.37/0.61 thf(fact_3834_power__eq__0__iff,axiom,
% 0.37/0.61 ! [A: complex,N: nat] :
% 0.37/0.61 ( ( ( power_power_complex @ A @ N )
% 0.37/0.61 = zero_zero_complex )
% 0.37/0.61 = ( ( A = zero_zero_complex )
% 0.37/0.61 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_eq_0_iff
% 0.37/0.61 thf(fact_3835_power__eq__0__iff,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ( power_power_int @ A @ N )
% 0.37/0.61 = zero_zero_int )
% 0.37/0.61 = ( ( A = zero_zero_int )
% 0.37/0.61 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_eq_0_iff
% 0.37/0.61 thf(fact_3836_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ( ( finite_card_literal @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bot_set_literal ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3837_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.61 => ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bot_set_list_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3838_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.61 => ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bot_set_set_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3839_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_complex] :
% 0.37/0.61 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.61 => ( ( ( finite_card_complex @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bot_set_complex ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3840_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_Code_integer] :
% 0.37/0.61 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.61 => ( ( ( finite4902975817058060853nteger @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bo3990330152332043303nteger ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3841_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ( ( finite_card_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bot_set_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3842_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ( ( finite_card_int @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bot_set_int ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3843_card__0__eq,axiom,
% 0.37/0.61 ! [A4: set_o] :
% 0.37/0.61 ( ( finite_finite_o @ A4 )
% 0.37/0.61 => ( ( ( finite_card_o @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( A4 = bot_bot_set_o ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_0_eq
% 0.37/0.61 thf(fact_3844_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_o,X: $o] :
% 0.37/0.61 ( ( finite_finite_o @ A4 )
% 0.37/0.61 => ( ~ ( member_o @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_o @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3845_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.61 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.61 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.61 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3846_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_real,X: real] :
% 0.37/0.61 ( ( finite_finite_real @ A4 )
% 0.37/0.61 => ( ~ ( member_real @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3847_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_literal,X: literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ~ ( member_literal @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_literal @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3848_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.61 => ( ~ ( member_list_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3849_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.61 => ( ~ ( member_set_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3850_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_nat,X: nat] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ~ ( member_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3851_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_int,X: int] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ~ ( member_int @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3852_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_complex,X: complex] :
% 0.37/0.61 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.61 => ( ~ ( member_complex @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3853_card__insert__disjoint,axiom,
% 0.37/0.61 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.61 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.61 => ( ~ ( member_Code_integer @ X @ A4 )
% 0.37/0.61 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_disjoint
% 0.37/0.61 thf(fact_3854_power__strict__decreasing__iff,axiom,
% 0.37/0.61 ! [B: real,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.61 => ( ( ord_less_real @ B @ one_one_real )
% 0.37/0.61 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 0.37/0.61 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_decreasing_iff
% 0.37/0.61 thf(fact_3855_power__strict__decreasing__iff,axiom,
% 0.37/0.61 ! [B: rat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.37/0.61 => ( ( ord_less_rat @ B @ one_one_rat )
% 0.37/0.61 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.37/0.61 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_decreasing_iff
% 0.37/0.61 thf(fact_3856_power__strict__decreasing__iff,axiom,
% 0.37/0.61 ! [B: nat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.61 => ( ( ord_less_nat @ B @ one_one_nat )
% 0.37/0.61 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.37/0.61 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_decreasing_iff
% 0.37/0.61 thf(fact_3857_power__strict__decreasing__iff,axiom,
% 0.37/0.61 ! [B: int,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.61 => ( ( ord_less_int @ B @ one_one_int )
% 0.37/0.61 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.37/0.61 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_decreasing_iff
% 0.37/0.61 thf(fact_3858_power__mono__iff,axiom,
% 0.37/0.61 ! [A: real,B: real,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.61 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono_iff
% 0.37/0.61 thf(fact_3859_power__mono__iff,axiom,
% 0.37/0.61 ! [A: rat,B: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono_iff
% 0.37/0.61 thf(fact_3860_power__mono__iff,axiom,
% 0.37/0.61 ! [A: nat,B: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono_iff
% 0.37/0.61 thf(fact_3861_power__mono__iff,axiom,
% 0.37/0.61 ! [A: int,B: int,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.61 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.37/0.61 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono_iff
% 0.37/0.61 thf(fact_3862_power__increasing__iff,axiom,
% 0.37/0.61 ! [B: real,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.61 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 0.37/0.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_increasing_iff
% 0.37/0.61 thf(fact_3863_power__increasing__iff,axiom,
% 0.37/0.61 ! [B: rat,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_rat @ one_one_rat @ B )
% 0.37/0.61 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.37/0.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_increasing_iff
% 0.37/0.61 thf(fact_3864_power__increasing__iff,axiom,
% 0.37/0.61 ! [B: nat,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_nat @ one_one_nat @ B )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.37/0.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_increasing_iff
% 0.37/0.61 thf(fact_3865_power__increasing__iff,axiom,
% 0.37/0.61 ! [B: int,X: nat,Y: nat] :
% 0.37/0.61 ( ( ord_less_int @ one_one_int @ B )
% 0.37/0.61 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.37/0.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_increasing_iff
% 0.37/0.61 thf(fact_3866_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: $o,A4: set_o,B4: set_o] :
% 0.37/0.61 ( ( member_o @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_o @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3867_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_VEBT_VEBT @ A @ B4 )
% 0.37/0.61 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3868_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: real,A4: set_real,B4: set_real] :
% 0.37/0.61 ( ( member_real @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_real @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3869_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: int,A4: set_int,B4: set_int] :
% 0.37/0.61 ( ( member_int @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_int @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3870_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: complex,A4: set_complex,B4: set_complex] :
% 0.37/0.61 ( ( member_complex @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_complex @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3871_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: literal,A4: set_literal,B4: set_literal] :
% 0.37/0.61 ( ( member_literal @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_literal @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3872_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: list_nat,A4: set_list_nat,B4: set_list_nat] :
% 0.37/0.61 ( ( member_list_nat @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_list_nat @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3873_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 0.37/0.61 ( ( member_set_nat @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_set_nat @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3874_card__Diff__insert,axiom,
% 0.37/0.61 ! [A: nat,A4: set_nat,B4: set_nat] :
% 0.37/0.61 ( ( member_nat @ A @ A4 )
% 0.37/0.61 => ( ~ ( member_nat @ A @ B4 )
% 0.37/0.61 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) ) )
% 0.37/0.61 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Diff_insert
% 0.37/0.61 thf(fact_3875_finite__enumerate__mono__iff,axiom,
% 0.37/0.61 ! [S3: set_nat,M: nat,N: nat] :
% 0.37/0.61 ( ( finite_finite_nat @ S3 )
% 0.37/0.61 => ( ( ord_less_nat @ M @ ( finite_card_nat @ S3 ) )
% 0.37/0.61 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.37/0.61 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) )
% 0.37/0.61 = ( ord_less_nat @ M @ N ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_enumerate_mono_iff
% 0.37/0.61 thf(fact_3876_size__neq__size__imp__neq,axiom,
% 0.37/0.61 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 0.37/0.61 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 0.37/0.61 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 0.37/0.61 => ( X != Y ) ) ).
% 0.37/0.61
% 0.37/0.61 % size_neq_size_imp_neq
% 0.37/0.61 thf(fact_3877_size__neq__size__imp__neq,axiom,
% 0.37/0.61 ! [X: list_real,Y: list_real] :
% 0.37/0.61 ( ( ( size_size_list_real @ X )
% 0.37/0.61 != ( size_size_list_real @ Y ) )
% 0.37/0.61 => ( X != Y ) ) ).
% 0.37/0.61
% 0.37/0.61 % size_neq_size_imp_neq
% 0.37/0.61 thf(fact_3878_size__neq__size__imp__neq,axiom,
% 0.37/0.61 ! [X: list_o,Y: list_o] :
% 0.37/0.61 ( ( ( size_size_list_o @ X )
% 0.37/0.61 != ( size_size_list_o @ Y ) )
% 0.37/0.61 => ( X != Y ) ) ).
% 0.37/0.61
% 0.37/0.61 % size_neq_size_imp_neq
% 0.37/0.61 thf(fact_3879_size__neq__size__imp__neq,axiom,
% 0.37/0.61 ! [X: list_nat,Y: list_nat] :
% 0.37/0.61 ( ( ( size_size_list_nat @ X )
% 0.37/0.61 != ( size_size_list_nat @ Y ) )
% 0.37/0.61 => ( X != Y ) ) ).
% 0.37/0.61
% 0.37/0.61 % size_neq_size_imp_neq
% 0.37/0.61 thf(fact_3880_size__neq__size__imp__neq,axiom,
% 0.37/0.61 ! [X: num,Y: num] :
% 0.37/0.61 ( ( ( size_size_num @ X )
% 0.37/0.61 != ( size_size_num @ Y ) )
% 0.37/0.61 => ( X != Y ) ) ).
% 0.37/0.61
% 0.37/0.61 % size_neq_size_imp_neq
% 0.37/0.61 thf(fact_3881_count__le__length,axiom,
% 0.37/0.61 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs @ X ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_le_length
% 0.37/0.61 thf(fact_3882_count__le__length,axiom,
% 0.37/0.61 ! [Xs: list_real,X: real] : ( ord_less_eq_nat @ ( count_list_real @ Xs @ X ) @ ( size_size_list_real @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_le_length
% 0.37/0.61 thf(fact_3883_count__le__length,axiom,
% 0.37/0.61 ! [Xs: list_o,X: $o] : ( ord_less_eq_nat @ ( count_list_o @ Xs @ X ) @ ( size_size_list_o @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_le_length
% 0.37/0.61 thf(fact_3884_count__le__length,axiom,
% 0.37/0.61 ! [Xs: list_nat,X: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs @ X ) @ ( size_size_list_nat @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % count_le_length
% 0.37/0.61 thf(fact_3885_card__length,axiom,
% 0.37/0.61 ! [Xs: list_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( set_complex2 @ Xs ) ) @ ( size_s3451745648224563538omplex @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3886_card__length,axiom,
% 0.37/0.61 ! [Xs: list_literal] : ( ord_less_eq_nat @ ( finite_card_literal @ ( set_literal2 @ Xs ) ) @ ( size_s2501651207091587910iteral @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3887_card__length,axiom,
% 0.37/0.61 ! [Xs: list_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( set_list_nat2 @ Xs ) ) @ ( size_s3023201423986296836st_nat @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3888_card__length,axiom,
% 0.37/0.61 ! [Xs: list_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( set_set_nat2 @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3889_card__length,axiom,
% 0.37/0.61 ! [Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3890_card__length,axiom,
% 0.37/0.61 ! [Xs: list_real] : ( ord_less_eq_nat @ ( finite_card_real @ ( set_real2 @ Xs ) ) @ ( size_size_list_real @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3891_card__length,axiom,
% 0.37/0.61 ! [Xs: list_o] : ( ord_less_eq_nat @ ( finite_card_o @ ( set_o2 @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3892_card__length,axiom,
% 0.37/0.61 ! [Xs: list_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( set_nat2 @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_length
% 0.37/0.61 thf(fact_3893_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( A != zero_zero_rat )
% 0.37/0.61 => ( ( power_power_rat @ A @ N )
% 0.37/0.61 != zero_zero_rat ) ) ).
% 0.37/0.61
% 0.37/0.61 % semiring_1_no_zero_divisors_class.power_not_zero
% 0.37/0.61 thf(fact_3894_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( A != zero_zero_nat )
% 0.37/0.61 => ( ( power_power_nat @ A @ N )
% 0.37/0.61 != zero_zero_nat ) ) ).
% 0.37/0.61
% 0.37/0.61 % semiring_1_no_zero_divisors_class.power_not_zero
% 0.37/0.61 thf(fact_3895_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( A != zero_zero_real )
% 0.37/0.61 => ( ( power_power_real @ A @ N )
% 0.37/0.61 != zero_zero_real ) ) ).
% 0.37/0.61
% 0.37/0.61 % semiring_1_no_zero_divisors_class.power_not_zero
% 0.37/0.61 thf(fact_3896_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 0.37/0.61 ! [A: complex,N: nat] :
% 0.37/0.61 ( ( A != zero_zero_complex )
% 0.37/0.61 => ( ( power_power_complex @ A @ N )
% 0.37/0.61 != zero_zero_complex ) ) ).
% 0.37/0.61
% 0.37/0.61 % semiring_1_no_zero_divisors_class.power_not_zero
% 0.37/0.61 thf(fact_3897_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( A != zero_zero_int )
% 0.37/0.61 => ( ( power_power_int @ A @ N )
% 0.37/0.61 != zero_zero_int ) ) ).
% 0.37/0.61
% 0.37/0.61 % semiring_1_no_zero_divisors_class.power_not_zero
% 0.37/0.61 thf(fact_3898_length__induct,axiom,
% 0.37/0.61 ! [P2: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 0.37/0.61 ( ! [Xs3: list_VEBT_VEBT] :
% 0.37/0.61 ( ! [Ys2: list_VEBT_VEBT] :
% 0.37/0.61 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Ys2 ) )
% 0.37/0.61 => ( P2 @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_induct
% 0.37/0.61 thf(fact_3899_length__induct,axiom,
% 0.37/0.61 ! [P2: list_real > $o,Xs: list_real] :
% 0.37/0.61 ( ! [Xs3: list_real] :
% 0.37/0.61 ( ! [Ys2: list_real] :
% 0.37/0.61 ( ( ord_less_nat @ ( size_size_list_real @ Ys2 ) @ ( size_size_list_real @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Ys2 ) )
% 0.37/0.61 => ( P2 @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_induct
% 0.37/0.61 thf(fact_3900_length__induct,axiom,
% 0.37/0.61 ! [P2: list_o > $o,Xs: list_o] :
% 0.37/0.61 ( ! [Xs3: list_o] :
% 0.37/0.61 ( ! [Ys2: list_o] :
% 0.37/0.61 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Ys2 ) )
% 0.37/0.61 => ( P2 @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_induct
% 0.37/0.61 thf(fact_3901_length__induct,axiom,
% 0.37/0.61 ! [P2: list_nat > $o,Xs: list_nat] :
% 0.37/0.61 ( ! [Xs3: list_nat] :
% 0.37/0.61 ( ! [Ys2: list_nat] :
% 0.37/0.61 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Ys2 ) )
% 0.37/0.61 => ( P2 @ Xs3 ) )
% 0.37/0.61 => ( P2 @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_induct
% 0.37/0.61 thf(fact_3902_finite__maxlen,axiom,
% 0.37/0.61 ! [M7: set_list_VEBT_VEBT] :
% 0.37/0.61 ( ( finite3004134309566078307T_VEBT @ M7 )
% 0.37/0.61 => ? [N2: nat] :
% 0.37/0.61 ! [X5: list_VEBT_VEBT] :
% 0.37/0.61 ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 0.37/0.61 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N2 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_maxlen
% 0.37/0.61 thf(fact_3903_finite__maxlen,axiom,
% 0.37/0.61 ! [M7: set_list_real] :
% 0.37/0.61 ( ( finite306553202115118035t_real @ M7 )
% 0.37/0.61 => ? [N2: nat] :
% 0.37/0.61 ! [X5: list_real] :
% 0.37/0.61 ( ( member_list_real @ X5 @ M7 )
% 0.37/0.61 => ( ord_less_nat @ ( size_size_list_real @ X5 ) @ N2 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_maxlen
% 0.37/0.61 thf(fact_3904_finite__maxlen,axiom,
% 0.37/0.61 ! [M7: set_list_o] :
% 0.37/0.61 ( ( finite_finite_list_o @ M7 )
% 0.37/0.61 => ? [N2: nat] :
% 0.37/0.61 ! [X5: list_o] :
% 0.37/0.61 ( ( member_list_o @ X5 @ M7 )
% 0.37/0.61 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N2 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_maxlen
% 0.37/0.61 thf(fact_3905_finite__maxlen,axiom,
% 0.37/0.61 ! [M7: set_list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ M7 )
% 0.37/0.61 => ? [N2: nat] :
% 0.37/0.61 ! [X5: list_nat] :
% 0.37/0.61 ( ( member_list_nat @ X5 @ M7 )
% 0.37/0.61 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N2 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_maxlen
% 0.37/0.61 thf(fact_3906_zero__le__power,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.61 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_le_power
% 0.37/0.61 thf(fact_3907_zero__le__power,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_le_power
% 0.37/0.61 thf(fact_3908_zero__le__power,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_le_power
% 0.37/0.61 thf(fact_3909_zero__le__power,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.61 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_le_power
% 0.37/0.61 thf(fact_3910_power__mono,axiom,
% 0.37/0.61 ! [A: real,B: real,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.61 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.61 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono
% 0.37/0.61 thf(fact_3911_power__mono,axiom,
% 0.37/0.61 ! [A: rat,B: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.61 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono
% 0.37/0.61 thf(fact_3912_power__mono,axiom,
% 0.37/0.61 ! [A: nat,B: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.61 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono
% 0.37/0.61 thf(fact_3913_power__mono,axiom,
% 0.37/0.61 ! [A: int,B: int,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.61 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_mono
% 0.37/0.61 thf(fact_3914_zero__less__power,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.61 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_less_power
% 0.37/0.61 thf(fact_3915_zero__less__power,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.61 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_less_power
% 0.37/0.61 thf(fact_3916_zero__less__power,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.61 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_less_power
% 0.37/0.61 thf(fact_3917_zero__less__power,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.61 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % zero_less_power
% 0.37/0.61 thf(fact_3918_one__le__power,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_real @ one_one_real @ A )
% 0.37/0.61 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % one_le_power
% 0.37/0.61 thf(fact_3919_one__le__power,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.37/0.61 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % one_le_power
% 0.37/0.61 thf(fact_3920_one__le__power,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.37/0.61 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % one_le_power
% 0.37/0.61 thf(fact_3921_one__le__power,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_int @ one_one_int @ A )
% 0.37/0.61 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % one_le_power
% 0.37/0.61 thf(fact_3922_card__subset__eq,axiom,
% 0.37/0.61 ! [B4: set_literal,A4: set_literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.61 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 0.37/0.61 => ( ( ( finite_card_literal @ A4 )
% 0.37/0.61 = ( finite_card_literal @ B4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_subset_eq
% 0.37/0.61 thf(fact_3923_card__subset__eq,axiom,
% 0.37/0.61 ! [B4: set_list_nat,A4: set_list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.61 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 0.37/0.61 => ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.61 = ( finite_card_list_nat @ B4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_subset_eq
% 0.37/0.61 thf(fact_3924_card__subset__eq,axiom,
% 0.37/0.61 ! [B4: set_set_nat,A4: set_set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.61 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 0.37/0.61 => ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.61 = ( finite_card_set_nat @ B4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_subset_eq
% 0.37/0.61 thf(fact_3925_card__subset__eq,axiom,
% 0.37/0.61 ! [B4: set_nat,A4: set_nat] :
% 0.37/0.61 ( ( finite_finite_nat @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.61 => ( ( ( finite_card_nat @ A4 )
% 0.37/0.61 = ( finite_card_nat @ B4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_subset_eq
% 0.37/0.61 thf(fact_3926_card__subset__eq,axiom,
% 0.37/0.61 ! [B4: set_complex,A4: set_complex] :
% 0.37/0.61 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.61 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.61 => ( ( ( finite_card_complex @ A4 )
% 0.37/0.61 = ( finite_card_complex @ B4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_subset_eq
% 0.37/0.61 thf(fact_3927_card__subset__eq,axiom,
% 0.37/0.61 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.37/0.61 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.61 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.61 => ( ( ( finite4902975817058060853nteger @ A4 )
% 0.37/0.61 = ( finite4902975817058060853nteger @ B4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_subset_eq
% 0.37/0.61 thf(fact_3928_card__subset__eq,axiom,
% 0.37/0.61 ! [B4: set_int,A4: set_int] :
% 0.37/0.61 ( ( finite_finite_int @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.61 => ( ( ( finite_card_int @ A4 )
% 0.37/0.61 = ( finite_card_int @ B4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_subset_eq
% 0.37/0.61 thf(fact_3929_infinite__arbitrarily__large,axiom,
% 0.37/0.61 ! [A4: set_literal,N: nat] :
% 0.37/0.61 ( ~ ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ? [B8: set_literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ B8 )
% 0.37/0.61 & ( ( finite_card_literal @ B8 )
% 0.37/0.61 = N )
% 0.37/0.61 & ( ord_le7307670543136651348iteral @ B8 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % infinite_arbitrarily_large
% 0.37/0.61 thf(fact_3930_infinite__arbitrarily__large,axiom,
% 0.37/0.61 ! [A4: set_list_nat,N: nat] :
% 0.37/0.61 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.61 => ? [B8: set_list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ B8 )
% 0.37/0.61 & ( ( finite_card_list_nat @ B8 )
% 0.37/0.61 = N )
% 0.37/0.61 & ( ord_le6045566169113846134st_nat @ B8 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % infinite_arbitrarily_large
% 0.37/0.61 thf(fact_3931_infinite__arbitrarily__large,axiom,
% 0.37/0.61 ! [A4: set_set_nat,N: nat] :
% 0.37/0.61 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.61 => ? [B8: set_set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ B8 )
% 0.37/0.61 & ( ( finite_card_set_nat @ B8 )
% 0.37/0.61 = N )
% 0.37/0.61 & ( ord_le6893508408891458716et_nat @ B8 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % infinite_arbitrarily_large
% 0.37/0.61 thf(fact_3932_infinite__arbitrarily__large,axiom,
% 0.37/0.61 ! [A4: set_nat,N: nat] :
% 0.37/0.61 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.61 => ? [B8: set_nat] :
% 0.37/0.61 ( ( finite_finite_nat @ B8 )
% 0.37/0.61 & ( ( finite_card_nat @ B8 )
% 0.37/0.61 = N )
% 0.37/0.61 & ( ord_less_eq_set_nat @ B8 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % infinite_arbitrarily_large
% 0.37/0.61 thf(fact_3933_infinite__arbitrarily__large,axiom,
% 0.37/0.61 ! [A4: set_complex,N: nat] :
% 0.37/0.61 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.37/0.61 => ? [B8: set_complex] :
% 0.37/0.61 ( ( finite3207457112153483333omplex @ B8 )
% 0.37/0.61 & ( ( finite_card_complex @ B8 )
% 0.37/0.61 = N )
% 0.37/0.61 & ( ord_le211207098394363844omplex @ B8 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % infinite_arbitrarily_large
% 0.37/0.61 thf(fact_3934_infinite__arbitrarily__large,axiom,
% 0.37/0.61 ! [A4: set_Code_integer,N: nat] :
% 0.37/0.61 ( ~ ( finite6017078050557962740nteger @ A4 )
% 0.37/0.61 => ? [B8: set_Code_integer] :
% 0.37/0.61 ( ( finite6017078050557962740nteger @ B8 )
% 0.37/0.61 & ( ( finite4902975817058060853nteger @ B8 )
% 0.37/0.61 = N )
% 0.37/0.61 & ( ord_le7084787975880047091nteger @ B8 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % infinite_arbitrarily_large
% 0.37/0.61 thf(fact_3935_infinite__arbitrarily__large,axiom,
% 0.37/0.61 ! [A4: set_int,N: nat] :
% 0.37/0.61 ( ~ ( finite_finite_int @ A4 )
% 0.37/0.61 => ? [B8: set_int] :
% 0.37/0.61 ( ( finite_finite_int @ B8 )
% 0.37/0.61 & ( ( finite_card_int @ B8 )
% 0.37/0.61 = N )
% 0.37/0.61 & ( ord_less_eq_set_int @ B8 @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % infinite_arbitrarily_large
% 0.37/0.61 thf(fact_3936_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,R: vEBT_VEBT > vEBT_VEBT > $o] :
% 0.37/0.61 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.61 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.37/0.61 => ? [B9: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: vEBT_VEBT,A22: vEBT_VEBT,B3: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ A1 @ A4 )
% 0.37/0.61 => ( ( member_VEBT_VEBT @ A22 @ A4 )
% 0.37/0.61 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3937_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_real,A4: set_VEBT_VEBT,R: vEBT_VEBT > real > $o] :
% 0.37/0.61 ( ( finite_finite_real @ B4 )
% 0.37/0.61 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.37/0.61 => ? [B9: real] :
% 0.37/0.61 ( ( member_real @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: vEBT_VEBT,A22: vEBT_VEBT,B3: real] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ A1 @ A4 )
% 0.37/0.61 => ( ( member_VEBT_VEBT @ A22 @ A4 )
% 0.37/0.61 => ( ( member_real @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite_card_real @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3938_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_VEBT_VEBT,A4: set_real,R: real > vEBT_VEBT > $o] :
% 0.37/0.61 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.61 => ( ! [A3: real] :
% 0.37/0.61 ( ( member_real @ A3 @ A4 )
% 0.37/0.61 => ? [B9: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: real,A22: real,B3: vEBT_VEBT] :
% 0.37/0.61 ( ( member_real @ A1 @ A4 )
% 0.37/0.61 => ( ( member_real @ A22 @ A4 )
% 0.37/0.61 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3939_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_real,A4: set_real,R: real > real > $o] :
% 0.37/0.61 ( ( finite_finite_real @ B4 )
% 0.37/0.61 => ( ! [A3: real] :
% 0.37/0.61 ( ( member_real @ A3 @ A4 )
% 0.37/0.61 => ? [B9: real] :
% 0.37/0.61 ( ( member_real @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: real,A22: real,B3: real] :
% 0.37/0.61 ( ( member_real @ A1 @ A4 )
% 0.37/0.61 => ( ( member_real @ A22 @ A4 )
% 0.37/0.61 => ( ( member_real @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3940_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_VEBT_VEBT,A4: set_int,R: int > vEBT_VEBT > $o] :
% 0.37/0.61 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.61 => ( ! [A3: int] :
% 0.37/0.61 ( ( member_int @ A3 @ A4 )
% 0.37/0.61 => ? [B9: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: int,A22: int,B3: vEBT_VEBT] :
% 0.37/0.61 ( ( member_int @ A1 @ A4 )
% 0.37/0.61 => ( ( member_int @ A22 @ A4 )
% 0.37/0.61 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3941_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_real,A4: set_int,R: int > real > $o] :
% 0.37/0.61 ( ( finite_finite_real @ B4 )
% 0.37/0.61 => ( ! [A3: int] :
% 0.37/0.61 ( ( member_int @ A3 @ A4 )
% 0.37/0.61 => ? [B9: real] :
% 0.37/0.61 ( ( member_real @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: int,A22: int,B3: real] :
% 0.37/0.61 ( ( member_int @ A1 @ A4 )
% 0.37/0.61 => ( ( member_int @ A22 @ A4 )
% 0.37/0.61 => ( ( member_real @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_real @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3942_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_literal,A4: set_VEBT_VEBT,R: vEBT_VEBT > literal > $o] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.61 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.37/0.61 => ? [B9: literal] :
% 0.37/0.61 ( ( member_literal @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: vEBT_VEBT,A22: vEBT_VEBT,B3: literal] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ A1 @ A4 )
% 0.37/0.61 => ( ( member_VEBT_VEBT @ A22 @ A4 )
% 0.37/0.61 => ( ( member_literal @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3943_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_literal,A4: set_real,R: real > literal > $o] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.61 => ( ! [A3: real] :
% 0.37/0.61 ( ( member_real @ A3 @ A4 )
% 0.37/0.61 => ? [B9: literal] :
% 0.37/0.61 ( ( member_literal @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: real,A22: real,B3: literal] :
% 0.37/0.61 ( ( member_real @ A1 @ A4 )
% 0.37/0.61 => ( ( member_real @ A22 @ A4 )
% 0.37/0.61 => ( ( member_literal @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3944_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_literal,A4: set_int,R: int > literal > $o] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.61 => ( ! [A3: int] :
% 0.37/0.61 ( ( member_int @ A3 @ A4 )
% 0.37/0.61 => ? [B9: literal] :
% 0.37/0.61 ( ( member_literal @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: int,A22: int,B3: literal] :
% 0.37/0.61 ( ( member_int @ A1 @ A4 )
% 0.37/0.61 => ( ( member_int @ A22 @ A4 )
% 0.37/0.61 => ( ( member_literal @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3945_card__le__if__inj__on__rel,axiom,
% 0.37/0.61 ! [B4: set_VEBT_VEBT,A4: set_complex,R: complex > vEBT_VEBT > $o] :
% 0.37/0.61 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.61 => ( ! [A3: complex] :
% 0.37/0.61 ( ( member_complex @ A3 @ A4 )
% 0.37/0.61 => ? [B9: vEBT_VEBT] :
% 0.37/0.61 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 0.37/0.61 & ( R @ A3 @ B9 ) ) )
% 0.37/0.61 => ( ! [A1: complex,A22: complex,B3: vEBT_VEBT] :
% 0.37/0.61 ( ( member_complex @ A1 @ A4 )
% 0.37/0.61 => ( ( member_complex @ A22 @ A4 )
% 0.37/0.61 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 0.37/0.61 => ( ( R @ A1 @ B3 )
% 0.37/0.61 => ( ( R @ A22 @ B3 )
% 0.37/0.61 => ( A1 = A22 ) ) ) ) ) )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_le_if_inj_on_rel
% 0.37/0.61 thf(fact_3946_empty__in__Fpow,axiom,
% 0.37/0.61 ! [A4: set_nat] : ( member_set_nat @ bot_bot_set_nat @ ( finite_Fpow_nat @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % empty_in_Fpow
% 0.37/0.61 thf(fact_3947_empty__in__Fpow,axiom,
% 0.37/0.61 ! [A4: set_int] : ( member_set_int @ bot_bot_set_int @ ( finite_Fpow_int @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % empty_in_Fpow
% 0.37/0.61 thf(fact_3948_empty__in__Fpow,axiom,
% 0.37/0.61 ! [A4: set_o] : ( member_set_o @ bot_bot_set_o @ ( finite_Fpow_o @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % empty_in_Fpow
% 0.37/0.61 thf(fact_3949_card__insert__le,axiom,
% 0.37/0.61 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3950_card__insert__le,axiom,
% 0.37/0.61 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3951_card__insert__le,axiom,
% 0.37/0.61 ! [A4: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ A4 ) @ ( finite_card_o @ ( insert_o @ X @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3952_card__insert__le,axiom,
% 0.37/0.61 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ ( insert_complex @ X @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3953_card__insert__le,axiom,
% 0.37/0.61 ! [A4: set_literal,X: literal] : ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ ( insert_literal @ X @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3954_card__insert__le,axiom,
% 0.37/0.61 ! [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 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3955_card__insert__le,axiom,
% 0.37/0.61 ! [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 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3956_card__insert__le,axiom,
% 0.37/0.61 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_le
% 0.37/0.61 thf(fact_3957_power__Suc,axiom,
% 0.37/0.61 ! [A: complex,N: nat] :
% 0.37/0.61 ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc
% 0.37/0.61 thf(fact_3958_power__Suc,axiom,
% 0.37/0.61 ! [A: assn,N: nat] :
% 0.37/0.61 ( ( power_power_assn @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc
% 0.37/0.61 thf(fact_3959_power__Suc,axiom,
% 0.37/0.61 ! [A: uint32,N: nat] :
% 0.37/0.61 ( ( power_power_uint32 @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_uint32 @ A @ ( power_power_uint32 @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc
% 0.37/0.61 thf(fact_3960_power__Suc,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( power_power_real @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc
% 0.37/0.61 thf(fact_3961_power__Suc,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc
% 0.37/0.61 thf(fact_3962_power__Suc,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( power_power_int @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc
% 0.37/0.61 thf(fact_3963_power__Suc2,axiom,
% 0.37/0.61 ! [A: complex,N: nat] :
% 0.37/0.61 ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc2
% 0.37/0.61 thf(fact_3964_power__Suc2,axiom,
% 0.37/0.61 ! [A: assn,N: nat] :
% 0.37/0.61 ( ( power_power_assn @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_assn @ ( power_power_assn @ A @ N ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc2
% 0.37/0.61 thf(fact_3965_power__Suc2,axiom,
% 0.37/0.61 ! [A: uint32,N: nat] :
% 0.37/0.61 ( ( power_power_uint32 @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_uint32 @ ( power_power_uint32 @ A @ N ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc2
% 0.37/0.61 thf(fact_3966_power__Suc2,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( power_power_real @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc2
% 0.37/0.61 thf(fact_3967_power__Suc2,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc2
% 0.37/0.61 thf(fact_3968_power__Suc2,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( power_power_int @ A @ ( suc @ N ) )
% 0.37/0.61 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_Suc2
% 0.37/0.61 thf(fact_3969_Fpow__mono,axiom,
% 0.37/0.61 ! [A4: set_int,B4: set_int] :
% 0.37/0.61 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.61 => ( ord_le4403425263959731960et_int @ ( finite_Fpow_int @ A4 ) @ ( finite_Fpow_int @ B4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % Fpow_mono
% 0.37/0.61 thf(fact_3970_power__0,axiom,
% 0.37/0.61 ! [A: uint32] :
% 0.37/0.61 ( ( power_power_uint32 @ A @ zero_zero_nat )
% 0.37/0.61 = one_one_uint32 ) ).
% 0.37/0.61
% 0.37/0.61 % power_0
% 0.37/0.61 thf(fact_3971_power__0,axiom,
% 0.37/0.61 ! [A: rat] :
% 0.37/0.61 ( ( power_power_rat @ A @ zero_zero_nat )
% 0.37/0.61 = one_one_rat ) ).
% 0.37/0.61
% 0.37/0.61 % power_0
% 0.37/0.61 thf(fact_3972_power__0,axiom,
% 0.37/0.61 ! [A: nat] :
% 0.37/0.61 ( ( power_power_nat @ A @ zero_zero_nat )
% 0.37/0.61 = one_one_nat ) ).
% 0.37/0.61
% 0.37/0.61 % power_0
% 0.37/0.61 thf(fact_3973_power__0,axiom,
% 0.37/0.61 ! [A: real] :
% 0.37/0.61 ( ( power_power_real @ A @ zero_zero_nat )
% 0.37/0.61 = one_one_real ) ).
% 0.37/0.61
% 0.37/0.61 % power_0
% 0.37/0.61 thf(fact_3974_power__0,axiom,
% 0.37/0.61 ! [A: complex] :
% 0.37/0.61 ( ( power_power_complex @ A @ zero_zero_nat )
% 0.37/0.61 = one_one_complex ) ).
% 0.37/0.61
% 0.37/0.61 % power_0
% 0.37/0.61 thf(fact_3975_power__0,axiom,
% 0.37/0.61 ! [A: int] :
% 0.37/0.61 ( ( power_power_int @ A @ zero_zero_nat )
% 0.37/0.61 = one_one_int ) ).
% 0.37/0.61
% 0.37/0.61 % power_0
% 0.37/0.61 thf(fact_3976_nat__power__less__imp__less,axiom,
% 0.37/0.61 ! [I: nat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ I )
% 0.37/0.61 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.37/0.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % nat_power_less_imp_less
% 0.37/0.61 thf(fact_3977_length__removeAll__less__eq,axiom,
% 0.37/0.61 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_removeAll_less_eq
% 0.37/0.61 thf(fact_3978_length__removeAll__less__eq,axiom,
% 0.37/0.61 ! [X: real,Xs: list_real] : ( ord_less_eq_nat @ ( size_size_list_real @ ( removeAll_real @ X @ Xs ) ) @ ( size_size_list_real @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_removeAll_less_eq
% 0.37/0.61 thf(fact_3979_length__removeAll__less__eq,axiom,
% 0.37/0.61 ! [X: $o,Xs: list_o] : ( ord_less_eq_nat @ ( size_size_list_o @ ( removeAll_o @ X @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_removeAll_less_eq
% 0.37/0.61 thf(fact_3980_length__removeAll__less__eq,axiom,
% 0.37/0.61 ! [X: nat,Xs: list_nat] : ( ord_less_eq_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 0.37/0.61
% 0.37/0.61 % length_removeAll_less_eq
% 0.37/0.61 thf(fact_3981_is__singleton__altdef,axiom,
% 0.37/0.61 ( is_singleton_complex
% 0.37/0.61 = ( ^ [A6: set_complex] :
% 0.37/0.61 ( ( finite_card_complex @ A6 )
% 0.37/0.61 = one_one_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % is_singleton_altdef
% 0.37/0.61 thf(fact_3982_is__singleton__altdef,axiom,
% 0.37/0.61 ( is_singleton_literal
% 0.37/0.61 = ( ^ [A6: set_literal] :
% 0.37/0.61 ( ( finite_card_literal @ A6 )
% 0.37/0.61 = one_one_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % is_singleton_altdef
% 0.37/0.61 thf(fact_3983_is__singleton__altdef,axiom,
% 0.37/0.61 ( is_sin2641923865335537900st_nat
% 0.37/0.61 = ( ^ [A6: set_list_nat] :
% 0.37/0.61 ( ( finite_card_list_nat @ A6 )
% 0.37/0.61 = one_one_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % is_singleton_altdef
% 0.37/0.61 thf(fact_3984_is__singleton__altdef,axiom,
% 0.37/0.61 ( is_singleton_set_nat
% 0.37/0.61 = ( ^ [A6: set_set_nat] :
% 0.37/0.61 ( ( finite_card_set_nat @ A6 )
% 0.37/0.61 = one_one_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % is_singleton_altdef
% 0.37/0.61 thf(fact_3985_is__singleton__altdef,axiom,
% 0.37/0.61 ( is_singleton_nat
% 0.37/0.61 = ( ^ [A6: set_nat] :
% 0.37/0.61 ( ( finite_card_nat @ A6 )
% 0.37/0.61 = one_one_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % is_singleton_altdef
% 0.37/0.61 thf(fact_3986_power__less__imp__less__base,axiom,
% 0.37/0.61 ! [A: real,N: nat,B: real] :
% 0.37/0.61 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.37/0.61 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.61 => ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_base
% 0.37/0.61 thf(fact_3987_power__less__imp__less__base,axiom,
% 0.37/0.61 ! [A: rat,N: nat,B: rat] :
% 0.37/0.61 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.37/0.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.61 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_base
% 0.37/0.61 thf(fact_3988_power__less__imp__less__base,axiom,
% 0.37/0.61 ! [A: nat,N: nat,B: nat] :
% 0.37/0.61 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.37/0.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.61 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_base
% 0.37/0.61 thf(fact_3989_power__less__imp__less__base,axiom,
% 0.37/0.61 ! [A: int,N: nat,B: int] :
% 0.37/0.61 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.37/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.61 => ( ord_less_int @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_base
% 0.37/0.61 thf(fact_3990_card__ge__0__finite,axiom,
% 0.37/0.61 ! [A4: set_literal] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 0.37/0.61 => ( finite5847741373460823677iteral @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_ge_0_finite
% 0.37/0.61 thf(fact_3991_card__ge__0__finite,axiom,
% 0.37/0.61 ! [A4: set_list_nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 0.37/0.61 => ( finite8100373058378681591st_nat @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_ge_0_finite
% 0.37/0.61 thf(fact_3992_card__ge__0__finite,axiom,
% 0.37/0.61 ! [A4: set_set_nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 0.37/0.61 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_ge_0_finite
% 0.37/0.61 thf(fact_3993_card__ge__0__finite,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 0.37/0.61 => ( finite_finite_nat @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_ge_0_finite
% 0.37/0.61 thf(fact_3994_card__ge__0__finite,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 0.37/0.61 => ( finite_finite_int @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_ge_0_finite
% 0.37/0.61 thf(fact_3995_card__ge__0__finite,axiom,
% 0.37/0.61 ! [A4: set_complex] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.37/0.61 => ( finite3207457112153483333omplex @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_ge_0_finite
% 0.37/0.61 thf(fact_3996_card__ge__0__finite,axiom,
% 0.37/0.61 ! [A4: set_Code_integer] :
% 0.37/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A4 ) )
% 0.37/0.61 => ( finite6017078050557962740nteger @ A4 ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_ge_0_finite
% 0.37/0.61 thf(fact_3997_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_literal] :
% 0.37/0.61 ( ( ( finite_card_literal @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bot_set_literal )
% 0.37/0.61 | ~ ( finite5847741373460823677iteral @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_3998_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_list_nat] :
% 0.37/0.61 ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bot_set_list_nat )
% 0.37/0.61 | ~ ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_3999_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_set_nat] :
% 0.37/0.61 ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bot_set_set_nat )
% 0.37/0.61 | ~ ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_4000_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_complex] :
% 0.37/0.61 ( ( ( finite_card_complex @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bot_set_complex )
% 0.37/0.61 | ~ ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_4001_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_Code_integer] :
% 0.37/0.61 ( ( ( finite4902975817058060853nteger @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bo3990330152332043303nteger )
% 0.37/0.61 | ~ ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_4002_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( ( finite_card_nat @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bot_set_nat )
% 0.37/0.61 | ~ ( finite_finite_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_4003_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( ( finite_card_int @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bot_set_int )
% 0.37/0.61 | ~ ( finite_finite_int @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_4004_card__eq__0__iff,axiom,
% 0.37/0.61 ! [A4: set_o] :
% 0.37/0.61 ( ( ( finite_card_o @ A4 )
% 0.37/0.61 = zero_zero_nat )
% 0.37/0.61 = ( ( A4 = bot_bot_set_o )
% 0.37/0.61 | ~ ( finite_finite_o @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_eq_0_iff
% 0.37/0.61 thf(fact_4005_power__le__one,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.61 => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.37/0.61 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_one
% 0.37/0.61 thf(fact_4006_power__le__one,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.61 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.37/0.61 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_one
% 0.37/0.61 thf(fact_4007_power__le__one,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.61 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.37/0.61 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_one
% 0.37/0.61 thf(fact_4008_power__le__one,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.61 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.37/0.61 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_one
% 0.37/0.61 thf(fact_4009_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_o,X: $o] :
% 0.37/0.61 ( ( finite_finite_o @ A4 )
% 0.37/0.61 => ( ( ( member_o @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_o @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_o @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_o @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4010_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.61 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.61 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.61 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.61 = ( finite7802652506058667612T_VEBT @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.61 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4011_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_real,X: real] :
% 0.37/0.61 ( ( finite_finite_real @ A4 )
% 0.37/0.61 => ( ( ( member_real @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_real @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_real @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4012_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_literal,X: literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ( ( member_literal @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_literal @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_literal @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_literal @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4013_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.61 => ( ( ( member_list_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_list_nat @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_list_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4014_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.61 => ( ( ( member_set_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_set_nat @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_set_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4015_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_nat,X: nat] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ( ( member_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_nat @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_nat @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4016_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_int,X: int] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ( ( member_int @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_int @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_int @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4017_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_complex,X: complex] :
% 0.37/0.61 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.61 => ( ( ( member_complex @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.37/0.61 = ( finite_card_complex @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_complex @ X @ A4 )
% 0.37/0.61 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4018_card__insert__if,axiom,
% 0.37/0.61 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.61 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.61 => ( ( ( member_Code_integer @ X @ A4 )
% 0.37/0.61 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.61 = ( finite4902975817058060853nteger @ A4 ) ) )
% 0.37/0.61 & ( ~ ( member_Code_integer @ X @ A4 )
% 0.37/0.61 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.61 = ( suc @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_insert_if
% 0.37/0.61 thf(fact_4019_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_o,K: nat] :
% 0.37/0.61 ( ( ( finite_card_o @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: $o,B6: set_o] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_o @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_o @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_o @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite_finite_o @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4020_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_VEBT_VEBT,K: nat] :
% 0.37/0.61 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_VEBT_VEBT @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_VEBT_VEBT @ B7 @ B6 )
% 0.37/0.61 & ( ( finite7802652506058667612T_VEBT @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite5795047828879050333T_VEBT @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4021_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_real,K: nat] :
% 0.37/0.61 ( ( ( finite_card_real @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: real,B6: set_real] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_real @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_real @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_real @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite_finite_real @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4022_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_literal,K: nat] :
% 0.37/0.61 ( ( ( finite_card_literal @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: literal,B6: set_literal] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_literal @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_literal @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_literal @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite5847741373460823677iteral @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4023_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_list_nat,K: nat] :
% 0.37/0.61 ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: list_nat,B6: set_list_nat] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_list_nat @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_list_nat @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_list_nat @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4024_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_set_nat,K: nat] :
% 0.37/0.61 ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: set_nat,B6: set_set_nat] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_set_nat @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_set_nat @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_set_nat @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4025_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_nat,K: nat] :
% 0.37/0.61 ( ( ( finite_card_nat @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: nat,B6: set_nat] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_nat @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_nat @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_nat @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4026_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_int,K: nat] :
% 0.37/0.61 ( ( ( finite_card_int @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: int,B6: set_int] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_int @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_int @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_int @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite_finite_int @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4027_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_complex,K: nat] :
% 0.37/0.61 ( ( ( finite_card_complex @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: complex,B6: set_complex] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_complex @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_complex @ B7 @ B6 )
% 0.37/0.61 & ( ( finite_card_complex @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4028_card__Suc__eq__finite,axiom,
% 0.37/0.61 ! [A4: set_Code_integer,K: nat] :
% 0.37/0.61 ( ( ( finite4902975817058060853nteger @ A4 )
% 0.37/0.61 = ( suc @ K ) )
% 0.37/0.61 = ( ? [B7: code_integer,B6: set_Code_integer] :
% 0.37/0.61 ( ( A4
% 0.37/0.61 = ( insert_Code_integer @ B7 @ B6 ) )
% 0.37/0.61 & ~ ( member_Code_integer @ B7 @ B6 )
% 0.37/0.61 & ( ( finite4902975817058060853nteger @ B6 )
% 0.37/0.61 = K )
% 0.37/0.61 & ( finite6017078050557962740nteger @ B6 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_Suc_eq_finite
% 0.37/0.61 thf(fact_4029_power__inject__base,axiom,
% 0.37/0.61 ! [A: real,N: nat,B: real] :
% 0.37/0.61 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 0.37/0.61 = ( power_power_real @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.61 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.61 => ( A = B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_base
% 0.37/0.61 thf(fact_4030_power__inject__base,axiom,
% 0.37/0.61 ! [A: rat,N: nat,B: rat] :
% 0.37/0.61 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.37/0.61 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.61 => ( A = B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_base
% 0.37/0.61 thf(fact_4031_power__inject__base,axiom,
% 0.37/0.61 ! [A: nat,N: nat,B: nat] :
% 0.37/0.61 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.37/0.61 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.61 => ( A = B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_base
% 0.37/0.61 thf(fact_4032_power__inject__base,axiom,
% 0.37/0.61 ! [A: int,N: nat,B: int] :
% 0.37/0.61 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 0.37/0.61 = ( power_power_int @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.61 => ( A = B ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_inject_base
% 0.37/0.61 thf(fact_4033_power__le__imp__le__base,axiom,
% 0.37/0.61 ! [A: real,N: nat,B: real] :
% 0.37/0.61 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.61 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_imp_le_base
% 0.37/0.61 thf(fact_4034_power__le__imp__le__base,axiom,
% 0.37/0.61 ! [A: rat,N: nat,B: rat] :
% 0.37/0.61 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.61 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_imp_le_base
% 0.37/0.61 thf(fact_4035_power__le__imp__le__base,axiom,
% 0.37/0.61 ! [A: nat,N: nat,B: nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.61 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_imp_le_base
% 0.37/0.61 thf(fact_4036_power__le__imp__le__base,axiom,
% 0.37/0.61 ! [A: int,N: nat,B: int] :
% 0.37/0.61 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 0.37/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.61 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_le_imp_le_base
% 0.37/0.61 thf(fact_4037_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_literal,F: literal > complex] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_complex @ ( image_5274195009022015549omplex @ F @ A4 ) ) @ ( finite_card_literal @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4038_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_literal,F: literal > literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_literal @ ( image_8195128725298311301iteral @ F @ A4 ) ) @ ( finite_card_literal @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4039_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_literal,F: literal > nat] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_literal_nat @ F @ A4 ) ) @ ( finite_card_literal @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4040_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_nat,F: nat > int] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_nat_int @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4041_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_nat,F: nat > complex] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_complex @ ( image_nat_complex @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4042_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_nat,F: nat > literal] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_literal @ ( image_nat_literal @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4043_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_nat,F: nat > nat] :
% 0.37/0.61 ( ( finite_finite_nat @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4044_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_int,F: int > int] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_int_int @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4045_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_int,F: int > complex] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_complex @ ( image_int_complex @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4046_card__image__le,axiom,
% 0.37/0.61 ! [A4: set_int,F: int > literal] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_literal @ ( image_int_literal @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_image_le
% 0.37/0.61 thf(fact_4047_power__gt1__lemma,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.61 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1_lemma
% 0.37/0.61 thf(fact_4048_power__gt1__lemma,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.61 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1_lemma
% 0.37/0.61 thf(fact_4049_power__gt1__lemma,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.61 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1_lemma
% 0.37/0.61 thf(fact_4050_power__gt1__lemma,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.61 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1_lemma
% 0.37/0.61 thf(fact_4051_power__less__power__Suc,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.61 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_power_Suc
% 0.37/0.61 thf(fact_4052_power__less__power__Suc,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.61 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_power_Suc
% 0.37/0.61 thf(fact_4053_power__less__power__Suc,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.61 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_power_Suc
% 0.37/0.61 thf(fact_4054_power__less__power__Suc,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.61 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_power_Suc
% 0.37/0.61 thf(fact_4055_finite__if__finite__subsets__card__bdd,axiom,
% 0.37/0.61 ! [F2: set_literal,C3: nat] :
% 0.37/0.61 ( ! [G2: set_literal] :
% 0.37/0.61 ( ( ord_le7307670543136651348iteral @ G2 @ F2 )
% 0.37/0.61 => ( ( finite5847741373460823677iteral @ G2 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_literal @ G2 ) @ C3 ) ) )
% 0.37/0.61 => ( ( finite5847741373460823677iteral @ F2 )
% 0.37/0.61 & ( ord_less_eq_nat @ ( finite_card_literal @ F2 ) @ C3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_if_finite_subsets_card_bdd
% 0.37/0.61 thf(fact_4056_finite__if__finite__subsets__card__bdd,axiom,
% 0.37/0.61 ! [F2: set_list_nat,C3: nat] :
% 0.37/0.61 ( ! [G2: set_list_nat] :
% 0.37/0.61 ( ( ord_le6045566169113846134st_nat @ G2 @ F2 )
% 0.37/0.61 => ( ( finite8100373058378681591st_nat @ G2 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G2 ) @ C3 ) ) )
% 0.37/0.61 => ( ( finite8100373058378681591st_nat @ F2 )
% 0.37/0.61 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F2 ) @ C3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_if_finite_subsets_card_bdd
% 0.37/0.61 thf(fact_4057_finite__if__finite__subsets__card__bdd,axiom,
% 0.37/0.61 ! [F2: set_set_nat,C3: nat] :
% 0.37/0.61 ( ! [G2: set_set_nat] :
% 0.37/0.61 ( ( ord_le6893508408891458716et_nat @ G2 @ F2 )
% 0.37/0.61 => ( ( finite1152437895449049373et_nat @ G2 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G2 ) @ C3 ) ) )
% 0.37/0.61 => ( ( finite1152437895449049373et_nat @ F2 )
% 0.37/0.61 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F2 ) @ C3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_if_finite_subsets_card_bdd
% 0.37/0.61 thf(fact_4058_finite__if__finite__subsets__card__bdd,axiom,
% 0.37/0.61 ! [F2: set_nat,C3: nat] :
% 0.37/0.61 ( ! [G2: set_nat] :
% 0.37/0.61 ( ( ord_less_eq_set_nat @ G2 @ F2 )
% 0.37/0.61 => ( ( finite_finite_nat @ G2 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_nat @ G2 ) @ C3 ) ) )
% 0.37/0.61 => ( ( finite_finite_nat @ F2 )
% 0.37/0.61 & ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_if_finite_subsets_card_bdd
% 0.37/0.61 thf(fact_4059_finite__if__finite__subsets__card__bdd,axiom,
% 0.37/0.61 ! [F2: set_complex,C3: nat] :
% 0.37/0.61 ( ! [G2: set_complex] :
% 0.37/0.61 ( ( ord_le211207098394363844omplex @ G2 @ F2 )
% 0.37/0.61 => ( ( finite3207457112153483333omplex @ G2 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_complex @ G2 ) @ C3 ) ) )
% 0.37/0.61 => ( ( finite3207457112153483333omplex @ F2 )
% 0.37/0.61 & ( ord_less_eq_nat @ ( finite_card_complex @ F2 ) @ C3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_if_finite_subsets_card_bdd
% 0.37/0.61 thf(fact_4060_finite__if__finite__subsets__card__bdd,axiom,
% 0.37/0.61 ! [F2: set_Code_integer,C3: nat] :
% 0.37/0.61 ( ! [G2: set_Code_integer] :
% 0.37/0.61 ( ( ord_le7084787975880047091nteger @ G2 @ F2 )
% 0.37/0.61 => ( ( finite6017078050557962740nteger @ G2 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ G2 ) @ C3 ) ) )
% 0.37/0.61 => ( ( finite6017078050557962740nteger @ F2 )
% 0.37/0.61 & ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ F2 ) @ C3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_if_finite_subsets_card_bdd
% 0.37/0.61 thf(fact_4061_finite__if__finite__subsets__card__bdd,axiom,
% 0.37/0.61 ! [F2: set_int,C3: nat] :
% 0.37/0.61 ( ! [G2: set_int] :
% 0.37/0.61 ( ( ord_less_eq_set_int @ G2 @ F2 )
% 0.37/0.61 => ( ( finite_finite_int @ G2 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ G2 ) @ C3 ) ) )
% 0.37/0.61 => ( ( finite_finite_int @ F2 )
% 0.37/0.61 & ( ord_less_eq_nat @ ( finite_card_int @ F2 ) @ C3 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % finite_if_finite_subsets_card_bdd
% 0.37/0.61 thf(fact_4062_card__seteq,axiom,
% 0.37/0.61 ! [B4: set_literal,A4: set_literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.61 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_literal @ A4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_seteq
% 0.37/0.61 thf(fact_4063_card__seteq,axiom,
% 0.37/0.61 ! [B4: set_list_nat,A4: set_list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.61 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B4 ) @ ( finite_card_list_nat @ A4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_seteq
% 0.37/0.61 thf(fact_4064_card__seteq,axiom,
% 0.37/0.61 ! [B4: set_set_nat,A4: set_set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.61 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B4 ) @ ( finite_card_set_nat @ A4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_seteq
% 0.37/0.61 thf(fact_4065_card__seteq,axiom,
% 0.37/0.61 ! [B4: set_nat,A4: set_nat] :
% 0.37/0.61 ( ( finite_finite_nat @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_nat @ A4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_seteq
% 0.37/0.61 thf(fact_4066_card__seteq,axiom,
% 0.37/0.61 ! [B4: set_complex,A4: set_complex] :
% 0.37/0.61 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.61 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_complex @ A4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_seteq
% 0.37/0.61 thf(fact_4067_card__seteq,axiom,
% 0.37/0.61 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.37/0.61 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.61 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ B4 ) @ ( finite4902975817058060853nteger @ A4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_seteq
% 0.37/0.61 thf(fact_4068_card__seteq,axiom,
% 0.37/0.61 ! [B4: set_int,A4: set_int] :
% 0.37/0.61 ( ( finite_finite_int @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_nat @ ( finite_card_int @ B4 ) @ ( finite_card_int @ A4 ) )
% 0.37/0.61 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_seteq
% 0.37/0.61 thf(fact_4069_card__mono,axiom,
% 0.37/0.61 ! [B4: set_literal,A4: set_literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.61 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_mono
% 0.37/0.61 thf(fact_4070_card__mono,axiom,
% 0.37/0.61 ! [B4: set_list_nat,A4: set_list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.61 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_mono
% 0.37/0.61 thf(fact_4071_card__mono,axiom,
% 0.37/0.61 ! [B4: set_set_nat,A4: set_set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.61 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_mono
% 0.37/0.61 thf(fact_4072_card__mono,axiom,
% 0.37/0.61 ! [B4: set_nat,A4: set_nat] :
% 0.37/0.61 ( ( finite_finite_nat @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_mono
% 0.37/0.61 thf(fact_4073_card__mono,axiom,
% 0.37/0.61 ! [B4: set_complex,A4: set_complex] :
% 0.37/0.61 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.61 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_mono
% 0.37/0.61 thf(fact_4074_card__mono,axiom,
% 0.37/0.61 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.37/0.61 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.61 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_mono
% 0.37/0.61 thf(fact_4075_card__mono,axiom,
% 0.37/0.61 ! [B4: set_int,A4: set_int] :
% 0.37/0.61 ( ( finite_finite_int @ B4 )
% 0.37/0.61 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.61 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_mono
% 0.37/0.61 thf(fact_4076_obtain__subset__with__card__n,axiom,
% 0.37/0.61 ! [N: nat,S3: set_literal] :
% 0.37/0.61 ( ( ord_less_eq_nat @ N @ ( finite_card_literal @ S3 ) )
% 0.37/0.61 => ~ ! [T4: set_literal] :
% 0.37/0.61 ( ( ord_le7307670543136651348iteral @ T4 @ S3 )
% 0.37/0.61 => ( ( ( finite_card_literal @ T4 )
% 0.37/0.61 = N )
% 0.37/0.61 => ~ ( finite5847741373460823677iteral @ T4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % obtain_subset_with_card_n
% 0.37/0.61 thf(fact_4077_obtain__subset__with__card__n,axiom,
% 0.37/0.61 ! [N: nat,S3: set_list_nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ S3 ) )
% 0.37/0.61 => ~ ! [T4: set_list_nat] :
% 0.37/0.61 ( ( ord_le6045566169113846134st_nat @ T4 @ S3 )
% 0.37/0.61 => ( ( ( finite_card_list_nat @ T4 )
% 0.37/0.61 = N )
% 0.37/0.61 => ~ ( finite8100373058378681591st_nat @ T4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % obtain_subset_with_card_n
% 0.37/0.61 thf(fact_4078_obtain__subset__with__card__n,axiom,
% 0.37/0.61 ! [N: nat,S3: set_set_nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ S3 ) )
% 0.37/0.61 => ~ ! [T4: set_set_nat] :
% 0.37/0.61 ( ( ord_le6893508408891458716et_nat @ T4 @ S3 )
% 0.37/0.61 => ( ( ( finite_card_set_nat @ T4 )
% 0.37/0.61 = N )
% 0.37/0.61 => ~ ( finite1152437895449049373et_nat @ T4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % obtain_subset_with_card_n
% 0.37/0.61 thf(fact_4079_obtain__subset__with__card__n,axiom,
% 0.37/0.61 ! [N: nat,S3: set_nat] :
% 0.37/0.61 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.37/0.61 => ~ ! [T4: set_nat] :
% 0.37/0.61 ( ( ord_less_eq_set_nat @ T4 @ S3 )
% 0.37/0.61 => ( ( ( finite_card_nat @ T4 )
% 0.37/0.61 = N )
% 0.37/0.61 => ~ ( finite_finite_nat @ T4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % obtain_subset_with_card_n
% 0.37/0.61 thf(fact_4080_obtain__subset__with__card__n,axiom,
% 0.37/0.61 ! [N: nat,S3: set_complex] :
% 0.37/0.61 ( ( ord_less_eq_nat @ N @ ( finite_card_complex @ S3 ) )
% 0.37/0.61 => ~ ! [T4: set_complex] :
% 0.37/0.61 ( ( ord_le211207098394363844omplex @ T4 @ S3 )
% 0.37/0.61 => ( ( ( finite_card_complex @ T4 )
% 0.37/0.61 = N )
% 0.37/0.61 => ~ ( finite3207457112153483333omplex @ T4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % obtain_subset_with_card_n
% 0.37/0.61 thf(fact_4081_obtain__subset__with__card__n,axiom,
% 0.37/0.61 ! [N: nat,S3: set_Code_integer] :
% 0.37/0.61 ( ( ord_less_eq_nat @ N @ ( finite4902975817058060853nteger @ S3 ) )
% 0.37/0.61 => ~ ! [T4: set_Code_integer] :
% 0.37/0.61 ( ( ord_le7084787975880047091nteger @ T4 @ S3 )
% 0.37/0.61 => ( ( ( finite4902975817058060853nteger @ T4 )
% 0.37/0.61 = N )
% 0.37/0.61 => ~ ( finite6017078050557962740nteger @ T4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % obtain_subset_with_card_n
% 0.37/0.61 thf(fact_4082_obtain__subset__with__card__n,axiom,
% 0.37/0.61 ! [N: nat,S3: set_int] :
% 0.37/0.61 ( ( ord_less_eq_nat @ N @ ( finite_card_int @ S3 ) )
% 0.37/0.61 => ~ ! [T4: set_int] :
% 0.37/0.61 ( ( ord_less_eq_set_int @ T4 @ S3 )
% 0.37/0.61 => ( ( ( finite_card_int @ T4 )
% 0.37/0.61 = N )
% 0.37/0.61 => ~ ( finite_finite_int @ T4 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % obtain_subset_with_card_n
% 0.37/0.61 thf(fact_4083_power__gt1,axiom,
% 0.37/0.61 ! [A: real,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.61 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1
% 0.37/0.61 thf(fact_4084_power__gt1,axiom,
% 0.37/0.61 ! [A: rat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.61 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1
% 0.37/0.61 thf(fact_4085_power__gt1,axiom,
% 0.37/0.61 ! [A: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.61 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1
% 0.37/0.61 thf(fact_4086_power__gt1,axiom,
% 0.37/0.61 ! [A: int,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.61 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_gt1
% 0.37/0.61 thf(fact_4087_power__0__left,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( ( N = zero_zero_nat )
% 0.37/0.61 => ( ( power_power_uint32 @ zero_zero_uint32 @ N )
% 0.37/0.61 = one_one_uint32 ) )
% 0.37/0.61 & ( ( N != zero_zero_nat )
% 0.37/0.61 => ( ( power_power_uint32 @ zero_zero_uint32 @ N )
% 0.37/0.61 = zero_zero_uint32 ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_left
% 0.37/0.61 thf(fact_4088_power__0__left,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( ( N = zero_zero_nat )
% 0.37/0.61 => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.37/0.61 = one_one_rat ) )
% 0.37/0.61 & ( ( N != zero_zero_nat )
% 0.37/0.61 => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.37/0.61 = zero_zero_rat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_left
% 0.37/0.61 thf(fact_4089_power__0__left,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( ( N = zero_zero_nat )
% 0.37/0.61 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.37/0.61 = one_one_nat ) )
% 0.37/0.61 & ( ( N != zero_zero_nat )
% 0.37/0.61 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.37/0.61 = zero_zero_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_left
% 0.37/0.61 thf(fact_4090_power__0__left,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( ( N = zero_zero_nat )
% 0.37/0.61 => ( ( power_power_real @ zero_zero_real @ N )
% 0.37/0.61 = one_one_real ) )
% 0.37/0.61 & ( ( N != zero_zero_nat )
% 0.37/0.61 => ( ( power_power_real @ zero_zero_real @ N )
% 0.37/0.61 = zero_zero_real ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_left
% 0.37/0.61 thf(fact_4091_power__0__left,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( ( N = zero_zero_nat )
% 0.37/0.61 => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.37/0.61 = one_one_complex ) )
% 0.37/0.61 & ( ( N != zero_zero_nat )
% 0.37/0.61 => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.37/0.61 = zero_zero_complex ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_left
% 0.37/0.61 thf(fact_4092_power__0__left,axiom,
% 0.37/0.61 ! [N: nat] :
% 0.37/0.61 ( ( ( N = zero_zero_nat )
% 0.37/0.61 => ( ( power_power_int @ zero_zero_int @ N )
% 0.37/0.61 = one_one_int ) )
% 0.37/0.61 & ( ( N != zero_zero_nat )
% 0.37/0.61 => ( ( power_power_int @ zero_zero_int @ N )
% 0.37/0.61 = zero_zero_int ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_0_left
% 0.37/0.61 thf(fact_4093_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_VEBT_VEBT] :
% 0.37/0.61 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4094_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_complex] :
% 0.37/0.61 ( ( ( finite_card_complex @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: complex] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4095_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_literal] :
% 0.37/0.61 ( ( ( finite_card_literal @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: literal] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_literal @ X3 @ bot_bot_set_literal ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4096_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_list_nat] :
% 0.37/0.61 ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: list_nat] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_list_nat @ X3 @ bot_bot_set_list_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4097_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_set_nat] :
% 0.37/0.61 ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: set_nat] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4098_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_nat] :
% 0.37/0.61 ( ( ( finite_card_nat @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: nat] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4099_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_int] :
% 0.37/0.61 ( ( ( finite_card_int @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: int] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4100_card__1__singletonE,axiom,
% 0.37/0.61 ! [A4: set_o] :
% 0.37/0.61 ( ( ( finite_card_o @ A4 )
% 0.37/0.61 = one_one_nat )
% 0.37/0.61 => ~ ! [X3: $o] :
% 0.37/0.61 ( A4
% 0.37/0.61 != ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_1_singletonE
% 0.37/0.61 thf(fact_4101_power__strict__increasing,axiom,
% 0.37/0.61 ! [N: nat,N8: nat,A: real] :
% 0.37/0.61 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.61 => ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.61 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N8 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing
% 0.37/0.61 thf(fact_4102_power__strict__increasing,axiom,
% 0.37/0.61 ! [N: nat,N8: nat,A: rat] :
% 0.37/0.61 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.61 => ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.61 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N8 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing
% 0.37/0.61 thf(fact_4103_power__strict__increasing,axiom,
% 0.37/0.61 ! [N: nat,N8: nat,A: nat] :
% 0.37/0.61 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.61 => ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.61 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N8 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing
% 0.37/0.61 thf(fact_4104_power__strict__increasing,axiom,
% 0.37/0.61 ! [N: nat,N8: nat,A: int] :
% 0.37/0.61 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.61 => ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.61 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N8 ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_strict_increasing
% 0.37/0.61 thf(fact_4105_power__less__imp__less__exp,axiom,
% 0.37/0.61 ! [A: real,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.61 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.37/0.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_exp
% 0.37/0.61 thf(fact_4106_power__less__imp__less__exp,axiom,
% 0.37/0.61 ! [A: rat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.61 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.37/0.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_exp
% 0.37/0.61 thf(fact_4107_power__less__imp__less__exp,axiom,
% 0.37/0.61 ! [A: nat,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.61 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.37/0.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_exp
% 0.37/0.61 thf(fact_4108_power__less__imp__less__exp,axiom,
% 0.37/0.61 ! [A: int,M: nat,N: nat] :
% 0.37/0.61 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.61 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.37/0.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % power_less_imp_less_exp
% 0.37/0.61 thf(fact_4109_card__less__sym__Diff,axiom,
% 0.37/0.61 ! [A4: set_literal,B4: set_literal] :
% 0.37/0.61 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.61 => ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.61 => ( ( ord_less_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) )
% 0.37/0.61 => ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_less_sym_Diff
% 0.37/0.61 thf(fact_4110_card__less__sym__Diff,axiom,
% 0.37/0.61 ! [A4: set_list_nat,B4: set_list_nat] :
% 0.37/0.61 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.61 => ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.61 => ( ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) )
% 0.37/0.61 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_less_sym_Diff
% 0.37/0.61 thf(fact_4111_card__less__sym__Diff,axiom,
% 0.37/0.61 ! [A4: set_set_nat,B4: set_set_nat] :
% 0.37/0.61 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.61 => ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.61 => ( ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) )
% 0.37/0.61 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.61
% 0.37/0.61 % card_less_sym_Diff
% 0.37/0.61 thf(fact_4112_card__less__sym__Diff,axiom,
% 0.37/0.61 ! [A4: set_int,B4: set_int] :
% 0.37/0.61 ( ( finite_finite_int @ A4 )
% 0.37/0.61 => ( ( finite_finite_int @ B4 )
% 0.37/0.61 => ( ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) )
% 0.37/0.61 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_less_sym_Diff
% 0.37/0.62 thf(fact_4113_card__less__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_complex,B4: set_complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_less_sym_Diff
% 0.37/0.62 thf(fact_4114_card__less__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) )
% 0.37/0.62 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_less_sym_Diff
% 0.37/0.62 thf(fact_4115_card__less__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_nat,B4: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( finite_finite_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_less_sym_Diff
% 0.37/0.62 thf(fact_4116_zero__power,axiom,
% 0.37/0.62 ! [N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( power_power_uint32 @ zero_zero_uint32 @ N )
% 0.37/0.62 = zero_zero_uint32 ) ) ).
% 0.37/0.62
% 0.37/0.62 % zero_power
% 0.37/0.62 thf(fact_4117_zero__power,axiom,
% 0.37/0.62 ! [N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.37/0.62 = zero_zero_rat ) ) ).
% 0.37/0.62
% 0.37/0.62 % zero_power
% 0.37/0.62 thf(fact_4118_zero__power,axiom,
% 0.37/0.62 ! [N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.37/0.62 = zero_zero_nat ) ) ).
% 0.37/0.62
% 0.37/0.62 % zero_power
% 0.37/0.62 thf(fact_4119_zero__power,axiom,
% 0.37/0.62 ! [N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( power_power_real @ zero_zero_real @ N )
% 0.37/0.62 = zero_zero_real ) ) ).
% 0.37/0.62
% 0.37/0.62 % zero_power
% 0.37/0.62 thf(fact_4120_zero__power,axiom,
% 0.37/0.62 ! [N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.37/0.62 = zero_zero_complex ) ) ).
% 0.37/0.62
% 0.37/0.62 % zero_power
% 0.37/0.62 thf(fact_4121_zero__power,axiom,
% 0.37/0.62 ! [N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( power_power_int @ zero_zero_int @ N )
% 0.37/0.62 = zero_zero_int ) ) ).
% 0.37/0.62
% 0.37/0.62 % zero_power
% 0.37/0.62 thf(fact_4122_power__increasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: real] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_real @ one_one_real @ A )
% 0.37/0.62 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N8 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_increasing
% 0.37/0.62 thf(fact_4123_power__increasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: rat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.37/0.62 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N8 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_increasing
% 0.37/0.62 thf(fact_4124_power__increasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.37/0.62 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N8 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_increasing
% 0.37/0.62 thf(fact_4125_power__increasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: int] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.37/0.62 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N8 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_increasing
% 0.37/0.62 thf(fact_4126_card__le__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_literal,B4: set_literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_sym_Diff
% 0.37/0.62 thf(fact_4127_card__le__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_list_nat,B4: set_list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_sym_Diff
% 0.37/0.62 thf(fact_4128_card__le__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_set_nat,B4: set_set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_sym_Diff
% 0.37/0.62 thf(fact_4129_card__le__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_int,B4: set_int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( finite_finite_int @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_sym_Diff
% 0.37/0.62 thf(fact_4130_card__le__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_complex,B4: set_complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_sym_Diff
% 0.37/0.62 thf(fact_4131_card__le__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_sym_Diff
% 0.37/0.62 thf(fact_4132_card__le__sym__Diff,axiom,
% 0.37/0.62 ! [A4: set_nat,B4: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( finite_finite_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_sym_Diff
% 0.37/0.62 thf(fact_4133_psubset__card__mono,axiom,
% 0.37/0.62 ! [B4: set_literal,A4: set_literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.62 => ( ( ord_less_set_literal @ A4 @ B4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % psubset_card_mono
% 0.37/0.62 thf(fact_4134_psubset__card__mono,axiom,
% 0.37/0.62 ! [B4: set_list_nat,A4: set_list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.62 => ( ( ord_le1190675801316882794st_nat @ A4 @ B4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % psubset_card_mono
% 0.37/0.62 thf(fact_4135_psubset__card__mono,axiom,
% 0.37/0.62 ! [B4: set_set_nat,A4: set_set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_set_set_nat @ A4 @ B4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % psubset_card_mono
% 0.37/0.62 thf(fact_4136_psubset__card__mono,axiom,
% 0.37/0.62 ! [B4: set_nat,A4: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_set_nat @ A4 @ B4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % psubset_card_mono
% 0.37/0.62 thf(fact_4137_psubset__card__mono,axiom,
% 0.37/0.62 ! [B4: set_int,A4: set_int] :
% 0.37/0.62 ( ( finite_finite_int @ B4 )
% 0.37/0.62 => ( ( ord_less_set_int @ A4 @ B4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % psubset_card_mono
% 0.37/0.62 thf(fact_4138_psubset__card__mono,axiom,
% 0.37/0.62 ! [B4: set_complex,A4: set_complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.62 => ( ( ord_less_set_complex @ A4 @ B4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % psubset_card_mono
% 0.37/0.62 thf(fact_4139_psubset__card__mono,axiom,
% 0.37/0.62 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.62 => ( ( ord_le1307284697595431911nteger @ A4 @ B4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % psubset_card_mono
% 0.37/0.62 thf(fact_4140_length__pos__if__in__set,axiom,
% 0.37/0.62 ! [X: int,Xs: list_int] :
% 0.37/0.62 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_pos_if_in_set
% 0.37/0.62 thf(fact_4141_length__pos__if__in__set,axiom,
% 0.37/0.62 ! [X: set_nat,Xs: list_set_nat] :
% 0.37/0.62 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_pos_if_in_set
% 0.37/0.62 thf(fact_4142_length__pos__if__in__set,axiom,
% 0.37/0.62 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_pos_if_in_set
% 0.37/0.62 thf(fact_4143_length__pos__if__in__set,axiom,
% 0.37/0.62 ! [X: real,Xs: list_real] :
% 0.37/0.62 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_pos_if_in_set
% 0.37/0.62 thf(fact_4144_length__pos__if__in__set,axiom,
% 0.37/0.62 ! [X: $o,Xs: list_o] :
% 0.37/0.62 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_pos_if_in_set
% 0.37/0.62 thf(fact_4145_length__pos__if__in__set,axiom,
% 0.37/0.62 ! [X: nat,Xs: list_nat] :
% 0.37/0.62 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_pos_if_in_set
% 0.37/0.62 thf(fact_4146_power__gt__expt,axiom,
% 0.37/0.62 ! [N: nat,K: nat] :
% 0.37/0.62 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.62 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_gt_expt
% 0.37/0.62 thf(fact_4147_nat__one__le__power,axiom,
% 0.37/0.62 ! [I: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 0.37/0.62 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nat_one_le_power
% 0.37/0.62 thf(fact_4148_finite__enum__ext,axiom,
% 0.37/0.62 ! [X6: set_nat,Y7: set_nat] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X6 ) )
% 0.37/0.62 => ( ( infini8530281810654367211te_nat @ X6 @ I2 )
% 0.37/0.62 = ( infini8530281810654367211te_nat @ Y7 @ I2 ) ) )
% 0.37/0.62 => ( ( finite_finite_nat @ X6 )
% 0.37/0.62 => ( ( finite_finite_nat @ Y7 )
% 0.37/0.62 => ( ( ( finite_card_nat @ X6 )
% 0.37/0.62 = ( finite_card_nat @ Y7 ) )
% 0.37/0.62 => ( X6 = Y7 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % finite_enum_ext
% 0.37/0.62 thf(fact_4149_finite__enumerate__Ex,axiom,
% 0.37/0.62 ! [S3: set_nat,S: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ S3 )
% 0.37/0.62 => ( ( member_nat @ S @ S3 )
% 0.37/0.62 => ? [N2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S3 ) )
% 0.37/0.62 & ( ( infini8530281810654367211te_nat @ S3 @ N2 )
% 0.37/0.62 = S ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % finite_enumerate_Ex
% 0.37/0.62 thf(fact_4150_finite__enumerate__in__set,axiom,
% 0.37/0.62 ! [S3: set_nat,N: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ S3 )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.37/0.62 => ( member_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ S3 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % finite_enumerate_in_set
% 0.37/0.62 thf(fact_4151_length__removeAll__less,axiom,
% 0.37/0.62 ! [X: int,Xs: list_int] :
% 0.37/0.62 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ ( size_size_list_int @ ( removeAll_int @ X @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_removeAll_less
% 0.37/0.62 thf(fact_4152_length__removeAll__less,axiom,
% 0.37/0.62 ! [X: set_nat,Xs: list_set_nat] :
% 0.37/0.62 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ ( size_s3254054031482475050et_nat @ ( removeAll_set_nat @ X @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_removeAll_less
% 0.37/0.62 thf(fact_4153_length__removeAll__less,axiom,
% 0.37/0.62 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_removeAll_less
% 0.37/0.62 thf(fact_4154_length__removeAll__less,axiom,
% 0.37/0.62 ! [X: real,Xs: list_real] :
% 0.37/0.62 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ ( size_size_list_real @ ( removeAll_real @ X @ Xs ) ) @ ( size_size_list_real @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_removeAll_less
% 0.37/0.62 thf(fact_4155_length__removeAll__less,axiom,
% 0.37/0.62 ! [X: $o,Xs: list_o] :
% 0.37/0.62 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ ( size_size_list_o @ ( removeAll_o @ X @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_removeAll_less
% 0.37/0.62 thf(fact_4156_length__removeAll__less,axiom,
% 0.37/0.62 ! [X: nat,Xs: list_nat] :
% 0.37/0.62 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.62 => ( ord_less_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_removeAll_less
% 0.37/0.62 thf(fact_4157_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_literal] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bot_set_literal )
% 0.37/0.62 & ( finite5847741373460823677iteral @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4158_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_list_nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bot_set_list_nat )
% 0.37/0.62 & ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4159_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_set_nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bot_set_set_nat )
% 0.37/0.62 & ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4160_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_complex] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bot_set_complex )
% 0.37/0.62 & ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4161_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_Code_integer] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.62 & ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4162_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bot_set_nat )
% 0.37/0.62 & ( finite_finite_nat @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4163_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_int] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bot_set_int )
% 0.37/0.62 & ( finite_finite_int @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4164_card__gt__0__iff,axiom,
% 0.37/0.62 ! [A4: set_o] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A4 ) )
% 0.37/0.62 = ( ( A4 != bot_bot_set_o )
% 0.37/0.62 & ( finite_finite_o @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_gt_0_iff
% 0.37/0.62 thf(fact_4165_card__le__Suc0__iff__eq,axiom,
% 0.37/0.62 ! [A4: set_literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ! [X4: literal] :
% 0.37/0.62 ( ( member_literal @ X4 @ A4 )
% 0.37/0.62 => ! [Y4: literal] :
% 0.37/0.62 ( ( member_literal @ Y4 @ A4 )
% 0.37/0.62 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc0_iff_eq
% 0.37/0.62 thf(fact_4166_card__le__Suc0__iff__eq,axiom,
% 0.37/0.62 ! [A4: set_list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ! [X4: list_nat] :
% 0.37/0.62 ( ( member_list_nat @ X4 @ A4 )
% 0.37/0.62 => ! [Y4: list_nat] :
% 0.37/0.62 ( ( member_list_nat @ Y4 @ A4 )
% 0.37/0.62 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc0_iff_eq
% 0.37/0.62 thf(fact_4167_card__le__Suc0__iff__eq,axiom,
% 0.37/0.62 ! [A4: set_set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ! [X4: set_nat] :
% 0.37/0.62 ( ( member_set_nat @ X4 @ A4 )
% 0.37/0.62 => ! [Y4: set_nat] :
% 0.37/0.62 ( ( member_set_nat @ Y4 @ A4 )
% 0.37/0.62 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc0_iff_eq
% 0.37/0.62 thf(fact_4168_card__le__Suc0__iff__eq,axiom,
% 0.37/0.62 ! [A4: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ! [X4: nat] :
% 0.37/0.62 ( ( member_nat @ X4 @ A4 )
% 0.37/0.62 => ! [Y4: nat] :
% 0.37/0.62 ( ( member_nat @ Y4 @ A4 )
% 0.37/0.62 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc0_iff_eq
% 0.37/0.62 thf(fact_4169_card__le__Suc0__iff__eq,axiom,
% 0.37/0.62 ! [A4: set_int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ! [X4: int] :
% 0.37/0.62 ( ( member_int @ X4 @ A4 )
% 0.37/0.62 => ! [Y4: int] :
% 0.37/0.62 ( ( member_int @ Y4 @ A4 )
% 0.37/0.62 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc0_iff_eq
% 0.37/0.62 thf(fact_4170_card__le__Suc0__iff__eq,axiom,
% 0.37/0.62 ! [A4: set_complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ! [X4: complex] :
% 0.37/0.62 ( ( member_complex @ X4 @ A4 )
% 0.37/0.62 => ! [Y4: complex] :
% 0.37/0.62 ( ( member_complex @ Y4 @ A4 )
% 0.37/0.62 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc0_iff_eq
% 0.37/0.62 thf(fact_4171_card__le__Suc0__iff__eq,axiom,
% 0.37/0.62 ! [A4: set_Code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ! [X4: code_integer] :
% 0.37/0.62 ( ( member_Code_integer @ X4 @ A4 )
% 0.37/0.62 => ! [Y4: code_integer] :
% 0.37/0.62 ( ( member_Code_integer @ Y4 @ A4 )
% 0.37/0.62 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc0_iff_eq
% 0.37/0.62 thf(fact_4172_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,K: nat] :
% 0.37/0.62 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_VEBT_VEBT @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_VEBT_VEBT @ B7 @ B6 )
% 0.37/0.62 & ( ( finite7802652506058667612T_VEBT @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4173_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_real,K: nat] :
% 0.37/0.62 ( ( ( finite_card_real @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: real,B6: set_real] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_real @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_real @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_real @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_real ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4174_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_complex,K: nat] :
% 0.37/0.62 ( ( ( finite_card_complex @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: complex,B6: set_complex] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_complex @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_complex @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_complex @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_complex ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4175_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_literal,K: nat] :
% 0.37/0.62 ( ( ( finite_card_literal @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: literal,B6: set_literal] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_literal @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_literal @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_literal @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_literal ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4176_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_list_nat,K: nat] :
% 0.37/0.62 ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: list_nat,B6: set_list_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_list_nat @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_list_nat @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_list_nat @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_list_nat ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4177_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_set_nat,K: nat] :
% 0.37/0.62 ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: set_nat,B6: set_set_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_set_nat @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_set_nat @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_set_nat @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_set_nat ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4178_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_nat,K: nat] :
% 0.37/0.62 ( ( ( finite_card_nat @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: nat,B6: set_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_nat @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_nat @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_nat @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_nat ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4179_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_int,K: nat] :
% 0.37/0.62 ( ( ( finite_card_int @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: int,B6: set_int] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_int @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_int @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_int @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_int ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4180_card__Suc__eq,axiom,
% 0.37/0.62 ! [A4: set_o,K: nat] :
% 0.37/0.62 ( ( ( finite_card_o @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 = ( ? [B7: $o,B6: set_o] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_o @ B7 @ B6 ) )
% 0.37/0.62 & ~ ( member_o @ B7 @ B6 )
% 0.37/0.62 & ( ( finite_card_o @ B6 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B6 = bot_bot_set_o ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_eq
% 0.37/0.62 thf(fact_4181_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,K: nat] :
% 0.37/0.62 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: vEBT_VEBT,B8: set_VEBT_VEBT] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_VEBT_VEBT @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_VEBT_VEBT @ B3 @ B8 )
% 0.37/0.62 & ( ( finite7802652506058667612T_VEBT @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4182_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_real,K: nat] :
% 0.37/0.62 ( ( ( finite_card_real @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: real,B8: set_real] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_real @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_real @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_real @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_real ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4183_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_complex,K: nat] :
% 0.37/0.62 ( ( ( finite_card_complex @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: complex,B8: set_complex] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_complex @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_complex @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_complex @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_complex ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4184_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_literal,K: nat] :
% 0.37/0.62 ( ( ( finite_card_literal @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: literal,B8: set_literal] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_literal @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_literal @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_literal @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_literal ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4185_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_list_nat,K: nat] :
% 0.37/0.62 ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: list_nat,B8: set_list_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_list_nat @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_list_nat @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_list_nat @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_list_nat ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4186_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_set_nat,K: nat] :
% 0.37/0.62 ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: set_nat,B8: set_set_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_set_nat @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_set_nat @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_set_nat @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_set_nat ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4187_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_nat,K: nat] :
% 0.37/0.62 ( ( ( finite_card_nat @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: nat,B8: set_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_nat @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_nat @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_nat @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_nat ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4188_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_int,K: nat] :
% 0.37/0.62 ( ( ( finite_card_int @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: int,B8: set_int] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_int @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_int @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_int @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_int ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4189_card__eq__SucD,axiom,
% 0.37/0.62 ! [A4: set_o,K: nat] :
% 0.37/0.62 ( ( ( finite_card_o @ A4 )
% 0.37/0.62 = ( suc @ K ) )
% 0.37/0.62 => ? [B3: $o,B8: set_o] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_o @ B3 @ B8 ) )
% 0.37/0.62 & ~ ( member_o @ B3 @ B8 )
% 0.37/0.62 & ( ( finite_card_o @ B8 )
% 0.37/0.62 = K )
% 0.37/0.62 & ( ( K = zero_zero_nat )
% 0.37/0.62 => ( B8 = bot_bot_set_o ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_eq_SucD
% 0.37/0.62 thf(fact_4190_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT] :
% 0.37/0.62 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: vEBT_VEBT] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4191_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_complex] :
% 0.37/0.62 ( ( ( finite_card_complex @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: complex] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4192_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_literal] :
% 0.37/0.62 ( ( ( finite_card_literal @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: literal] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_literal @ X4 @ bot_bot_set_literal ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4193_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_list_nat] :
% 0.37/0.62 ( ( ( finite_card_list_nat @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: list_nat] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4194_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_set_nat] :
% 0.37/0.62 ( ( ( finite_card_set_nat @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: set_nat] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4195_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_nat] :
% 0.37/0.62 ( ( ( finite_card_nat @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: nat] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4196_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_int] :
% 0.37/0.62 ( ( ( finite_card_int @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: int] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4197_card__1__singleton__iff,axiom,
% 0.37/0.62 ! [A4: set_o] :
% 0.37/0.62 ( ( ( finite_card_o @ A4 )
% 0.37/0.62 = ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( ? [X4: $o] :
% 0.37/0.62 ( A4
% 0.37/0.62 = ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singleton_iff
% 0.37/0.62 thf(fact_4198_power__Suc__less,axiom,
% 0.37/0.62 ! [A: real,N: nat] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_real @ A @ one_one_real )
% 0.37/0.62 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less
% 0.37/0.62 thf(fact_4199_power__Suc__less,axiom,
% 0.37/0.62 ! [A: rat,N: nat] :
% 0.37/0.62 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.37/0.62 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less
% 0.37/0.62 thf(fact_4200_power__Suc__less,axiom,
% 0.37/0.62 ! [A: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.37/0.62 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less
% 0.37/0.62 thf(fact_4201_power__Suc__less,axiom,
% 0.37/0.62 ! [A: int,N: nat] :
% 0.37/0.62 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_int @ A @ one_one_int )
% 0.37/0.62 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less
% 0.37/0.62 thf(fact_4202_power__Suc__le__self,axiom,
% 0.37/0.62 ! [A: real,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.37/0.62 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_le_self
% 0.37/0.62 thf(fact_4203_power__Suc__le__self,axiom,
% 0.37/0.62 ! [A: rat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.37/0.62 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_le_self
% 0.37/0.62 thf(fact_4204_power__Suc__le__self,axiom,
% 0.37/0.62 ! [A: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.37/0.62 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_le_self
% 0.37/0.62 thf(fact_4205_power__Suc__le__self,axiom,
% 0.37/0.62 ! [A: int,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.37/0.62 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_le_self
% 0.37/0.62 thf(fact_4206_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_o] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_o @ A4 ) )
% 0.37/0.62 = ( ? [A7: $o,B6: set_o] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_o @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_o @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_o @ B6 ) )
% 0.37/0.62 & ( finite_finite_o @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4207_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_VEBT_VEBT] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 0.37/0.62 = ( ? [A7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_VEBT_VEBT @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_VEBT_VEBT @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite7802652506058667612T_VEBT @ B6 ) )
% 0.37/0.62 & ( finite5795047828879050333T_VEBT @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4208_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_real] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_real @ A4 ) )
% 0.37/0.62 = ( ? [A7: real,B6: set_real] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_real @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_real @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_real @ B6 ) )
% 0.37/0.62 & ( finite_finite_real @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4209_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_literal] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_literal @ A4 ) )
% 0.37/0.62 = ( ? [A7: literal,B6: set_literal] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_literal @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_literal @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_literal @ B6 ) )
% 0.37/0.62 & ( finite5847741373460823677iteral @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4210_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_list_nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_list_nat @ A4 ) )
% 0.37/0.62 = ( ? [A7: list_nat,B6: set_list_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_list_nat @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_list_nat @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ B6 ) )
% 0.37/0.62 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4211_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_set_nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_set_nat @ A4 ) )
% 0.37/0.62 = ( ? [A7: set_nat,B6: set_set_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_set_nat @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_set_nat @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ B6 ) )
% 0.37/0.62 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4212_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_nat @ A4 ) )
% 0.37/0.62 = ( ? [A7: nat,B6: set_nat] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_nat @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_nat @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_nat @ B6 ) )
% 0.37/0.62 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4213_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_int] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_int @ A4 ) )
% 0.37/0.62 = ( ? [A7: int,B6: set_int] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_int @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_int @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_int @ B6 ) )
% 0.37/0.62 & ( finite_finite_int @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4214_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_complex] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_complex @ A4 ) )
% 0.37/0.62 = ( ? [A7: complex,B6: set_complex] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_complex @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_complex @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite_card_complex @ B6 ) )
% 0.37/0.62 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4215_card__le__Suc__iff,axiom,
% 0.37/0.62 ! [N: nat,A4: set_Code_integer] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite4902975817058060853nteger @ A4 ) )
% 0.37/0.62 = ( ? [A7: code_integer,B6: set_Code_integer] :
% 0.37/0.62 ( ( A4
% 0.37/0.62 = ( insert_Code_integer @ A7 @ B6 ) )
% 0.37/0.62 & ~ ( member_Code_integer @ A7 @ B6 )
% 0.37/0.62 & ( ord_less_eq_nat @ N @ ( finite4902975817058060853nteger @ B6 ) )
% 0.37/0.62 & ( finite6017078050557962740nteger @ B6 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_iff
% 0.37/0.62 thf(fact_4216_power__Suc__less__one,axiom,
% 0.37/0.62 ! [A: real,N: nat] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_real @ A @ one_one_real )
% 0.37/0.62 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less_one
% 0.37/0.62 thf(fact_4217_power__Suc__less__one,axiom,
% 0.37/0.62 ! [A: rat,N: nat] :
% 0.37/0.62 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.37/0.62 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less_one
% 0.37/0.62 thf(fact_4218_power__Suc__less__one,axiom,
% 0.37/0.62 ! [A: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.37/0.62 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less_one
% 0.37/0.62 thf(fact_4219_power__Suc__less__one,axiom,
% 0.37/0.62 ! [A: int,N: nat] :
% 0.37/0.62 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_int @ A @ one_one_int )
% 0.37/0.62 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_Suc_less_one
% 0.37/0.62 thf(fact_4220_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_literal,B4: set_complex,F: literal > complex] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_5274195009022015549omplex @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4221_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_literal,B4: set_literal,F: literal > literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( ord_le7307670543136651348iteral @ B4 @ ( image_8195128725298311301iteral @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4222_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_literal,B4: set_nat,F: literal > nat] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_set_nat @ B4 @ ( image_literal_nat @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4223_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_nat,B4: set_complex,F: nat > complex] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_nat_complex @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4224_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_nat,B4: set_literal,F: nat > literal] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( ord_le7307670543136651348iteral @ B4 @ ( image_nat_literal @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4225_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_nat,B4: set_nat,F: nat > nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4226_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_int,B4: set_complex,F: int > complex] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_int_complex @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4227_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_int,B4: set_literal,F: int > literal] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( ord_le7307670543136651348iteral @ B4 @ ( image_int_literal @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4228_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_int,B4: set_nat,F: int > nat] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4229_surj__card__le,axiom,
% 0.37/0.62 ! [A4: set_complex,B4: set_complex,F: complex > complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_complex @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % surj_card_le
% 0.37/0.62 thf(fact_4230_power__strict__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: real] :
% 0.37/0.62 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_real @ A @ one_one_real )
% 0.37/0.62 => ( ord_less_real @ ( power_power_real @ A @ N8 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_decreasing
% 0.37/0.62 thf(fact_4231_power__strict__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: rat] :
% 0.37/0.62 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.37/0.62 => ( ord_less_rat @ ( power_power_rat @ A @ N8 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_decreasing
% 0.37/0.62 thf(fact_4232_power__strict__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: nat] :
% 0.37/0.62 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.37/0.62 => ( ord_less_nat @ ( power_power_nat @ A @ N8 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_decreasing
% 0.37/0.62 thf(fact_4233_power__strict__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: int] :
% 0.37/0.62 ( ( ord_less_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_int @ A @ one_one_int )
% 0.37/0.62 => ( ord_less_int @ ( power_power_int @ A @ N8 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_decreasing
% 0.37/0.62 thf(fact_4234_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.62 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.62 => ( ( ( finite7802652506058667612T_VEBT @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_VEBT_VEBT @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4235_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_real,X: real] :
% 0.37/0.62 ( ( finite_finite_real @ S3 )
% 0.37/0.62 => ( ( ( finite_card_real @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_real @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4236_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_literal,X: literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ S3 )
% 0.37/0.62 => ( ( ( finite_card_literal @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_literal @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_literal @ X @ bot_bot_set_literal ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4237_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_list_nat,X: list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ S3 )
% 0.37/0.62 => ( ( ( finite_card_list_nat @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_list_nat @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4238_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_set_nat,X: set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ S3 )
% 0.37/0.62 => ( ( ( finite_card_set_nat @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_set_nat @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4239_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_complex,X: complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.62 => ( ( ( finite_card_complex @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_complex @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4240_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_Code_integer,X: code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.62 => ( ( ( finite4902975817058060853nteger @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_Code_integer @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4241_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_nat,X: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ S3 )
% 0.37/0.62 => ( ( ( finite_card_nat @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_nat @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4242_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_int,X: int] :
% 0.37/0.62 ( ( finite_finite_int @ S3 )
% 0.37/0.62 => ( ( ( finite_card_int @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_int @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4243_card__1__singletonI,axiom,
% 0.37/0.62 ! [S3: set_o,X: $o] :
% 0.37/0.62 ( ( finite_finite_o @ S3 )
% 0.37/0.62 => ( ( ( finite_card_o @ S3 )
% 0.37/0.62 = one_one_nat )
% 0.37/0.62 => ( ( member_o @ X @ S3 )
% 0.37/0.62 => ( S3
% 0.37/0.62 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_1_singletonI
% 0.37/0.62 thf(fact_4244_power__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: real] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.37/0.62 => ( ord_less_eq_real @ ( power_power_real @ A @ N8 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_decreasing
% 0.37/0.62 thf(fact_4245_power__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: rat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.37/0.62 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N8 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_decreasing
% 0.37/0.62 thf(fact_4246_power__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.37/0.62 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N8 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_decreasing
% 0.37/0.62 thf(fact_4247_power__decreasing,axiom,
% 0.37/0.62 ! [N: nat,N8: nat,A: int] :
% 0.37/0.62 ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.62 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.37/0.62 => ( ord_less_eq_int @ ( power_power_int @ A @ N8 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_decreasing
% 0.37/0.62 thf(fact_4248_power__eq__imp__eq__base,axiom,
% 0.37/0.62 ! [A: real,N: nat,B: real] :
% 0.37/0.62 ( ( ( power_power_real @ A @ N )
% 0.37/0.62 = ( power_power_real @ B @ N ) )
% 0.37/0.62 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_imp_eq_base
% 0.37/0.62 thf(fact_4249_power__eq__imp__eq__base,axiom,
% 0.37/0.62 ! [A: rat,N: nat,B: rat] :
% 0.37/0.62 ( ( ( power_power_rat @ A @ N )
% 0.37/0.62 = ( power_power_rat @ B @ N ) )
% 0.37/0.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_imp_eq_base
% 0.37/0.62 thf(fact_4250_power__eq__imp__eq__base,axiom,
% 0.37/0.62 ! [A: nat,N: nat,B: nat] :
% 0.37/0.62 ( ( ( power_power_nat @ A @ N )
% 0.37/0.62 = ( power_power_nat @ B @ N ) )
% 0.37/0.62 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_imp_eq_base
% 0.37/0.62 thf(fact_4251_power__eq__imp__eq__base,axiom,
% 0.37/0.62 ! [A: int,N: nat,B: int] :
% 0.37/0.62 ( ( ( power_power_int @ A @ N )
% 0.37/0.62 = ( power_power_int @ B @ N ) )
% 0.37/0.62 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_imp_eq_base
% 0.37/0.62 thf(fact_4252_power__eq__iff__eq__base,axiom,
% 0.37/0.62 ! [N: nat,A: real,B: real] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.37/0.62 => ( ( ( power_power_real @ A @ N )
% 0.37/0.62 = ( power_power_real @ B @ N ) )
% 0.37/0.62 = ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_iff_eq_base
% 0.37/0.62 thf(fact_4253_power__eq__iff__eq__base,axiom,
% 0.37/0.62 ! [N: nat,A: rat,B: rat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.37/0.62 => ( ( ( power_power_rat @ A @ N )
% 0.37/0.62 = ( power_power_rat @ B @ N ) )
% 0.37/0.62 = ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_iff_eq_base
% 0.37/0.62 thf(fact_4254_power__eq__iff__eq__base,axiom,
% 0.37/0.62 ! [N: nat,A: nat,B: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.37/0.62 => ( ( ( power_power_nat @ A @ N )
% 0.37/0.62 = ( power_power_nat @ B @ N ) )
% 0.37/0.62 = ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_iff_eq_base
% 0.37/0.62 thf(fact_4255_power__eq__iff__eq__base,axiom,
% 0.37/0.62 ! [N: nat,A: int,B: int] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.62 => ( ( ( power_power_int @ A @ N )
% 0.37/0.62 = ( power_power_int @ B @ N ) )
% 0.37/0.62 = ( A = B ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_iff_eq_base
% 0.37/0.62 thf(fact_4256_power__le__imp__le__exp,axiom,
% 0.37/0.62 ! [A: real,M: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.62 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 0.37/0.62 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_le_imp_le_exp
% 0.37/0.62 thf(fact_4257_power__le__imp__le__exp,axiom,
% 0.37/0.62 ! [A: rat,M: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.62 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.37/0.62 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_le_imp_le_exp
% 0.37/0.62 thf(fact_4258_power__le__imp__le__exp,axiom,
% 0.37/0.62 ! [A: nat,M: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.37/0.62 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_le_imp_le_exp
% 0.37/0.62 thf(fact_4259_power__le__imp__le__exp,axiom,
% 0.37/0.62 ! [A: int,M: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.62 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.37/0.62 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_le_imp_le_exp
% 0.37/0.62 thf(fact_4260_self__le__power,axiom,
% 0.37/0.62 ! [A: real,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_real @ one_one_real @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % self_le_power
% 0.37/0.62 thf(fact_4261_self__le__power,axiom,
% 0.37/0.62 ! [A: rat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % self_le_power
% 0.37/0.62 thf(fact_4262_self__le__power,axiom,
% 0.37/0.62 ! [A: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % self_le_power
% 0.37/0.62 thf(fact_4263_self__le__power,axiom,
% 0.37/0.62 ! [A: int,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_int @ one_one_int @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % self_le_power
% 0.37/0.62 thf(fact_4264_one__less__power,axiom,
% 0.37/0.62 ! [A: real,N: nat] :
% 0.37/0.62 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % one_less_power
% 0.37/0.62 thf(fact_4265_one__less__power,axiom,
% 0.37/0.62 ! [A: rat,N: nat] :
% 0.37/0.62 ( ( ord_less_rat @ one_one_rat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % one_less_power
% 0.37/0.62 thf(fact_4266_one__less__power,axiom,
% 0.37/0.62 ! [A: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ one_one_nat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % one_less_power
% 0.37/0.62 thf(fact_4267_one__less__power,axiom,
% 0.37/0.62 ! [A: int,N: nat] :
% 0.37/0.62 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % one_less_power
% 0.37/0.62 thf(fact_4268_card__Diff1__le,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4269_card__Diff1__le,axiom,
% 0.37/0.62 ! [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 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4270_card__Diff1__le,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal] : ( ord_less_eq_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4271_card__Diff1__le,axiom,
% 0.37/0.62 ! [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 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4272_card__Diff1__le,axiom,
% 0.37/0.62 ! [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 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4273_card__Diff1__le,axiom,
% 0.37/0.62 ! [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 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4274_card__Diff1__le,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4275_card__Diff1__le,axiom,
% 0.37/0.62 ! [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 ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_le
% 0.37/0.62 thf(fact_4276_card__Diff__subset,axiom,
% 0.37/0.62 ! [B4: set_literal,A4: set_literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.62 => ( ( ord_le7307670543136651348iteral @ B4 @ A4 )
% 0.37/0.62 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_subset
% 0.37/0.62 thf(fact_4277_card__Diff__subset,axiom,
% 0.37/0.62 ! [B4: set_list_nat,A4: set_list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.62 => ( ( ord_le6045566169113846134st_nat @ B4 @ A4 )
% 0.37/0.62 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_subset
% 0.37/0.62 thf(fact_4278_card__Diff__subset,axiom,
% 0.37/0.62 ! [B4: set_set_nat,A4: set_set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.62 => ( ( ord_le6893508408891458716et_nat @ B4 @ A4 )
% 0.37/0.62 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_subset
% 0.37/0.62 thf(fact_4279_card__Diff__subset,axiom,
% 0.37/0.62 ! [B4: set_complex,A4: set_complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.62 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.62 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_subset
% 0.37/0.62 thf(fact_4280_card__Diff__subset,axiom,
% 0.37/0.62 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.62 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.62 => ( ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_subset
% 0.37/0.62 thf(fact_4281_card__Diff__subset,axiom,
% 0.37/0.62 ! [B4: set_nat,A4: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.62 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_subset
% 0.37/0.62 thf(fact_4282_card__Diff__subset,axiom,
% 0.37/0.62 ! [B4: set_int,A4: set_int] :
% 0.37/0.62 ( ( finite_finite_int @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.37/0.62 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_subset
% 0.37/0.62 thf(fact_4283_diff__card__le__card__Diff,axiom,
% 0.37/0.62 ! [B4: set_literal,A4: set_literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % diff_card_le_card_Diff
% 0.37/0.62 thf(fact_4284_diff__card__le__card__Diff,axiom,
% 0.37/0.62 ! [B4: set_list_nat,A4: set_list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % diff_card_le_card_Diff
% 0.37/0.62 thf(fact_4285_diff__card__le__card__Diff,axiom,
% 0.37/0.62 ! [B4: set_set_nat,A4: set_set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % diff_card_le_card_Diff
% 0.37/0.62 thf(fact_4286_diff__card__le__card__Diff,axiom,
% 0.37/0.62 ! [B4: set_int,A4: set_int] :
% 0.37/0.62 ( ( finite_finite_int @ B4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % diff_card_le_card_Diff
% 0.37/0.62 thf(fact_4287_diff__card__le__card__Diff,axiom,
% 0.37/0.62 ! [B4: set_complex,A4: set_complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % diff_card_le_card_Diff
% 0.37/0.62 thf(fact_4288_diff__card__le__card__Diff,axiom,
% 0.37/0.62 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % diff_card_le_card_Diff
% 0.37/0.62 thf(fact_4289_diff__card__le__card__Diff,axiom,
% 0.37/0.62 ! [B4: set_nat,A4: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ B4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % diff_card_le_card_Diff
% 0.37/0.62 thf(fact_4290_card__psubset,axiom,
% 0.37/0.62 ! [B4: set_literal,A4: set_literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ B4 )
% 0.37/0.62 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) )
% 0.37/0.62 => ( ord_less_set_literal @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_psubset
% 0.37/0.62 thf(fact_4291_card__psubset,axiom,
% 0.37/0.62 ! [B4: set_list_nat,A4: set_list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ B4 )
% 0.37/0.62 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) )
% 0.37/0.62 => ( ord_le1190675801316882794st_nat @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_psubset
% 0.37/0.62 thf(fact_4292_card__psubset,axiom,
% 0.37/0.62 ! [B4: set_set_nat,A4: set_set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ B4 )
% 0.37/0.62 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) )
% 0.37/0.62 => ( ord_less_set_set_nat @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_psubset
% 0.37/0.62 thf(fact_4293_card__psubset,axiom,
% 0.37/0.62 ! [B4: set_nat,A4: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) )
% 0.37/0.62 => ( ord_less_set_nat @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_psubset
% 0.37/0.62 thf(fact_4294_card__psubset,axiom,
% 0.37/0.62 ! [B4: set_complex,A4: set_complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) )
% 0.37/0.62 => ( ord_less_set_complex @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_psubset
% 0.37/0.62 thf(fact_4295_card__psubset,axiom,
% 0.37/0.62 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.62 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) )
% 0.37/0.62 => ( ord_le1307284697595431911nteger @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_psubset
% 0.37/0.62 thf(fact_4296_card__psubset,axiom,
% 0.37/0.62 ! [B4: set_int,A4: set_int] :
% 0.37/0.62 ( ( finite_finite_int @ B4 )
% 0.37/0.62 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 0.37/0.62 => ( ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) )
% 0.37/0.62 => ( ord_less_set_int @ A4 @ B4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_psubset
% 0.37/0.62 thf(fact_4297_finite__enumerate__mono,axiom,
% 0.37/0.62 ! [M: nat,N: nat,S3: set_nat] :
% 0.37/0.62 ( ( ord_less_nat @ M @ N )
% 0.37/0.62 => ( ( finite_finite_nat @ S3 )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.37/0.62 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % finite_enumerate_mono
% 0.37/0.62 thf(fact_4298_nat__mult__power__less__eq,axiom,
% 0.37/0.62 ! [B: nat,A: nat,N: nat,M: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.37/0.62 => ( ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ B @ N ) ) @ ( power_power_nat @ B @ M ) )
% 0.37/0.62 = ( ord_less_nat @ A @ ( power_power_nat @ B @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nat_mult_power_less_eq
% 0.37/0.62 thf(fact_4299_card__le__Suc__Max,axiom,
% 0.37/0.62 ! [S3: set_nat] :
% 0.37/0.62 ( ( finite_finite_nat @ S3 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_le_Suc_Max
% 0.37/0.62 thf(fact_4300_finite__le__enumerate,axiom,
% 0.37/0.62 ! [S3: set_nat,N: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ S3 )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.37/0.62 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % finite_le_enumerate
% 0.37/0.62 thf(fact_4301_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o] :
% 0.37/0.62 ( ( finite_finite_o @ A4 )
% 0.37/0.62 => ( ~ ( member_o @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_o @ ( insert_o @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_o @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4302_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.62 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4303_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_real,X: real] :
% 0.37/0.62 ( ( finite_finite_real @ A4 )
% 0.37/0.62 => ( ~ ( member_real @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_real @ ( insert_real @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_real @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4304_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ~ ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_literal @ ( insert_literal @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_literal @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4305_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ~ ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4306_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ~ ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4307_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_nat,X: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ~ ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4308_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_int,X: int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ~ ( member_int @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4309_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_complex,X: complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ~ ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite_card_complex @ ( insert_complex @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite_card_complex @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4310_card__insert__disjoint_H,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ~ ( member_Code_integer @ X @ A4 )
% 0.37/0.62 => ( ( minus_minus_nat @ ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.62 = ( finite4902975817058060853nteger @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_insert_disjoint'
% 0.37/0.62 thf(fact_4311_power__strict__mono,axiom,
% 0.37/0.62 ! [A: real,B: real,N: nat] :
% 0.37/0.62 ( ( ord_less_real @ A @ B )
% 0.37/0.62 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_mono
% 0.37/0.62 thf(fact_4312_power__strict__mono,axiom,
% 0.37/0.62 ! [A: rat,B: rat,N: nat] :
% 0.37/0.62 ( ( ord_less_rat @ A @ B )
% 0.37/0.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_mono
% 0.37/0.62 thf(fact_4313_power__strict__mono,axiom,
% 0.37/0.62 ! [A: nat,B: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_nat @ A @ B )
% 0.37/0.62 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_mono
% 0.37/0.62 thf(fact_4314_power__strict__mono,axiom,
% 0.37/0.62 ! [A: int,B: int,N: nat] :
% 0.37/0.62 ( ( ord_less_int @ A @ B )
% 0.37/0.62 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_strict_mono
% 0.37/0.62 thf(fact_4315_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.62 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ( finite7802652506058667612T_VEBT @ A4 )
% 0.37/0.62 = ( suc @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4316_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_real,X: real] :
% 0.37/0.62 ( ( finite_finite_real @ A4 )
% 0.37/0.62 => ( ( member_real @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_real @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4317_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_literal @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4318_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_list_nat @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4319_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_set_nat @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4320_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_complex,X: complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_complex @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4321_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.62 => ( ( finite4902975817058060853nteger @ A4 )
% 0.37/0.62 = ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4322_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_int,X: int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( member_int @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_int @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4323_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o] :
% 0.37/0.62 ( ( finite_finite_o @ A4 )
% 0.37/0.62 => ( ( member_o @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_o @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4324_card_Oremove,axiom,
% 0.37/0.62 ! [A4: set_nat,X: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_nat @ A4 )
% 0.37/0.62 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.remove
% 0.37/0.62 thf(fact_4325_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.62 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4326_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4327_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4328_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4329_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_complex,X: complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4330_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4331_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_int,X: int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4332_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o] :
% 0.37/0.62 ( ( finite_finite_o @ A4 )
% 0.37/0.62 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4333_card_Oinsert__remove,axiom,
% 0.37/0.62 ! [A4: set_nat,X: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.62 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card.insert_remove
% 0.37/0.62 thf(fact_4334_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.62 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 0.37/0.62 = ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4335_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_real,X: real] :
% 0.37/0.62 ( ( finite_finite_real @ A4 )
% 0.37/0.62 => ( ( member_real @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 0.37/0.62 = ( finite_card_real @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4336_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) )
% 0.37/0.62 = ( finite_card_literal @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4337_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) )
% 0.37/0.62 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4338_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 0.37/0.62 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4339_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_complex,X: complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 0.37/0.62 = ( finite_card_complex @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4340_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) )
% 0.37/0.62 = ( finite4902975817058060853nteger @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4341_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_int,X: int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( member_int @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 0.37/0.62 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4342_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o] :
% 0.37/0.62 ( ( finite_finite_o @ A4 )
% 0.37/0.62 => ( ( member_o @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) )
% 0.37/0.62 = ( finite_card_o @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4343_card__Suc__Diff1,axiom,
% 0.37/0.62 ! [A4: set_nat,X: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 0.37/0.62 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Suc_Diff1
% 0.37/0.62 thf(fact_4344_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.62 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4345_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_real,X: real] :
% 0.37/0.62 ( ( finite_finite_real @ A4 )
% 0.37/0.62 => ( ( member_real @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4346_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4347_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4348_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4349_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_complex,X: complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4350_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4351_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_int,X: int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( member_int @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4352_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o] :
% 0.37/0.62 ( ( finite_finite_o @ A4 )
% 0.37/0.62 => ( ( member_o @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4353_card__Diff1__less,axiom,
% 0.37/0.62 ! [A4: set_nat,X: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less
% 0.37/0.62 thf(fact_4354_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.62 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.62 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ( member_VEBT_VEBT @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ ( insert_VEBT_VEBT @ Y @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4355_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_real,X: real,Y: real] :
% 0.37/0.62 ( ( finite_finite_real @ A4 )
% 0.37/0.62 => ( ( member_real @ X @ A4 )
% 0.37/0.62 => ( ( member_real @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ ( insert_real @ Y @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4356_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal,Y: literal] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ( member_literal @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) @ ( insert_literal @ Y @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4357_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_list_nat,X: list_nat,Y: list_nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ( member_list_nat @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) @ ( insert_list_nat @ Y @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4358_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_set_nat,X: set_nat,Y: set_nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ( member_set_nat @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ ( insert_set_nat @ Y @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4359_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_complex,X: complex,Y: complex] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ( member_complex @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ ( insert_complex @ Y @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4360_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,X: code_integer,Y: code_integer] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.62 => ( ( member_Code_integer @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) @ ( insert_Code_integer @ Y @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4361_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_int,X: int,Y: int] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ( member_int @ X @ A4 )
% 0.37/0.62 => ( ( member_int @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ ( insert_int @ Y @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4362_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o,Y: $o] :
% 0.37/0.62 ( ( finite_finite_o @ A4 )
% 0.37/0.62 => ( ( member_o @ X @ A4 )
% 0.37/0.62 => ( ( member_o @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ ( insert_o @ Y @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4363_card__Diff2__less,axiom,
% 0.37/0.62 ! [A4: set_nat,X: nat,Y: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ( member_nat @ Y @ A4 )
% 0.37/0.62 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff2_less
% 0.37/0.62 thf(fact_4364_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 0.37/0.62 = ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.62 & ( member_VEBT_VEBT @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4365_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_real,X: real] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) )
% 0.37/0.62 = ( ( finite_finite_real @ A4 )
% 0.37/0.62 & ( member_real @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4366_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_literal,X: literal] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) )
% 0.37/0.62 = ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 & ( member_literal @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4367_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_list_nat,X: list_nat] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) )
% 0.37/0.62 = ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 & ( member_list_nat @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4368_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_set_nat,X: set_nat] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) )
% 0.37/0.62 = ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 & ( member_set_nat @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4369_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_complex,X: complex] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) )
% 0.37/0.62 = ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 & ( member_complex @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4370_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A4 ) )
% 0.37/0.62 = ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 & ( member_Code_integer @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4371_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_int,X: int] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) )
% 0.37/0.62 = ( ( finite_finite_int @ A4 )
% 0.37/0.62 & ( member_int @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4372_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_o,X: $o] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) )
% 0.37/0.62 = ( ( finite_finite_o @ A4 )
% 0.37/0.62 & ( member_o @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4373_card__Diff1__less__iff,axiom,
% 0.37/0.62 ! [A4: set_nat,X: nat] :
% 0.37/0.62 ( ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) )
% 0.37/0.62 = ( ( finite_finite_nat @ A4 )
% 0.37/0.62 & ( member_nat @ X @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff1_less_iff
% 0.37/0.62 thf(fact_4374_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.62 ( ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.62 = ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4375_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: real,A4: set_real] :
% 0.37/0.62 ( ( ( member_real @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_real @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_real @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 0.37/0.62 = ( finite_card_real @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4376_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: complex,A4: set_complex] :
% 0.37/0.62 ( ( ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 0.37/0.62 = ( finite_card_complex @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4377_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: literal,A4: set_literal] :
% 0.37/0.62 ( ( ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 0.37/0.62 = ( finite_card_literal @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4378_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: list_nat,A4: set_list_nat] :
% 0.37/0.62 ( ( ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 0.37/0.62 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4379_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: set_nat,A4: set_set_nat] :
% 0.37/0.62 ( ( ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 0.37/0.62 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4380_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: int,A4: set_int] :
% 0.37/0.62 ( ( ( member_int @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_int @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_int @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.37/0.62 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4381_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: $o,A4: set_o] :
% 0.37/0.62 ( ( ( member_o @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_o @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_o @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.37/0.62 = ( finite_card_o @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4382_card__Diff__singleton__if,axiom,
% 0.37/0.62 ! [X: nat,A4: set_nat] :
% 0.37/0.62 ( ( ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ one_one_nat ) ) )
% 0.37/0.62 & ( ~ ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.37/0.62 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton_if
% 0.37/0.62 thf(fact_4383_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.62 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4384_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: real,A4: set_real] :
% 0.37/0.62 ( ( member_real @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_real @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4385_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: complex,A4: set_complex] :
% 0.37/0.62 ( ( member_complex @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4386_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: literal,A4: set_literal] :
% 0.37/0.62 ( ( member_literal @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4387_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: list_nat,A4: set_list_nat] :
% 0.37/0.62 ( ( member_list_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4388_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: set_nat,A4: set_set_nat] :
% 0.37/0.62 ( ( member_set_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4389_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: int,A4: set_int] :
% 0.37/0.62 ( ( member_int @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_int @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4390_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: $o,A4: set_o] :
% 0.37/0.62 ( ( member_o @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_o @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4391_card__Diff__singleton,axiom,
% 0.37/0.62 ! [X: nat,A4: set_nat] :
% 0.37/0.62 ( ( member_nat @ X @ A4 )
% 0.37/0.62 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.37/0.62 = ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ one_one_nat ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Diff_singleton
% 0.37/0.62 thf(fact_4392_the__default_Osimps_I1_J,axiom,
% 0.37/0.62 ! [Uu2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.37/0.62 ( ( the_de3812365490807259288at_nat @ Uu2 @ ( some_P7363390416028606310at_nat @ X ) )
% 0.37/0.62 = X ) ).
% 0.37/0.62
% 0.37/0.62 % the_default.simps(1)
% 0.37/0.62 thf(fact_4393_the__default_Osimps_I1_J,axiom,
% 0.37/0.62 ! [Uu2: nat,X: nat] :
% 0.37/0.62 ( ( the_default_nat @ Uu2 @ ( some_nat @ X ) )
% 0.37/0.62 = X ) ).
% 0.37/0.62
% 0.37/0.62 % the_default.simps(1)
% 0.37/0.62 thf(fact_4394_power__eq__if,axiom,
% 0.37/0.62 ( power_power_rat
% 0.37/0.62 = ( ^ [P7: rat,M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P7 @ ( power_power_rat @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_if
% 0.37/0.62 thf(fact_4395_power__eq__if,axiom,
% 0.37/0.62 ( power_power_complex
% 0.37/0.62 = ( ^ [P7: complex,M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P7 @ ( power_power_complex @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_if
% 0.37/0.62 thf(fact_4396_power__eq__if,axiom,
% 0.37/0.62 ( power_power_assn
% 0.37/0.62 = ( ^ [P7: assn,M5: nat] : ( if_assn @ ( M5 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P7 @ ( power_power_assn @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_if
% 0.37/0.62 thf(fact_4397_power__eq__if,axiom,
% 0.37/0.62 ( power_power_uint32
% 0.37/0.62 = ( ^ [P7: uint32,M5: nat] : ( if_uint32 @ ( M5 = zero_zero_nat ) @ one_one_uint32 @ ( times_times_uint32 @ P7 @ ( power_power_uint32 @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_if
% 0.37/0.62 thf(fact_4398_power__eq__if,axiom,
% 0.37/0.62 ( power_power_real
% 0.37/0.62 = ( ^ [P7: real,M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P7 @ ( power_power_real @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_if
% 0.37/0.62 thf(fact_4399_power__eq__if,axiom,
% 0.37/0.62 ( power_power_nat
% 0.37/0.62 = ( ^ [P7: nat,M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P7 @ ( power_power_nat @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_if
% 0.37/0.62 thf(fact_4400_power__eq__if,axiom,
% 0.37/0.62 ( power_power_int
% 0.37/0.62 = ( ^ [P7: int,M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P7 @ ( power_power_int @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_eq_if
% 0.37/0.62 thf(fact_4401_the__default_Osimps_I2_J,axiom,
% 0.37/0.62 ! [X: product_prod_nat_nat] :
% 0.37/0.62 ( ( the_de3812365490807259288at_nat @ X @ none_P5556105721700978146at_nat )
% 0.37/0.62 = X ) ).
% 0.37/0.62
% 0.37/0.62 % the_default.simps(2)
% 0.37/0.62 thf(fact_4402_the__default_Osimps_I2_J,axiom,
% 0.37/0.62 ! [X: nat] :
% 0.37/0.62 ( ( the_default_nat @ X @ none_nat )
% 0.37/0.62 = X ) ).
% 0.37/0.62
% 0.37/0.62 % the_default.simps(2)
% 0.37/0.62 thf(fact_4403_power__minus__mult,axiom,
% 0.37/0.62 ! [N: nat,A: complex] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.37/0.62 = ( power_power_complex @ A @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_minus_mult
% 0.37/0.62 thf(fact_4404_power__minus__mult,axiom,
% 0.37/0.62 ! [N: nat,A: assn] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.37/0.62 = ( power_power_assn @ A @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_minus_mult
% 0.37/0.62 thf(fact_4405_power__minus__mult,axiom,
% 0.37/0.62 ! [N: nat,A: uint32] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( times_times_uint32 @ ( power_power_uint32 @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.37/0.62 = ( power_power_uint32 @ A @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_minus_mult
% 0.37/0.62 thf(fact_4406_power__minus__mult,axiom,
% 0.37/0.62 ! [N: nat,A: real] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.37/0.62 = ( power_power_real @ A @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_minus_mult
% 0.37/0.62 thf(fact_4407_power__minus__mult,axiom,
% 0.37/0.62 ! [N: nat,A: nat] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.37/0.62 = ( power_power_nat @ A @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_minus_mult
% 0.37/0.62 thf(fact_4408_power__minus__mult,axiom,
% 0.37/0.62 ! [N: nat,A: int] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.37/0.62 = ( power_power_int @ A @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % power_minus_mult
% 0.37/0.62 thf(fact_4409_finite__enumerate__step,axiom,
% 0.37/0.62 ! [S3: set_nat,N: nat] :
% 0.37/0.62 ( ( finite_finite_nat @ S3 )
% 0.37/0.62 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite_card_nat @ S3 ) )
% 0.37/0.62 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % finite_enumerate_step
% 0.37/0.62 thf(fact_4410_finite__enum__subset,axiom,
% 0.37/0.62 ! [X6: set_nat,Y7: set_nat] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X6 ) )
% 0.37/0.62 => ( ( infini8530281810654367211te_nat @ X6 @ I2 )
% 0.37/0.62 = ( infini8530281810654367211te_nat @ Y7 @ I2 ) ) )
% 0.37/0.62 => ( ( finite_finite_nat @ X6 )
% 0.37/0.62 => ( ( finite_finite_nat @ Y7 )
% 0.37/0.62 => ( ( ord_less_eq_nat @ ( finite_card_nat @ X6 ) @ ( finite_card_nat @ Y7 ) )
% 0.37/0.62 => ( ord_less_eq_set_nat @ X6 @ Y7 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % finite_enum_subset
% 0.37/0.62 thf(fact_4411_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.37/0.62 ! [K: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.62 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 0.37/0.62 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % neg_one_power_add_eq_neg_one_power_diff
% 0.37/0.62 thf(fact_4412_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.37/0.62 ! [K: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.62 => ( ( power_power_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ ( plus_plus_nat @ N @ K ) )
% 0.37/0.62 = ( power_power_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % neg_one_power_add_eq_neg_one_power_diff
% 0.37/0.62 thf(fact_4413_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.37/0.62 ! [K: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.62 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 0.37/0.62 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % neg_one_power_add_eq_neg_one_power_diff
% 0.37/0.62 thf(fact_4414_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.37/0.62 ! [K: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.62 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 0.37/0.62 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % neg_one_power_add_eq_neg_one_power_diff
% 0.37/0.62 thf(fact_4415_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.37/0.62 ! [K: nat,N: nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.62 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 0.37/0.62 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % neg_one_power_add_eq_neg_one_power_diff
% 0.37/0.62 thf(fact_4416_inthall,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o,N: nat] :
% 0.37/0.62 ( ! [X3: vEBT_VEBTi] :
% 0.37/0.62 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % inthall
% 0.37/0.62 thf(fact_4417_inthall,axiom,
% 0.37/0.62 ! [Xs: list_int,P2: int > $o,N: nat] :
% 0.37/0.62 ( ! [X3: int] :
% 0.37/0.62 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_int @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % inthall
% 0.37/0.62 thf(fact_4418_inthall,axiom,
% 0.37/0.62 ! [Xs: list_set_nat,P2: set_nat > $o,N: nat] :
% 0.37/0.62 ( ! [X3: set_nat] :
% 0.37/0.62 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % inthall
% 0.37/0.62 thf(fact_4419_inthall,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o,N: nat] :
% 0.37/0.62 ( ! [X3: vEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % inthall
% 0.37/0.62 thf(fact_4420_inthall,axiom,
% 0.37/0.62 ! [Xs: list_real,P2: real > $o,N: nat] :
% 0.37/0.62 ( ! [X3: real] :
% 0.37/0.62 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_real @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % inthall
% 0.37/0.62 thf(fact_4421_inthall,axiom,
% 0.37/0.62 ! [Xs: list_o,P2: $o > $o,N: nat] :
% 0.37/0.62 ( ! [X3: $o] :
% 0.37/0.62 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_o @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % inthall
% 0.37/0.62 thf(fact_4422_inthall,axiom,
% 0.37/0.62 ! [Xs: list_nat,P2: nat > $o,N: nat] :
% 0.37/0.62 ( ! [X3: nat] :
% 0.37/0.62 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % inthall
% 0.37/0.62 thf(fact_4423_slice__len,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.62 ( ( ord_less_eq_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( ( size_s6755466524823107622T_VEBT @ ( slice_VEBT_VEBT @ From @ To @ Xs ) )
% 0.37/0.62 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_len
% 0.37/0.62 thf(fact_4424_slice__len,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_real] :
% 0.37/0.62 ( ( ord_less_eq_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( ( size_size_list_real @ ( slice_real @ From @ To @ Xs ) )
% 0.37/0.62 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_len
% 0.37/0.62 thf(fact_4425_slice__len,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_o] :
% 0.37/0.62 ( ( ord_less_eq_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( ( size_size_list_o @ ( slice_o @ From @ To @ Xs ) )
% 0.37/0.62 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_len
% 0.37/0.62 thf(fact_4426_slice__len,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( ( size_size_list_nat @ ( slice_nat @ From @ To @ Xs ) )
% 0.37/0.62 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_len
% 0.37/0.62 thf(fact_4427_card__Min__le__sum,axiom,
% 0.37/0.62 ! [A4: set_literal,F: literal > nat] :
% 0.37/0.62 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_literal @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_literal_nat @ F @ A4 ) ) ) @ ( groups8652099787943017962al_nat @ F @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Min_le_sum
% 0.37/0.62 thf(fact_4428_card__Min__le__sum,axiom,
% 0.37/0.62 ! [A4: set_list_nat,F: list_nat > nat] :
% 0.37/0.62 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_list_nat @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_list_nat_nat @ F @ A4 ) ) ) @ ( groups4396056296759096172at_nat @ F @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Min_le_sum
% 0.37/0.62 thf(fact_4429_card__Min__le__sum,axiom,
% 0.37/0.62 ! [A4: set_set_nat,F: set_nat > nat] :
% 0.37/0.62 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_set_nat @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_set_nat_nat @ F @ A4 ) ) ) @ ( groups8294997508430121362at_nat @ F @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Min_le_sum
% 0.37/0.62 thf(fact_4430_card__Min__le__sum,axiom,
% 0.37/0.62 ! [A4: set_int,F: int > nat] :
% 0.37/0.62 ( ( finite_finite_int @ A4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_int @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_int_nat @ F @ A4 ) ) ) @ ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Min_le_sum
% 0.37/0.62 thf(fact_4431_card__Min__le__sum,axiom,
% 0.37/0.62 ! [A4: set_complex,F: complex > nat] :
% 0.37/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_complex @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_complex_nat @ F @ A4 ) ) ) @ ( groups5693394587270226106ex_nat @ F @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Min_le_sum
% 0.37/0.62 thf(fact_4432_card__Min__le__sum,axiom,
% 0.37/0.62 ! [A4: set_Code_integer,F: code_integer > nat] :
% 0.37/0.62 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_951025933927791156er_nat @ F @ A4 ) ) ) @ ( groups7237345082560585321er_nat @ F @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Min_le_sum
% 0.37/0.62 thf(fact_4433_card__Min__le__sum,axiom,
% 0.37/0.62 ! [A4: set_nat,F: nat > nat] :
% 0.37/0.62 ( ( finite_finite_nat @ A4 )
% 0.37/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_nat @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_nat_nat @ F @ A4 ) ) ) @ ( groups3542108847815614940at_nat @ F @ A4 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % card_Min_le_sum
% 0.37/0.62 thf(fact_4434_realpow__pos__nth,axiom,
% 0.37/0.62 ! [N: nat,A: real] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.62 => ? [R4: real] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.37/0.62 & ( ( power_power_real @ R4 @ N )
% 0.37/0.62 = A ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % realpow_pos_nth
% 0.37/0.62 thf(fact_4435_realpow__pos__nth__unique,axiom,
% 0.37/0.62 ! [N: nat,A: real] :
% 0.37/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.62 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.62 => ? [X3: real] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.37/0.62 & ( ( power_power_real @ X3 @ N )
% 0.37/0.62 = A )
% 0.37/0.62 & ! [Y5: real] :
% 0.37/0.62 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 0.37/0.62 & ( ( power_power_real @ Y5 @ N )
% 0.37/0.62 = A ) )
% 0.37/0.62 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % realpow_pos_nth_unique
% 0.37/0.62 thf(fact_4436_length__mul__elem,axiom,
% 0.37/0.62 ! [Xs: list_list_VEBT_VEBT,N: nat] :
% 0.37/0.62 ( ! [X3: list_VEBT_VEBT] :
% 0.37/0.62 ( ( member2936631157270082147T_VEBT @ X3 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 => ( ( size_s6755466524823107622T_VEBT @ X3 )
% 0.37/0.62 = N ) )
% 0.37/0.62 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 0.37/0.62 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_mul_elem
% 0.37/0.62 thf(fact_4437_length__mul__elem,axiom,
% 0.37/0.62 ! [Xs: list_list_real,N: nat] :
% 0.37/0.62 ( ! [X3: list_real] :
% 0.37/0.62 ( ( member_list_real @ X3 @ ( set_list_real2 @ Xs ) )
% 0.37/0.62 => ( ( size_size_list_real @ X3 )
% 0.37/0.62 = N ) )
% 0.37/0.62 => ( ( size_size_list_real @ ( concat_real @ Xs ) )
% 0.37/0.62 = ( times_times_nat @ ( size_s6660260683639930848t_real @ Xs ) @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_mul_elem
% 0.37/0.62 thf(fact_4438_length__mul__elem,axiom,
% 0.37/0.62 ! [Xs: list_list_o,N: nat] :
% 0.37/0.62 ( ! [X3: list_o] :
% 0.37/0.62 ( ( member_list_o @ X3 @ ( set_list_o2 @ Xs ) )
% 0.37/0.62 => ( ( size_size_list_o @ X3 )
% 0.37/0.62 = N ) )
% 0.37/0.62 => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 0.37/0.62 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_mul_elem
% 0.37/0.62 thf(fact_4439_length__mul__elem,axiom,
% 0.37/0.62 ! [Xs: list_list_nat,N: nat] :
% 0.37/0.62 ( ! [X3: list_nat] :
% 0.37/0.62 ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xs ) )
% 0.37/0.62 => ( ( size_size_list_nat @ X3 )
% 0.37/0.62 = N ) )
% 0.37/0.62 => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 0.37/0.62 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % length_mul_elem
% 0.37/0.62 thf(fact_4440_rotate1__length01,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBT] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat )
% 0.37/0.62 => ( ( rotate1_VEBT_VEBT @ Xs )
% 0.37/0.62 = Xs ) ) ).
% 0.37/0.62
% 0.37/0.62 % rotate1_length01
% 0.37/0.62 thf(fact_4441_rotate1__length01,axiom,
% 0.37/0.62 ! [Xs: list_real] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ one_one_nat )
% 0.37/0.62 => ( ( rotate1_real @ Xs )
% 0.37/0.62 = Xs ) ) ).
% 0.37/0.62
% 0.37/0.62 % rotate1_length01
% 0.37/0.62 thf(fact_4442_rotate1__length01,axiom,
% 0.37/0.62 ! [Xs: list_o] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 0.37/0.62 => ( ( rotate1_o @ Xs )
% 0.37/0.62 = Xs ) ) ).
% 0.37/0.62
% 0.37/0.62 % rotate1_length01
% 0.37/0.62 thf(fact_4443_rotate1__length01,axiom,
% 0.37/0.62 ! [Xs: list_nat] :
% 0.37/0.62 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 0.37/0.62 => ( ( rotate1_nat @ Xs )
% 0.37/0.62 = Xs ) ) ).
% 0.37/0.62
% 0.37/0.62 % rotate1_length01
% 0.37/0.62 thf(fact_4444_not__real__square__gt__zero,axiom,
% 0.37/0.62 ! [X: real] :
% 0.37/0.62 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 0.37/0.62 = ( X = zero_zero_real ) ) ).
% 0.37/0.62
% 0.37/0.62 % not_real_square_gt_zero
% 0.37/0.62 thf(fact_4445_slice__complete,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBT] :
% 0.37/0.62 ( ( slice_VEBT_VEBT @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ Xs )
% 0.37/0.62 = Xs ) ).
% 0.37/0.62
% 0.37/0.62 % slice_complete
% 0.37/0.62 thf(fact_4446_slice__complete,axiom,
% 0.37/0.62 ! [Xs: list_real] :
% 0.37/0.62 ( ( slice_real @ zero_zero_nat @ ( size_size_list_real @ Xs ) @ Xs )
% 0.37/0.62 = Xs ) ).
% 0.37/0.62
% 0.37/0.62 % slice_complete
% 0.37/0.62 thf(fact_4447_slice__complete,axiom,
% 0.37/0.62 ! [Xs: list_o] :
% 0.37/0.62 ( ( slice_o @ zero_zero_nat @ ( size_size_list_o @ Xs ) @ Xs )
% 0.37/0.62 = Xs ) ).
% 0.37/0.62
% 0.37/0.62 % slice_complete
% 0.37/0.62 thf(fact_4448_slice__complete,axiom,
% 0.37/0.62 ! [Xs: list_nat] :
% 0.37/0.62 ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) @ Xs )
% 0.37/0.62 = Xs ) ).
% 0.37/0.62
% 0.37/0.62 % slice_complete
% 0.37/0.62 thf(fact_4449_real__add__le__0__iff,axiom,
% 0.37/0.62 ! [X: real,Y: real] :
% 0.37/0.62 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 0.37/0.62 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % real_add_le_0_iff
% 0.37/0.62 thf(fact_4450_real__0__le__add__iff,axiom,
% 0.37/0.62 ! [X: real,Y: real] :
% 0.37/0.62 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 0.37/0.62 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 0.37/0.62
% 0.37/0.62 % real_0_le_add_iff
% 0.37/0.62 thf(fact_4451_less__eq__real__def,axiom,
% 0.37/0.62 ( ord_less_eq_real
% 0.37/0.62 = ( ^ [X4: real,Y4: real] :
% 0.37/0.62 ( ( ord_less_real @ X4 @ Y4 )
% 0.37/0.62 | ( X4 = Y4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % less_eq_real_def
% 0.37/0.62 thf(fact_4452_real__arch__pow,axiom,
% 0.37/0.62 ! [X: real,Y: real] :
% 0.37/0.62 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.62 => ? [N2: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % real_arch_pow
% 0.37/0.62 thf(fact_4453_real__arch__pow__inv,axiom,
% 0.37/0.62 ! [Y: real,X: real] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.62 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.62 => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X @ N2 ) @ Y ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % real_arch_pow_inv
% 0.37/0.62 thf(fact_4454_real__add__less__0__iff,axiom,
% 0.37/0.62 ! [X: real,Y: real] :
% 0.37/0.62 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 0.37/0.62 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % real_add_less_0_iff
% 0.37/0.62 thf(fact_4455_real__0__less__add__iff,axiom,
% 0.37/0.62 ! [X: real,Y: real] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 0.37/0.62 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 0.37/0.62
% 0.37/0.62 % real_0_less_add_iff
% 0.37/0.62 thf(fact_4456_nth__equalityI,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 0.37/0.62 ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.62 = ( size_s7982070591426661849_VEBTi @ Ys ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 => ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.62 = ( nth_VEBT_VEBTi @ Ys @ I2 ) ) )
% 0.37/0.62 => ( Xs = Ys ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_equalityI
% 0.37/0.62 thf(fact_4457_nth__equalityI,axiom,
% 0.37/0.62 ! [Xs: list_int,Ys: list_int] :
% 0.37/0.62 ( ( ( size_size_list_int @ Xs )
% 0.37/0.62 = ( size_size_list_int @ Ys ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 => ( ( nth_int @ Xs @ I2 )
% 0.37/0.62 = ( nth_int @ Ys @ I2 ) ) )
% 0.37/0.62 => ( Xs = Ys ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_equalityI
% 0.37/0.62 thf(fact_4458_nth__equalityI,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.37/0.62 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.62 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 0.37/0.62 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 0.37/0.62 => ( Xs = Ys ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_equalityI
% 0.37/0.62 thf(fact_4459_nth__equalityI,axiom,
% 0.37/0.62 ! [Xs: list_real,Ys: list_real] :
% 0.37/0.62 ( ( ( size_size_list_real @ Xs )
% 0.37/0.62 = ( size_size_list_real @ Ys ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( ( nth_real @ Xs @ I2 )
% 0.37/0.62 = ( nth_real @ Ys @ I2 ) ) )
% 0.37/0.62 => ( Xs = Ys ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_equalityI
% 0.37/0.62 thf(fact_4460_nth__equalityI,axiom,
% 0.37/0.62 ! [Xs: list_o,Ys: list_o] :
% 0.37/0.62 ( ( ( size_size_list_o @ Xs )
% 0.37/0.62 = ( size_size_list_o @ Ys ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( ( nth_o @ Xs @ I2 )
% 0.37/0.62 = ( nth_o @ Ys @ I2 ) ) )
% 0.37/0.62 => ( Xs = Ys ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_equalityI
% 0.37/0.62 thf(fact_4461_nth__equalityI,axiom,
% 0.37/0.62 ! [Xs: list_nat,Ys: list_nat] :
% 0.37/0.62 ( ( ( size_size_list_nat @ Xs )
% 0.37/0.62 = ( size_size_list_nat @ Ys ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( ( nth_nat @ Xs @ I2 )
% 0.37/0.62 = ( nth_nat @ Ys @ I2 ) ) )
% 0.37/0.62 => ( Xs = Ys ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_equalityI
% 0.37/0.62 thf(fact_4462_Skolem__list__nth,axiom,
% 0.37/0.62 ! [K: nat,P2: nat > vEBT_VEBTi > $o] :
% 0.37/0.62 ( ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ? [X8: vEBT_VEBTi] : ( P2 @ I3 @ X8 ) ) )
% 0.37/0.62 = ( ? [Xs2: list_VEBT_VEBTi] :
% 0.37/0.62 ( ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 0.37/0.62 = K )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ( P2 @ I3 @ ( nth_VEBT_VEBTi @ Xs2 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % Skolem_list_nth
% 0.37/0.62 thf(fact_4463_Skolem__list__nth,axiom,
% 0.37/0.62 ! [K: nat,P2: nat > int > $o] :
% 0.37/0.62 ( ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ? [X8: int] : ( P2 @ I3 @ X8 ) ) )
% 0.37/0.62 = ( ? [Xs2: list_int] :
% 0.37/0.62 ( ( ( size_size_list_int @ Xs2 )
% 0.37/0.62 = K )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ( P2 @ I3 @ ( nth_int @ Xs2 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % Skolem_list_nth
% 0.37/0.62 thf(fact_4464_Skolem__list__nth,axiom,
% 0.37/0.62 ! [K: nat,P2: nat > vEBT_VEBT > $o] :
% 0.37/0.62 ( ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ? [X8: vEBT_VEBT] : ( P2 @ I3 @ X8 ) ) )
% 0.37/0.62 = ( ? [Xs2: list_VEBT_VEBT] :
% 0.37/0.62 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.37/0.62 = K )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ( P2 @ I3 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % Skolem_list_nth
% 0.37/0.62 thf(fact_4465_Skolem__list__nth,axiom,
% 0.37/0.62 ! [K: nat,P2: nat > real > $o] :
% 0.37/0.62 ( ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ? [X8: real] : ( P2 @ I3 @ X8 ) ) )
% 0.37/0.62 = ( ? [Xs2: list_real] :
% 0.37/0.62 ( ( ( size_size_list_real @ Xs2 )
% 0.37/0.62 = K )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ( P2 @ I3 @ ( nth_real @ Xs2 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % Skolem_list_nth
% 0.37/0.62 thf(fact_4466_Skolem__list__nth,axiom,
% 0.37/0.62 ! [K: nat,P2: nat > $o > $o] :
% 0.37/0.62 ( ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ? [X8: $o] : ( P2 @ I3 @ X8 ) ) )
% 0.37/0.62 = ( ? [Xs2: list_o] :
% 0.37/0.62 ( ( ( size_size_list_o @ Xs2 )
% 0.37/0.62 = K )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ( P2 @ I3 @ ( nth_o @ Xs2 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % Skolem_list_nth
% 0.37/0.62 thf(fact_4467_Skolem__list__nth,axiom,
% 0.37/0.62 ! [K: nat,P2: nat > nat > $o] :
% 0.37/0.62 ( ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ? [X8: nat] : ( P2 @ I3 @ X8 ) ) )
% 0.37/0.62 = ( ? [Xs2: list_nat] :
% 0.37/0.62 ( ( ( size_size_list_nat @ Xs2 )
% 0.37/0.62 = K )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ K )
% 0.37/0.62 => ( P2 @ I3 @ ( nth_nat @ Xs2 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % Skolem_list_nth
% 0.37/0.62 thf(fact_4468_list__eq__iff__nth__eq,axiom,
% 0.37/0.62 ( ( ^ [Y6: list_VEBT_VEBTi,Z4: list_VEBT_VEBTi] : ( Y6 = Z4 ) )
% 0.37/0.62 = ( ^ [Xs2: list_VEBT_VEBTi,Ys3: list_VEBT_VEBTi] :
% 0.37/0.62 ( ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 0.37/0.62 = ( size_s7982070591426661849_VEBTi @ Ys3 ) )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 0.37/0.62 => ( ( nth_VEBT_VEBTi @ Xs2 @ I3 )
% 0.37/0.62 = ( nth_VEBT_VEBTi @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_eq_iff_nth_eq
% 0.37/0.62 thf(fact_4469_list__eq__iff__nth__eq,axiom,
% 0.37/0.62 ( ( ^ [Y6: list_int,Z4: list_int] : ( Y6 = Z4 ) )
% 0.37/0.62 = ( ^ [Xs2: list_int,Ys3: list_int] :
% 0.37/0.62 ( ( ( size_size_list_int @ Xs2 )
% 0.37/0.62 = ( size_size_list_int @ Ys3 ) )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.37/0.62 => ( ( nth_int @ Xs2 @ I3 )
% 0.37/0.62 = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_eq_iff_nth_eq
% 0.37/0.62 thf(fact_4470_list__eq__iff__nth__eq,axiom,
% 0.37/0.62 ( ( ^ [Y6: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y6 = Z4 ) )
% 0.37/0.62 = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.37/0.62 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.37/0.62 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.37/0.62 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 0.37/0.62 = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_eq_iff_nth_eq
% 0.37/0.62 thf(fact_4471_list__eq__iff__nth__eq,axiom,
% 0.37/0.62 ( ( ^ [Y6: list_real,Z4: list_real] : ( Y6 = Z4 ) )
% 0.37/0.62 = ( ^ [Xs2: list_real,Ys3: list_real] :
% 0.37/0.62 ( ( ( size_size_list_real @ Xs2 )
% 0.37/0.62 = ( size_size_list_real @ Ys3 ) )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 0.37/0.62 => ( ( nth_real @ Xs2 @ I3 )
% 0.37/0.62 = ( nth_real @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_eq_iff_nth_eq
% 0.37/0.62 thf(fact_4472_list__eq__iff__nth__eq,axiom,
% 0.37/0.62 ( ( ^ [Y6: list_o,Z4: list_o] : ( Y6 = Z4 ) )
% 0.37/0.62 = ( ^ [Xs2: list_o,Ys3: list_o] :
% 0.37/0.62 ( ( ( size_size_list_o @ Xs2 )
% 0.37/0.62 = ( size_size_list_o @ Ys3 ) )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.37/0.62 => ( ( nth_o @ Xs2 @ I3 )
% 0.37/0.62 = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_eq_iff_nth_eq
% 0.37/0.62 thf(fact_4473_list__eq__iff__nth__eq,axiom,
% 0.37/0.62 ( ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 ) )
% 0.37/0.62 = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 0.37/0.62 ( ( ( size_size_list_nat @ Xs2 )
% 0.37/0.62 = ( size_size_list_nat @ Ys3 ) )
% 0.37/0.62 & ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.37/0.62 => ( ( nth_nat @ Xs2 @ I3 )
% 0.37/0.62 = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_eq_iff_nth_eq
% 0.37/0.62 thf(fact_4474_obtain__list__from__elements,axiom,
% 0.37/0.62 ! [N: nat,P2: vEBT_VEBTi > nat > $o] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.62 => ? [Li: vEBT_VEBTi] : ( P2 @ Li @ I2 ) )
% 0.37/0.62 => ~ ! [L2: list_VEBT_VEBTi] :
% 0.37/0.62 ( ( ( size_s7982070591426661849_VEBTi @ L2 )
% 0.37/0.62 = N )
% 0.37/0.62 => ~ ! [I4: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I4 @ N )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBTi @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % obtain_list_from_elements
% 0.37/0.62 thf(fact_4475_obtain__list__from__elements,axiom,
% 0.37/0.62 ! [N: nat,P2: int > nat > $o] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.62 => ? [Li: int] : ( P2 @ Li @ I2 ) )
% 0.37/0.62 => ~ ! [L2: list_int] :
% 0.37/0.62 ( ( ( size_size_list_int @ L2 )
% 0.37/0.62 = N )
% 0.37/0.62 => ~ ! [I4: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I4 @ N )
% 0.37/0.62 => ( P2 @ ( nth_int @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % obtain_list_from_elements
% 0.37/0.62 thf(fact_4476_obtain__list__from__elements,axiom,
% 0.37/0.62 ! [N: nat,P2: vEBT_VEBT > nat > $o] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.62 => ? [Li: vEBT_VEBT] : ( P2 @ Li @ I2 ) )
% 0.37/0.62 => ~ ! [L2: list_VEBT_VEBT] :
% 0.37/0.62 ( ( ( size_s6755466524823107622T_VEBT @ L2 )
% 0.37/0.62 = N )
% 0.37/0.62 => ~ ! [I4: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I4 @ N )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBT @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % obtain_list_from_elements
% 0.37/0.62 thf(fact_4477_obtain__list__from__elements,axiom,
% 0.37/0.62 ! [N: nat,P2: real > nat > $o] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.62 => ? [Li: real] : ( P2 @ Li @ I2 ) )
% 0.37/0.62 => ~ ! [L2: list_real] :
% 0.37/0.62 ( ( ( size_size_list_real @ L2 )
% 0.37/0.62 = N )
% 0.37/0.62 => ~ ! [I4: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I4 @ N )
% 0.37/0.62 => ( P2 @ ( nth_real @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % obtain_list_from_elements
% 0.37/0.62 thf(fact_4478_obtain__list__from__elements,axiom,
% 0.37/0.62 ! [N: nat,P2: $o > nat > $o] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.62 => ? [Li: $o] : ( P2 @ Li @ I2 ) )
% 0.37/0.62 => ~ ! [L2: list_o] :
% 0.37/0.62 ( ( ( size_size_list_o @ L2 )
% 0.37/0.62 = N )
% 0.37/0.62 => ~ ! [I4: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I4 @ N )
% 0.37/0.62 => ( P2 @ ( nth_o @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % obtain_list_from_elements
% 0.37/0.62 thf(fact_4479_obtain__list__from__elements,axiom,
% 0.37/0.62 ! [N: nat,P2: nat > nat > $o] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.62 => ? [Li: nat] : ( P2 @ Li @ I2 ) )
% 0.37/0.62 => ~ ! [L2: list_nat] :
% 0.37/0.62 ( ( ( size_size_list_nat @ L2 )
% 0.37/0.62 = N )
% 0.37/0.62 => ~ ! [I4: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I4 @ N )
% 0.37/0.62 => ( P2 @ ( nth_nat @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % obtain_list_from_elements
% 0.37/0.62 thf(fact_4480_slice__nth,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_VEBT_VEBTi,I: nat] :
% 0.37/0.62 ( ( ord_less_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.37/0.62 => ( ( nth_VEBT_VEBTi @ ( slice_VEBT_VEBTi @ From @ To @ Xs ) @ I )
% 0.37/0.62 = ( nth_VEBT_VEBTi @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_nth
% 0.37/0.62 thf(fact_4481_slice__nth,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_int,I: nat] :
% 0.37/0.62 ( ( ord_less_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.37/0.62 => ( ( nth_int @ ( slice_int @ From @ To @ Xs ) @ I )
% 0.37/0.62 = ( nth_int @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_nth
% 0.37/0.62 thf(fact_4482_slice__nth,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_VEBT_VEBT,I: nat] :
% 0.37/0.62 ( ( ord_less_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.37/0.62 => ( ( nth_VEBT_VEBT @ ( slice_VEBT_VEBT @ From @ To @ Xs ) @ I )
% 0.37/0.62 = ( nth_VEBT_VEBT @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_nth
% 0.37/0.62 thf(fact_4483_slice__nth,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_real,I: nat] :
% 0.37/0.62 ( ( ord_less_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.37/0.62 => ( ( nth_real @ ( slice_real @ From @ To @ Xs ) @ I )
% 0.37/0.62 = ( nth_real @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_nth
% 0.37/0.62 thf(fact_4484_slice__nth,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_o,I: nat] :
% 0.37/0.62 ( ( ord_less_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.37/0.62 => ( ( nth_o @ ( slice_o @ From @ To @ Xs ) @ I )
% 0.37/0.62 = ( nth_o @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_nth
% 0.37/0.62 thf(fact_4485_slice__nth,axiom,
% 0.37/0.62 ! [From: nat,To: nat,Xs: list_nat,I: nat] :
% 0.37/0.62 ( ( ord_less_nat @ From @ To )
% 0.37/0.62 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 0.37/0.62 => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs ) @ I )
% 0.37/0.62 = ( nth_nat @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % slice_nth
% 0.37/0.62 thf(fact_4486_all__set__conv__nth,axiom,
% 0.37/0.62 ! [L: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o] :
% 0.37/0.62 ( ( ! [X4: vEBT_VEBTi] :
% 0.37/0.62 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ L ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBTi @ L @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_nth
% 0.37/0.62 thf(fact_4487_all__set__conv__nth,axiom,
% 0.37/0.62 ! [L: list_int,P2: int > $o] :
% 0.37/0.62 ( ( ! [X4: int] :
% 0.37/0.62 ( ( member_int @ X4 @ ( set_int2 @ L ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 0.37/0.62 => ( P2 @ ( nth_int @ L @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_nth
% 0.37/0.62 thf(fact_4488_all__set__conv__nth,axiom,
% 0.37/0.62 ! [L: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.62 ( ( ! [X4: vEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ L ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBT @ L @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_nth
% 0.37/0.62 thf(fact_4489_all__set__conv__nth,axiom,
% 0.37/0.62 ! [L: list_real,P2: real > $o] :
% 0.37/0.62 ( ( ! [X4: real] :
% 0.37/0.62 ( ( member_real @ X4 @ ( set_real2 @ L ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ L ) )
% 0.37/0.62 => ( P2 @ ( nth_real @ L @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_nth
% 0.37/0.62 thf(fact_4490_all__set__conv__nth,axiom,
% 0.37/0.62 ! [L: list_o,P2: $o > $o] :
% 0.37/0.62 ( ( ! [X4: $o] :
% 0.37/0.62 ( ( member_o @ X4 @ ( set_o2 @ L ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ L ) )
% 0.37/0.62 => ( P2 @ ( nth_o @ L @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_nth
% 0.37/0.62 thf(fact_4491_all__set__conv__nth,axiom,
% 0.37/0.62 ! [L: list_nat,P2: nat > $o] :
% 0.37/0.62 ( ( ! [X4: nat] :
% 0.37/0.62 ( ( member_nat @ X4 @ ( set_nat2 @ L ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ L ) )
% 0.37/0.62 => ( P2 @ ( nth_nat @ L @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_nth
% 0.37/0.62 thf(fact_4492_nth__mem,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_VEBT_VEBTi] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 => ( member_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N ) @ ( set_VEBT_VEBTi2 @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_mem
% 0.37/0.62 thf(fact_4493_nth__mem,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_int] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_mem
% 0.37/0.62 thf(fact_4494_nth__mem,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_set_nat] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.62 => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_mem
% 0.37/0.62 thf(fact_4495_nth__mem,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_mem
% 0.37/0.62 thf(fact_4496_nth__mem,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_real] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_mem
% 0.37/0.62 thf(fact_4497_nth__mem,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_o] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_mem
% 0.37/0.62 thf(fact_4498_nth__mem,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_nat] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % nth_mem
% 0.37/0.62 thf(fact_4499_list__ball__nth,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 => ( ! [X3: vEBT_VEBTi] :
% 0.37/0.62 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_ball_nth
% 0.37/0.62 thf(fact_4500_list__ball__nth,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_int,P2: int > $o] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 => ( ! [X3: int] :
% 0.37/0.62 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( P2 @ ( nth_int @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_ball_nth
% 0.37/0.62 thf(fact_4501_list__ball__nth,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_ball_nth
% 0.37/0.62 thf(fact_4502_list__ball__nth,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_real,P2: real > $o] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( ! [X3: real] :
% 0.37/0.62 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( P2 @ ( nth_real @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_ball_nth
% 0.37/0.62 thf(fact_4503_list__ball__nth,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_o,P2: $o > $o] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( ! [X3: $o] :
% 0.37/0.62 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( P2 @ ( nth_o @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_ball_nth
% 0.37/0.62 thf(fact_4504_list__ball__nth,axiom,
% 0.37/0.62 ! [N: nat,Xs: list_nat,P2: nat > $o] :
% 0.37/0.62 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( ! [X3: nat] :
% 0.37/0.62 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X3 ) )
% 0.37/0.62 => ( P2 @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % list_ball_nth
% 0.37/0.62 thf(fact_4505_in__set__conv__nth,axiom,
% 0.37/0.62 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 0.37/0.62 ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 0.37/0.62 = ( ? [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 & ( ( nth_VEBT_VEBTi @ Xs @ I3 )
% 0.37/0.62 = X ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % in_set_conv_nth
% 0.37/0.62 thf(fact_4506_in__set__conv__nth,axiom,
% 0.37/0.62 ! [X: int,Xs: list_int] :
% 0.37/0.62 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.62 = ( ? [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 & ( ( nth_int @ Xs @ I3 )
% 0.37/0.62 = X ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % in_set_conv_nth
% 0.37/0.62 thf(fact_4507_in__set__conv__nth,axiom,
% 0.37/0.62 ! [X: set_nat,Xs: list_set_nat] :
% 0.37/0.62 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.37/0.62 = ( ? [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.62 & ( ( nth_set_nat @ Xs @ I3 )
% 0.37/0.62 = X ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % in_set_conv_nth
% 0.37/0.62 thf(fact_4508_in__set__conv__nth,axiom,
% 0.37/0.62 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 = ( ? [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 & ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 0.37/0.62 = X ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % in_set_conv_nth
% 0.37/0.62 thf(fact_4509_in__set__conv__nth,axiom,
% 0.37/0.62 ! [X: real,Xs: list_real] :
% 0.37/0.62 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.37/0.62 = ( ? [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 & ( ( nth_real @ Xs @ I3 )
% 0.37/0.62 = X ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % in_set_conv_nth
% 0.37/0.62 thf(fact_4510_in__set__conv__nth,axiom,
% 0.37/0.62 ! [X: $o,Xs: list_o] :
% 0.37/0.62 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.37/0.62 = ( ? [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 & ( ( nth_o @ Xs @ I3 )
% 0.37/0.62 = X ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % in_set_conv_nth
% 0.37/0.62 thf(fact_4511_in__set__conv__nth,axiom,
% 0.37/0.62 ! [X: nat,Xs: list_nat] :
% 0.37/0.62 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.62 = ( ? [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 & ( ( nth_nat @ Xs @ I3 )
% 0.37/0.62 = X ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % in_set_conv_nth
% 0.37/0.62 thf(fact_4512_all__nth__imp__all__set,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o,X: vEBT_VEBTi] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) ) )
% 0.37/0.62 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_nth_imp_all_set
% 0.37/0.62 thf(fact_4513_all__nth__imp__all__set,axiom,
% 0.37/0.62 ! [Xs: list_int,P2: int > $o,X: int] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_int @ Xs @ I2 ) ) )
% 0.37/0.62 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_nth_imp_all_set
% 0.37/0.62 thf(fact_4514_all__nth__imp__all__set,axiom,
% 0.37/0.62 ! [Xs: list_set_nat,P2: set_nat > $o,X: set_nat] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_set_nat @ Xs @ I2 ) ) )
% 0.37/0.62 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_nth_imp_all_set
% 0.37/0.62 thf(fact_4515_all__nth__imp__all__set,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) )
% 0.37/0.62 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_nth_imp_all_set
% 0.37/0.62 thf(fact_4516_all__nth__imp__all__set,axiom,
% 0.37/0.62 ! [Xs: list_real,P2: real > $o,X: real] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_real @ Xs @ I2 ) ) )
% 0.37/0.62 => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_nth_imp_all_set
% 0.37/0.62 thf(fact_4517_all__nth__imp__all__set,axiom,
% 0.37/0.62 ! [Xs: list_o,P2: $o > $o,X: $o] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_o @ Xs @ I2 ) ) )
% 0.37/0.62 => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_nth_imp_all_set
% 0.37/0.62 thf(fact_4518_all__nth__imp__all__set,axiom,
% 0.37/0.62 ! [Xs: list_nat,P2: nat > $o,X: nat] :
% 0.37/0.62 ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_nat @ Xs @ I2 ) ) )
% 0.37/0.62 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_nth_imp_all_set
% 0.37/0.62 thf(fact_4519_all__set__conv__all__nth,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o] :
% 0.37/0.62 ( ( ! [X4: vEBT_VEBTi] :
% 0.37/0.62 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_all_nth
% 0.37/0.62 thf(fact_4520_all__set__conv__all__nth,axiom,
% 0.37/0.62 ! [Xs: list_int,P2: int > $o] :
% 0.37/0.62 ( ( ! [X4: int] :
% 0.37/0.62 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_int @ Xs @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_all_nth
% 0.37/0.62 thf(fact_4521_all__set__conv__all__nth,axiom,
% 0.37/0.62 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.62 ( ( ! [X4: vEBT_VEBT] :
% 0.37/0.62 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_all_nth
% 0.37/0.62 thf(fact_4522_all__set__conv__all__nth,axiom,
% 0.37/0.62 ! [Xs: list_real,P2: real > $o] :
% 0.37/0.62 ( ( ! [X4: real] :
% 0.37/0.62 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_real @ Xs @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_all_nth
% 0.37/0.62 thf(fact_4523_all__set__conv__all__nth,axiom,
% 0.37/0.62 ! [Xs: list_o,P2: $o > $o] :
% 0.37/0.62 ( ( ! [X4: $o] :
% 0.37/0.62 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_o @ Xs @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_all_nth
% 0.37/0.62 thf(fact_4524_all__set__conv__all__nth,axiom,
% 0.37/0.62 ! [Xs: list_nat,P2: nat > $o] :
% 0.37/0.62 ( ( ! [X4: nat] :
% 0.37/0.62 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.37/0.62 => ( P2 @ X4 ) ) )
% 0.37/0.62 = ( ! [I3: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.62 => ( P2 @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % all_set_conv_all_nth
% 0.37/0.62 thf(fact_4525_realpow__pos__nth2,axiom,
% 0.37/0.62 ! [A: real,N: nat] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.62 => ? [R4: real] :
% 0.37/0.62 ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.37/0.62 & ( ( power_power_real @ R4 @ ( suc @ N ) )
% 0.37/0.62 = A ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % realpow_pos_nth2
% 0.37/0.62 thf(fact_4526_VEBT_Osize_I4_J,axiom,
% 0.37/0.62 ! [X21: $o,X22: $o] :
% 0.37/0.62 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 0.37/0.62 = zero_zero_nat ) ).
% 0.37/0.62
% 0.37/0.62 % VEBT.size(4)
% 0.37/0.62 thf(fact_4527_set__image__eq__pointwiseI,axiom,
% 0.37/0.62 ! [L: list_int,L3: list_int,F: int > nat] :
% 0.37/0.62 ( ( ( size_size_list_int @ L )
% 0.37/0.62 = ( size_size_list_int @ L3 ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ L ) )
% 0.37/0.62 => ( ( F @ ( nth_int @ L @ I2 ) )
% 0.37/0.62 = ( F @ ( nth_int @ L3 @ I2 ) ) ) )
% 0.37/0.62 => ( ( image_int_nat @ F @ ( set_int2 @ L ) )
% 0.37/0.62 = ( image_int_nat @ F @ ( set_int2 @ L3 ) ) ) ) ) ).
% 0.37/0.62
% 0.37/0.62 % set_image_eq_pointwiseI
% 0.37/0.62 thf(fact_4528_set__image__eq__pointwiseI,axiom,
% 0.37/0.62 ! [L: list_int,L3: list_int,F: int > int] :
% 0.37/0.62 ( ( ( size_size_list_int @ L )
% 0.37/0.62 = ( size_size_list_int @ L3 ) )
% 0.37/0.62 => ( ! [I2: nat] :
% 0.37/0.62 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ L ) )
% 0.37/0.62 => ( ( F @ ( nth_int @ L @ I2 ) )
% 0.37/0.62 = ( F @ ( nth_int @ L3 @ I2 ) ) ) )
% 0.37/0.62 => ( ( image_int_int @ F @ ( set_int2 @ L ) )
% 0.37/0.62 = ( image_int_int @ F @ ( set_int2 @ L3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % set_image_eq_pointwiseI
% 0.37/0.63 thf(fact_4529_set__image__eq__pointwiseI,axiom,
% 0.37/0.63 ! [L: list_nat,L3: list_nat,F: nat > set_nat] :
% 0.37/0.63 ( ( ( size_size_list_nat @ L )
% 0.37/0.63 = ( size_size_list_nat @ L3 ) )
% 0.37/0.63 => ( ! [I2: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ L ) )
% 0.37/0.63 => ( ( F @ ( nth_nat @ L @ I2 ) )
% 0.37/0.63 = ( F @ ( nth_nat @ L3 @ I2 ) ) ) )
% 0.37/0.63 => ( ( image_nat_set_nat @ F @ ( set_nat2 @ L ) )
% 0.37/0.63 = ( image_nat_set_nat @ F @ ( set_nat2 @ L3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % set_image_eq_pointwiseI
% 0.37/0.63 thf(fact_4530_set__image__eq__pointwiseI,axiom,
% 0.37/0.63 ! [L: list_nat,L3: list_nat,F: nat > nat] :
% 0.37/0.63 ( ( ( size_size_list_nat @ L )
% 0.37/0.63 = ( size_size_list_nat @ L3 ) )
% 0.37/0.63 => ( ! [I2: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ L ) )
% 0.37/0.63 => ( ( F @ ( nth_nat @ L @ I2 ) )
% 0.37/0.63 = ( F @ ( nth_nat @ L3 @ I2 ) ) ) )
% 0.37/0.63 => ( ( image_nat_nat @ F @ ( set_nat2 @ L ) )
% 0.37/0.63 = ( image_nat_nat @ F @ ( set_nat2 @ L3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % set_image_eq_pointwiseI
% 0.37/0.63 thf(fact_4531_set__image__eq__pointwiseI,axiom,
% 0.37/0.63 ! [L: list_nat,L3: list_nat,F: nat > int] :
% 0.37/0.63 ( ( ( size_size_list_nat @ L )
% 0.37/0.63 = ( size_size_list_nat @ L3 ) )
% 0.37/0.63 => ( ! [I2: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ L ) )
% 0.37/0.63 => ( ( F @ ( nth_nat @ L @ I2 ) )
% 0.37/0.63 = ( F @ ( nth_nat @ L3 @ I2 ) ) ) )
% 0.37/0.63 => ( ( image_nat_int @ F @ ( set_nat2 @ L ) )
% 0.37/0.63 = ( image_nat_int @ F @ ( set_nat2 @ L3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % set_image_eq_pointwiseI
% 0.37/0.63 thf(fact_4532_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: vEBT_VEBTi > nat,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 0.37/0.63 ( ( member_nat @ ( F @ X ) @ ( image_VEBT_VEBTi_nat @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4533_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: int > nat,X: int,L: list_int] :
% 0.37/0.63 ( ( member_nat @ ( F @ X ) @ ( image_int_nat @ F @ ( set_int2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_int @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4534_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: vEBT_VEBTi > vEBT_VEBT,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ ( F @ X ) @ ( image_7547481670047419768T_VEBT @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4535_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: int > vEBT_VEBT,X: int,L: list_int] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ ( F @ X ) @ ( image_int_VEBT_VEBT @ F @ ( set_int2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_int @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4536_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: vEBT_VEBTi > real,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 0.37/0.63 ( ( member_real @ ( F @ X ) @ ( image_6202559892754154600i_real @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4537_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: int > real,X: int,L: list_int] :
% 0.37/0.63 ( ( member_real @ ( F @ X ) @ ( image_int_real @ F @ ( set_int2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_int @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4538_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: vEBT_VEBTi > int,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 0.37/0.63 ( ( member_int @ ( F @ X ) @ ( image_VEBT_VEBTi_int @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4539_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: int > int,X: int,L: list_int] :
% 0.37/0.63 ( ( member_int @ ( F @ X ) @ ( image_int_int @ F @ ( set_int2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_int @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4540_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: vEBT_VEBT > nat,X: vEBT_VEBT,L: list_VEBT_VEBT] :
% 0.37/0.63 ( ( member_nat @ ( F @ X ) @ ( image_VEBT_VEBT_nat @ F @ ( set_VEBT_VEBT2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_VEBT_VEBT @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4541_in__set__image__conv__nth,axiom,
% 0.37/0.63 ! [F: vEBT_VEBT > vEBT_VEBT,X: vEBT_VEBT,L: list_VEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ ( F @ X ) @ ( image_3375948659692109573T_VEBT @ F @ ( set_VEBT_VEBT2 @ L ) ) )
% 0.37/0.63 = ( ? [I3: nat] :
% 0.37/0.63 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.63 & ( ( F @ ( nth_VEBT_VEBT @ L @ I3 ) )
% 0.37/0.63 = ( F @ X ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % in_set_image_conv_nth
% 0.37/0.63 thf(fact_4542_sum__count__set,axiom,
% 0.37/0.63 ! [Xs: list_complex,X6: set_complex] :
% 0.37/0.63 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ X6 )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ X6 )
% 0.37/0.63 => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs ) @ X6 )
% 0.37/0.63 = ( size_s3451745648224563538omplex @ Xs ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_count_set
% 0.37/0.63 thf(fact_4543_sum__count__set,axiom,
% 0.37/0.63 ! [Xs: list_Code_integer,X6: set_Code_integer] :
% 0.37/0.63 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs ) @ X6 )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ X6 )
% 0.37/0.63 => ( ( groups7237345082560585321er_nat @ ( count_3970941599679287265nteger @ Xs ) @ X6 )
% 0.37/0.63 = ( size_s3445333598471063425nteger @ Xs ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_count_set
% 0.37/0.63 thf(fact_4544_sum__count__set,axiom,
% 0.37/0.63 ! [Xs: list_VEBT_VEBT,X6: set_VEBT_VEBT] :
% 0.37/0.63 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ X6 )
% 0.37/0.63 => ( ( finite5795047828879050333T_VEBT @ X6 )
% 0.37/0.63 => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs ) @ X6 )
% 0.37/0.63 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_count_set
% 0.37/0.63 thf(fact_4545_sum__count__set,axiom,
% 0.37/0.63 ! [Xs: list_real,X6: set_real] :
% 0.37/0.63 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ X6 )
% 0.37/0.63 => ( ( finite_finite_real @ X6 )
% 0.37/0.63 => ( ( groups1935376822645274424al_nat @ ( count_list_real @ Xs ) @ X6 )
% 0.37/0.63 = ( size_size_list_real @ Xs ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_count_set
% 0.37/0.63 thf(fact_4546_sum__count__set,axiom,
% 0.37/0.63 ! [Xs: list_o,X6: set_o] :
% 0.37/0.63 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ X6 )
% 0.37/0.63 => ( ( finite_finite_o @ X6 )
% 0.37/0.63 => ( ( groups8507830703676809646_o_nat @ ( count_list_o @ Xs ) @ X6 )
% 0.37/0.63 = ( size_size_list_o @ Xs ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_count_set
% 0.37/0.63 thf(fact_4547_sum__count__set,axiom,
% 0.37/0.63 ! [Xs: list_int,X6: set_int] :
% 0.37/0.63 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ X6 )
% 0.37/0.63 => ( ( finite_finite_int @ X6 )
% 0.37/0.63 => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs ) @ X6 )
% 0.37/0.63 = ( size_size_list_int @ Xs ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_count_set
% 0.37/0.63 thf(fact_4548_sum__count__set,axiom,
% 0.37/0.63 ! [Xs: list_nat,X6: set_nat] :
% 0.37/0.63 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ X6 )
% 0.37/0.63 => ( ( finite_finite_nat @ X6 )
% 0.37/0.63 => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs ) @ X6 )
% 0.37/0.63 = ( size_size_list_nat @ Xs ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_count_set
% 0.37/0.63 thf(fact_4549_sum__le__card__Max,axiom,
% 0.37/0.63 ! [A4: set_literal,F: literal > nat] :
% 0.37/0.63 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups8652099787943017962al_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_literal @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_literal_nat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_card_Max
% 0.37/0.63 thf(fact_4550_sum__le__card__Max,axiom,
% 0.37/0.63 ! [A4: set_list_nat,F: list_nat > nat] :
% 0.37/0.63 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups4396056296759096172at_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_list_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_list_nat_nat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_card_Max
% 0.37/0.63 thf(fact_4551_sum__le__card__Max,axiom,
% 0.37/0.63 ! [A4: set_set_nat,F: set_nat > nat] :
% 0.37/0.63 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_set_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_set_nat_nat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_card_Max
% 0.37/0.63 thf(fact_4552_sum__le__card__Max,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > nat] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_int @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_card_Max
% 0.37/0.63 thf(fact_4553_sum__le__card__Max,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > nat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_complex @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_complex_nat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_card_Max
% 0.37/0.63 thf(fact_4554_sum__le__card__Max,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > nat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( times_times_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_951025933927791156er_nat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_card_Max
% 0.37/0.63 thf(fact_4555_sum__le__card__Max,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > nat] :
% 0.37/0.63 ( ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_card_Max
% 0.37/0.63 thf(fact_4556_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_o,X: $o,G: $o > real] :
% 0.37/0.63 ( ( finite_finite_o @ A4 )
% 0.37/0.63 => ( ~ ( member_o @ X @ A4 )
% 0.37/0.63 => ( ( groups8691415230153176458o_real @ G @ ( insert_o @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups8691415230153176458o_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4557_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.63 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4558_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_real,X: real,G: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ~ ( member_real @ X @ A4 )
% 0.37/0.63 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4559_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_int,X: int,G: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ~ ( member_int @ X @ A4 )
% 0.37/0.63 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4560_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_complex,X: complex,G: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ~ ( member_complex @ X @ A4 )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4561_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,X: code_integer,G: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ~ ( member_Code_integer @ X @ A4 )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4562_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_o,X: $o,G: $o > rat] :
% 0.37/0.63 ( ( finite_finite_o @ A4 )
% 0.37/0.63 => ( ~ ( member_o @ X @ A4 )
% 0.37/0.63 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4563_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.63 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4564_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_real,X: real,G: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ~ ( member_real @ X @ A4 )
% 0.37/0.63 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4565_sum_Oinsert,axiom,
% 0.37/0.63 ! [A4: set_nat,X: nat,G: nat > rat] :
% 0.37/0.63 ( ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ~ ( member_nat @ X @ A4 )
% 0.37/0.63 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert
% 0.37/0.63 thf(fact_4566_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_nat,G: nat > uint32] :
% 0.37/0.63 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ( groups833757482993574392uint32 @ G @ A4 )
% 0.37/0.63 = zero_zero_uint32 ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4567_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_int,G: int > uint32] :
% 0.37/0.63 ( ~ ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( groups5712668689793887828uint32 @ G @ A4 )
% 0.37/0.63 = zero_zero_uint32 ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4568_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_complex,G: complex > uint32] :
% 0.37/0.63 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( groups8736914816313324502uint32 @ G @ A4 )
% 0.37/0.63 = zero_zero_uint32 ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4569_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,G: code_integer > uint32] :
% 0.37/0.63 ( ~ ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( groups8847630953604152069uint32 @ G @ A4 )
% 0.37/0.63 = zero_zero_uint32 ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4570_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_int,G: int > real] :
% 0.37/0.63 ( ~ ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( groups8778361861064173332t_real @ G @ A4 )
% 0.37/0.63 = zero_zero_real ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4571_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_complex,G: complex > real] :
% 0.37/0.63 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 0.37/0.63 = zero_zero_real ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4572_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,G: code_integer > real] :
% 0.37/0.63 ( ~ ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 0.37/0.63 = zero_zero_real ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4573_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_nat,G: nat > rat] :
% 0.37/0.63 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 0.37/0.63 = zero_zero_rat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4574_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_int,G: int > rat] :
% 0.37/0.63 ( ~ ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( groups3906332499630173760nt_rat @ G @ A4 )
% 0.37/0.63 = zero_zero_rat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4575_sum_Oinfinite,axiom,
% 0.37/0.63 ! [A4: set_complex,G: complex > rat] :
% 0.37/0.63 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 0.37/0.63 = zero_zero_rat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.infinite
% 0.37/0.63 thf(fact_4576_sum__eq__0__iff,axiom,
% 0.37/0.63 ! [F2: set_int,F: int > nat] :
% 0.37/0.63 ( ( finite_finite_int @ F2 )
% 0.37/0.63 => ( ( ( groups4541462559716669496nt_nat @ F @ F2 )
% 0.37/0.63 = zero_zero_nat )
% 0.37/0.63 = ( ! [X4: int] :
% 0.37/0.63 ( ( member_int @ X4 @ F2 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_0_iff
% 0.37/0.63 thf(fact_4577_sum__eq__0__iff,axiom,
% 0.37/0.63 ! [F2: set_complex,F: complex > nat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ F2 )
% 0.37/0.63 => ( ( ( groups5693394587270226106ex_nat @ F @ F2 )
% 0.37/0.63 = zero_zero_nat )
% 0.37/0.63 = ( ! [X4: complex] :
% 0.37/0.63 ( ( member_complex @ X4 @ F2 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_0_iff
% 0.37/0.63 thf(fact_4578_sum__eq__0__iff,axiom,
% 0.37/0.63 ! [F2: set_Code_integer,F: code_integer > nat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ F2 )
% 0.37/0.63 => ( ( ( groups7237345082560585321er_nat @ F @ F2 )
% 0.37/0.63 = zero_zero_nat )
% 0.37/0.63 = ( ! [X4: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X4 @ F2 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_0_iff
% 0.37/0.63 thf(fact_4579_sum__eq__0__iff,axiom,
% 0.37/0.63 ! [F2: set_nat,F: nat > nat] :
% 0.37/0.63 ( ( finite_finite_nat @ F2 )
% 0.37/0.63 => ( ( ( groups3542108847815614940at_nat @ F @ F2 )
% 0.37/0.63 = zero_zero_nat )
% 0.37/0.63 = ( ! [X4: nat] :
% 0.37/0.63 ( ( member_nat @ X4 @ F2 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_0_iff
% 0.37/0.63 thf(fact_4580_sum_Oempty,axiom,
% 0.37/0.63 ! [G: nat > uint32] :
% 0.37/0.63 ( ( groups833757482993574392uint32 @ G @ bot_bot_set_nat )
% 0.37/0.63 = zero_zero_uint32 ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4581_sum_Oempty,axiom,
% 0.37/0.63 ! [G: nat > rat] :
% 0.37/0.63 ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 0.37/0.63 = zero_zero_rat ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4582_sum_Oempty,axiom,
% 0.37/0.63 ! [G: nat > int] :
% 0.37/0.63 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 0.37/0.63 = zero_zero_int ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4583_sum_Oempty,axiom,
% 0.37/0.63 ! [G: int > uint32] :
% 0.37/0.63 ( ( groups5712668689793887828uint32 @ G @ bot_bot_set_int )
% 0.37/0.63 = zero_zero_uint32 ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4584_sum_Oempty,axiom,
% 0.37/0.63 ! [G: int > real] :
% 0.37/0.63 ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 0.37/0.63 = zero_zero_real ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4585_sum_Oempty,axiom,
% 0.37/0.63 ! [G: int > rat] :
% 0.37/0.63 ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 0.37/0.63 = zero_zero_rat ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4586_sum_Oempty,axiom,
% 0.37/0.63 ! [G: int > nat] :
% 0.37/0.63 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 0.37/0.63 = zero_zero_nat ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4587_sum_Oempty,axiom,
% 0.37/0.63 ! [G: $o > uint32] :
% 0.37/0.63 ( ( groups7241207224191747786uint32 @ G @ bot_bot_set_o )
% 0.37/0.63 = zero_zero_uint32 ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4588_sum_Oempty,axiom,
% 0.37/0.63 ! [G: $o > real] :
% 0.37/0.63 ( ( groups8691415230153176458o_real @ G @ bot_bot_set_o )
% 0.37/0.63 = zero_zero_real ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4589_sum_Oempty,axiom,
% 0.37/0.63 ! [G: $o > rat] :
% 0.37/0.63 ( ( groups7872700643590313910_o_rat @ G @ bot_bot_set_o )
% 0.37/0.63 = zero_zero_rat ) ).
% 0.37/0.63
% 0.37/0.63 % sum.empty
% 0.37/0.63 thf(fact_4590_member__le__sum,axiom,
% 0.37/0.63 ! [I: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I @ A4 )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4591_member__le__sum,axiom,
% 0.37/0.63 ! [I: real,A4: set_real,F: real > real] :
% 0.37/0.63 ( ( member_real @ I @ A4 )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4592_member__le__sum,axiom,
% 0.37/0.63 ! [I: complex,A4: set_complex,F: complex > real] :
% 0.37/0.63 ( ( member_complex @ I @ A4 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4593_member__le__sum,axiom,
% 0.37/0.63 ! [I: code_integer,A4: set_Code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( member_Code_integer @ I @ A4 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ I @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ I ) @ ( groups1270011288395367621r_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4594_member__le__sum,axiom,
% 0.37/0.63 ! [I: int,A4: set_int,F: int > real] :
% 0.37/0.63 ( ( member_int @ I @ A4 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4595_member__le__sum,axiom,
% 0.37/0.63 ! [I: $o,A4: set_o,F: $o > real] :
% 0.37/0.63 ( ( member_o @ I @ A4 )
% 0.37/0.63 => ( ! [X3: $o] :
% 0.37/0.63 ( ( member_o @ X3 @ ( minus_minus_set_o @ A4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite_finite_o @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8691415230153176458o_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4596_member__le__sum,axiom,
% 0.37/0.63 ! [I: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I @ A4 )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4597_member__le__sum,axiom,
% 0.37/0.63 ! [I: real,A4: set_real,F: real > rat] :
% 0.37/0.63 ( ( member_real @ I @ A4 )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4598_member__le__sum,axiom,
% 0.37/0.63 ! [I: complex,A4: set_complex,F: complex > rat] :
% 0.37/0.63 ( ( member_complex @ I @ A4 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4599_member__le__sum,axiom,
% 0.37/0.63 ! [I: code_integer,A4: set_Code_integer,F: code_integer > rat] :
% 0.37/0.63 ( ( member_Code_integer @ I @ A4 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ I @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups6602215022474089585er_rat @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % member_le_sum
% 0.37/0.63 thf(fact_4600_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.37/0.63 => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( groups2240296850493347238T_real @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4601_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_real,A4: set_real,B: real,F: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ B4 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 0.37/0.63 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4602_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_complex,A4: set_complex,B: complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.63 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4603_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_Code_integer,A4: set_Code_integer,B: code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.63 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4604_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.37/0.63 => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ ( groups136491112297645522BT_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4605_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_real,A4: set_real,B: real,F: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ B4 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 0.37/0.63 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4606_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_complex,A4: set_complex,B: complex,F: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.63 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4607_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_Code_integer,A4: set_Code_integer,B: code_integer,F: code_integer > rat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.63 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4608_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_nat,A4: set_nat,B: nat,F: nat > rat] :
% 0.37/0.63 ( ( finite_finite_nat @ B4 )
% 0.37/0.63 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.63 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4609_sum__strict__mono2,axiom,
% 0.37/0.63 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.37/0.63 => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 0.37/0.63 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 0.37/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( groups771621172384141258BT_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono2
% 0.37/0.63 thf(fact_4610_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( ( member_VEBT_VEBT @ A @ A4 )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.63 = ( minus_minus_uint32 @ ( groups8325533452322294502uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.63 = ( groups8325533452322294502uint32 @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4611_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_real,A: real,F: real > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ( ( member_real @ A @ A4 )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.37/0.63 = ( minus_minus_uint32 @ ( groups5944083974425963860uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_real @ A @ A4 )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.37/0.63 = ( groups5944083974425963860uint32 @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4612_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_complex,A: complex,F: complex > uint32] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( ( member_complex @ A @ A4 )
% 0.37/0.63 => ( ( groups8736914816313324502uint32 @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.37/0.63 = ( minus_minus_uint32 @ ( groups8736914816313324502uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_complex @ A @ A4 )
% 0.37/0.63 => ( ( groups8736914816313324502uint32 @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4613_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,A: code_integer,F: code_integer > uint32] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( ( member_Code_integer @ A @ A4 )
% 0.37/0.63 => ( ( groups8847630953604152069uint32 @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.63 = ( minus_minus_uint32 @ ( groups8847630953604152069uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_Code_integer @ A @ A4 )
% 0.37/0.63 => ( ( groups8847630953604152069uint32 @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4614_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_int,A: int,F: int > uint32] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( ( member_int @ A @ A4 )
% 0.37/0.63 => ( ( groups5712668689793887828uint32 @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.37/0.63 = ( minus_minus_uint32 @ ( groups5712668689793887828uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_int @ A @ A4 )
% 0.37/0.63 => ( ( groups5712668689793887828uint32 @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.37/0.63 = ( groups5712668689793887828uint32 @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4615_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_o,A: $o,F: $o > uint32] :
% 0.37/0.63 ( ( finite_finite_o @ A4 )
% 0.37/0.63 => ( ( ( member_o @ A @ A4 )
% 0.37/0.63 => ( ( groups7241207224191747786uint32 @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.37/0.63 = ( minus_minus_uint32 @ ( groups7241207224191747786uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_o @ A @ A4 )
% 0.37/0.63 => ( ( groups7241207224191747786uint32 @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.37/0.63 = ( groups7241207224191747786uint32 @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4616_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( ( member_VEBT_VEBT @ A @ A4 )
% 0.37/0.63 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.63 = ( minus_minus_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 0.37/0.63 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.63 = ( groups2240296850493347238T_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4617_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_real,A: real,F: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ( ( member_real @ A @ A4 )
% 0.37/0.63 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.37/0.63 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_real @ A @ A4 )
% 0.37/0.63 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.37/0.63 = ( groups8097168146408367636l_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4618_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_complex,A: complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( ( member_complex @ A @ A4 )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.37/0.63 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_complex @ A @ A4 )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.37/0.63 = ( groups5808333547571424918x_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4619_sum__diff1,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,A: code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( ( member_Code_integer @ A @ A4 )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.63 = ( minus_minus_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.63 & ( ~ ( member_Code_integer @ A @ A4 )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.63 = ( groups1270011288395367621r_real @ F @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_diff1
% 0.37/0.63 thf(fact_4620_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4621_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_complex,G: complex > real,X: complex] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4622_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,G: code_integer > real,X: code_integer] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4623_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > rat,X: vEBT_VEBT] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4624_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_complex,G: complex > rat,X: complex] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4625_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,G: code_integer > rat,X: code_integer] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4626_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > nat,X: vEBT_VEBT] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4627_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_complex,G: complex > nat,X: complex] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4628_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,G: code_integer > nat,X: code_integer] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4629_sum_Oinsert__remove,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > int,X: vEBT_VEBT] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_remove
% 0.37/0.63 thf(fact_4630_complete__real,axiom,
% 0.37/0.63 ! [S3: set_real] :
% 0.37/0.63 ( ? [X5: real] : ( member_real @ X5 @ S3 )
% 0.37/0.63 => ( ? [Z5: real] :
% 0.37/0.63 ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ S3 )
% 0.37/0.63 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 0.37/0.63 => ? [Y3: real] :
% 0.37/0.63 ( ! [X5: real] :
% 0.37/0.63 ( ( member_real @ X5 @ S3 )
% 0.37/0.63 => ( ord_less_eq_real @ X5 @ Y3 ) )
% 0.37/0.63 & ! [Z5: real] :
% 0.37/0.63 ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ S3 )
% 0.37/0.63 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 0.37/0.63 => ( ord_less_eq_real @ Y3 @ Z5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % complete_real
% 0.37/0.63 thf(fact_4631_real__minus__mult__self__le,axiom,
% 0.37/0.63 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 0.37/0.63
% 0.37/0.63 % real_minus_mult_self_le
% 0.37/0.63 thf(fact_4632_sum__cong__Suc,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 0.37/0.63 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 0.37/0.63 => ( ( F @ ( suc @ X3 ) )
% 0.37/0.63 = ( G @ ( suc @ X3 ) ) ) )
% 0.37/0.63 => ( ( groups3542108847815614940at_nat @ F @ A4 )
% 0.37/0.63 = ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_cong_Suc
% 0.37/0.63 thf(fact_4633_sum__cong__Suc,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > real,G: nat > real] :
% 0.37/0.63 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 0.37/0.63 => ( ( F @ ( suc @ X3 ) )
% 0.37/0.63 = ( G @ ( suc @ X3 ) ) ) )
% 0.37/0.63 => ( ( groups6591440286371151544t_real @ F @ A4 )
% 0.37/0.63 = ( groups6591440286371151544t_real @ G @ A4 ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_cong_Suc
% 0.37/0.63 thf(fact_4634_sum_Oneutral,axiom,
% 0.37/0.63 ! [A4: set_nat,G: nat > nat] :
% 0.37/0.63 ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ A4 )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_nat ) )
% 0.37/0.63 => ( ( groups3542108847815614940at_nat @ G @ A4 )
% 0.37/0.63 = zero_zero_nat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.neutral
% 0.37/0.63 thf(fact_4635_sum_Oneutral,axiom,
% 0.37/0.63 ! [A4: set_complex,G: complex > complex] :
% 0.37/0.63 ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_complex ) )
% 0.37/0.63 => ( ( groups7754918857620584856omplex @ G @ A4 )
% 0.37/0.63 = zero_zero_complex ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.neutral
% 0.37/0.63 thf(fact_4636_sum_Oneutral,axiom,
% 0.37/0.63 ! [A4: set_nat,G: nat > real] :
% 0.37/0.63 ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ A4 )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( groups6591440286371151544t_real @ G @ A4 )
% 0.37/0.63 = zero_zero_real ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.neutral
% 0.37/0.63 thf(fact_4637_sum_Oneutral,axiom,
% 0.37/0.63 ! [A4: set_int,G: int > int] :
% 0.37/0.63 ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_int ) )
% 0.37/0.63 => ( ( groups4538972089207619220nt_int @ G @ A4 )
% 0.37/0.63 = zero_zero_int ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.neutral
% 0.37/0.63 thf(fact_4638_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: nat > uint32,A4: set_nat] :
% 0.37/0.63 ( ( ( groups833757482993574392uint32 @ G @ A4 )
% 0.37/0.63 != zero_zero_uint32 )
% 0.37/0.63 => ~ ! [A3: nat] :
% 0.37/0.63 ( ( member_nat @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4639_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: vEBT_VEBT > uint32,A4: set_VEBT_VEBT] :
% 0.37/0.63 ( ( ( groups8325533452322294502uint32 @ G @ A4 )
% 0.37/0.63 != zero_zero_uint32 )
% 0.37/0.63 => ~ ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4640_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: real > uint32,A4: set_real] :
% 0.37/0.63 ( ( ( groups5944083974425963860uint32 @ G @ A4 )
% 0.37/0.63 != zero_zero_uint32 )
% 0.37/0.63 => ~ ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4641_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: int > uint32,A4: set_int] :
% 0.37/0.63 ( ( ( groups5712668689793887828uint32 @ G @ A4 )
% 0.37/0.63 != zero_zero_uint32 )
% 0.37/0.63 => ~ ! [A3: int] :
% 0.37/0.63 ( ( member_int @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4642_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: vEBT_VEBT > real,A4: set_VEBT_VEBT] :
% 0.37/0.63 ( ( ( groups2240296850493347238T_real @ G @ A4 )
% 0.37/0.63 != zero_zero_real )
% 0.37/0.63 => ~ ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4643_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: real > real,A4: set_real] :
% 0.37/0.63 ( ( ( groups8097168146408367636l_real @ G @ A4 )
% 0.37/0.63 != zero_zero_real )
% 0.37/0.63 => ~ ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4644_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: int > real,A4: set_int] :
% 0.37/0.63 ( ( ( groups8778361861064173332t_real @ G @ A4 )
% 0.37/0.63 != zero_zero_real )
% 0.37/0.63 => ~ ! [A3: int] :
% 0.37/0.63 ( ( member_int @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4645_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: nat > rat,A4: set_nat] :
% 0.37/0.63 ( ( ( groups2906978787729119204at_rat @ G @ A4 )
% 0.37/0.63 != zero_zero_rat )
% 0.37/0.63 => ~ ! [A3: nat] :
% 0.37/0.63 ( ( member_nat @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_rat ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4646_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: vEBT_VEBT > rat,A4: set_VEBT_VEBT] :
% 0.37/0.63 ( ( ( groups136491112297645522BT_rat @ G @ A4 )
% 0.37/0.63 != zero_zero_rat )
% 0.37/0.63 => ~ ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_rat ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4647_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.37/0.63 ! [G: real > rat,A4: set_real] :
% 0.37/0.63 ( ( ( groups1300246762558778688al_rat @ G @ A4 )
% 0.37/0.63 != zero_zero_rat )
% 0.37/0.63 => ~ ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ A4 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_rat ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.not_neutral_contains_not_neutral
% 0.37/0.63 thf(fact_4648_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ zero_zero_real ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4649_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > real] :
% 0.37/0.63 ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ zero_zero_real ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4650_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > real] :
% 0.37/0.63 ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ zero_zero_real ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4651_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > rat] :
% 0.37/0.63 ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.37/0.63 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4652_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.63 ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.37/0.63 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4653_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > rat] :
% 0.37/0.63 ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.37/0.63 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4654_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > rat] :
% 0.37/0.63 ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 0.37/0.63 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4655_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.63 ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4656_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > nat] :
% 0.37/0.63 ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4657_sum__nonpos,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > nat] :
% 0.37/0.63 ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 0.37/0.63 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonpos
% 0.37/0.63 thf(fact_4658_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4659_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > real] :
% 0.37/0.63 ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4660_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > real] :
% 0.37/0.63 ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4661_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > rat] :
% 0.37/0.63 ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4662_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.63 ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4663_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > rat] :
% 0.37/0.63 ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4664_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > rat] :
% 0.37/0.63 ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4665_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.63 ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4666_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > nat] :
% 0.37/0.63 ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4667_sum__nonneg,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > nat] :
% 0.37/0.63 ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg
% 0.37/0.63 thf(fact_4668_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: vEBT_VEBT > rat,I5: set_VEBT_VEBT,G: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 0.37/0.63 ( ( ( groups136491112297645522BT_rat @ F @ I5 )
% 0.37/0.63 = ( groups136491112297645522BT_rat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_VEBT_VEBT @ I @ I5 )
% 0.37/0.63 => ( ( finite5795047828879050333T_VEBT @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4669_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 0.37/0.63 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 0.37/0.63 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: real] :
% 0.37/0.63 ( ( member_real @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_real @ I @ I5 )
% 0.37/0.63 => ( ( finite_finite_real @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4670_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 0.37/0.63 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 0.37/0.63 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: nat] :
% 0.37/0.63 ( ( member_nat @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_nat @ I @ I5 )
% 0.37/0.63 => ( ( finite_finite_nat @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4671_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 0.37/0.63 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 0.37/0.63 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: int] :
% 0.37/0.63 ( ( member_int @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_int @ I @ I5 )
% 0.37/0.63 => ( ( finite_finite_int @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4672_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 0.37/0.63 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 0.37/0.63 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: complex] :
% 0.37/0.63 ( ( member_complex @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_complex @ I @ I5 )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4673_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: code_integer > rat,I5: set_Code_integer,G: code_integer > rat,I: code_integer] :
% 0.37/0.63 ( ( ( groups6602215022474089585er_rat @ F @ I5 )
% 0.37/0.63 = ( groups6602215022474089585er_rat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_Code_integer @ I @ I5 )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4674_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: vEBT_VEBT > nat,I5: set_VEBT_VEBT,G: vEBT_VEBT > nat,I: vEBT_VEBT] :
% 0.37/0.63 ( ( ( groups771621172384141258BT_nat @ F @ I5 )
% 0.37/0.63 = ( groups771621172384141258BT_nat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_VEBT_VEBT @ I @ I5 )
% 0.37/0.63 => ( ( finite5795047828879050333T_VEBT @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4675_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 0.37/0.63 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 0.37/0.63 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: real] :
% 0.37/0.63 ( ( member_real @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_real @ I @ I5 )
% 0.37/0.63 => ( ( finite_finite_real @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4676_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 0.37/0.63 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 0.37/0.63 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: int] :
% 0.37/0.63 ( ( member_int @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_int @ I @ I5 )
% 0.37/0.63 => ( ( finite_finite_int @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4677_sum__mono__inv,axiom,
% 0.37/0.63 ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 0.37/0.63 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 0.37/0.63 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 0.37/0.63 => ( ! [I2: complex] :
% 0.37/0.63 ( ( member_complex @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.63 => ( ( member_complex @ I @ I5 )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ I5 )
% 0.37/0.63 => ( ( F @ I )
% 0.37/0.63 = ( G @ I ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_mono_inv
% 0.37/0.63 thf(fact_4678_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups2240296850493347238T_real @ F @ A4 )
% 0.37/0.63 = zero_zero_real )
% 0.37/0.63 = ( ! [X4: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4679_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups8097168146408367636l_real @ F @ A4 )
% 0.37/0.63 = zero_zero_real )
% 0.37/0.63 = ( ! [X4: real] :
% 0.37/0.63 ( ( member_real @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4680_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups8778361861064173332t_real @ F @ A4 )
% 0.37/0.63 = zero_zero_real )
% 0.37/0.63 = ( ! [X4: int] :
% 0.37/0.63 ( ( member_int @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4681_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups5808333547571424918x_real @ F @ A4 )
% 0.37/0.63 = zero_zero_real )
% 0.37/0.63 = ( ! [X4: complex] :
% 0.37/0.63 ( ( member_complex @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4682_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups1270011288395367621r_real @ F @ A4 )
% 0.37/0.63 = zero_zero_real )
% 0.37/0.63 = ( ! [X4: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4683_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups136491112297645522BT_rat @ F @ A4 )
% 0.37/0.63 = zero_zero_rat )
% 0.37/0.63 = ( ! [X4: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_rat ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4684_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups1300246762558778688al_rat @ F @ A4 )
% 0.37/0.63 = zero_zero_rat )
% 0.37/0.63 = ( ! [X4: real] :
% 0.37/0.63 ( ( member_real @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_rat ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4685_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > rat] :
% 0.37/0.63 ( ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups2906978787729119204at_rat @ F @ A4 )
% 0.37/0.63 = zero_zero_rat )
% 0.37/0.63 = ( ! [X4: nat] :
% 0.37/0.63 ( ( member_nat @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_rat ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4686_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > rat] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups3906332499630173760nt_rat @ F @ A4 )
% 0.37/0.63 = zero_zero_rat )
% 0.37/0.63 = ( ! [X4: int] :
% 0.37/0.63 ( ( member_int @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_rat ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4687_sum__nonneg__eq__0__iff,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 0.37/0.63 => ( ( ( groups5058264527183730370ex_rat @ F @ A4 )
% 0.37/0.63 = zero_zero_rat )
% 0.37/0.63 = ( ! [X4: complex] :
% 0.37/0.63 ( ( member_complex @ X4 @ A4 )
% 0.37/0.63 => ( ( F @ X4 )
% 0.37/0.63 = zero_zero_rat ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_nonneg_eq_0_iff
% 0.37/0.63 thf(fact_4688_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ S )
% 0.37/0.63 => ( ( finite_finite_int @ T )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ S )
% 0.37/0.63 => ? [Xa: int] :
% 0.37/0.63 ( ( member_int @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4689_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ S )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ T )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ S )
% 0.37/0.63 => ? [Xa: complex] :
% 0.37/0.63 ( ( member_complex @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4690_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_int,T: set_Code_integer,G: code_integer > real,I: code_integer > int,F: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ S )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ T )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ S )
% 0.37/0.63 => ? [Xa: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4691_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ S )
% 0.37/0.63 => ( ( finite_finite_int @ T )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ S )
% 0.37/0.63 => ? [Xa: int] :
% 0.37/0.63 ( ( member_int @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4692_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ S )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ T )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ S )
% 0.37/0.63 => ? [Xa: complex] :
% 0.37/0.63 ( ( member_complex @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4693_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_complex,T: set_Code_integer,G: code_integer > real,I: code_integer > complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ S )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ T )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ S )
% 0.37/0.63 => ? [Xa: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4694_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_Code_integer,T: set_int,G: int > real,I: int > code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ S )
% 0.37/0.63 => ( ( finite_finite_int @ T )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ S )
% 0.37/0.63 => ? [Xa: int] :
% 0.37/0.63 ( ( member_int @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4695_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_Code_integer,T: set_complex,G: complex > real,I: complex > code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ S )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ T )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ S )
% 0.37/0.63 => ? [Xa: complex] :
% 0.37/0.63 ( ( member_complex @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4696_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_Code_integer,T: set_Code_integer,G: code_integer > real,I: code_integer > code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ S )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ T )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ S )
% 0.37/0.63 => ? [Xa: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4697_sum__le__included,axiom,
% 0.37/0.63 ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 0.37/0.63 ( ( finite_finite_nat @ S )
% 0.37/0.63 => ( ( finite_finite_nat @ T )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ T )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ S )
% 0.37/0.63 => ? [Xa: nat] :
% 0.37/0.63 ( ( member_nat @ Xa @ T )
% 0.37/0.63 & ( ( I @ Xa )
% 0.37/0.63 = X3 )
% 0.37/0.63 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 0.37/0.63 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_le_included
% 0.37/0.63 thf(fact_4698_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > real,G: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: int] :
% 0.37/0.63 ( ( member_int @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4699_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > real,G: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: complex] :
% 0.37/0.63 ( ( member_complex @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4700_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4701_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 0.37/0.63 ( ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: nat] :
% 0.37/0.63 ( ( member_nat @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4702_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > rat,G: int > rat] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: int] :
% 0.37/0.63 ( ( member_int @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4703_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > rat,G: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: complex] :
% 0.37/0.63 ( ( member_complex @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4704_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4705_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > nat,G: int > nat] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: int] :
% 0.37/0.63 ( ( member_int @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4706_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > nat,G: complex > nat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: complex] :
% 0.37/0.63 ( ( member_complex @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4707_sum__strict__mono__ex1,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ? [X5: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X5 @ A4 )
% 0.37/0.63 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 0.37/0.63 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono_ex1
% 0.37/0.63 thf(fact_4708_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: uint32 > uint32 > $o,S3: set_nat,H2: nat > uint32,G: nat > uint32] :
% 0.37/0.63 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 0.37/0.63 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite_finite_nat @ S3 )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups833757482993574392uint32 @ H2 @ S3 ) @ ( groups833757482993574392uint32 @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4709_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: uint32 > uint32 > $o,S3: set_int,H2: int > uint32,G: int > uint32] :
% 0.37/0.63 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 0.37/0.63 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite_finite_int @ S3 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups5712668689793887828uint32 @ H2 @ S3 ) @ ( groups5712668689793887828uint32 @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4710_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: uint32 > uint32 > $o,S3: set_complex,H2: complex > uint32,G: complex > uint32] :
% 0.37/0.63 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 0.37/0.63 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups8736914816313324502uint32 @ H2 @ S3 ) @ ( groups8736914816313324502uint32 @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4711_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: uint32 > uint32 > $o,S3: set_Code_integer,H2: code_integer > uint32,G: code_integer > uint32] :
% 0.37/0.63 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 0.37/0.63 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups8847630953604152069uint32 @ H2 @ S3 ) @ ( groups8847630953604152069uint32 @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4712_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 0.37/0.63 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 0.37/0.63 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite_finite_int @ S3 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups8778361861064173332t_real @ H2 @ S3 ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4713_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 0.37/0.63 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 0.37/0.63 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4714_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: real > real > $o,S3: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 0.37/0.63 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 0.37/0.63 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups1270011288395367621r_real @ H2 @ S3 ) @ ( groups1270011288395367621r_real @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4715_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 0.37/0.63 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.37/0.63 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite_finite_nat @ S3 )
% 0.37/0.63 => ( ! [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4716_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 0.37/0.63 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.37/0.63 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite_finite_int @ S3 )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups3906332499630173760nt_rat @ H2 @ S3 ) @ ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4717_sum_Orelated,axiom,
% 0.37/0.63 ! [R2: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 0.37/0.63 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.37/0.63 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.37/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.37/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.37/0.63 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ S3 )
% 0.37/0.63 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( R2 @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.related
% 0.37/0.63 thf(fact_4718_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bo8194388402131092736T_VEBT )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4719_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > real,G: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bot_set_real )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4720_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > real,G: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bot_set_complex )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4721_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4722_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > real,G: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bot_set_int )
% 0.37/0.63 => ( ! [X3: int] :
% 0.37/0.63 ( ( member_int @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4723_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_o,F: $o > real,G: $o > real] :
% 0.37/0.63 ( ( finite_finite_o @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bot_set_o )
% 0.37/0.63 => ( ! [X3: $o] :
% 0.37/0.63 ( ( member_o @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_real @ ( groups8691415230153176458o_real @ F @ A4 ) @ ( groups8691415230153176458o_real @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4724_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bo8194388402131092736T_VEBT )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4725_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_real,F: real > rat,G: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bot_set_real )
% 0.37/0.63 => ( ! [X3: real] :
% 0.37/0.63 ( ( member_real @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4726_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > rat,G: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bot_set_complex )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4727_sum__strict__mono,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ A4 )
% 0.37/0.63 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 0.37/0.63 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_strict_mono
% 0.37/0.63 thf(fact_4728_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_o,X: $o,G: $o > real] :
% 0.37/0.63 ( ( finite_finite_o @ A4 )
% 0.37/0.63 => ( ( ( member_o @ X @ A4 )
% 0.37/0.63 => ( ( groups8691415230153176458o_real @ G @ ( insert_o @ X @ A4 ) )
% 0.37/0.63 = ( groups8691415230153176458o_real @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_o @ X @ A4 )
% 0.37/0.63 => ( ( groups8691415230153176458o_real @ G @ ( insert_o @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups8691415230153176458o_real @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4729_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.63 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( groups2240296850493347238T_real @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.63 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4730_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_real,X: real,G: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ( ( member_real @ X @ A4 )
% 0.37/0.63 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A4 ) )
% 0.37/0.63 = ( groups8097168146408367636l_real @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_real @ X @ A4 )
% 0.37/0.63 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4731_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_int,X: int,G: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( ( member_int @ X @ A4 )
% 0.37/0.63 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A4 ) )
% 0.37/0.63 = ( groups8778361861064173332t_real @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_int @ X @ A4 )
% 0.37/0.63 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4732_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_complex,X: complex,G: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( ( member_complex @ X @ A4 )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 0.37/0.63 = ( groups5808333547571424918x_real @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_complex @ X @ A4 )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4733_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,X: code_integer,G: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( ( member_Code_integer @ X @ A4 )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.63 = ( groups1270011288395367621r_real @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_Code_integer @ X @ A4 )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4734_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_o,X: $o,G: $o > rat] :
% 0.37/0.63 ( ( finite_finite_o @ A4 )
% 0.37/0.63 => ( ( ( member_o @ X @ A4 )
% 0.37/0.63 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 0.37/0.63 = ( groups7872700643590313910_o_rat @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_o @ X @ A4 )
% 0.37/0.63 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4735_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.63 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.63 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( groups136491112297645522BT_rat @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.63 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4736_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_real,X: real,G: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ A4 )
% 0.37/0.63 => ( ( ( member_real @ X @ A4 )
% 0.37/0.63 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A4 ) )
% 0.37/0.63 = ( groups1300246762558778688al_rat @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_real @ X @ A4 )
% 0.37/0.63 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4737_sum_Oinsert__if,axiom,
% 0.37/0.63 ! [A4: set_nat,X: nat,G: nat > rat] :
% 0.37/0.63 ( ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ( ( member_nat @ X @ A4 )
% 0.37/0.63 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 0.37/0.63 = ( groups2906978787729119204at_rat @ G @ A4 ) ) )
% 0.37/0.63 & ( ~ ( member_nat @ X @ A4 )
% 0.37/0.63 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 0.37/0.63 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.insert_if
% 0.37/0.63 thf(fact_4738_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_VEBT_VEBT,T5: set_VEBT_VEBT,S3: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ S7 )
% 0.37/0.63 => ( ( finite5795047828879050333T_VEBT @ T5 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 0.37/0.63 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8325533452322294502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4739_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_VEBT_VEBT,T5: set_real,S3: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T3: set_real,G: vEBT_VEBT > uint32,H2: real > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ S7 )
% 0.37/0.63 => ( ( finite_finite_real @ T5 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 0.37/0.63 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 0.37/0.63 = ( groups5944083974425963860uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4740_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_real,T5: set_VEBT_VEBT,S3: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T3: set_VEBT_VEBT,G: real > uint32,H2: vEBT_VEBT > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ S7 )
% 0.37/0.63 => ( ( finite5795047828879050333T_VEBT @ T5 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 0.37/0.63 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8325533452322294502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4741_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_real,T5: set_real,S3: set_real,I: real > real,J: real > real,T3: set_real,G: real > uint32,H2: real > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ S7 )
% 0.37/0.63 => ( ( finite_finite_real @ T5 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 0.37/0.63 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 0.37/0.63 = ( groups5944083974425963860uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4742_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_VEBT_VEBT,T5: set_int,S3: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T3: set_int,G: vEBT_VEBT > uint32,H2: int > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ S7 )
% 0.37/0.63 => ( ( finite_finite_int @ T5 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: int] :
% 0.37/0.63 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: int] :
% 0.37/0.63 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 0.37/0.63 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: int] :
% 0.37/0.63 ( ( member_int @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 0.37/0.63 = ( groups5712668689793887828uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4743_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_real,T5: set_int,S3: set_real,I: int > real,J: real > int,T3: set_int,G: real > uint32,H2: int > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ S7 )
% 0.37/0.63 => ( ( finite_finite_int @ T5 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: int] :
% 0.37/0.63 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: int] :
% 0.37/0.63 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 0.37/0.63 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: int] :
% 0.37/0.63 ( ( member_int @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 0.37/0.63 = ( groups5712668689793887828uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4744_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_VEBT_VEBT,T5: set_complex,S3: set_VEBT_VEBT,I: complex > vEBT_VEBT,J: vEBT_VEBT > complex,T3: set_complex,G: vEBT_VEBT > uint32,H2: complex > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ S7 )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ T5 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 0.37/0.63 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4745_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_real,T5: set_complex,S3: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > uint32,H2: complex > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ S7 )
% 0.37/0.63 => ( ( finite3207457112153483333omplex @ T5 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 0.37/0.63 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4746_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_VEBT_VEBT,T5: set_Code_integer,S3: set_VEBT_VEBT,I: code_integer > vEBT_VEBT,J: vEBT_VEBT > code_integer,T3: set_Code_integer,G: vEBT_VEBT > uint32,H2: code_integer > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ S7 )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ T5 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 0.37/0.63 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 0.37/0.63 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4747_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.37/0.63 ! [S7: set_real,T5: set_Code_integer,S3: set_real,I: code_integer > real,J: real > code_integer,T3: set_Code_integer,G: real > uint32,H2: code_integer > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ S7 )
% 0.37/0.63 => ( ( finite6017078050557962740nteger @ T5 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( ( I @ ( J @ A3 ) )
% 0.37/0.63 = A3 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 0.37/0.63 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T3 @ T5 ) ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 0.37/0.63 => ( ( J @ ( I @ B3 ) )
% 0.37/0.63 = B3 ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 0.37/0.63 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S7 )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ T5 )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ S3 )
% 0.37/0.63 => ( ( H2 @ ( J @ A3 ) )
% 0.37/0.63 = ( G @ A3 ) ) )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.reindex_bij_witness_not_neutral
% 0.37/0.63 thf(fact_4748_sum__SucD,axiom,
% 0.37/0.63 ! [F: nat > nat,A4: set_nat,N: nat] :
% 0.37/0.63 ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 0.37/0.63 = ( suc @ N ) )
% 0.37/0.63 => ? [X3: nat] :
% 0.37/0.63 ( ( member_nat @ X3 @ A4 )
% 0.37/0.63 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_SucD
% 0.37/0.63 thf(fact_4749_sum__eq__Suc0__iff,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > nat] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 = ( ? [X4: int] :
% 0.37/0.63 ( ( member_int @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 & ! [Y4: int] :
% 0.37/0.63 ( ( member_int @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_Suc0_iff
% 0.37/0.63 thf(fact_4750_sum__eq__Suc0__iff,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > nat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( ( groups5693394587270226106ex_nat @ F @ A4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 = ( ? [X4: complex] :
% 0.37/0.63 ( ( member_complex @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 & ! [Y4: complex] :
% 0.37/0.63 ( ( member_complex @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_Suc0_iff
% 0.37/0.63 thf(fact_4751_sum__eq__Suc0__iff,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > nat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( ( groups7237345082560585321er_nat @ F @ A4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 = ( ? [X4: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 & ! [Y4: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_Suc0_iff
% 0.37/0.63 thf(fact_4752_sum__eq__Suc0__iff,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > nat] :
% 0.37/0.63 ( ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 = ( ? [X4: nat] :
% 0.37/0.63 ( ( member_nat @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = ( suc @ zero_zero_nat ) )
% 0.37/0.63 & ! [Y4: nat] :
% 0.37/0.63 ( ( member_nat @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_Suc0_iff
% 0.37/0.63 thf(fact_4753_sum__eq__1__iff,axiom,
% 0.37/0.63 ! [A4: set_int,F: int > nat] :
% 0.37/0.63 ( ( finite_finite_int @ A4 )
% 0.37/0.63 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 = ( ? [X4: int] :
% 0.37/0.63 ( ( member_int @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 & ! [Y4: int] :
% 0.37/0.63 ( ( member_int @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_1_iff
% 0.37/0.63 thf(fact_4754_sum__eq__1__iff,axiom,
% 0.37/0.63 ! [A4: set_complex,F: complex > nat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.63 => ( ( ( groups5693394587270226106ex_nat @ F @ A4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 = ( ? [X4: complex] :
% 0.37/0.63 ( ( member_complex @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 & ! [Y4: complex] :
% 0.37/0.63 ( ( member_complex @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_1_iff
% 0.37/0.63 thf(fact_4755_sum__eq__1__iff,axiom,
% 0.37/0.63 ! [A4: set_Code_integer,F: code_integer > nat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.63 => ( ( ( groups7237345082560585321er_nat @ F @ A4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 = ( ? [X4: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 & ! [Y4: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_1_iff
% 0.37/0.63 thf(fact_4756_sum__eq__1__iff,axiom,
% 0.37/0.63 ! [A4: set_nat,F: nat > nat] :
% 0.37/0.63 ( ( finite_finite_nat @ A4 )
% 0.37/0.63 => ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 = ( ? [X4: nat] :
% 0.37/0.63 ( ( member_nat @ X4 @ A4 )
% 0.37/0.63 & ( ( F @ X4 )
% 0.37/0.63 = one_one_nat )
% 0.37/0.63 & ! [Y4: nat] :
% 0.37/0.63 ( ( member_nat @ Y4 @ A4 )
% 0.37/0.63 => ( ( X4 != Y4 )
% 0.37/0.63 => ( ( F @ Y4 )
% 0.37/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_eq_1_iff
% 0.37/0.63 thf(fact_4757_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ I5 )
% 0.37/0.63 => ( ( member_VEBT_VEBT @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4758_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_real,I: real,F: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ I5 )
% 0.37/0.63 => ( ( member_real @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: real] :
% 0.37/0.63 ( ( member_real @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4759_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_int,I: int,F: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ I5 )
% 0.37/0.63 => ( ( member_int @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: int] :
% 0.37/0.63 ( ( member_int @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4760_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_complex,I: complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ I5 )
% 0.37/0.63 => ( ( member_complex @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: complex] :
% 0.37/0.63 ( ( member_complex @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4761_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_Code_integer,I: code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ I5 )
% 0.37/0.63 => ( ( member_Code_integer @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups1270011288395367621r_real @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4762_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ I5 )
% 0.37/0.63 => ( ( member_VEBT_VEBT @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4763_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_real,I: real,F: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ I5 )
% 0.37/0.63 => ( ( member_real @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: real] :
% 0.37/0.63 ( ( member_real @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4764_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_nat,I: nat,F: nat > rat] :
% 0.37/0.63 ( ( finite_finite_nat @ I5 )
% 0.37/0.63 => ( ( member_nat @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: nat] :
% 0.37/0.63 ( ( member_nat @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4765_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_int,I: int,F: int > rat] :
% 0.37/0.63 ( ( finite_finite_int @ I5 )
% 0.37/0.63 => ( ( member_int @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: int] :
% 0.37/0.63 ( ( member_int @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4766_sum__pos2,axiom,
% 0.37/0.63 ! [I5: set_complex,I: complex,F: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ I5 )
% 0.37/0.63 => ( ( member_complex @ I @ I5 )
% 0.37/0.63 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 0.37/0.63 => ( ! [I2: complex] :
% 0.37/0.63 ( ( member_complex @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos2
% 0.37/0.63 thf(fact_4767_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bo8194388402131092736T_VEBT )
% 0.37/0.63 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4768_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_real,F: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bot_set_real )
% 0.37/0.63 => ( ! [I2: real] :
% 0.37/0.63 ( ( member_real @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4769_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_complex,F: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bot_set_complex )
% 0.37/0.63 => ( ! [I2: complex] :
% 0.37/0.63 ( ( member_complex @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4770_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_Code_integer,F: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bo3990330152332043303nteger )
% 0.37/0.63 => ( ! [I2: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups1270011288395367621r_real @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4771_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_int,F: int > real] :
% 0.37/0.63 ( ( finite_finite_int @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bot_set_int )
% 0.37/0.63 => ( ! [I2: int] :
% 0.37/0.63 ( ( member_int @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4772_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_o,F: $o > real] :
% 0.37/0.63 ( ( finite_finite_o @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bot_set_o )
% 0.37/0.63 => ( ! [I2: $o] :
% 0.37/0.63 ( ( member_o @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4773_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bo8194388402131092736T_VEBT )
% 0.37/0.63 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4774_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_real,F: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bot_set_real )
% 0.37/0.63 => ( ! [I2: real] :
% 0.37/0.63 ( ( member_real @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4775_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_complex,F: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bot_set_complex )
% 0.37/0.63 => ( ! [I2: complex] :
% 0.37/0.63 ( ( member_complex @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4776_sum__pos,axiom,
% 0.37/0.63 ! [I5: set_Code_integer,F: code_integer > rat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ I5 )
% 0.37/0.63 => ( ( I5 != bot_bo3990330152332043303nteger )
% 0.37/0.63 => ( ! [I2: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ I2 @ I5 )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.63 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I5 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum_pos
% 0.37/0.63 thf(fact_4777_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups8325533452322294502uint32 @ G @ A4 )
% 0.37/0.63 = ( groups8325533452322294502uint32 @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups8325533452322294502uint32 @ G @ C3 )
% 0.37/0.63 = ( groups8325533452322294502uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4778_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_real,A4: set_real,B4: set_real,G: real > uint32,H2: real > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups5944083974425963860uint32 @ G @ A4 )
% 0.37/0.63 = ( groups5944083974425963860uint32 @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups5944083974425963860uint32 @ G @ C3 )
% 0.37/0.63 = ( groups5944083974425963860uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4779_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > uint32,H2: complex > uint32] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: complex] :
% 0.37/0.63 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups8736914816313324502uint32 @ G @ A4 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups8736914816313324502uint32 @ G @ C3 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4780_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > uint32,H2: code_integer > uint32] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups8847630953604152069uint32 @ G @ A4 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups8847630953604152069uint32 @ G @ C3 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4781_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups2240296850493347238T_real @ G @ A4 )
% 0.37/0.63 = ( groups2240296850493347238T_real @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups2240296850493347238T_real @ G @ C3 )
% 0.37/0.63 = ( groups2240296850493347238T_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4782_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_real,A4: set_real,B4: set_real,G: real > real,H2: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups8097168146408367636l_real @ G @ A4 )
% 0.37/0.63 = ( groups8097168146408367636l_real @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups8097168146408367636l_real @ G @ C3 )
% 0.37/0.63 = ( groups8097168146408367636l_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4783_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: complex] :
% 0.37/0.63 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups5808333547571424918x_real @ G @ A4 )
% 0.37/0.63 = ( groups5808333547571424918x_real @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups5808333547571424918x_real @ G @ C3 )
% 0.37/0.63 = ( groups5808333547571424918x_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4784_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups1270011288395367621r_real @ G @ A4 )
% 0.37/0.63 = ( groups1270011288395367621r_real @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups1270011288395367621r_real @ G @ C3 )
% 0.37/0.63 = ( groups1270011288395367621r_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4785_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( ( groups136491112297645522BT_rat @ G @ A4 )
% 0.37/0.63 = ( groups136491112297645522BT_rat @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups136491112297645522BT_rat @ G @ C3 )
% 0.37/0.63 = ( groups136491112297645522BT_rat @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4786_sum_Osame__carrier,axiom,
% 0.37/0.63 ! [C3: set_real,A4: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( ( groups1300246762558778688al_rat @ G @ A4 )
% 0.37/0.63 = ( groups1300246762558778688al_rat @ H2 @ B4 ) )
% 0.37/0.63 = ( ( groups1300246762558778688al_rat @ G @ C3 )
% 0.37/0.63 = ( groups1300246762558778688al_rat @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrier
% 0.37/0.63 thf(fact_4787_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups8325533452322294502uint32 @ G @ C3 )
% 0.37/0.63 = ( groups8325533452322294502uint32 @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ G @ A4 )
% 0.37/0.63 = ( groups8325533452322294502uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4788_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_real,A4: set_real,B4: set_real,G: real > uint32,H2: real > uint32] :
% 0.37/0.63 ( ( finite_finite_real @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups5944083974425963860uint32 @ G @ C3 )
% 0.37/0.63 = ( groups5944083974425963860uint32 @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups5944083974425963860uint32 @ G @ A4 )
% 0.37/0.63 = ( groups5944083974425963860uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4789_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > uint32,H2: complex > uint32] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: complex] :
% 0.37/0.63 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups8736914816313324502uint32 @ G @ C3 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups8736914816313324502uint32 @ G @ A4 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4790_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > uint32,H2: code_integer > uint32] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( ( groups8847630953604152069uint32 @ G @ C3 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups8847630953604152069uint32 @ G @ A4 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4791_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups2240296850493347238T_real @ G @ C3 )
% 0.37/0.63 = ( groups2240296850493347238T_real @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups2240296850493347238T_real @ G @ A4 )
% 0.37/0.63 = ( groups2240296850493347238T_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4792_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_real,A4: set_real,B4: set_real,G: real > real,H2: real > real] :
% 0.37/0.63 ( ( finite_finite_real @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups8097168146408367636l_real @ G @ C3 )
% 0.37/0.63 = ( groups8097168146408367636l_real @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups8097168146408367636l_real @ G @ A4 )
% 0.37/0.63 = ( groups8097168146408367636l_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4793_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: complex] :
% 0.37/0.63 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: complex] :
% 0.37/0.63 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups5808333547571424918x_real @ G @ C3 )
% 0.37/0.63 = ( groups5808333547571424918x_real @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 0.37/0.63 = ( groups5808333547571424918x_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4794_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ! [B3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( ( groups1270011288395367621r_real @ G @ C3 )
% 0.37/0.63 = ( groups1270011288395367621r_real @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 0.37/0.63 = ( groups1270011288395367621r_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4795_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( ( groups136491112297645522BT_rat @ G @ C3 )
% 0.37/0.63 = ( groups136491112297645522BT_rat @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups136491112297645522BT_rat @ G @ A4 )
% 0.37/0.63 = ( groups136491112297645522BT_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4796_sum_Osame__carrierI,axiom,
% 0.37/0.63 ! [C3: set_real,A4: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 0.37/0.63 ( ( finite_finite_real @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 0.37/0.63 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 0.37/0.63 => ( ! [A3: real] :
% 0.37/0.63 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 0.37/0.63 => ( ( G @ A3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ! [B3: real] :
% 0.37/0.63 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 0.37/0.63 => ( ( H2 @ B3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( ( groups1300246762558778688al_rat @ G @ C3 )
% 0.37/0.63 = ( groups1300246762558778688al_rat @ H2 @ C3 ) )
% 0.37/0.63 => ( ( groups1300246762558778688al_rat @ G @ A4 )
% 0.37/0.63 = ( groups1300246762558778688al_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.same_carrierI
% 0.37/0.63 thf(fact_4797_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > uint32] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( groups8736914816313324502uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4798_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > uint32] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( groups8847630953604152069uint32 @ G @ S3 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4799_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 0.37/0.63 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4800_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ S3 )
% 0.37/0.63 = ( groups1270011288395367621r_real @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4801_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( groups5058264527183730370ex_rat @ G @ S3 )
% 0.37/0.63 = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4802_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > rat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( groups6602215022474089585er_rat @ G @ S3 )
% 0.37/0.63 = ( groups6602215022474089585er_rat @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4803_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_nat ) )
% 0.37/0.63 => ( ( groups5693394587270226106ex_nat @ G @ S3 )
% 0.37/0.63 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4804_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > nat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_nat ) )
% 0.37/0.63 => ( ( groups7237345082560585321er_nat @ G @ S3 )
% 0.37/0.63 = ( groups7237345082560585321er_nat @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4805_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_int ) )
% 0.37/0.63 => ( ( groups5690904116761175830ex_int @ G @ S3 )
% 0.37/0.63 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4806_sum_Omono__neutral__left,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > int] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_int ) )
% 0.37/0.63 => ( ( groups7234854612051535045er_int @ G @ S3 )
% 0.37/0.63 = ( groups7234854612051535045er_int @ G @ T3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_left
% 0.37/0.63 thf(fact_4807_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > uint32] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( groups8736914816313324502uint32 @ G @ T3 )
% 0.37/0.63 = ( groups8736914816313324502uint32 @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4808_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > uint32] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ( groups8847630953604152069uint32 @ G @ T3 )
% 0.37/0.63 = ( groups8847630953604152069uint32 @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4809_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 0.37/0.63 = ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4810_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > real] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_real ) )
% 0.37/0.63 => ( ( groups1270011288395367621r_real @ G @ T3 )
% 0.37/0.63 = ( groups1270011288395367621r_real @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4811_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 0.37/0.63 = ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4812_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > rat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_rat ) )
% 0.37/0.63 => ( ( groups6602215022474089585er_rat @ G @ T3 )
% 0.37/0.63 = ( groups6602215022474089585er_rat @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4813_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_nat ) )
% 0.37/0.63 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 0.37/0.63 = ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4814_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > nat] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_nat ) )
% 0.37/0.63 => ( ( groups7237345082560585321er_nat @ G @ T3 )
% 0.37/0.63 = ( groups7237345082560585321er_nat @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4815_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 0.37/0.63 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.63 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: complex] :
% 0.37/0.63 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_int ) )
% 0.37/0.63 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 0.37/0.63 = ( groups5690904116761175830ex_int @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4816_sum_Omono__neutral__right,axiom,
% 0.37/0.63 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > int] :
% 0.37/0.63 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.63 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: code_integer] :
% 0.37/0.63 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = zero_zero_int ) )
% 0.37/0.63 => ( ( groups7234854612051535045er_int @ G @ T3 )
% 0.37/0.63 = ( groups7234854612051535045er_int @ G @ S3 ) ) ) ) ) ).
% 0.37/0.63
% 0.37/0.63 % sum.mono_neutral_right
% 0.37/0.63 thf(fact_4817_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.63 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > uint32,G: vEBT_VEBT > uint32] :
% 0.37/0.63 ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.63 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 0.37/0.63 => ( ( H2 @ X3 )
% 0.37/0.63 = zero_zero_uint32 ) )
% 0.37/0.63 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.63 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 0.37/0.63 => ( ( G @ X3 )
% 0.37/0.63 = ( H2 @ X3 ) ) )
% 0.37/0.63 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 0.37/0.64 = ( groups8325533452322294502uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4818_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_real,S3: set_real,H2: real > uint32,G: real > uint32] :
% 0.37/0.64 ( ( finite_finite_real @ T3 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_uint32 ) )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 0.37/0.64 = ( groups5944083974425963860uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4819_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_complex,S3: set_complex,H2: complex > uint32,G: complex > uint32] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_uint32 ) )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups8736914816313324502uint32 @ G @ S3 )
% 0.37/0.64 = ( groups8736914816313324502uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4820_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_Code_integer,S3: set_Code_integer,H2: code_integer > uint32,G: code_integer > uint32] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_uint32 ) )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups8847630953604152069uint32 @ G @ S3 )
% 0.37/0.64 = ( groups8847630953604152069uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4821_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups2240296850493347238T_real @ G @ S3 )
% 0.37/0.64 = ( groups2240296850493347238T_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4822_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_real,S3: set_real,H2: real > real,G: real > real] :
% 0.37/0.64 ( ( finite_finite_real @ T3 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups8097168146408367636l_real @ G @ S3 )
% 0.37/0.64 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4823_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 0.37/0.64 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4824_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_Code_integer,S3: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups1270011288395367621r_real @ G @ S3 )
% 0.37/0.64 = ( groups1270011288395367621r_real @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4825_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_rat ) )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups136491112297645522BT_rat @ G @ S3 )
% 0.37/0.64 = ( groups136491112297645522BT_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4826_sum_Omono__neutral__cong__left,axiom,
% 0.37/0.64 ! [T3: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 0.37/0.64 ( ( finite_finite_real @ T3 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 0.37/0.64 => ( ( H2 @ X3 )
% 0.37/0.64 = zero_zero_rat ) )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups1300246762558778688al_rat @ G @ S3 )
% 0.37/0.64 = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_left
% 0.37/0.64 thf(fact_4827_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_uint32 ) )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups8325533452322294502uint32 @ G @ T3 )
% 0.37/0.64 = ( groups8325533452322294502uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4828_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_real,S3: set_real,G: real > uint32,H2: real > uint32] :
% 0.37/0.64 ( ( finite_finite_real @ T3 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_uint32 ) )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups5944083974425963860uint32 @ G @ T3 )
% 0.37/0.64 = ( groups5944083974425963860uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4829_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_complex,S3: set_complex,G: complex > uint32,H2: complex > uint32] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_uint32 ) )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups8736914816313324502uint32 @ G @ T3 )
% 0.37/0.64 = ( groups8736914816313324502uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4830_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > uint32,H2: code_integer > uint32] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_uint32 ) )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups8847630953604152069uint32 @ G @ T3 )
% 0.37/0.64 = ( groups8847630953604152069uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4831_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups2240296850493347238T_real @ G @ T3 )
% 0.37/0.64 = ( groups2240296850493347238T_real @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4832_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_real,S3: set_real,G: real > real,H2: real > real] :
% 0.37/0.64 ( ( finite_finite_real @ T3 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 0.37/0.64 = ( groups8097168146408367636l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4833_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: complex] :
% 0.37/0.64 ( ( member_complex @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 0.37/0.64 = ( groups5808333547571424918x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4834_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_real ) )
% 0.37/0.64 => ( ! [X3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups1270011288395367621r_real @ G @ T3 )
% 0.37/0.64 = ( groups1270011288395367621r_real @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4835_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_rat ) )
% 0.37/0.64 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups136491112297645522BT_rat @ G @ T3 )
% 0.37/0.64 = ( groups136491112297645522BT_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4836_sum_Omono__neutral__cong__right,axiom,
% 0.37/0.64 ! [T3: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 0.37/0.64 ( ( finite_finite_real @ T3 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = zero_zero_rat ) )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( member_real @ X3 @ S3 )
% 0.37/0.64 => ( ( G @ X3 )
% 0.37/0.64 = ( H2 @ X3 ) ) )
% 0.37/0.64 => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 0.37/0.64 = ( groups1300246762558778688al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.mono_neutral_cong_right
% 0.37/0.64 thf(fact_4837_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_complex,A4: set_complex,G: complex > real] :
% 0.37/0.64 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 0.37/0.64 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5808333547571424918x_real @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4838_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > real] :
% 0.37/0.64 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 0.37/0.64 = ( plus_plus_real @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups1270011288395367621r_real @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4839_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_complex,A4: set_complex,G: complex > rat] :
% 0.37/0.64 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5058264527183730370ex_rat @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4840_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > rat] :
% 0.37/0.64 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups6602215022474089585er_rat @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4841_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_complex,A4: set_complex,G: complex > nat] :
% 0.37/0.64 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( groups5693394587270226106ex_nat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5693394587270226106ex_nat @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4842_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > nat] :
% 0.37/0.64 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( groups7237345082560585321er_nat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups7237345082560585321er_nat @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4843_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_complex,A4: set_complex,G: complex > int] :
% 0.37/0.64 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( groups5690904116761175830ex_int @ G @ A4 )
% 0.37/0.64 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5690904116761175830ex_int @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4844_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > int] :
% 0.37/0.64 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( groups7234854612051535045er_int @ G @ A4 )
% 0.37/0.64 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups7234854612051535045er_int @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4845_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_nat,A4: set_nat,G: nat > rat] :
% 0.37/0.64 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.64 => ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups2906978787729119204at_rat @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4846_sum_Osubset__diff,axiom,
% 0.37/0.64 ! [B4: set_nat,A4: set_nat,G: nat > int] :
% 0.37/0.64 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.64 => ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( groups3539618377306564664at_int @ G @ A4 )
% 0.37/0.64 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups3539618377306564664at_int @ G @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.subset_diff
% 0.37/0.64 thf(fact_4847_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_complex,B4: set_complex,F: complex > uint32] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( groups8736914816313324502uint32 @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_uint32 @ ( groups8736914816313324502uint32 @ F @ A4 ) @ ( groups8736914816313324502uint32 @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4848_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,B4: set_Code_integer,F: code_integer > uint32] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( groups8847630953604152069uint32 @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_uint32 @ ( groups8847630953604152069uint32 @ F @ A4 ) @ ( groups8847630953604152069uint32 @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4849_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_complex,B4: set_complex,F: complex > real] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4850_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,B4: set_Code_integer,F: code_integer > real] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4851_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_complex,B4: set_complex,F: complex > int] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ ( groups5690904116761175830ex_int @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4852_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,B4: set_Code_integer,F: code_integer > int] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_int @ ( groups7234854612051535045er_int @ F @ A4 ) @ ( groups7234854612051535045er_int @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4853_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_nat,B4: set_nat,F: nat > uint32] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.64 => ( ( groups833757482993574392uint32 @ F @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_uint32 @ ( groups833757482993574392uint32 @ F @ A4 ) @ ( groups833757482993574392uint32 @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4854_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_nat,B4: set_nat,F: nat > int] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.64 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4855_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_int,B4: set_int,F: int > uint32] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.37/0.64 => ( ( groups5712668689793887828uint32 @ F @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_uint32 @ ( groups5712668689793887828uint32 @ F @ A4 ) @ ( groups5712668689793887828uint32 @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4856_sum__diff,axiom,
% 0.37/0.64 ! [A4: set_int,B4: set_int,F: int > real] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.37/0.64 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff
% 0.37/0.64 thf(fact_4857_sum__diff__nat,axiom,
% 0.37/0.64 ! [B4: set_complex,A4: set_complex,F: complex > nat] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.64 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff_nat
% 0.37/0.64 thf(fact_4858_sum__diff__nat,axiom,
% 0.37/0.64 ! [B4: set_Code_integer,A4: set_Code_integer,F: code_integer > nat] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff_nat
% 0.37/0.64 thf(fact_4859_sum__diff__nat,axiom,
% 0.37/0.64 ! [B4: set_int,A4: set_int,F: int > nat] :
% 0.37/0.64 ( ( finite_finite_int @ B4 )
% 0.37/0.64 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.37/0.64 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff_nat
% 0.37/0.64 thf(fact_4860_sum__diff__nat,axiom,
% 0.37/0.64 ! [B4: set_nat,A4: set_nat,F: nat > nat] :
% 0.37/0.64 ( ( finite_finite_nat @ B4 )
% 0.37/0.64 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.64 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff_nat
% 0.37/0.64 thf(fact_4861_sum__diff1__nat,axiom,
% 0.37/0.64 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.64 ( ( ( member_VEBT_VEBT @ A @ A4 )
% 0.37/0.64 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.64 & ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 0.37/0.64 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.64 = ( groups771621172384141258BT_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff1_nat
% 0.37/0.64 thf(fact_4862_sum__diff1__nat,axiom,
% 0.37/0.64 ! [A: real,A4: set_real,F: real > nat] :
% 0.37/0.64 ( ( ( member_real @ A @ A4 )
% 0.37/0.64 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.64 & ( ~ ( member_real @ A @ A4 )
% 0.37/0.64 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.37/0.64 = ( groups1935376822645274424al_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff1_nat
% 0.37/0.64 thf(fact_4863_sum__diff1__nat,axiom,
% 0.37/0.64 ! [A: set_nat,A4: set_set_nat,F: set_nat > nat] :
% 0.37/0.64 ( ( ( member_set_nat @ A @ A4 )
% 0.37/0.64 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.64 & ( ~ ( member_set_nat @ A @ A4 )
% 0.37/0.64 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.37/0.64 = ( groups8294997508430121362at_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff1_nat
% 0.37/0.64 thf(fact_4864_sum__diff1__nat,axiom,
% 0.37/0.64 ! [A: int,A4: set_int,F: int > nat] :
% 0.37/0.64 ( ( ( member_int @ A @ A4 )
% 0.37/0.64 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.64 & ( ~ ( member_int @ A @ A4 )
% 0.37/0.64 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.37/0.64 = ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff1_nat
% 0.37/0.64 thf(fact_4865_sum__diff1__nat,axiom,
% 0.37/0.64 ! [A: $o,A4: set_o,F: $o > nat] :
% 0.37/0.64 ( ( ( member_o @ A @ A4 )
% 0.37/0.64 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.64 & ( ~ ( member_o @ A @ A4 )
% 0.37/0.64 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.37/0.64 = ( groups8507830703676809646_o_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff1_nat
% 0.37/0.64 thf(fact_4866_sum__diff1__nat,axiom,
% 0.37/0.64 ! [A: nat,A4: set_nat,F: nat > nat] :
% 0.37/0.64 ( ( ( member_nat @ A @ A4 )
% 0.37/0.64 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.37/0.64 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 0.37/0.64 & ( ~ ( member_nat @ A @ A4 )
% 0.37/0.64 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.37/0.64 = ( groups3542108847815614940at_nat @ F @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_diff1_nat
% 0.37/0.64 thf(fact_4867_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( groups2240296850493347238T_real @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4868_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_real,A4: set_real,F: real > real] :
% 0.37/0.64 ( ( finite_finite_real @ B4 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: real] :
% 0.37/0.64 ( ( member_real @ B3 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4869_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_complex,A4: set_complex,F: complex > real] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: complex] :
% 0.37/0.64 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4870_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_Code_integer,A4: set_Code_integer,F: code_integer > real] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4871_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ ( groups136491112297645522BT_rat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4872_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_real,A4: set_real,F: real > rat] :
% 0.37/0.64 ( ( finite_finite_real @ B4 )
% 0.37/0.64 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: real] :
% 0.37/0.64 ( ( member_real @ B3 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4873_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_complex,A4: set_complex,F: complex > rat] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.64 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: complex] :
% 0.37/0.64 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4874_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_Code_integer,A4: set_Code_integer,F: code_integer > rat] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: code_integer] :
% 0.37/0.64 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4875_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_nat,A4: set_nat,F: nat > rat] :
% 0.37/0.64 ( ( finite_finite_nat @ B4 )
% 0.37/0.64 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: nat] :
% 0.37/0.64 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4876_sum__mono2,axiom,
% 0.37/0.64 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ B4 )
% 0.37/0.64 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 0.37/0.64 => ( ! [B3: vEBT_VEBT] :
% 0.37/0.64 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 0.37/0.64 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 0.37/0.64 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( groups771621172384141258BT_nat @ F @ B4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum_mono2
% 0.37/0.64 thf(fact_4877_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.64 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.64 => ( ( groups2240296850493347238T_real @ G @ A4 )
% 0.37/0.64 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4878_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_real,X: real,G: real > real] :
% 0.37/0.64 ( ( finite_finite_real @ A4 )
% 0.37/0.64 => ( ( member_real @ X @ A4 )
% 0.37/0.64 => ( ( groups8097168146408367636l_real @ G @ A4 )
% 0.37/0.64 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4879_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_complex,X: complex,G: complex > real] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( member_complex @ X @ A4 )
% 0.37/0.64 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 0.37/0.64 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4880_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,X: code_integer,G: code_integer > real] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.64 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 0.37/0.64 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4881_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.64 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.64 => ( ( groups136491112297645522BT_rat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4882_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_real,X: real,G: real > rat] :
% 0.37/0.64 ( ( finite_finite_real @ A4 )
% 0.37/0.64 => ( ( member_real @ X @ A4 )
% 0.37/0.64 => ( ( groups1300246762558778688al_rat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4883_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_complex,X: complex,G: complex > rat] :
% 0.37/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.64 => ( ( member_complex @ X @ A4 )
% 0.37/0.64 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4884_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.64 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4885_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 0.37/0.64 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.64 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.64 => ( ( groups771621172384141258BT_nat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4886_sum_Oremove,axiom,
% 0.37/0.64 ! [A4: set_real,X: real,G: real > nat] :
% 0.37/0.64 ( ( finite_finite_real @ A4 )
% 0.37/0.64 => ( ( member_real @ X @ A4 )
% 0.37/0.64 => ( ( groups1935376822645274424al_nat @ G @ A4 )
% 0.37/0.64 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sum.remove
% 0.37/0.64 thf(fact_4887_max__idx__list,axiom,
% 0.37/0.64 ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 0.37/0.64 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 0.37/0.64 => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_idx_list
% 0.37/0.64 thf(fact_4888_cnt__non__neg,axiom,
% 0.37/0.64 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ zero_zero_real @ ( vEBT_VEBT_cnt @ T ) ) ).
% 0.37/0.64
% 0.37/0.64 % cnt_non_neg
% 0.37/0.64 thf(fact_4889_height__i__max,axiom,
% 0.37/0.64 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 0.37/0.64 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 0.37/0.64 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % height_i_max
% 0.37/0.64 thf(fact_4890_Bolzano,axiom,
% 0.37/0.64 ! [A: real,B: real,P2: real > real > $o] :
% 0.37/0.64 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.64 => ( ! [A3: real,B3: real,C: real] :
% 0.37/0.64 ( ( P2 @ A3 @ B3 )
% 0.37/0.64 => ( ( P2 @ B3 @ C )
% 0.37/0.64 => ( ( ord_less_eq_real @ A3 @ B3 )
% 0.37/0.64 => ( ( ord_less_eq_real @ B3 @ C )
% 0.37/0.64 => ( P2 @ A3 @ C ) ) ) ) )
% 0.37/0.64 => ( ! [X3: real] :
% 0.37/0.64 ( ( ord_less_eq_real @ A @ X3 )
% 0.37/0.64 => ( ( ord_less_eq_real @ X3 @ B )
% 0.37/0.64 => ? [D3: real] :
% 0.37/0.64 ( ( ord_less_real @ zero_zero_real @ D3 )
% 0.37/0.64 & ! [A3: real,B3: real] :
% 0.37/0.64 ( ( ( ord_less_eq_real @ A3 @ X3 )
% 0.37/0.64 & ( ord_less_eq_real @ X3 @ B3 )
% 0.37/0.64 & ( ord_less_real @ ( minus_minus_real @ B3 @ A3 ) @ D3 ) )
% 0.37/0.64 => ( P2 @ A3 @ B3 ) ) ) ) )
% 0.37/0.64 => ( P2 @ A @ B ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Bolzano
% 0.37/0.64 thf(fact_4891_option_Osize_I3_J,axiom,
% 0.37/0.64 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 0.37/0.64 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size(3)
% 0.37/0.64 thf(fact_4892_option_Osize_I3_J,axiom,
% 0.37/0.64 ( ( size_size_option_nat @ none_nat )
% 0.37/0.64 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size(3)
% 0.37/0.64 thf(fact_4893_option_Osize_I4_J,axiom,
% 0.37/0.64 ! [X2: product_prod_nat_nat] :
% 0.37/0.64 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 0.37/0.64 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size(4)
% 0.37/0.64 thf(fact_4894_option_Osize_I4_J,axiom,
% 0.37/0.64 ! [X2: nat] :
% 0.37/0.64 ( ( size_size_option_nat @ ( some_nat @ X2 ) )
% 0.37/0.64 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size(4)
% 0.37/0.64 thf(fact_4895_max__bot,axiom,
% 0.37/0.64 ! [X: set_nat] :
% 0.37/0.64 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot
% 0.37/0.64 thf(fact_4896_max__bot,axiom,
% 0.37/0.64 ! [X: assn] :
% 0.37/0.64 ( ( ord_max_assn @ bot_bot_assn @ X )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot
% 0.37/0.64 thf(fact_4897_max__bot,axiom,
% 0.37/0.64 ! [X: set_int] :
% 0.37/0.64 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot
% 0.37/0.64 thf(fact_4898_max__bot,axiom,
% 0.37/0.64 ! [X: set_o] :
% 0.37/0.64 ( ( ord_max_set_o @ bot_bot_set_o @ X )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot
% 0.37/0.64 thf(fact_4899_max__bot,axiom,
% 0.37/0.64 ! [X: nat] :
% 0.37/0.64 ( ( ord_max_nat @ bot_bot_nat @ X )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot
% 0.37/0.64 thf(fact_4900_max__bot2,axiom,
% 0.37/0.64 ! [X: set_nat] :
% 0.37/0.64 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot2
% 0.37/0.64 thf(fact_4901_max__bot2,axiom,
% 0.37/0.64 ! [X: assn] :
% 0.37/0.64 ( ( ord_max_assn @ X @ bot_bot_assn )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot2
% 0.37/0.64 thf(fact_4902_max__bot2,axiom,
% 0.37/0.64 ! [X: set_int] :
% 0.37/0.64 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot2
% 0.37/0.64 thf(fact_4903_max__bot2,axiom,
% 0.37/0.64 ! [X: set_o] :
% 0.37/0.64 ( ( ord_max_set_o @ X @ bot_bot_set_o )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot2
% 0.37/0.64 thf(fact_4904_max__bot2,axiom,
% 0.37/0.64 ! [X: nat] :
% 0.37/0.64 ( ( ord_max_nat @ X @ bot_bot_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % max_bot2
% 0.37/0.64 thf(fact_4905_max__Suc__Suc,axiom,
% 0.37/0.64 ! [M: nat,N: nat] :
% 0.37/0.64 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.37/0.64 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_Suc_Suc
% 0.37/0.64 thf(fact_4906_max__nat_Oeq__neutr__iff,axiom,
% 0.37/0.64 ! [A: nat,B: nat] :
% 0.37/0.64 ( ( ( ord_max_nat @ A @ B )
% 0.37/0.64 = zero_zero_nat )
% 0.37/0.64 = ( ( A = zero_zero_nat )
% 0.37/0.64 & ( B = zero_zero_nat ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_nat.eq_neutr_iff
% 0.37/0.64 thf(fact_4907_max__nat_Oleft__neutral,axiom,
% 0.37/0.64 ! [A: nat] :
% 0.37/0.64 ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.37/0.64 = A ) ).
% 0.37/0.64
% 0.37/0.64 % max_nat.left_neutral
% 0.37/0.64 thf(fact_4908_max__nat_Oneutr__eq__iff,axiom,
% 0.37/0.64 ! [A: nat,B: nat] :
% 0.37/0.64 ( ( zero_zero_nat
% 0.37/0.64 = ( ord_max_nat @ A @ B ) )
% 0.37/0.64 = ( ( A = zero_zero_nat )
% 0.37/0.64 & ( B = zero_zero_nat ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_nat.neutr_eq_iff
% 0.37/0.64 thf(fact_4909_max__nat_Oright__neutral,axiom,
% 0.37/0.64 ! [A: nat] :
% 0.37/0.64 ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.37/0.64 = A ) ).
% 0.37/0.64
% 0.37/0.64 % max_nat.right_neutral
% 0.37/0.64 thf(fact_4910_max__0L,axiom,
% 0.37/0.64 ! [N: nat] :
% 0.37/0.64 ( ( ord_max_nat @ zero_zero_nat @ N )
% 0.37/0.64 = N ) ).
% 0.37/0.64
% 0.37/0.64 % max_0L
% 0.37/0.64 thf(fact_4911_max__0R,axiom,
% 0.37/0.64 ! [N: nat] :
% 0.37/0.64 ( ( ord_max_nat @ N @ zero_zero_nat )
% 0.37/0.64 = N ) ).
% 0.37/0.64
% 0.37/0.64 % max_0R
% 0.37/0.64 thf(fact_4912_max__0__1_I2_J,axiom,
% 0.37/0.64 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 0.37/0.64 = one_one_real ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(2)
% 0.37/0.64 thf(fact_4913_max__0__1_I2_J,axiom,
% 0.37/0.64 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 0.37/0.64 = one_one_rat ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(2)
% 0.37/0.64 thf(fact_4914_max__0__1_I2_J,axiom,
% 0.37/0.64 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 0.37/0.64 = one_one_nat ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(2)
% 0.37/0.64 thf(fact_4915_max__0__1_I2_J,axiom,
% 0.37/0.64 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 0.37/0.64 = one_one_Code_integer ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(2)
% 0.37/0.64 thf(fact_4916_max__0__1_I2_J,axiom,
% 0.37/0.64 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 0.37/0.64 = one_one_int ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(2)
% 0.37/0.64 thf(fact_4917_max__0__1_I1_J,axiom,
% 0.37/0.64 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 0.37/0.64 = one_one_real ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(1)
% 0.37/0.64 thf(fact_4918_max__0__1_I1_J,axiom,
% 0.37/0.64 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 0.37/0.64 = one_one_rat ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(1)
% 0.37/0.64 thf(fact_4919_max__0__1_I1_J,axiom,
% 0.37/0.64 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 0.37/0.64 = one_one_nat ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(1)
% 0.37/0.64 thf(fact_4920_max__0__1_I1_J,axiom,
% 0.37/0.64 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 0.37/0.64 = one_one_Code_integer ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(1)
% 0.37/0.64 thf(fact_4921_max__0__1_I1_J,axiom,
% 0.37/0.64 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 0.37/0.64 = one_one_int ) ).
% 0.37/0.64
% 0.37/0.64 % max_0_1(1)
% 0.37/0.64 thf(fact_4922_Max__insert,axiom,
% 0.37/0.64 ! [A4: set_o,X: $o] :
% 0.37/0.64 ( ( finite_finite_o @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_o )
% 0.37/0.64 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max_insert
% 0.37/0.64 thf(fact_4923_Max__insert,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max_insert
% 0.37/0.64 thf(fact_4924_Max__insert,axiom,
% 0.37/0.64 ! [A4: set_int,X: int] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_int )
% 0.37/0.64 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max_insert
% 0.37/0.64 thf(fact_4925_Max__insert,axiom,
% 0.37/0.64 ! [A4: set_nat,X: nat] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.64 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max_insert
% 0.37/0.64 thf(fact_4926_max__def,axiom,
% 0.37/0.64 ( ord_max_Code_integer
% 0.37/0.64 = ( ^ [A7: code_integer,B7: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_def
% 0.37/0.64 thf(fact_4927_max__def,axiom,
% 0.37/0.64 ( ord_max_set_int
% 0.37/0.64 = ( ^ [A7: set_int,B7: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_def
% 0.37/0.64 thf(fact_4928_max__def,axiom,
% 0.37/0.64 ( ord_max_rat
% 0.37/0.64 = ( ^ [A7: rat,B7: rat] : ( if_rat @ ( ord_less_eq_rat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_def
% 0.37/0.64 thf(fact_4929_max__def,axiom,
% 0.37/0.64 ( ord_max_num
% 0.37/0.64 = ( ^ [A7: num,B7: num] : ( if_num @ ( ord_less_eq_num @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_def
% 0.37/0.64 thf(fact_4930_max__def,axiom,
% 0.37/0.64 ( ord_max_nat
% 0.37/0.64 = ( ^ [A7: nat,B7: nat] : ( if_nat @ ( ord_less_eq_nat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_def
% 0.37/0.64 thf(fact_4931_max__def,axiom,
% 0.37/0.64 ( ord_max_int
% 0.37/0.64 = ( ^ [A7: int,B7: int] : ( if_int @ ( ord_less_eq_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_def
% 0.37/0.64 thf(fact_4932_max__absorb1,axiom,
% 0.37/0.64 ! [Y: code_integer,X: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ Y @ X )
% 0.37/0.64 => ( ( ord_max_Code_integer @ X @ Y )
% 0.37/0.64 = X ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb1
% 0.37/0.64 thf(fact_4933_max__absorb1,axiom,
% 0.37/0.64 ! [Y: set_int,X: set_int] :
% 0.37/0.64 ( ( ord_less_eq_set_int @ Y @ X )
% 0.37/0.64 => ( ( ord_max_set_int @ X @ Y )
% 0.37/0.64 = X ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb1
% 0.37/0.64 thf(fact_4934_max__absorb1,axiom,
% 0.37/0.64 ! [Y: rat,X: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ Y @ X )
% 0.37/0.64 => ( ( ord_max_rat @ X @ Y )
% 0.37/0.64 = X ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb1
% 0.37/0.64 thf(fact_4935_max__absorb1,axiom,
% 0.37/0.64 ! [Y: num,X: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ Y @ X )
% 0.37/0.64 => ( ( ord_max_num @ X @ Y )
% 0.37/0.64 = X ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb1
% 0.37/0.64 thf(fact_4936_max__absorb1,axiom,
% 0.37/0.64 ! [Y: nat,X: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ Y @ X )
% 0.37/0.64 => ( ( ord_max_nat @ X @ Y )
% 0.37/0.64 = X ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb1
% 0.37/0.64 thf(fact_4937_max__absorb1,axiom,
% 0.37/0.64 ! [Y: int,X: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ Y @ X )
% 0.37/0.64 => ( ( ord_max_int @ X @ Y )
% 0.37/0.64 = X ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb1
% 0.37/0.64 thf(fact_4938_max__absorb2,axiom,
% 0.37/0.64 ! [X: code_integer,Y: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 0.37/0.64 => ( ( ord_max_Code_integer @ X @ Y )
% 0.37/0.64 = Y ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb2
% 0.37/0.64 thf(fact_4939_max__absorb2,axiom,
% 0.37/0.64 ! [X: set_int,Y: set_int] :
% 0.37/0.64 ( ( ord_less_eq_set_int @ X @ Y )
% 0.37/0.64 => ( ( ord_max_set_int @ X @ Y )
% 0.37/0.64 = Y ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb2
% 0.37/0.64 thf(fact_4940_max__absorb2,axiom,
% 0.37/0.64 ! [X: rat,Y: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ X @ Y )
% 0.37/0.64 => ( ( ord_max_rat @ X @ Y )
% 0.37/0.64 = Y ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb2
% 0.37/0.64 thf(fact_4941_max__absorb2,axiom,
% 0.37/0.64 ! [X: num,Y: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ X @ Y )
% 0.37/0.64 => ( ( ord_max_num @ X @ Y )
% 0.37/0.64 = Y ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb2
% 0.37/0.64 thf(fact_4942_max__absorb2,axiom,
% 0.37/0.64 ! [X: nat,Y: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ X @ Y )
% 0.37/0.64 => ( ( ord_max_nat @ X @ Y )
% 0.37/0.64 = Y ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb2
% 0.37/0.64 thf(fact_4943_max__absorb2,axiom,
% 0.37/0.64 ! [X: int,Y: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ X @ Y )
% 0.37/0.64 => ( ( ord_max_int @ X @ Y )
% 0.37/0.64 = Y ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_absorb2
% 0.37/0.64 thf(fact_4944_max__add__distrib__right,axiom,
% 0.37/0.64 ! [X: real,Y: real,Z: real] :
% 0.37/0.64 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 0.37/0.64 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_right
% 0.37/0.64 thf(fact_4945_max__add__distrib__right,axiom,
% 0.37/0.64 ! [X: rat,Y: rat,Z: rat] :
% 0.37/0.64 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 0.37/0.64 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_right
% 0.37/0.64 thf(fact_4946_max__add__distrib__right,axiom,
% 0.37/0.64 ! [X: nat,Y: nat,Z: nat] :
% 0.37/0.64 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 0.37/0.64 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_right
% 0.37/0.64 thf(fact_4947_max__add__distrib__right,axiom,
% 0.37/0.64 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.37/0.64 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 0.37/0.64 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_right
% 0.37/0.64 thf(fact_4948_max__add__distrib__right,axiom,
% 0.37/0.64 ! [X: int,Y: int,Z: int] :
% 0.37/0.64 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 0.37/0.64 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_right
% 0.37/0.64 thf(fact_4949_max__add__distrib__left,axiom,
% 0.37/0.64 ! [X: real,Y: real,Z: real] :
% 0.37/0.64 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_left
% 0.37/0.64 thf(fact_4950_max__add__distrib__left,axiom,
% 0.37/0.64 ! [X: rat,Y: rat,Z: rat] :
% 0.37/0.64 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_left
% 0.37/0.64 thf(fact_4951_max__add__distrib__left,axiom,
% 0.37/0.64 ! [X: nat,Y: nat,Z: nat] :
% 0.37/0.64 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_left
% 0.37/0.64 thf(fact_4952_max__add__distrib__left,axiom,
% 0.37/0.64 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.37/0.64 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_left
% 0.37/0.64 thf(fact_4953_max__add__distrib__left,axiom,
% 0.37/0.64 ! [X: int,Y: int,Z: int] :
% 0.37/0.64 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_add_distrib_left
% 0.37/0.64 thf(fact_4954_max__diff__distrib__left,axiom,
% 0.37/0.64 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.37/0.64 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_diff_distrib_left
% 0.37/0.64 thf(fact_4955_max__diff__distrib__left,axiom,
% 0.37/0.64 ! [X: real,Y: real,Z: real] :
% 0.37/0.64 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_diff_distrib_left
% 0.37/0.64 thf(fact_4956_max__diff__distrib__left,axiom,
% 0.37/0.64 ! [X: int,Y: int,Z: int] :
% 0.37/0.64 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.37/0.64 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_diff_distrib_left
% 0.37/0.64 thf(fact_4957_nat__add__max__right,axiom,
% 0.37/0.64 ! [M: nat,N: nat,Q3: nat] :
% 0.37/0.64 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 0.37/0.64 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nat_add_max_right
% 0.37/0.64 thf(fact_4958_nat__add__max__left,axiom,
% 0.37/0.64 ! [M: nat,N: nat,Q3: nat] :
% 0.37/0.64 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 0.37/0.64 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nat_add_max_left
% 0.37/0.64 thf(fact_4959_nat__mult__max__right,axiom,
% 0.37/0.64 ! [M: nat,N: nat,Q3: nat] :
% 0.37/0.64 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 0.37/0.64 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nat_mult_max_right
% 0.37/0.64 thf(fact_4960_nat__mult__max__left,axiom,
% 0.37/0.64 ! [M: nat,N: nat,Q3: nat] :
% 0.37/0.64 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 0.37/0.64 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nat_mult_max_left
% 0.37/0.64 thf(fact_4961_nat__minus__add__max,axiom,
% 0.37/0.64 ! [N: nat,M: nat] :
% 0.37/0.64 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 0.37/0.64 = ( ord_max_nat @ N @ M ) ) ).
% 0.37/0.64
% 0.37/0.64 % nat_minus_add_max
% 0.37/0.64 thf(fact_4962_Max_Oin__idem,axiom,
% 0.37/0.64 ! [A4: set_real,X: real] :
% 0.37/0.64 ( ( finite_finite_real @ A4 )
% 0.37/0.64 => ( ( member_real @ X @ A4 )
% 0.37/0.64 => ( ( ord_max_real @ X @ ( lattic4275903605611617917x_real @ A4 ) )
% 0.37/0.64 = ( lattic4275903605611617917x_real @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.in_idem
% 0.37/0.64 thf(fact_4963_Max_Oin__idem,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.64 => ( ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A4 ) )
% 0.37/0.64 = ( lattic4901227151466704046nteger @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.in_idem
% 0.37/0.64 thf(fact_4964_Max_Oin__idem,axiom,
% 0.37/0.64 ! [A4: set_int,X: int] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( member_int @ X @ A4 )
% 0.37/0.64 => ( ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) )
% 0.37/0.64 = ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.in_idem
% 0.37/0.64 thf(fact_4965_Max_Oin__idem,axiom,
% 0.37/0.64 ! [A4: set_nat,X: nat] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( member_nat @ X @ A4 )
% 0.37/0.64 => ( ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 0.37/0.64 = ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.in_idem
% 0.37/0.64 thf(fact_4966_VEBT__internal_Ocnt_Osimps_I1_J,axiom,
% 0.37/0.64 ! [A: $o,B: $o] :
% 0.37/0.64 ( ( vEBT_VEBT_cnt @ ( vEBT_Leaf @ A @ B ) )
% 0.37/0.64 = one_one_real ) ).
% 0.37/0.64
% 0.37/0.64 % VEBT_internal.cnt.simps(1)
% 0.37/0.64 thf(fact_4967_hom__Max__commute,axiom,
% 0.37/0.64 ! [H2: $o > $o,N8: set_o] :
% 0.37/0.64 ( ! [X3: $o,Y3: $o] :
% 0.37/0.64 ( ( H2 @ ( ord_max_o @ X3 @ Y3 ) )
% 0.37/0.64 = ( ord_max_o @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 0.37/0.64 => ( ( finite_finite_o @ N8 )
% 0.37/0.64 => ( ( N8 != bot_bot_set_o )
% 0.37/0.64 => ( ( H2 @ ( lattic1921953407002678535_Max_o @ N8 ) )
% 0.37/0.64 = ( lattic1921953407002678535_Max_o @ ( image_o_o @ H2 @ N8 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % hom_Max_commute
% 0.37/0.64 thf(fact_4968_hom__Max__commute,axiom,
% 0.37/0.64 ! [H2: code_integer > code_integer,N8: set_Code_integer] :
% 0.37/0.64 ( ! [X3: code_integer,Y3: code_integer] :
% 0.37/0.64 ( ( H2 @ ( ord_max_Code_integer @ X3 @ Y3 ) )
% 0.37/0.64 = ( ord_max_Code_integer @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 0.37/0.64 => ( ( finite6017078050557962740nteger @ N8 )
% 0.37/0.64 => ( ( N8 != bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( H2 @ ( lattic4901227151466704046nteger @ N8 ) )
% 0.37/0.64 = ( lattic4901227151466704046nteger @ ( image_4470545334726330049nteger @ H2 @ N8 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % hom_Max_commute
% 0.37/0.64 thf(fact_4969_hom__Max__commute,axiom,
% 0.37/0.64 ! [H2: int > int,N8: set_int] :
% 0.37/0.64 ( ! [X3: int,Y3: int] :
% 0.37/0.64 ( ( H2 @ ( ord_max_int @ X3 @ Y3 ) )
% 0.37/0.64 = ( ord_max_int @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 0.37/0.64 => ( ( finite_finite_int @ N8 )
% 0.37/0.64 => ( ( N8 != bot_bot_set_int )
% 0.37/0.64 => ( ( H2 @ ( lattic8263393255366662781ax_int @ N8 ) )
% 0.37/0.64 = ( lattic8263393255366662781ax_int @ ( image_int_int @ H2 @ N8 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % hom_Max_commute
% 0.37/0.64 thf(fact_4970_hom__Max__commute,axiom,
% 0.37/0.64 ! [H2: nat > nat,N8: set_nat] :
% 0.37/0.64 ( ! [X3: nat,Y3: nat] :
% 0.37/0.64 ( ( H2 @ ( ord_max_nat @ X3 @ Y3 ) )
% 0.37/0.64 = ( ord_max_nat @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 0.37/0.64 => ( ( finite_finite_nat @ N8 )
% 0.37/0.64 => ( ( N8 != bot_bot_set_nat )
% 0.37/0.64 => ( ( H2 @ ( lattic8265883725875713057ax_nat @ N8 ) )
% 0.37/0.64 = ( lattic8265883725875713057ax_nat @ ( image_nat_nat @ H2 @ N8 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % hom_Max_commute
% 0.37/0.64 thf(fact_4971_Max_Osubset,axiom,
% 0.37/0.64 ! [A4: set_o,B4: set_o] :
% 0.37/0.64 ( ( finite_finite_o @ A4 )
% 0.37/0.64 => ( ( B4 != bot_bot_set_o )
% 0.37/0.64 => ( ( ord_less_eq_set_o @ B4 @ A4 )
% 0.37/0.64 => ( ( ord_max_o @ ( lattic1921953407002678535_Max_o @ B4 ) @ ( lattic1921953407002678535_Max_o @ A4 ) )
% 0.37/0.64 = ( lattic1921953407002678535_Max_o @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.subset
% 0.37/0.64 thf(fact_4972_Max_Osubset,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( B4 != bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 0.37/0.64 => ( ( ord_max_Code_integer @ ( lattic4901227151466704046nteger @ B4 ) @ ( lattic4901227151466704046nteger @ A4 ) )
% 0.37/0.64 = ( lattic4901227151466704046nteger @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.subset
% 0.37/0.64 thf(fact_4973_Max_Osubset,axiom,
% 0.37/0.64 ! [A4: set_int,B4: set_int] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( B4 != bot_bot_set_int )
% 0.37/0.64 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.37/0.64 => ( ( ord_max_int @ ( lattic8263393255366662781ax_int @ B4 ) @ ( lattic8263393255366662781ax_int @ A4 ) )
% 0.37/0.64 = ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.subset
% 0.37/0.64 thf(fact_4974_Max_Osubset,axiom,
% 0.37/0.64 ! [A4: set_nat,B4: set_nat] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( B4 != bot_bot_set_nat )
% 0.37/0.64 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.64 => ( ( ord_max_nat @ ( lattic8265883725875713057ax_nat @ B4 ) @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 0.37/0.64 = ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.subset
% 0.37/0.64 thf(fact_4975_Max_Oclosed,axiom,
% 0.37/0.64 ! [A4: set_real] :
% 0.37/0.64 ( ( finite_finite_real @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_real )
% 0.37/0.64 => ( ! [X3: real,Y3: real] : ( member_real @ ( ord_max_real @ X3 @ Y3 ) @ ( insert_real @ X3 @ ( insert_real @ Y3 @ bot_bot_set_real ) ) )
% 0.37/0.64 => ( member_real @ ( lattic4275903605611617917x_real @ A4 ) @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.closed
% 0.37/0.64 thf(fact_4976_Max_Oclosed,axiom,
% 0.37/0.64 ! [A4: set_o] :
% 0.37/0.64 ( ( finite_finite_o @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_o )
% 0.37/0.64 => ( ! [X3: $o,Y3: $o] : ( member_o @ ( ord_max_o @ X3 @ Y3 ) @ ( insert_o @ X3 @ ( insert_o @ Y3 @ bot_bot_set_o ) ) )
% 0.37/0.64 => ( member_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.closed
% 0.37/0.64 thf(fact_4977_Max_Oclosed,axiom,
% 0.37/0.64 ! [A4: set_Code_integer] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ! [X3: code_integer,Y3: code_integer] : ( member_Code_integer @ ( ord_max_Code_integer @ X3 @ Y3 ) @ ( insert_Code_integer @ X3 @ ( insert_Code_integer @ Y3 @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.64 => ( member_Code_integer @ ( lattic4901227151466704046nteger @ A4 ) @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.closed
% 0.37/0.64 thf(fact_4978_Max_Oclosed,axiom,
% 0.37/0.64 ! [A4: set_int] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_int )
% 0.37/0.64 => ( ! [X3: int,Y3: int] : ( member_int @ ( ord_max_int @ X3 @ Y3 ) @ ( insert_int @ X3 @ ( insert_int @ Y3 @ bot_bot_set_int ) ) )
% 0.37/0.64 => ( member_int @ ( lattic8263393255366662781ax_int @ A4 ) @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.closed
% 0.37/0.64 thf(fact_4979_Max_Oclosed,axiom,
% 0.37/0.64 ! [A4: set_nat] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.64 => ( ! [X3: nat,Y3: nat] : ( member_nat @ ( ord_max_nat @ X3 @ Y3 ) @ ( insert_nat @ X3 @ ( insert_nat @ Y3 @ bot_bot_set_nat ) ) )
% 0.37/0.64 => ( member_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ A4 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.closed
% 0.37/0.64 thf(fact_4980_Max_Oinsert__not__elem,axiom,
% 0.37/0.64 ! [A4: set_real,X: real] :
% 0.37/0.64 ( ( finite_finite_real @ A4 )
% 0.37/0.64 => ( ~ ( member_real @ X @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_real )
% 0.37/0.64 => ( ( lattic4275903605611617917x_real @ ( insert_real @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_real @ X @ ( lattic4275903605611617917x_real @ A4 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_not_elem
% 0.37/0.64 thf(fact_4981_Max_Oinsert__not__elem,axiom,
% 0.37/0.64 ! [A4: set_o,X: $o] :
% 0.37/0.64 ( ( finite_finite_o @ A4 )
% 0.37/0.64 => ( ~ ( member_o @ X @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_o )
% 0.37/0.64 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_not_elem
% 0.37/0.64 thf(fact_4982_Max_Oinsert__not__elem,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ~ ( member_Code_integer @ X @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_not_elem
% 0.37/0.64 thf(fact_4983_Max_Oinsert__not__elem,axiom,
% 0.37/0.64 ! [A4: set_int,X: int] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ~ ( member_int @ X @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_int )
% 0.37/0.64 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_not_elem
% 0.37/0.64 thf(fact_4984_Max_Oinsert__not__elem,axiom,
% 0.37/0.64 ! [A4: set_nat,X: nat] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ~ ( member_nat @ X @ A4 )
% 0.37/0.64 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.64 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_not_elem
% 0.37/0.64 thf(fact_4985_Max_Oinsert__remove,axiom,
% 0.37/0.64 ! [A4: set_o,X: $o] :
% 0.37/0.64 ( ( finite_finite_o @ A4 )
% 0.37/0.64 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A4 ) )
% 0.37/0.64 = ( ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.37/0.64 = bot_bot_set_o )
% 0.37/0.64 => X )
% 0.37/0.64 & ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.37/0.64 != bot_bot_set_o )
% 0.37/0.64 => ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_remove
% 0.37/0.64 thf(fact_4986_Max_Oinsert__remove,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 0.37/0.64 = bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.64 = X ) )
% 0.37/0.64 & ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 0.37/0.64 != bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_remove
% 0.37/0.64 thf(fact_4987_Max_Oinsert__remove,axiom,
% 0.37/0.64 ! [A4: set_int,X: int] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.37/0.64 = bot_bot_set_int )
% 0.37/0.64 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.64 = X ) )
% 0.37/0.64 & ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.37/0.64 != bot_bot_set_int )
% 0.37/0.64 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_remove
% 0.37/0.64 thf(fact_4988_Max_Oinsert__remove,axiom,
% 0.37/0.64 ! [A4: set_nat,X: nat] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.37/0.64 = bot_bot_set_nat )
% 0.37/0.64 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.64 = X ) )
% 0.37/0.64 & ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.37/0.64 != bot_bot_set_nat )
% 0.37/0.64 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 0.37/0.64 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.insert_remove
% 0.37/0.64 thf(fact_4989_Max_Oremove,axiom,
% 0.37/0.64 ! [A4: set_real,X: real] :
% 0.37/0.64 ( ( finite_finite_real @ A4 )
% 0.37/0.64 => ( ( member_real @ X @ A4 )
% 0.37/0.64 => ( ( ( ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.37/0.64 = bot_bot_set_real )
% 0.37/0.64 => ( ( lattic4275903605611617917x_real @ A4 )
% 0.37/0.64 = X ) )
% 0.37/0.64 & ( ( ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.37/0.64 != bot_bot_set_real )
% 0.37/0.64 => ( ( lattic4275903605611617917x_real @ A4 )
% 0.37/0.64 = ( ord_max_real @ X @ ( lattic4275903605611617917x_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.remove
% 0.37/0.64 thf(fact_4990_Max_Oremove,axiom,
% 0.37/0.64 ! [A4: set_o,X: $o] :
% 0.37/0.64 ( ( finite_finite_o @ A4 )
% 0.37/0.64 => ( ( member_o @ X @ A4 )
% 0.37/0.64 => ( ( lattic1921953407002678535_Max_o @ A4 )
% 0.37/0.64 = ( ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.37/0.64 = bot_bot_set_o )
% 0.37/0.64 => X )
% 0.37/0.64 & ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.37/0.64 != bot_bot_set_o )
% 0.37/0.64 => ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.remove
% 0.37/0.64 thf(fact_4991_Max_Oremove,axiom,
% 0.37/0.64 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.64 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.64 => ( ( member_Code_integer @ X @ A4 )
% 0.37/0.64 => ( ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 0.37/0.64 = bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( lattic4901227151466704046nteger @ A4 )
% 0.37/0.64 = X ) )
% 0.37/0.64 & ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 0.37/0.64 != bot_bo3990330152332043303nteger )
% 0.37/0.64 => ( ( lattic4901227151466704046nteger @ A4 )
% 0.37/0.64 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.remove
% 0.37/0.64 thf(fact_4992_Max_Oremove,axiom,
% 0.37/0.64 ! [A4: set_int,X: int] :
% 0.37/0.64 ( ( finite_finite_int @ A4 )
% 0.37/0.64 => ( ( member_int @ X @ A4 )
% 0.37/0.64 => ( ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.37/0.64 = bot_bot_set_int )
% 0.37/0.64 => ( ( lattic8263393255366662781ax_int @ A4 )
% 0.37/0.64 = X ) )
% 0.37/0.64 & ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.37/0.64 != bot_bot_set_int )
% 0.37/0.64 => ( ( lattic8263393255366662781ax_int @ A4 )
% 0.37/0.64 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.remove
% 0.37/0.64 thf(fact_4993_Max_Oremove,axiom,
% 0.37/0.64 ! [A4: set_nat,X: nat] :
% 0.37/0.64 ( ( finite_finite_nat @ A4 )
% 0.37/0.64 => ( ( member_nat @ X @ A4 )
% 0.37/0.64 => ( ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.37/0.64 = bot_bot_set_nat )
% 0.37/0.64 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 0.37/0.64 = X ) )
% 0.37/0.64 & ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.37/0.64 != bot_bot_set_nat )
% 0.37/0.64 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 0.37/0.64 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Max.remove
% 0.37/0.64 thf(fact_4994_max_Oabsorb3,axiom,
% 0.37/0.64 ! [B: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.37/0.64 => ( ( ord_max_Code_integer @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb3
% 0.37/0.64 thf(fact_4995_max_Oabsorb3,axiom,
% 0.37/0.64 ! [B: real,A: real] :
% 0.37/0.64 ( ( ord_less_real @ B @ A )
% 0.37/0.64 => ( ( ord_max_real @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb3
% 0.37/0.64 thf(fact_4996_max_Oabsorb3,axiom,
% 0.37/0.64 ! [B: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_rat @ B @ A )
% 0.37/0.64 => ( ( ord_max_rat @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb3
% 0.37/0.64 thf(fact_4997_max_Oabsorb3,axiom,
% 0.37/0.64 ! [B: num,A: num] :
% 0.37/0.64 ( ( ord_less_num @ B @ A )
% 0.37/0.64 => ( ( ord_max_num @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb3
% 0.37/0.64 thf(fact_4998_max_Oabsorb3,axiom,
% 0.37/0.64 ! [B: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_nat @ B @ A )
% 0.37/0.64 => ( ( ord_max_nat @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb3
% 0.37/0.64 thf(fact_4999_max_Oabsorb3,axiom,
% 0.37/0.64 ! [B: int,A: int] :
% 0.37/0.64 ( ( ord_less_int @ B @ A )
% 0.37/0.64 => ( ( ord_max_int @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb3
% 0.37/0.64 thf(fact_5000_max_Oabsorb4,axiom,
% 0.37/0.64 ! [A: code_integer,B: code_integer] :
% 0.37/0.64 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.37/0.64 => ( ( ord_max_Code_integer @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb4
% 0.37/0.64 thf(fact_5001_max_Oabsorb4,axiom,
% 0.37/0.64 ! [A: real,B: real] :
% 0.37/0.64 ( ( ord_less_real @ A @ B )
% 0.37/0.64 => ( ( ord_max_real @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb4
% 0.37/0.64 thf(fact_5002_max_Oabsorb4,axiom,
% 0.37/0.64 ! [A: rat,B: rat] :
% 0.37/0.64 ( ( ord_less_rat @ A @ B )
% 0.37/0.64 => ( ( ord_max_rat @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb4
% 0.37/0.64 thf(fact_5003_max_Oabsorb4,axiom,
% 0.37/0.64 ! [A: num,B: num] :
% 0.37/0.64 ( ( ord_less_num @ A @ B )
% 0.37/0.64 => ( ( ord_max_num @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb4
% 0.37/0.64 thf(fact_5004_max_Oabsorb4,axiom,
% 0.37/0.64 ! [A: nat,B: nat] :
% 0.37/0.64 ( ( ord_less_nat @ A @ B )
% 0.37/0.64 => ( ( ord_max_nat @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb4
% 0.37/0.64 thf(fact_5005_max_Oabsorb4,axiom,
% 0.37/0.64 ! [A: int,B: int] :
% 0.37/0.64 ( ( ord_less_int @ A @ B )
% 0.37/0.64 => ( ( ord_max_int @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb4
% 0.37/0.64 thf(fact_5006_max__less__iff__conj,axiom,
% 0.37/0.64 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 0.37/0.64 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 0.37/0.64 = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 0.37/0.64 & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_less_iff_conj
% 0.37/0.64 thf(fact_5007_max__less__iff__conj,axiom,
% 0.37/0.64 ! [X: real,Y: real,Z: real] :
% 0.37/0.64 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 0.37/0.64 = ( ( ord_less_real @ X @ Z )
% 0.37/0.64 & ( ord_less_real @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_less_iff_conj
% 0.37/0.64 thf(fact_5008_max__less__iff__conj,axiom,
% 0.37/0.64 ! [X: rat,Y: rat,Z: rat] :
% 0.37/0.64 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 0.37/0.64 = ( ( ord_less_rat @ X @ Z )
% 0.37/0.64 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_less_iff_conj
% 0.37/0.64 thf(fact_5009_max__less__iff__conj,axiom,
% 0.37/0.64 ! [X: num,Y: num,Z: num] :
% 0.37/0.64 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 0.37/0.64 = ( ( ord_less_num @ X @ Z )
% 0.37/0.64 & ( ord_less_num @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_less_iff_conj
% 0.37/0.64 thf(fact_5010_max__less__iff__conj,axiom,
% 0.37/0.64 ! [X: nat,Y: nat,Z: nat] :
% 0.37/0.64 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 0.37/0.64 = ( ( ord_less_nat @ X @ Z )
% 0.37/0.64 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_less_iff_conj
% 0.37/0.64 thf(fact_5011_max__less__iff__conj,axiom,
% 0.37/0.64 ! [X: int,Y: int,Z: int] :
% 0.37/0.64 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 0.37/0.64 = ( ( ord_less_int @ X @ Z )
% 0.37/0.64 & ( ord_less_int @ Y @ Z ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max_less_iff_conj
% 0.37/0.64 thf(fact_5012_max_Obounded__iff,axiom,
% 0.37/0.64 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A )
% 0.37/0.64 = ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.37/0.64 & ( ord_le3102999989581377725nteger @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.bounded_iff
% 0.37/0.64 thf(fact_5013_max_Obounded__iff,axiom,
% 0.37/0.64 ! [B: rat,C2: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 0.37/0.64 = ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.64 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.bounded_iff
% 0.37/0.64 thf(fact_5014_max_Obounded__iff,axiom,
% 0.37/0.64 ! [B: num,C2: num,A: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 0.37/0.64 = ( ( ord_less_eq_num @ B @ A )
% 0.37/0.64 & ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.bounded_iff
% 0.37/0.64 thf(fact_5015_max_Obounded__iff,axiom,
% 0.37/0.64 ! [B: nat,C2: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 0.37/0.64 = ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.64 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.bounded_iff
% 0.37/0.64 thf(fact_5016_max_Obounded__iff,axiom,
% 0.37/0.64 ! [B: int,C2: int,A: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 0.37/0.64 = ( ( ord_less_eq_int @ B @ A )
% 0.37/0.64 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.bounded_iff
% 0.37/0.64 thf(fact_5017_max_Oabsorb2,axiom,
% 0.37/0.64 ! [A: code_integer,B: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.37/0.64 => ( ( ord_max_Code_integer @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb2
% 0.37/0.64 thf(fact_5018_max_Oabsorb2,axiom,
% 0.37/0.64 ! [A: rat,B: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ A @ B )
% 0.37/0.64 => ( ( ord_max_rat @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb2
% 0.37/0.64 thf(fact_5019_max_Oabsorb2,axiom,
% 0.37/0.64 ! [A: num,B: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ A @ B )
% 0.37/0.64 => ( ( ord_max_num @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb2
% 0.37/0.64 thf(fact_5020_max_Oabsorb2,axiom,
% 0.37/0.64 ! [A: nat,B: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.64 => ( ( ord_max_nat @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb2
% 0.37/0.64 thf(fact_5021_max_Oabsorb2,axiom,
% 0.37/0.64 ! [A: int,B: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ A @ B )
% 0.37/0.64 => ( ( ord_max_int @ A @ B )
% 0.37/0.64 = B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb2
% 0.37/0.64 thf(fact_5022_max_Oabsorb1,axiom,
% 0.37/0.64 ! [B: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.37/0.64 => ( ( ord_max_Code_integer @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb1
% 0.37/0.64 thf(fact_5023_max_Oabsorb1,axiom,
% 0.37/0.64 ! [B: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.64 => ( ( ord_max_rat @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb1
% 0.37/0.64 thf(fact_5024_max_Oabsorb1,axiom,
% 0.37/0.64 ! [B: num,A: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ B @ A )
% 0.37/0.64 => ( ( ord_max_num @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb1
% 0.37/0.64 thf(fact_5025_max_Oabsorb1,axiom,
% 0.37/0.64 ! [B: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.64 => ( ( ord_max_nat @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb1
% 0.37/0.64 thf(fact_5026_max_Oabsorb1,axiom,
% 0.37/0.64 ! [B: int,A: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.64 => ( ( ord_max_int @ A @ B )
% 0.37/0.64 = A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb1
% 0.37/0.64 thf(fact_5027_option_Osize__gen_I2_J,axiom,
% 0.37/0.64 ! [X: product_prod_nat_nat > nat,X2: product_prod_nat_nat] :
% 0.37/0.64 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X2 ) )
% 0.37/0.64 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size_gen(2)
% 0.37/0.64 thf(fact_5028_option_Osize__gen_I2_J,axiom,
% 0.37/0.64 ! [X: nat > nat,X2: nat] :
% 0.37/0.64 ( ( size_option_nat @ X @ ( some_nat @ X2 ) )
% 0.37/0.64 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size_gen(2)
% 0.37/0.64 thf(fact_5029_option_Osize__gen_I1_J,axiom,
% 0.37/0.64 ! [X: product_prod_nat_nat > nat] :
% 0.37/0.64 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 0.37/0.64 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size_gen(1)
% 0.37/0.64 thf(fact_5030_option_Osize__gen_I1_J,axiom,
% 0.37/0.64 ! [X: nat > nat] :
% 0.37/0.64 ( ( size_option_nat @ X @ none_nat )
% 0.37/0.64 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.64
% 0.37/0.64 % option.size_gen(1)
% 0.37/0.64 thf(fact_5031_max_Omono,axiom,
% 0.37/0.64 ! [C2: code_integer,A: code_integer,D: code_integer,B: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 0.37/0.64 => ( ( ord_le3102999989581377725nteger @ D @ B )
% 0.37/0.64 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C2 @ D ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.mono
% 0.37/0.64 thf(fact_5032_max_Omono,axiom,
% 0.37/0.64 ! [C2: rat,A: rat,D: rat,B: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ C2 @ A )
% 0.37/0.64 => ( ( ord_less_eq_rat @ D @ B )
% 0.37/0.64 => ( ord_less_eq_rat @ ( ord_max_rat @ C2 @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.mono
% 0.37/0.64 thf(fact_5033_max_Omono,axiom,
% 0.37/0.64 ! [C2: num,A: num,D: num,B: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ C2 @ A )
% 0.37/0.64 => ( ( ord_less_eq_num @ D @ B )
% 0.37/0.64 => ( ord_less_eq_num @ ( ord_max_num @ C2 @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.mono
% 0.37/0.64 thf(fact_5034_max_Omono,axiom,
% 0.37/0.64 ! [C2: nat,A: nat,D: nat,B: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ C2 @ A )
% 0.37/0.64 => ( ( ord_less_eq_nat @ D @ B )
% 0.37/0.64 => ( ord_less_eq_nat @ ( ord_max_nat @ C2 @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.mono
% 0.37/0.64 thf(fact_5035_max_Omono,axiom,
% 0.37/0.64 ! [C2: int,A: int,D: int,B: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ C2 @ A )
% 0.37/0.64 => ( ( ord_less_eq_int @ D @ B )
% 0.37/0.64 => ( ord_less_eq_int @ ( ord_max_int @ C2 @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.mono
% 0.37/0.64 thf(fact_5036_max_OorderE,axiom,
% 0.37/0.64 ! [B: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.37/0.64 => ( A
% 0.37/0.64 = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderE
% 0.37/0.64 thf(fact_5037_max_OorderE,axiom,
% 0.37/0.64 ! [B: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.64 => ( A
% 0.37/0.64 = ( ord_max_rat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderE
% 0.37/0.64 thf(fact_5038_max_OorderE,axiom,
% 0.37/0.64 ! [B: num,A: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ B @ A )
% 0.37/0.64 => ( A
% 0.37/0.64 = ( ord_max_num @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderE
% 0.37/0.64 thf(fact_5039_max_OorderE,axiom,
% 0.37/0.64 ! [B: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.64 => ( A
% 0.37/0.64 = ( ord_max_nat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderE
% 0.37/0.64 thf(fact_5040_max_OorderE,axiom,
% 0.37/0.64 ! [B: int,A: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.64 => ( A
% 0.37/0.64 = ( ord_max_int @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderE
% 0.37/0.64 thf(fact_5041_max_OorderI,axiom,
% 0.37/0.64 ! [A: code_integer,B: code_integer] :
% 0.37/0.64 ( ( A
% 0.37/0.64 = ( ord_max_Code_integer @ A @ B ) )
% 0.37/0.64 => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderI
% 0.37/0.64 thf(fact_5042_max_OorderI,axiom,
% 0.37/0.64 ! [A: rat,B: rat] :
% 0.37/0.64 ( ( A
% 0.37/0.64 = ( ord_max_rat @ A @ B ) )
% 0.37/0.64 => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderI
% 0.37/0.64 thf(fact_5043_max_OorderI,axiom,
% 0.37/0.64 ! [A: num,B: num] :
% 0.37/0.64 ( ( A
% 0.37/0.64 = ( ord_max_num @ A @ B ) )
% 0.37/0.64 => ( ord_less_eq_num @ B @ A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderI
% 0.37/0.64 thf(fact_5044_max_OorderI,axiom,
% 0.37/0.64 ! [A: nat,B: nat] :
% 0.37/0.64 ( ( A
% 0.37/0.64 = ( ord_max_nat @ A @ B ) )
% 0.37/0.64 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderI
% 0.37/0.64 thf(fact_5045_max_OorderI,axiom,
% 0.37/0.64 ! [A: int,B: int] :
% 0.37/0.64 ( ( A
% 0.37/0.64 = ( ord_max_int @ A @ B ) )
% 0.37/0.64 => ( ord_less_eq_int @ B @ A ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.orderI
% 0.37/0.64 thf(fact_5046_max_OboundedE,axiom,
% 0.37/0.64 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.37/0.64 => ~ ( ord_le3102999989581377725nteger @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedE
% 0.37/0.64 thf(fact_5047_max_OboundedE,axiom,
% 0.37/0.64 ! [B: rat,C2: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.64 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedE
% 0.37/0.64 thf(fact_5048_max_OboundedE,axiom,
% 0.37/0.64 ! [B: num,C2: num,A: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_eq_num @ B @ A )
% 0.37/0.64 => ~ ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedE
% 0.37/0.64 thf(fact_5049_max_OboundedE,axiom,
% 0.37/0.64 ! [B: nat,C2: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.64 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedE
% 0.37/0.64 thf(fact_5050_max_OboundedE,axiom,
% 0.37/0.64 ! [B: int,C2: int,A: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_eq_int @ B @ A )
% 0.37/0.64 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedE
% 0.37/0.64 thf(fact_5051_max_OboundedI,axiom,
% 0.37/0.64 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.37/0.64 => ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 0.37/0.64 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedI
% 0.37/0.64 thf(fact_5052_max_OboundedI,axiom,
% 0.37/0.64 ! [B: rat,A: rat,C2: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.64 => ( ( ord_less_eq_rat @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedI
% 0.37/0.64 thf(fact_5053_max_OboundedI,axiom,
% 0.37/0.64 ! [B: num,A: num,C2: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ B @ A )
% 0.37/0.64 => ( ( ord_less_eq_num @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedI
% 0.37/0.64 thf(fact_5054_max_OboundedI,axiom,
% 0.37/0.64 ! [B: nat,A: nat,C2: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.64 => ( ( ord_less_eq_nat @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedI
% 0.37/0.64 thf(fact_5055_max_OboundedI,axiom,
% 0.37/0.64 ! [B: int,A: int,C2: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.64 => ( ( ord_less_eq_int @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.boundedI
% 0.37/0.64 thf(fact_5056_max_Oorder__iff,axiom,
% 0.37/0.64 ( ord_le3102999989581377725nteger
% 0.37/0.64 = ( ^ [B7: code_integer,A7: code_integer] :
% 0.37/0.64 ( A7
% 0.37/0.64 = ( ord_max_Code_integer @ A7 @ B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.order_iff
% 0.37/0.64 thf(fact_5057_max_Oorder__iff,axiom,
% 0.37/0.64 ( ord_less_eq_rat
% 0.37/0.64 = ( ^ [B7: rat,A7: rat] :
% 0.37/0.64 ( A7
% 0.37/0.64 = ( ord_max_rat @ A7 @ B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.order_iff
% 0.37/0.64 thf(fact_5058_max_Oorder__iff,axiom,
% 0.37/0.64 ( ord_less_eq_num
% 0.37/0.64 = ( ^ [B7: num,A7: num] :
% 0.37/0.64 ( A7
% 0.37/0.64 = ( ord_max_num @ A7 @ B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.order_iff
% 0.37/0.64 thf(fact_5059_max_Oorder__iff,axiom,
% 0.37/0.64 ( ord_less_eq_nat
% 0.37/0.64 = ( ^ [B7: nat,A7: nat] :
% 0.37/0.64 ( A7
% 0.37/0.64 = ( ord_max_nat @ A7 @ B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.order_iff
% 0.37/0.64 thf(fact_5060_max_Oorder__iff,axiom,
% 0.37/0.64 ( ord_less_eq_int
% 0.37/0.64 = ( ^ [B7: int,A7: int] :
% 0.37/0.64 ( A7
% 0.37/0.64 = ( ord_max_int @ A7 @ B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.order_iff
% 0.37/0.64 thf(fact_5061_max_Ocobounded1,axiom,
% 0.37/0.64 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded1
% 0.37/0.64 thf(fact_5062_max_Ocobounded1,axiom,
% 0.37/0.64 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded1
% 0.37/0.64 thf(fact_5063_max_Ocobounded1,axiom,
% 0.37/0.64 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded1
% 0.37/0.64 thf(fact_5064_max_Ocobounded1,axiom,
% 0.37/0.64 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded1
% 0.37/0.64 thf(fact_5065_max_Ocobounded1,axiom,
% 0.37/0.64 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded1
% 0.37/0.64 thf(fact_5066_max_Ocobounded2,axiom,
% 0.37/0.64 ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded2
% 0.37/0.64 thf(fact_5067_max_Ocobounded2,axiom,
% 0.37/0.64 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded2
% 0.37/0.64 thf(fact_5068_max_Ocobounded2,axiom,
% 0.37/0.64 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded2
% 0.37/0.64 thf(fact_5069_max_Ocobounded2,axiom,
% 0.37/0.64 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded2
% 0.37/0.64 thf(fact_5070_max_Ocobounded2,axiom,
% 0.37/0.64 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.cobounded2
% 0.37/0.64 thf(fact_5071_le__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 0.37/0.64 = ( ( ord_le3102999989581377725nteger @ Z @ X )
% 0.37/0.64 | ( ord_le3102999989581377725nteger @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % le_max_iff_disj
% 0.37/0.64 thf(fact_5072_le__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: rat,X: rat,Y: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_eq_rat @ Z @ X )
% 0.37/0.64 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % le_max_iff_disj
% 0.37/0.64 thf(fact_5073_le__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: num,X: num,Y: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_eq_num @ Z @ X )
% 0.37/0.64 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % le_max_iff_disj
% 0.37/0.64 thf(fact_5074_le__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: nat,X: nat,Y: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_eq_nat @ Z @ X )
% 0.37/0.64 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % le_max_iff_disj
% 0.37/0.64 thf(fact_5075_le__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: int,X: int,Y: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_eq_int @ Z @ X )
% 0.37/0.64 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % le_max_iff_disj
% 0.37/0.64 thf(fact_5076_max_Oabsorb__iff1,axiom,
% 0.37/0.64 ( ord_le3102999989581377725nteger
% 0.37/0.64 = ( ^ [B7: code_integer,A7: code_integer] :
% 0.37/0.64 ( ( ord_max_Code_integer @ A7 @ B7 )
% 0.37/0.64 = A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff1
% 0.37/0.64 thf(fact_5077_max_Oabsorb__iff1,axiom,
% 0.37/0.64 ( ord_less_eq_rat
% 0.37/0.64 = ( ^ [B7: rat,A7: rat] :
% 0.37/0.64 ( ( ord_max_rat @ A7 @ B7 )
% 0.37/0.64 = A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff1
% 0.37/0.64 thf(fact_5078_max_Oabsorb__iff1,axiom,
% 0.37/0.64 ( ord_less_eq_num
% 0.37/0.64 = ( ^ [B7: num,A7: num] :
% 0.37/0.64 ( ( ord_max_num @ A7 @ B7 )
% 0.37/0.64 = A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff1
% 0.37/0.64 thf(fact_5079_max_Oabsorb__iff1,axiom,
% 0.37/0.64 ( ord_less_eq_nat
% 0.37/0.64 = ( ^ [B7: nat,A7: nat] :
% 0.37/0.64 ( ( ord_max_nat @ A7 @ B7 )
% 0.37/0.64 = A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff1
% 0.37/0.64 thf(fact_5080_max_Oabsorb__iff1,axiom,
% 0.37/0.64 ( ord_less_eq_int
% 0.37/0.64 = ( ^ [B7: int,A7: int] :
% 0.37/0.64 ( ( ord_max_int @ A7 @ B7 )
% 0.37/0.64 = A7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff1
% 0.37/0.64 thf(fact_5081_max_Oabsorb__iff2,axiom,
% 0.37/0.64 ( ord_le3102999989581377725nteger
% 0.37/0.64 = ( ^ [A7: code_integer,B7: code_integer] :
% 0.37/0.64 ( ( ord_max_Code_integer @ A7 @ B7 )
% 0.37/0.64 = B7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff2
% 0.37/0.64 thf(fact_5082_max_Oabsorb__iff2,axiom,
% 0.37/0.64 ( ord_less_eq_rat
% 0.37/0.64 = ( ^ [A7: rat,B7: rat] :
% 0.37/0.64 ( ( ord_max_rat @ A7 @ B7 )
% 0.37/0.64 = B7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff2
% 0.37/0.64 thf(fact_5083_max_Oabsorb__iff2,axiom,
% 0.37/0.64 ( ord_less_eq_num
% 0.37/0.64 = ( ^ [A7: num,B7: num] :
% 0.37/0.64 ( ( ord_max_num @ A7 @ B7 )
% 0.37/0.64 = B7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff2
% 0.37/0.64 thf(fact_5084_max_Oabsorb__iff2,axiom,
% 0.37/0.64 ( ord_less_eq_nat
% 0.37/0.64 = ( ^ [A7: nat,B7: nat] :
% 0.37/0.64 ( ( ord_max_nat @ A7 @ B7 )
% 0.37/0.64 = B7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff2
% 0.37/0.64 thf(fact_5085_max_Oabsorb__iff2,axiom,
% 0.37/0.64 ( ord_less_eq_int
% 0.37/0.64 = ( ^ [A7: int,B7: int] :
% 0.37/0.64 ( ( ord_max_int @ A7 @ B7 )
% 0.37/0.64 = B7 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.absorb_iff2
% 0.37/0.64 thf(fact_5086_max_OcoboundedI1,axiom,
% 0.37/0.64 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 0.37/0.64 => ( ord_le3102999989581377725nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI1
% 0.37/0.64 thf(fact_5087_max_OcoboundedI1,axiom,
% 0.37/0.64 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI1
% 0.37/0.64 thf(fact_5088_max_OcoboundedI1,axiom,
% 0.37/0.64 ! [C2: num,A: num,B: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI1
% 0.37/0.64 thf(fact_5089_max_OcoboundedI1,axiom,
% 0.37/0.64 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI1
% 0.37/0.64 thf(fact_5090_max_OcoboundedI1,axiom,
% 0.37/0.64 ! [C2: int,A: int,B: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ C2 @ A )
% 0.37/0.64 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI1
% 0.37/0.64 thf(fact_5091_max_OcoboundedI2,axiom,
% 0.37/0.64 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le3102999989581377725nteger @ C2 @ B )
% 0.37/0.64 => ( ord_le3102999989581377725nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI2
% 0.37/0.64 thf(fact_5092_max_OcoboundedI2,axiom,
% 0.37/0.64 ! [C2: rat,B: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_eq_rat @ C2 @ B )
% 0.37/0.64 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI2
% 0.37/0.64 thf(fact_5093_max_OcoboundedI2,axiom,
% 0.37/0.64 ! [C2: num,B: num,A: num] :
% 0.37/0.64 ( ( ord_less_eq_num @ C2 @ B )
% 0.37/0.64 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI2
% 0.37/0.64 thf(fact_5094_max_OcoboundedI2,axiom,
% 0.37/0.64 ! [C2: nat,B: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ C2 @ B )
% 0.37/0.64 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI2
% 0.37/0.64 thf(fact_5095_max_OcoboundedI2,axiom,
% 0.37/0.64 ! [C2: int,B: int,A: int] :
% 0.37/0.64 ( ( ord_less_eq_int @ C2 @ B )
% 0.37/0.64 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.coboundedI2
% 0.37/0.64 thf(fact_5096_max_Ostrict__coboundedI2,axiom,
% 0.37/0.64 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le6747313008572928689nteger @ C2 @ B )
% 0.37/0.64 => ( ord_le6747313008572928689nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI2
% 0.37/0.64 thf(fact_5097_max_Ostrict__coboundedI2,axiom,
% 0.37/0.64 ! [C2: real,B: real,A: real] :
% 0.37/0.64 ( ( ord_less_real @ C2 @ B )
% 0.37/0.64 => ( ord_less_real @ C2 @ ( ord_max_real @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI2
% 0.37/0.64 thf(fact_5098_max_Ostrict__coboundedI2,axiom,
% 0.37/0.64 ! [C2: rat,B: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_rat @ C2 @ B )
% 0.37/0.64 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI2
% 0.37/0.64 thf(fact_5099_max_Ostrict__coboundedI2,axiom,
% 0.37/0.64 ! [C2: num,B: num,A: num] :
% 0.37/0.64 ( ( ord_less_num @ C2 @ B )
% 0.37/0.64 => ( ord_less_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI2
% 0.37/0.64 thf(fact_5100_max_Ostrict__coboundedI2,axiom,
% 0.37/0.64 ! [C2: nat,B: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_nat @ C2 @ B )
% 0.37/0.64 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI2
% 0.37/0.64 thf(fact_5101_max_Ostrict__coboundedI2,axiom,
% 0.37/0.64 ! [C2: int,B: int,A: int] :
% 0.37/0.64 ( ( ord_less_int @ C2 @ B )
% 0.37/0.64 => ( ord_less_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI2
% 0.37/0.64 thf(fact_5102_max_Ostrict__coboundedI1,axiom,
% 0.37/0.64 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 0.37/0.64 ( ( ord_le6747313008572928689nteger @ C2 @ A )
% 0.37/0.64 => ( ord_le6747313008572928689nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI1
% 0.37/0.64 thf(fact_5103_max_Ostrict__coboundedI1,axiom,
% 0.37/0.64 ! [C2: real,A: real,B: real] :
% 0.37/0.64 ( ( ord_less_real @ C2 @ A )
% 0.37/0.64 => ( ord_less_real @ C2 @ ( ord_max_real @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI1
% 0.37/0.64 thf(fact_5104_max_Ostrict__coboundedI1,axiom,
% 0.37/0.64 ! [C2: rat,A: rat,B: rat] :
% 0.37/0.64 ( ( ord_less_rat @ C2 @ A )
% 0.37/0.64 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI1
% 0.37/0.64 thf(fact_5105_max_Ostrict__coboundedI1,axiom,
% 0.37/0.64 ! [C2: num,A: num,B: num] :
% 0.37/0.64 ( ( ord_less_num @ C2 @ A )
% 0.37/0.64 => ( ord_less_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI1
% 0.37/0.64 thf(fact_5106_max_Ostrict__coboundedI1,axiom,
% 0.37/0.64 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.64 ( ( ord_less_nat @ C2 @ A )
% 0.37/0.64 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI1
% 0.37/0.64 thf(fact_5107_max_Ostrict__coboundedI1,axiom,
% 0.37/0.64 ! [C2: int,A: int,B: int] :
% 0.37/0.64 ( ( ord_less_int @ C2 @ A )
% 0.37/0.64 => ( ord_less_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_coboundedI1
% 0.37/0.64 thf(fact_5108_max_Ostrict__order__iff,axiom,
% 0.37/0.64 ( ord_le6747313008572928689nteger
% 0.37/0.64 = ( ^ [B7: code_integer,A7: code_integer] :
% 0.37/0.64 ( ( A7
% 0.37/0.64 = ( ord_max_Code_integer @ A7 @ B7 ) )
% 0.37/0.64 & ( A7 != B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_order_iff
% 0.37/0.64 thf(fact_5109_max_Ostrict__order__iff,axiom,
% 0.37/0.64 ( ord_less_real
% 0.37/0.64 = ( ^ [B7: real,A7: real] :
% 0.37/0.64 ( ( A7
% 0.37/0.64 = ( ord_max_real @ A7 @ B7 ) )
% 0.37/0.64 & ( A7 != B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_order_iff
% 0.37/0.64 thf(fact_5110_max_Ostrict__order__iff,axiom,
% 0.37/0.64 ( ord_less_rat
% 0.37/0.64 = ( ^ [B7: rat,A7: rat] :
% 0.37/0.64 ( ( A7
% 0.37/0.64 = ( ord_max_rat @ A7 @ B7 ) )
% 0.37/0.64 & ( A7 != B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_order_iff
% 0.37/0.64 thf(fact_5111_max_Ostrict__order__iff,axiom,
% 0.37/0.64 ( ord_less_num
% 0.37/0.64 = ( ^ [B7: num,A7: num] :
% 0.37/0.64 ( ( A7
% 0.37/0.64 = ( ord_max_num @ A7 @ B7 ) )
% 0.37/0.64 & ( A7 != B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_order_iff
% 0.37/0.64 thf(fact_5112_max_Ostrict__order__iff,axiom,
% 0.37/0.64 ( ord_less_nat
% 0.37/0.64 = ( ^ [B7: nat,A7: nat] :
% 0.37/0.64 ( ( A7
% 0.37/0.64 = ( ord_max_nat @ A7 @ B7 ) )
% 0.37/0.64 & ( A7 != B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_order_iff
% 0.37/0.64 thf(fact_5113_max_Ostrict__order__iff,axiom,
% 0.37/0.64 ( ord_less_int
% 0.37/0.64 = ( ^ [B7: int,A7: int] :
% 0.37/0.64 ( ( A7
% 0.37/0.64 = ( ord_max_int @ A7 @ B7 ) )
% 0.37/0.64 & ( A7 != B7 ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_order_iff
% 0.37/0.64 thf(fact_5114_max_Ostrict__boundedE,axiom,
% 0.37/0.64 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 0.37/0.64 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.37/0.64 => ~ ( ord_le6747313008572928689nteger @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_boundedE
% 0.37/0.64 thf(fact_5115_max_Ostrict__boundedE,axiom,
% 0.37/0.64 ! [B: real,C2: real,A: real] :
% 0.37/0.64 ( ( ord_less_real @ ( ord_max_real @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_real @ B @ A )
% 0.37/0.64 => ~ ( ord_less_real @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_boundedE
% 0.37/0.64 thf(fact_5116_max_Ostrict__boundedE,axiom,
% 0.37/0.64 ! [B: rat,C2: rat,A: rat] :
% 0.37/0.64 ( ( ord_less_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_rat @ B @ A )
% 0.37/0.64 => ~ ( ord_less_rat @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_boundedE
% 0.37/0.64 thf(fact_5117_max_Ostrict__boundedE,axiom,
% 0.37/0.64 ! [B: num,C2: num,A: num] :
% 0.37/0.64 ( ( ord_less_num @ ( ord_max_num @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_num @ B @ A )
% 0.37/0.64 => ~ ( ord_less_num @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_boundedE
% 0.37/0.64 thf(fact_5118_max_Ostrict__boundedE,axiom,
% 0.37/0.64 ! [B: nat,C2: nat,A: nat] :
% 0.37/0.64 ( ( ord_less_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_nat @ B @ A )
% 0.37/0.64 => ~ ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_boundedE
% 0.37/0.64 thf(fact_5119_max_Ostrict__boundedE,axiom,
% 0.37/0.64 ! [B: int,C2: int,A: int] :
% 0.37/0.64 ( ( ord_less_int @ ( ord_max_int @ B @ C2 ) @ A )
% 0.37/0.64 => ~ ( ( ord_less_int @ B @ A )
% 0.37/0.64 => ~ ( ord_less_int @ C2 @ A ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % max.strict_boundedE
% 0.37/0.64 thf(fact_5120_less__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 0.37/0.64 ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 0.37/0.64 = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 0.37/0.64 | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % less_max_iff_disj
% 0.37/0.64 thf(fact_5121_less__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: real,X: real,Y: real] :
% 0.37/0.64 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_real @ Z @ X )
% 0.37/0.64 | ( ord_less_real @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % less_max_iff_disj
% 0.37/0.64 thf(fact_5122_less__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: rat,X: rat,Y: rat] :
% 0.37/0.64 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_rat @ Z @ X )
% 0.37/0.64 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % less_max_iff_disj
% 0.37/0.64 thf(fact_5123_less__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: num,X: num,Y: num] :
% 0.37/0.64 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_num @ Z @ X )
% 0.37/0.64 | ( ord_less_num @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % less_max_iff_disj
% 0.37/0.64 thf(fact_5124_less__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: nat,X: nat,Y: nat] :
% 0.37/0.64 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_nat @ Z @ X )
% 0.37/0.64 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % less_max_iff_disj
% 0.37/0.64 thf(fact_5125_less__max__iff__disj,axiom,
% 0.37/0.64 ! [Z: int,X: int,Y: int] :
% 0.37/0.64 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 0.37/0.64 = ( ( ord_less_int @ Z @ X )
% 0.37/0.64 | ( ord_less_int @ Z @ Y ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % less_max_iff_disj
% 0.37/0.64 thf(fact_5126_sorted__in__between,axiom,
% 0.37/0.64 ! [I: nat,J: nat,L: list_o,X: $o] :
% 0.37/0.64 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.37/0.64 => ( ( ord_less_nat @ I @ J )
% 0.37/0.64 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 0.37/0.64 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 0.37/0.64 => ( ( ord_less_eq_o @ ( nth_o @ L @ I ) @ X )
% 0.37/0.64 => ( ( ord_less_o @ X @ ( nth_o @ L @ J ) )
% 0.37/0.64 => ~ ! [K2: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ I @ K2 )
% 0.37/0.64 => ( ( ord_less_nat @ K2 @ J )
% 0.37/0.64 => ( ( ord_less_eq_o @ ( nth_o @ L @ K2 ) @ X )
% 0.37/0.64 => ~ ( ord_less_o @ X @ ( nth_o @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_in_between
% 0.37/0.64 thf(fact_5127_sorted__in__between,axiom,
% 0.37/0.64 ! [I: nat,J: nat,L: list_real,X: real] :
% 0.37/0.64 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.37/0.64 => ( ( ord_less_nat @ I @ J )
% 0.37/0.64 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 0.37/0.64 => ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 0.37/0.64 => ( ( ord_less_eq_real @ ( nth_real @ L @ I ) @ X )
% 0.37/0.64 => ( ( ord_less_real @ X @ ( nth_real @ L @ J ) )
% 0.37/0.64 => ~ ! [K2: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ I @ K2 )
% 0.37/0.64 => ( ( ord_less_nat @ K2 @ J )
% 0.37/0.64 => ( ( ord_less_eq_real @ ( nth_real @ L @ K2 ) @ X )
% 0.37/0.64 => ~ ( ord_less_real @ X @ ( nth_real @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_in_between
% 0.37/0.64 thf(fact_5128_sorted__in__between,axiom,
% 0.37/0.64 ! [I: nat,J: nat,L: list_rat,X: rat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.37/0.64 => ( ( ord_less_nat @ I @ J )
% 0.37/0.64 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 0.37/0.64 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 0.37/0.64 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I ) @ X )
% 0.37/0.64 => ( ( ord_less_rat @ X @ ( nth_rat @ L @ J ) )
% 0.37/0.64 => ~ ! [K2: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ I @ K2 )
% 0.37/0.64 => ( ( ord_less_nat @ K2 @ J )
% 0.37/0.64 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ K2 ) @ X )
% 0.37/0.64 => ~ ( ord_less_rat @ X @ ( nth_rat @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_in_between
% 0.37/0.64 thf(fact_5129_sorted__in__between,axiom,
% 0.37/0.64 ! [I: nat,J: nat,L: list_num,X: num] :
% 0.37/0.64 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.37/0.64 => ( ( ord_less_nat @ I @ J )
% 0.37/0.64 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 0.37/0.64 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 0.37/0.64 => ( ( ord_less_eq_num @ ( nth_num @ L @ I ) @ X )
% 0.37/0.64 => ( ( ord_less_num @ X @ ( nth_num @ L @ J ) )
% 0.37/0.64 => ~ ! [K2: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ I @ K2 )
% 0.37/0.64 => ( ( ord_less_nat @ K2 @ J )
% 0.37/0.64 => ( ( ord_less_eq_num @ ( nth_num @ L @ K2 ) @ X )
% 0.37/0.64 => ~ ( ord_less_num @ X @ ( nth_num @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_in_between
% 0.37/0.64 thf(fact_5130_sorted__in__between,axiom,
% 0.37/0.64 ! [I: nat,J: nat,L: list_nat,X: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.37/0.64 => ( ( ord_less_nat @ I @ J )
% 0.37/0.64 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 0.37/0.64 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 0.37/0.64 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ X )
% 0.37/0.64 => ( ( ord_less_nat @ X @ ( nth_nat @ L @ J ) )
% 0.37/0.64 => ~ ! [K2: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ I @ K2 )
% 0.37/0.64 => ( ( ord_less_nat @ K2 @ J )
% 0.37/0.64 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ K2 ) @ X )
% 0.37/0.64 => ~ ( ord_less_nat @ X @ ( nth_nat @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_in_between
% 0.37/0.64 thf(fact_5131_sorted__in__between,axiom,
% 0.37/0.64 ! [I: nat,J: nat,L: list_int,X: int] :
% 0.37/0.64 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 0.37/0.64 => ( ( ord_less_nat @ I @ J )
% 0.37/0.64 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 0.37/0.64 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 0.37/0.64 => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ X )
% 0.37/0.64 => ( ( ord_less_int @ X @ ( nth_int @ L @ J ) )
% 0.37/0.64 => ~ ! [K2: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ I @ K2 )
% 0.37/0.64 => ( ( ord_less_nat @ K2 @ J )
% 0.37/0.64 => ( ( ord_less_eq_int @ ( nth_int @ L @ K2 ) @ X )
% 0.37/0.64 => ~ ( ord_less_int @ X @ ( nth_int @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_in_between
% 0.37/0.64 thf(fact_5132_nth__enumerate__eq,axiom,
% 0.37/0.64 ! [M: nat,Xs: list_VEBT_VEBTi,N: nat] :
% 0.37/0.64 ( ( ord_less_nat @ M @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( nth_Pr3244165891152107629_VEBTi @ ( enumerate_VEBT_VEBTi @ N @ Xs ) @ M )
% 0.37/0.64 = ( produc2649746096677893406_VEBTi @ ( plus_plus_nat @ N @ M ) @ ( nth_VEBT_VEBTi @ Xs @ M ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_enumerate_eq
% 0.37/0.64 thf(fact_5133_nth__enumerate__eq,axiom,
% 0.37/0.64 ! [M: nat,Xs: list_int,N: nat] :
% 0.37/0.64 ( ( ord_less_nat @ M @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs ) @ M )
% 0.37/0.64 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M ) @ ( nth_int @ Xs @ M ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_enumerate_eq
% 0.37/0.64 thf(fact_5134_nth__enumerate__eq,axiom,
% 0.37/0.64 ! [M: nat,Xs: list_VEBT_VEBT,N: nat] :
% 0.37/0.64 ( ( ord_less_nat @ M @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.64 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs ) @ M )
% 0.37/0.64 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N @ M ) @ ( nth_VEBT_VEBT @ Xs @ M ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_enumerate_eq
% 0.37/0.64 thf(fact_5135_nth__enumerate__eq,axiom,
% 0.37/0.64 ! [M: nat,Xs: list_real,N: nat] :
% 0.37/0.64 ( ( ord_less_nat @ M @ ( size_size_list_real @ Xs ) )
% 0.37/0.64 => ( ( nth_Pr7767817059697521252t_real @ ( enumerate_real @ N @ Xs ) @ M )
% 0.37/0.64 = ( produc7837566107596912789t_real @ ( plus_plus_nat @ N @ M ) @ ( nth_real @ Xs @ M ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_enumerate_eq
% 0.37/0.64 thf(fact_5136_nth__enumerate__eq,axiom,
% 0.37/0.64 ! [M: nat,Xs: list_o,N: nat] :
% 0.37/0.64 ( ( ord_less_nat @ M @ ( size_size_list_o @ Xs ) )
% 0.37/0.64 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N @ Xs ) @ M )
% 0.37/0.64 = ( product_Pair_nat_o @ ( plus_plus_nat @ N @ M ) @ ( nth_o @ Xs @ M ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_enumerate_eq
% 0.37/0.64 thf(fact_5137_nth__enumerate__eq,axiom,
% 0.37/0.64 ! [M: nat,Xs: list_nat,N: nat] :
% 0.37/0.64 ( ( ord_less_nat @ M @ ( size_size_list_nat @ Xs ) )
% 0.37/0.64 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs ) @ M )
% 0.37/0.64 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M ) @ ( nth_nat @ Xs @ M ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_enumerate_eq
% 0.37/0.64 thf(fact_5138_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5139_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > nat > assn,Xsi: list_nat] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5140_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5141_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > int > assn,Xsi: list_int] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5142_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5143_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > nat > assn,Xsi: list_nat] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5144_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5145_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > int > assn,Xsi: list_int] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5146_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5147_listI__assn__extract,axiom,
% 0.37/0.64 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > nat > assn,Xsi: list_nat] :
% 0.37/0.64 ( ( member_nat @ I @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.64 => ( ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_extract
% 0.37/0.64 thf(fact_5148_nth__step__trancl,axiom,
% 0.37/0.64 ! [Xs: list_VEBT_VEBTi,R2: set_Pr2227491710730465451_VEBTi,N: nat,M: nat] :
% 0.37/0.64 ( ! [N2: nat] :
% 0.37/0.64 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) @ one_one_nat ) )
% 0.37/0.64 => ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ ( suc @ N2 ) ) @ ( nth_VEBT_VEBTi @ Xs @ N2 ) ) @ R2 ) )
% 0.37/0.64 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( ord_less_nat @ M @ N )
% 0.37/0.64 => ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N ) @ ( nth_VEBT_VEBTi @ Xs @ M ) ) @ ( transi2803566869205510612_VEBTi @ R2 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_step_trancl
% 0.37/0.64 thf(fact_5149_nth__step__trancl,axiom,
% 0.37/0.64 ! [Xs: list_uint32,R2: set_Pr1773385645901665561uint32,N: nat,M: nat] :
% 0.37/0.64 ( ! [N2: nat] :
% 0.37/0.64 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_s4844771616002835472uint32 @ Xs ) @ one_one_nat ) )
% 0.37/0.64 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ ( suc @ N2 ) ) @ ( nth_uint32 @ Xs @ N2 ) ) @ R2 ) )
% 0.37/0.64 => ( ( ord_less_nat @ N @ ( size_s4844771616002835472uint32 @ Xs ) )
% 0.37/0.64 => ( ( ord_less_nat @ M @ N )
% 0.37/0.64 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ N ) @ ( nth_uint32 @ Xs @ M ) ) @ ( transi3114468042090999947uint32 @ R2 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_step_trancl
% 0.37/0.64 thf(fact_5150_nth__step__trancl,axiom,
% 0.37/0.64 ! [Xs: list_int,R2: set_Pr958786334691620121nt_int,N: nat,M: nat] :
% 0.37/0.64 ( ! [N2: nat] :
% 0.37/0.64 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) )
% 0.37/0.64 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ ( suc @ N2 ) ) @ ( nth_int @ Xs @ N2 ) ) @ R2 ) )
% 0.37/0.64 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( ord_less_nat @ M @ N )
% 0.37/0.64 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N ) @ ( nth_int @ Xs @ M ) ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_step_trancl
% 0.37/0.64 thf(fact_5151_nth__step__trancl,axiom,
% 0.37/0.64 ! [Xs: list_VEBT_VEBT,R2: set_Pr6192946355708809607T_VEBT,N: nat,M: nat] :
% 0.37/0.64 ( ! [N2: nat] :
% 0.37/0.64 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat ) )
% 0.37/0.64 => ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( suc @ N2 ) ) @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) @ R2 ) )
% 0.37/0.64 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.64 => ( ( ord_less_nat @ M @ N )
% 0.37/0.64 => ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( nth_VEBT_VEBT @ Xs @ M ) ) @ ( transi8906537157094044885T_VEBT @ R2 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_step_trancl
% 0.37/0.64 thf(fact_5152_nth__step__trancl,axiom,
% 0.37/0.64 ! [Xs: list_real,R2: set_Pr6218003697084177305l_real,N: nat,M: nat] :
% 0.37/0.64 ( ! [N2: nat] :
% 0.37/0.64 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_real @ Xs ) @ one_one_nat ) )
% 0.37/0.64 => ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ ( suc @ N2 ) ) @ ( nth_real @ Xs @ N2 ) ) @ R2 ) )
% 0.37/0.64 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.64 => ( ( ord_less_nat @ M @ N )
% 0.37/0.64 => ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ N ) @ ( nth_real @ Xs @ M ) ) @ ( transi1789104906590519371l_real @ R2 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_step_trancl
% 0.37/0.64 thf(fact_5153_nth__step__trancl,axiom,
% 0.37/0.64 ! [Xs: list_o,R2: set_Product_prod_o_o,N: nat,M: nat] :
% 0.37/0.64 ( ! [N2: nat] :
% 0.37/0.64 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_o @ Xs ) @ one_one_nat ) )
% 0.37/0.64 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ ( suc @ N2 ) ) @ ( nth_o @ Xs @ N2 ) ) @ R2 ) )
% 0.37/0.64 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.64 => ( ( ord_less_nat @ M @ N )
% 0.37/0.64 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ N ) @ ( nth_o @ Xs @ M ) ) @ ( transitive_trancl_o @ R2 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_step_trancl
% 0.37/0.64 thf(fact_5154_nth__step__trancl,axiom,
% 0.37/0.64 ! [Xs: list_nat,R2: set_Pr1261947904930325089at_nat,N: nat,M: nat] :
% 0.37/0.64 ( ! [N2: nat] :
% 0.37/0.64 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) )
% 0.37/0.64 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( suc @ N2 ) ) @ ( nth_nat @ Xs @ N2 ) ) @ R2 ) )
% 0.37/0.64 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.64 => ( ( ord_less_nat @ M @ N )
% 0.37/0.64 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N ) @ ( nth_nat @ Xs @ M ) ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_step_trancl
% 0.37/0.64 thf(fact_5155_nth__Cons__pos,axiom,
% 0.37/0.64 ! [N: nat,X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.64 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 0.37/0.64 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_pos
% 0.37/0.64 thf(fact_5156_nth__Cons__pos,axiom,
% 0.37/0.64 ! [N: nat,X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 0.37/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.64 => ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_pos
% 0.37/0.64 thf(fact_5157_nth__Cons__pos,axiom,
% 0.37/0.64 ! [N: nat,X: int,Xs: list_int] :
% 0.37/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.64 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 0.37/0.64 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_pos
% 0.37/0.64 thf(fact_5158_nth__Cons__pos,axiom,
% 0.37/0.64 ! [N: nat,X: nat,Xs: list_nat] :
% 0.37/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.64 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 0.37/0.64 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_pos
% 0.37/0.64 thf(fact_5159_nth__Cons__pos,axiom,
% 0.37/0.64 ! [N: nat,X: $o,Xs: list_o] :
% 0.37/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.64 => ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 0.37/0.64 = ( nth_o @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_pos
% 0.37/0.64 thf(fact_5160_length__nth__simps_I4_J,axiom,
% 0.37/0.64 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 0.37/0.64 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_VEBT_VEBT @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(4)
% 0.37/0.64 thf(fact_5161_length__nth__simps_I4_J,axiom,
% 0.37/0.64 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 0.37/0.64 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(4)
% 0.37/0.64 thf(fact_5162_length__nth__simps_I4_J,axiom,
% 0.37/0.64 ! [X: int,Xs: list_int,N: nat] :
% 0.37/0.64 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_int @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(4)
% 0.37/0.64 thf(fact_5163_length__nth__simps_I4_J,axiom,
% 0.37/0.64 ! [X: nat,Xs: list_nat,N: nat] :
% 0.37/0.64 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_nat @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(4)
% 0.37/0.64 thf(fact_5164_length__nth__simps_I4_J,axiom,
% 0.37/0.64 ! [X: $o,Xs: list_o,N: nat] :
% 0.37/0.64 ( ( nth_o @ ( cons_o @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_o @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(4)
% 0.37/0.64 thf(fact_5165_nth__Cons__Suc,axiom,
% 0.37/0.64 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 0.37/0.64 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_VEBT_VEBT @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_Suc
% 0.37/0.64 thf(fact_5166_nth__Cons__Suc,axiom,
% 0.37/0.64 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 0.37/0.64 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_Suc
% 0.37/0.64 thf(fact_5167_nth__Cons__Suc,axiom,
% 0.37/0.64 ! [X: int,Xs: list_int,N: nat] :
% 0.37/0.64 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_int @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_Suc
% 0.37/0.64 thf(fact_5168_nth__Cons__Suc,axiom,
% 0.37/0.64 ! [X: nat,Xs: list_nat,N: nat] :
% 0.37/0.64 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_nat @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_Suc
% 0.37/0.64 thf(fact_5169_nth__Cons__Suc,axiom,
% 0.37/0.64 ! [X: $o,Xs: list_o,N: nat] :
% 0.37/0.64 ( ( nth_o @ ( cons_o @ X @ Xs ) @ ( suc @ N ) )
% 0.37/0.64 = ( nth_o @ Xs @ N ) ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_Suc
% 0.37/0.64 thf(fact_5170_length__nth__simps_I3_J,axiom,
% 0.37/0.64 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.64 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(3)
% 0.37/0.64 thf(fact_5171_length__nth__simps_I3_J,axiom,
% 0.37/0.64 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 0.37/0.64 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(3)
% 0.37/0.64 thf(fact_5172_length__nth__simps_I3_J,axiom,
% 0.37/0.64 ! [X: int,Xs: list_int] :
% 0.37/0.64 ( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(3)
% 0.37/0.64 thf(fact_5173_length__nth__simps_I3_J,axiom,
% 0.37/0.64 ! [X: nat,Xs: list_nat] :
% 0.37/0.64 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(3)
% 0.37/0.64 thf(fact_5174_length__nth__simps_I3_J,axiom,
% 0.37/0.64 ! [X: $o,Xs: list_o] :
% 0.37/0.64 ( ( nth_o @ ( cons_o @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(3)
% 0.37/0.64 thf(fact_5175_nth__Cons__0,axiom,
% 0.37/0.64 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.64 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_0
% 0.37/0.64 thf(fact_5176_nth__Cons__0,axiom,
% 0.37/0.64 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 0.37/0.64 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_0
% 0.37/0.64 thf(fact_5177_nth__Cons__0,axiom,
% 0.37/0.64 ! [X: int,Xs: list_int] :
% 0.37/0.64 ( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_0
% 0.37/0.64 thf(fact_5178_nth__Cons__0,axiom,
% 0.37/0.64 ! [X: nat,Xs: list_nat] :
% 0.37/0.64 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_0
% 0.37/0.64 thf(fact_5179_nth__Cons__0,axiom,
% 0.37/0.64 ! [X: $o,Xs: list_o] :
% 0.37/0.64 ( ( nth_o @ ( cons_o @ X @ Xs ) @ zero_zero_nat )
% 0.37/0.64 = X ) ).
% 0.37/0.64
% 0.37/0.64 % nth_Cons_0
% 0.37/0.64 thf(fact_5180_trancl__single,axiom,
% 0.37/0.64 ! [A: uint32,B: uint32] :
% 0.37/0.64 ( ( transi3114468042090999947uint32 @ ( insert4454361187789264009uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ bot_bo8438649754162204037uint32 ) )
% 0.37/0.64 = ( insert4454361187789264009uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ bot_bo8438649754162204037uint32 ) ) ).
% 0.37/0.64
% 0.37/0.64 % trancl_single
% 0.37/0.64 thf(fact_5181_trancl__single,axiom,
% 0.37/0.64 ! [A: nat,B: nat] :
% 0.37/0.64 ( ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ bot_bo2099793752762293965at_nat ) )
% 0.37/0.64 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ bot_bo2099793752762293965at_nat ) ) ).
% 0.37/0.64
% 0.37/0.64 % trancl_single
% 0.37/0.64 thf(fact_5182_trancl__single,axiom,
% 0.37/0.64 ! [A: int,B: int] :
% 0.37/0.64 ( ( transi6261509568448316235cl_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ bot_bo1796632182523588997nt_int ) )
% 0.37/0.64 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ bot_bo1796632182523588997nt_int ) ) ).
% 0.37/0.64
% 0.37/0.64 % trancl_single
% 0.37/0.64 thf(fact_5183_listI__assn__finite,axiom,
% 0.37/0.64 ! [I5: set_nat,A4: vEBT_VEBT > vEBT_VEBTi > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi] :
% 0.37/0.64 ( ~ ( finite_finite_nat @ I5 )
% 0.37/0.64 => ( ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = bot_bot_assn ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_finite
% 0.37/0.64 thf(fact_5184_enumerate__simps_I2_J,axiom,
% 0.37/0.64 ! [N: nat,X: int,Xs: list_int] :
% 0.37/0.64 ( ( enumerate_int @ N @ ( cons_int @ X @ Xs ) )
% 0.37/0.64 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ N @ X ) @ ( enumerate_int @ ( suc @ N ) @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % enumerate_simps(2)
% 0.37/0.64 thf(fact_5185_enumerate__simps_I2_J,axiom,
% 0.37/0.64 ! [N: nat,X: $o,Xs: list_o] :
% 0.37/0.64 ( ( enumerate_o @ N @ ( cons_o @ X @ Xs ) )
% 0.37/0.64 = ( cons_P9142372351690779143_nat_o @ ( product_Pair_nat_o @ N @ X ) @ ( enumerate_o @ ( suc @ N ) @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % enumerate_simps(2)
% 0.37/0.64 thf(fact_5186_enumerate__simps_I2_J,axiom,
% 0.37/0.64 ! [N: nat,X: nat,Xs: list_nat] :
% 0.37/0.64 ( ( enumerate_nat @ N @ ( cons_nat @ X @ Xs ) )
% 0.37/0.64 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ N @ X ) @ ( enumerate_nat @ ( suc @ N ) @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % enumerate_simps(2)
% 0.37/0.64 thf(fact_5187_list__tail__coinc,axiom,
% 0.37/0.64 ! [N1: int,R1: list_int,N22: int,R22: list_int] :
% 0.37/0.64 ( ( ( cons_int @ N1 @ R1 )
% 0.37/0.64 = ( cons_int @ N22 @ R22 ) )
% 0.37/0.64 => ( ( N1 = N22 )
% 0.37/0.64 & ( R1 = R22 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % list_tail_coinc
% 0.37/0.64 thf(fact_5188_list__tail__coinc,axiom,
% 0.37/0.64 ! [N1: nat,R1: list_nat,N22: nat,R22: list_nat] :
% 0.37/0.64 ( ( ( cons_nat @ N1 @ R1 )
% 0.37/0.64 = ( cons_nat @ N22 @ R22 ) )
% 0.37/0.64 => ( ( N1 = N22 )
% 0.37/0.64 & ( R1 = R22 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % list_tail_coinc
% 0.37/0.64 thf(fact_5189_list__tail__coinc,axiom,
% 0.37/0.64 ! [N1: $o,R1: list_o,N22: $o,R22: list_o] :
% 0.37/0.64 ( ( ( cons_o @ N1 @ R1 )
% 0.37/0.64 = ( cons_o @ N22 @ R22 ) )
% 0.37/0.64 => ( ( N1 = N22 )
% 0.37/0.64 & ( R1 = R22 ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % list_tail_coinc
% 0.37/0.64 thf(fact_5190_sorted2,axiom,
% 0.37/0.64 ! [X: $o,Y: $o,Zs: list_o] :
% 0.37/0.64 ( ( sorted_wrt_o @ ord_less_eq_o @ ( cons_o @ X @ ( cons_o @ Y @ Zs ) ) )
% 0.37/0.64 = ( ( ord_less_eq_o @ X @ Y )
% 0.37/0.64 & ( sorted_wrt_o @ ord_less_eq_o @ ( cons_o @ Y @ Zs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted2
% 0.37/0.64 thf(fact_5191_sorted2,axiom,
% 0.37/0.64 ! [X: rat,Y: rat,Zs: list_rat] :
% 0.37/0.64 ( ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X @ ( cons_rat @ Y @ Zs ) ) )
% 0.37/0.64 = ( ( ord_less_eq_rat @ X @ Y )
% 0.37/0.64 & ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ Y @ Zs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted2
% 0.37/0.64 thf(fact_5192_sorted2,axiom,
% 0.37/0.64 ! [X: num,Y: num,Zs: list_num] :
% 0.37/0.64 ( ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X @ ( cons_num @ Y @ Zs ) ) )
% 0.37/0.64 = ( ( ord_less_eq_num @ X @ Y )
% 0.37/0.64 & ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ Y @ Zs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted2
% 0.37/0.64 thf(fact_5193_sorted2,axiom,
% 0.37/0.64 ! [X: nat,Y: nat,Zs: list_nat] :
% 0.37/0.64 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X @ ( cons_nat @ Y @ Zs ) ) )
% 0.37/0.64 = ( ( ord_less_eq_nat @ X @ Y )
% 0.37/0.64 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ Y @ Zs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted2
% 0.37/0.64 thf(fact_5194_sorted2,axiom,
% 0.37/0.64 ! [X: int,Y: int,Zs: list_int] :
% 0.37/0.64 ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X @ ( cons_int @ Y @ Zs ) ) )
% 0.37/0.64 = ( ( ord_less_eq_int @ X @ Y )
% 0.37/0.64 & ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ Y @ Zs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted2
% 0.37/0.64 thf(fact_5195_sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: real,Ys: list_real] :
% 0.37/0.64 ( ( sorted_wrt_real @ ord_less_eq_real @ ( cons_real @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: real] :
% 0.37/0.64 ( ( member_real @ X4 @ ( set_real2 @ Ys ) )
% 0.37/0.64 => ( ord_less_eq_real @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_real @ ord_less_eq_real @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_simps(2)
% 0.37/0.64 thf(fact_5196_sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: $o,Ys: list_o] :
% 0.37/0.64 ( ( sorted_wrt_o @ ord_less_eq_o @ ( cons_o @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: $o] :
% 0.37/0.64 ( ( member_o @ X4 @ ( set_o2 @ Ys ) )
% 0.37/0.64 => ( ord_less_eq_o @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_o @ ord_less_eq_o @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_simps(2)
% 0.37/0.64 thf(fact_5197_sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: rat,Ys: list_rat] :
% 0.37/0.64 ( ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: rat] :
% 0.37/0.64 ( ( member_rat @ X4 @ ( set_rat2 @ Ys ) )
% 0.37/0.64 => ( ord_less_eq_rat @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_rat @ ord_less_eq_rat @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_simps(2)
% 0.37/0.64 thf(fact_5198_sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: num,Ys: list_num] :
% 0.37/0.64 ( ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: num] :
% 0.37/0.64 ( ( member_num @ X4 @ ( set_num2 @ Ys ) )
% 0.37/0.64 => ( ord_less_eq_num @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_num @ ord_less_eq_num @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_simps(2)
% 0.37/0.64 thf(fact_5199_sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: nat,Ys: list_nat] :
% 0.37/0.64 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: nat] :
% 0.37/0.64 ( ( member_nat @ X4 @ ( set_nat2 @ Ys ) )
% 0.37/0.64 => ( ord_less_eq_nat @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_nat @ ord_less_eq_nat @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_simps(2)
% 0.37/0.64 thf(fact_5200_sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: int,Ys: list_int] :
% 0.37/0.64 ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: int] :
% 0.37/0.64 ( ( member_int @ X4 @ ( set_int2 @ Ys ) )
% 0.37/0.64 => ( ord_less_eq_int @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_int @ ord_less_eq_int @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % sorted_simps(2)
% 0.37/0.64 thf(fact_5201_strict__sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: $o,Ys: list_o] :
% 0.37/0.64 ( ( sorted_wrt_o @ ord_less_o @ ( cons_o @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: $o] :
% 0.37/0.64 ( ( member_o @ X4 @ ( set_o2 @ Ys ) )
% 0.37/0.64 => ( ord_less_o @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_o @ ord_less_o @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_simps(2)
% 0.37/0.64 thf(fact_5202_strict__sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: real,Ys: list_real] :
% 0.37/0.64 ( ( sorted_wrt_real @ ord_less_real @ ( cons_real @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: real] :
% 0.37/0.64 ( ( member_real @ X4 @ ( set_real2 @ Ys ) )
% 0.37/0.64 => ( ord_less_real @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_real @ ord_less_real @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_simps(2)
% 0.37/0.64 thf(fact_5203_strict__sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: rat,Ys: list_rat] :
% 0.37/0.64 ( ( sorted_wrt_rat @ ord_less_rat @ ( cons_rat @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: rat] :
% 0.37/0.64 ( ( member_rat @ X4 @ ( set_rat2 @ Ys ) )
% 0.37/0.64 => ( ord_less_rat @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_rat @ ord_less_rat @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_simps(2)
% 0.37/0.64 thf(fact_5204_strict__sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: num,Ys: list_num] :
% 0.37/0.64 ( ( sorted_wrt_num @ ord_less_num @ ( cons_num @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: num] :
% 0.37/0.64 ( ( member_num @ X4 @ ( set_num2 @ Ys ) )
% 0.37/0.64 => ( ord_less_num @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_num @ ord_less_num @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_simps(2)
% 0.37/0.64 thf(fact_5205_strict__sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: nat,Ys: list_nat] :
% 0.37/0.64 ( ( sorted_wrt_nat @ ord_less_nat @ ( cons_nat @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: nat] :
% 0.37/0.64 ( ( member_nat @ X4 @ ( set_nat2 @ Ys ) )
% 0.37/0.64 => ( ord_less_nat @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_nat @ ord_less_nat @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_simps(2)
% 0.37/0.64 thf(fact_5206_strict__sorted__simps_I2_J,axiom,
% 0.37/0.64 ! [X: int,Ys: list_int] :
% 0.37/0.64 ( ( sorted_wrt_int @ ord_less_int @ ( cons_int @ X @ Ys ) )
% 0.37/0.64 = ( ! [X4: int] :
% 0.37/0.64 ( ( member_int @ X4 @ ( set_int2 @ Ys ) )
% 0.37/0.64 => ( ord_less_int @ X @ X4 ) )
% 0.37/0.64 & ( sorted_wrt_int @ ord_less_int @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_simps(2)
% 0.37/0.64 thf(fact_5207_strict__sorted__imp__sorted,axiom,
% 0.37/0.64 ! [Xs: list_real] :
% 0.37/0.64 ( ( sorted_wrt_real @ ord_less_real @ Xs )
% 0.37/0.64 => ( sorted_wrt_real @ ord_less_eq_real @ Xs ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_imp_sorted
% 0.37/0.64 thf(fact_5208_strict__sorted__imp__sorted,axiom,
% 0.37/0.64 ! [Xs: list_rat] :
% 0.37/0.64 ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 0.37/0.64 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_imp_sorted
% 0.37/0.64 thf(fact_5209_strict__sorted__imp__sorted,axiom,
% 0.37/0.64 ! [Xs: list_num] :
% 0.37/0.64 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 0.37/0.64 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_imp_sorted
% 0.37/0.64 thf(fact_5210_strict__sorted__imp__sorted,axiom,
% 0.37/0.64 ! [Xs: list_nat] :
% 0.37/0.64 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 0.37/0.64 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_imp_sorted
% 0.37/0.64 thf(fact_5211_strict__sorted__imp__sorted,axiom,
% 0.37/0.64 ! [Xs: list_int] :
% 0.37/0.64 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 0.37/0.64 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_imp_sorted
% 0.37/0.64 thf(fact_5212_strict__sorted__equal,axiom,
% 0.37/0.64 ! [Xs: list_o,Ys: list_o] :
% 0.37/0.64 ( ( sorted_wrt_o @ ord_less_o @ Xs )
% 0.37/0.64 => ( ( sorted_wrt_o @ ord_less_o @ Ys )
% 0.37/0.64 => ( ( ( set_o2 @ Ys )
% 0.37/0.64 = ( set_o2 @ Xs ) )
% 0.37/0.64 => ( Ys = Xs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_equal
% 0.37/0.64 thf(fact_5213_strict__sorted__equal,axiom,
% 0.37/0.64 ! [Xs: list_real,Ys: list_real] :
% 0.37/0.64 ( ( sorted_wrt_real @ ord_less_real @ Xs )
% 0.37/0.64 => ( ( sorted_wrt_real @ ord_less_real @ Ys )
% 0.37/0.64 => ( ( ( set_real2 @ Ys )
% 0.37/0.64 = ( set_real2 @ Xs ) )
% 0.37/0.64 => ( Ys = Xs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_equal
% 0.37/0.64 thf(fact_5214_strict__sorted__equal,axiom,
% 0.37/0.64 ! [Xs: list_rat,Ys: list_rat] :
% 0.37/0.64 ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 0.37/0.64 => ( ( sorted_wrt_rat @ ord_less_rat @ Ys )
% 0.37/0.64 => ( ( ( set_rat2 @ Ys )
% 0.37/0.64 = ( set_rat2 @ Xs ) )
% 0.37/0.64 => ( Ys = Xs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_equal
% 0.37/0.64 thf(fact_5215_strict__sorted__equal,axiom,
% 0.37/0.64 ! [Xs: list_num,Ys: list_num] :
% 0.37/0.64 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 0.37/0.64 => ( ( sorted_wrt_num @ ord_less_num @ Ys )
% 0.37/0.64 => ( ( ( set_num2 @ Ys )
% 0.37/0.64 = ( set_num2 @ Xs ) )
% 0.37/0.64 => ( Ys = Xs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_equal
% 0.37/0.64 thf(fact_5216_strict__sorted__equal,axiom,
% 0.37/0.64 ! [Xs: list_nat,Ys: list_nat] :
% 0.37/0.64 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 0.37/0.64 => ( ( sorted_wrt_nat @ ord_less_nat @ Ys )
% 0.37/0.64 => ( ( ( set_nat2 @ Ys )
% 0.37/0.64 = ( set_nat2 @ Xs ) )
% 0.37/0.64 => ( Ys = Xs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_equal
% 0.37/0.64 thf(fact_5217_strict__sorted__equal,axiom,
% 0.37/0.64 ! [Xs: list_int,Ys: list_int] :
% 0.37/0.64 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 0.37/0.64 => ( ( sorted_wrt_int @ ord_less_int @ Ys )
% 0.37/0.64 => ( ( ( set_int2 @ Ys )
% 0.37/0.64 = ( set_int2 @ Xs ) )
% 0.37/0.64 => ( Ys = Xs ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % strict_sorted_equal
% 0.37/0.64 thf(fact_5218_length__nth__simps_I2_J,axiom,
% 0.37/0.64 ! [X: int,Xs: list_int] :
% 0.37/0.64 ( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
% 0.37/0.64 = ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(2)
% 0.37/0.64 thf(fact_5219_length__nth__simps_I2_J,axiom,
% 0.37/0.64 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.64 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) )
% 0.37/0.64 = ( suc @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(2)
% 0.37/0.64 thf(fact_5220_length__nth__simps_I2_J,axiom,
% 0.37/0.64 ! [X: real,Xs: list_real] :
% 0.37/0.64 ( ( size_size_list_real @ ( cons_real @ X @ Xs ) )
% 0.37/0.64 = ( suc @ ( size_size_list_real @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(2)
% 0.37/0.64 thf(fact_5221_length__nth__simps_I2_J,axiom,
% 0.37/0.64 ! [X: $o,Xs: list_o] :
% 0.37/0.64 ( ( size_size_list_o @ ( cons_o @ X @ Xs ) )
% 0.37/0.64 = ( suc @ ( size_size_list_o @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(2)
% 0.37/0.64 thf(fact_5222_length__nth__simps_I2_J,axiom,
% 0.37/0.64 ! [X: nat,Xs: list_nat] :
% 0.37/0.64 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs ) )
% 0.37/0.64 = ( suc @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_nth_simps(2)
% 0.37/0.64 thf(fact_5223_length__Suc__conv,axiom,
% 0.37/0.64 ! [Xs: list_int,N: nat] :
% 0.37/0.64 ( ( ( size_size_list_int @ Xs )
% 0.37/0.64 = ( suc @ N ) )
% 0.37/0.64 = ( ? [Y4: int,Ys3: list_int] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_int @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_int @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_Suc_conv
% 0.37/0.64 thf(fact_5224_length__Suc__conv,axiom,
% 0.37/0.64 ! [Xs: list_VEBT_VEBT,N: nat] :
% 0.37/0.64 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.64 = ( suc @ N ) )
% 0.37/0.64 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_Suc_conv
% 0.37/0.64 thf(fact_5225_length__Suc__conv,axiom,
% 0.37/0.64 ! [Xs: list_real,N: nat] :
% 0.37/0.64 ( ( ( size_size_list_real @ Xs )
% 0.37/0.64 = ( suc @ N ) )
% 0.37/0.64 = ( ? [Y4: real,Ys3: list_real] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_real @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_real @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_Suc_conv
% 0.37/0.64 thf(fact_5226_length__Suc__conv,axiom,
% 0.37/0.64 ! [Xs: list_o,N: nat] :
% 0.37/0.64 ( ( ( size_size_list_o @ Xs )
% 0.37/0.64 = ( suc @ N ) )
% 0.37/0.64 = ( ? [Y4: $o,Ys3: list_o] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_o @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_o @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_Suc_conv
% 0.37/0.64 thf(fact_5227_length__Suc__conv,axiom,
% 0.37/0.64 ! [Xs: list_nat,N: nat] :
% 0.37/0.64 ( ( ( size_size_list_nat @ Xs )
% 0.37/0.64 = ( suc @ N ) )
% 0.37/0.64 = ( ? [Y4: nat,Ys3: list_nat] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_nat @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_nat @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % length_Suc_conv
% 0.37/0.64 thf(fact_5228_Suc__length__conv,axiom,
% 0.37/0.64 ! [N: nat,Xs: list_int] :
% 0.37/0.64 ( ( ( suc @ N )
% 0.37/0.64 = ( size_size_list_int @ Xs ) )
% 0.37/0.64 = ( ? [Y4: int,Ys3: list_int] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_int @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_int @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Suc_length_conv
% 0.37/0.64 thf(fact_5229_Suc__length__conv,axiom,
% 0.37/0.64 ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.64 ( ( ( suc @ N )
% 0.37/0.64 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.64 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Suc_length_conv
% 0.37/0.64 thf(fact_5230_Suc__length__conv,axiom,
% 0.37/0.64 ! [N: nat,Xs: list_real] :
% 0.37/0.64 ( ( ( suc @ N )
% 0.37/0.64 = ( size_size_list_real @ Xs ) )
% 0.37/0.64 = ( ? [Y4: real,Ys3: list_real] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_real @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_real @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Suc_length_conv
% 0.37/0.64 thf(fact_5231_Suc__length__conv,axiom,
% 0.37/0.64 ! [N: nat,Xs: list_o] :
% 0.37/0.64 ( ( ( suc @ N )
% 0.37/0.64 = ( size_size_list_o @ Xs ) )
% 0.37/0.64 = ( ? [Y4: $o,Ys3: list_o] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_o @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_o @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Suc_length_conv
% 0.37/0.64 thf(fact_5232_Suc__length__conv,axiom,
% 0.37/0.64 ! [N: nat,Xs: list_nat] :
% 0.37/0.64 ( ( ( suc @ N )
% 0.37/0.64 = ( size_size_list_nat @ Xs ) )
% 0.37/0.64 = ( ? [Y4: nat,Ys3: list_nat] :
% 0.37/0.64 ( ( Xs
% 0.37/0.64 = ( cons_nat @ Y4 @ Ys3 ) )
% 0.37/0.64 & ( ( size_size_list_nat @ Ys3 )
% 0.37/0.64 = N ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % Suc_length_conv
% 0.37/0.64 thf(fact_5233_impossible__Cons,axiom,
% 0.37/0.64 ! [Xs: list_int,Ys: list_int,X: int] :
% 0.37/0.64 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) )
% 0.37/0.64 => ( Xs
% 0.37/0.64 != ( cons_int @ X @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % impossible_Cons
% 0.37/0.64 thf(fact_5234_impossible__Cons,axiom,
% 0.37/0.64 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.64 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.64 => ( Xs
% 0.37/0.64 != ( cons_VEBT_VEBT @ X @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % impossible_Cons
% 0.37/0.64 thf(fact_5235_impossible__Cons,axiom,
% 0.37/0.64 ! [Xs: list_real,Ys: list_real,X: real] :
% 0.37/0.64 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ ( size_size_list_real @ Ys ) )
% 0.37/0.64 => ( Xs
% 0.37/0.64 != ( cons_real @ X @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % impossible_Cons
% 0.37/0.64 thf(fact_5236_impossible__Cons,axiom,
% 0.37/0.64 ! [Xs: list_o,Ys: list_o,X: $o] :
% 0.37/0.64 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) )
% 0.37/0.64 => ( Xs
% 0.37/0.64 != ( cons_o @ X @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % impossible_Cons
% 0.37/0.64 thf(fact_5237_impossible__Cons,axiom,
% 0.37/0.64 ! [Xs: list_nat,Ys: list_nat,X: nat] :
% 0.37/0.64 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) )
% 0.37/0.64 => ( Xs
% 0.37/0.64 != ( cons_nat @ X @ Ys ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % impossible_Cons
% 0.37/0.64 thf(fact_5238_set__subset__Cons,axiom,
% 0.37/0.64 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % set_subset_Cons
% 0.37/0.64 thf(fact_5239_set__subset__Cons,axiom,
% 0.37/0.64 ! [Xs: list_real,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ ( set_real2 @ ( cons_real @ X @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % set_subset_Cons
% 0.37/0.64 thf(fact_5240_set__subset__Cons,axiom,
% 0.37/0.64 ! [Xs: list_nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ ( cons_nat @ X @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % set_subset_Cons
% 0.37/0.64 thf(fact_5241_set__subset__Cons,axiom,
% 0.37/0.64 ! [Xs: list_o,X: $o] : ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ ( set_o2 @ ( cons_o @ X @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % set_subset_Cons
% 0.37/0.64 thf(fact_5242_set__subset__Cons,axiom,
% 0.37/0.64 ! [Xs: list_int,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ ( set_int2 @ ( cons_int @ X @ Xs ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % set_subset_Cons
% 0.37/0.64 thf(fact_5243_listI__assn__cong,axiom,
% 0.37/0.64 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,A9: vEBT_VEBTi > vEBT_VEBTi > assn] :
% 0.37/0.64 ( ( I5 = I6 )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 0.37/0.64 => ( ! [I2: nat] :
% 0.37/0.64 ( ( member_nat @ I2 @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 0.37/0.64 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.64 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) )
% 0.37/0.64 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi @ I2 ) )
% 0.37/0.64 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.64 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( vEBT_L886525131989349516_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_cong
% 0.37/0.64 thf(fact_5244_listI__assn__cong,axiom,
% 0.37/0.64 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_int,Xsi2: list_int,A4: vEBT_VEBTi > int > assn,A9: vEBT_VEBTi > int > assn] :
% 0.37/0.64 ( ( I5 = I6 )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xsi )
% 0.37/0.64 = ( size_size_list_int @ Xsi2 ) )
% 0.37/0.64 => ( ! [I2: nat] :
% 0.37/0.64 ( ( member_nat @ I2 @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_size_list_int @ Xsi ) )
% 0.37/0.64 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.64 & ( ( nth_int @ Xsi @ I2 )
% 0.37/0.64 = ( nth_int @ Xsi2 @ I2 ) )
% 0.37/0.64 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_int @ Xsi @ I2 ) )
% 0.37/0.64 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_int @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.64 => ( ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( vEBT_L2806540629473551875Ti_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_cong
% 0.37/0.64 thf(fact_5245_listI__assn__cong,axiom,
% 0.37/0.64 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi,A4: int > vEBT_VEBTi > assn,A9: int > vEBT_VEBTi > assn] :
% 0.37/0.64 ( ( I5 = I6 )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.64 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 0.37/0.64 => ( ! [I2: nat] :
% 0.37/0.64 ( ( member_nat @ I2 @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 0.37/0.64 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.64 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.64 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) )
% 0.37/0.64 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi @ I2 ) )
% 0.37/0.64 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.64 => ( ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( vEBT_L114188773329725699_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_cong
% 0.37/0.64 thf(fact_5246_listI__assn__cong,axiom,
% 0.37/0.64 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_int,Xsi2: list_int,A4: int > int > assn,A9: int > int > assn] :
% 0.37/0.64 ( ( I5 = I6 )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.64 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xsi )
% 0.37/0.64 = ( size_size_list_int @ Xsi2 ) )
% 0.37/0.64 => ( ! [I2: nat] :
% 0.37/0.64 ( ( member_nat @ I2 @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.64 = ( size_size_list_int @ Xsi ) )
% 0.37/0.64 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.64 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.64 & ( ( nth_int @ Xsi @ I2 )
% 0.37/0.64 = ( nth_int @ Xsi2 @ I2 ) )
% 0.37/0.64 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Xsi @ I2 ) )
% 0.37/0.64 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_int @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.64 => ( ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( vEBT_L8888932350013902202nt_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_cong
% 0.37/0.64 thf(fact_5247_listI__assn__cong,axiom,
% 0.37/0.64 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A4: vEBT_VEBTi > vEBT_VEBT > assn,A9: vEBT_VEBTi > vEBT_VEBT > assn] :
% 0.37/0.64 ( ( I5 = I6 )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.64 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.64 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 0.37/0.64 => ( ! [I2: nat] :
% 0.37/0.64 ( ( member_nat @ I2 @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 0.37/0.64 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.64 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) )
% 0.37/0.64 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Xsi @ I2 ) )
% 0.37/0.64 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.64 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( vEBT_L2497118539674116125T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_cong
% 0.37/0.64 thf(fact_5248_listI__assn__cong,axiom,
% 0.37/0.64 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A4: int > vEBT_VEBT > assn,A9: int > vEBT_VEBT > assn] :
% 0.37/0.64 ( ( I5 = I6 )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.64 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.64 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.64 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 0.37/0.64 => ( ! [I2: nat] :
% 0.37/0.64 ( ( member_nat @ I2 @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.64 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.64 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 0.37/0.64 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.64 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.64 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) )
% 0.37/0.64 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Xsi @ I2 ) )
% 0.37/0.64 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.64 => ( ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.64 = ( vEBT_L2018189785592951398T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.64
% 0.37/0.64 % listI_assn_cong
% 0.37/0.64 thf(fact_5249_listI__assn__cong,axiom,
% 0.37/0.64 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_real,Xsi2: list_real,A4: vEBT_VEBTi > real > assn,A9: vEBT_VEBTi > real > assn] :
% 0.37/0.64 ( ( I5 = I6 )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.64 => ( ( ( size_size_list_real @ Xsi )
% 0.37/0.64 = ( size_size_list_real @ Xsi2 ) )
% 0.37/0.64 => ( ! [I2: nat] :
% 0.37/0.64 ( ( member_nat @ I2 @ I5 )
% 0.37/0.64 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.64 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.64 = ( size_size_list_real @ Xsi ) )
% 0.37/0.64 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.64 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.64 & ( ( nth_real @ Xsi @ I2 )
% 0.37/0.64 = ( nth_real @ Xsi2 @ I2 ) )
% 0.37/0.64 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_real @ Xsi @ I2 ) )
% 0.37/0.65 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_real @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L7728200936804140803i_real @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L7728200936804140803i_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_cong
% 0.37/0.65 thf(fact_5250_listI__assn__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_real,Xsi2: list_real,A4: int > real > assn,A9: int > real > assn] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_real @ Xsi )
% 0.37/0.65 = ( size_size_list_real @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_real @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.65 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_real @ Xsi @ I2 )
% 0.37/0.65 = ( nth_real @ Xsi2 @ I2 ) )
% 0.37/0.65 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_real @ Xsi @ I2 ) )
% 0.37/0.65 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_real @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L7077748017936769786t_real @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L7077748017936769786t_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_cong
% 0.37/0.65 thf(fact_5251_listI__assn__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_o,Xsi2: list_o,A4: vEBT_VEBTi > $o > assn,A9: vEBT_VEBTi > $o > assn] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_o @ Xsi )
% 0.37/0.65 = ( size_size_list_o @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_size_list_o @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_o @ Xsi @ I2 )
% 0.37/0.65 = ( nth_o @ Xsi2 @ I2 ) )
% 0.37/0.65 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_o @ Xsi @ I2 ) )
% 0.37/0.65 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_o @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L3328983362619735041EBTi_o @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L3328983362619735041EBTi_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_cong
% 0.37/0.65 thf(fact_5252_listI__assn__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_o,Xsi2: list_o,A4: int > $o > assn,A9: int > $o > assn] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_o @ Xsi )
% 0.37/0.65 = ( size_size_list_o @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_o @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.65 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_o @ Xsi @ I2 )
% 0.37/0.65 = ( nth_o @ Xsi2 @ I2 ) )
% 0.37/0.65 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_o @ Xsi @ I2 ) )
% 0.37/0.65 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_o @ Xsi2 @ I2 ) ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L3563379889750563018_int_o @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L3563379889750563018_int_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_cong
% 0.37/0.65 thf(fact_5253_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > vEBT_VEBTi > assn,A9: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L886525131989349516_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5254_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > int > assn,A9: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_int,Xsi2: list_int] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xsi )
% 0.37/0.65 = ( size_size_list_int @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_int @ Xsi @ I2 )
% 0.37/0.65 = ( nth_int @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L2806540629473551875Ti_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5255_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: int > vEBT_VEBTi > assn,A9: int > vEBT_VEBTi > assn,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.65 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L114188773329725699_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5256_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: int > int > assn,A9: int > int > assn,Xs: list_int,Xs4: list_int,Xsi: list_int,Xsi2: list_int] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xsi )
% 0.37/0.65 = ( size_size_list_int @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.65 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_int @ Xsi @ I2 )
% 0.37/0.65 = ( nth_int @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L8888932350013902202nt_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5257_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > vEBT_VEBT > assn,A9: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L2497118539674116125T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5258_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: int > vEBT_VEBT > assn,A9: int > vEBT_VEBT > assn,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.65 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L2018189785592951398T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5259_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > real > assn,A9: vEBT_VEBTi > real > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_real,Xsi2: list_real] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_real @ Xsi )
% 0.37/0.65 = ( size_size_list_real @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_size_list_real @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_real @ Xsi @ I2 )
% 0.37/0.65 = ( nth_real @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L7728200936804140803i_real @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L7728200936804140803i_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5260_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: int > real > assn,A9: int > real > assn,Xs: list_int,Xs4: list_int,Xsi: list_real,Xsi2: list_real] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_real @ Xsi )
% 0.37/0.65 = ( size_size_list_real @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_real @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.65 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_real @ Xsi @ I2 )
% 0.37/0.65 = ( nth_real @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L7077748017936769786t_real @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L7077748017936769786t_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5261_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > $o > assn,A9: vEBT_VEBTi > $o > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_o,Xsi2: list_o] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_o @ Xsi )
% 0.37/0.65 = ( size_size_list_o @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 0.37/0.65 = ( size_size_list_o @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_o @ Xsi @ I2 )
% 0.37/0.65 = ( nth_o @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L3328983362619735041EBTi_o @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L3328983362619735041EBTi_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5262_listI__assn__weak__cong,axiom,
% 0.37/0.65 ! [I5: set_nat,I6: set_nat,A4: int > $o > assn,A9: int > $o > assn,Xs: list_int,Xs4: list_int,Xsi: list_o,Xsi2: list_o] :
% 0.37/0.65 ( ( I5 = I6 )
% 0.37/0.65 => ( ( A4 = A9 )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_int @ Xs4 ) )
% 0.37/0.65 => ( ( ( size_size_list_o @ Xsi )
% 0.37/0.65 = ( size_size_list_o @ Xsi2 ) )
% 0.37/0.65 => ( ! [I2: nat] :
% 0.37/0.65 ( ( member_nat @ I2 @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( size_size_list_int @ Xs )
% 0.37/0.65 = ( size_size_list_o @ Xsi ) )
% 0.37/0.65 => ( ( ( nth_int @ Xs @ I2 )
% 0.37/0.65 = ( nth_int @ Xs4 @ I2 ) )
% 0.37/0.65 & ( ( nth_o @ Xsi @ I2 )
% 0.37/0.65 = ( nth_o @ Xsi2 @ I2 ) ) ) ) ) )
% 0.37/0.65 => ( ( vEBT_L3563379889750563018_int_o @ I5 @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L3563379889750563018_int_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_weak_cong
% 0.37/0.65 thf(fact_5263_sorted__wrt01,axiom,
% 0.37/0.65 ! [Xs: list_int,P2: int > int > $o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_int @ P2 @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt01
% 0.37/0.65 thf(fact_5264_sorted__wrt01,axiom,
% 0.37/0.65 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > vEBT_VEBT > $o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_VEBT_VEBT @ P2 @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt01
% 0.37/0.65 thf(fact_5265_sorted__wrt01,axiom,
% 0.37/0.65 ! [Xs: list_real,P2: real > real > $o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_real @ P2 @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt01
% 0.37/0.65 thf(fact_5266_sorted__wrt01,axiom,
% 0.37/0.65 ! [Xs: list_o,P2: $o > $o > $o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_o @ P2 @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt01
% 0.37/0.65 thf(fact_5267_sorted__wrt01,axiom,
% 0.37/0.65 ! [Xs: list_nat,P2: nat > nat > $o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_nat @ P2 @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt01
% 0.37/0.65 thf(fact_5268_sorted__wrt__iff__nth__less,axiom,
% 0.37/0.65 ( sorted9206477368072086664_VEBTi
% 0.37/0.65 = ( ^ [P5: vEBT_VEBTi > vEBT_VEBTi > $o,Xs2: list_VEBT_VEBTi] :
% 0.37/0.65 ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 0.37/0.65 => ( P5 @ ( nth_VEBT_VEBTi @ Xs2 @ I3 ) @ ( nth_VEBT_VEBTi @ Xs2 @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_iff_nth_less
% 0.37/0.65 thf(fact_5269_sorted__wrt__iff__nth__less,axiom,
% 0.37/0.65 ( sorted_wrt_int
% 0.37/0.65 = ( ^ [P5: int > int > $o,Xs2: list_int] :
% 0.37/0.65 ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs2 ) )
% 0.37/0.65 => ( P5 @ ( nth_int @ Xs2 @ I3 ) @ ( nth_int @ Xs2 @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_iff_nth_less
% 0.37/0.65 thf(fact_5270_sorted__wrt__iff__nth__less,axiom,
% 0.37/0.65 ( sorted_wrt_VEBT_VEBT
% 0.37/0.65 = ( ^ [P5: vEBT_VEBT > vEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 0.37/0.65 ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.37/0.65 => ( P5 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) @ ( nth_VEBT_VEBT @ Xs2 @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_iff_nth_less
% 0.37/0.65 thf(fact_5271_sorted__wrt__iff__nth__less,axiom,
% 0.37/0.65 ( sorted_wrt_real
% 0.37/0.65 = ( ^ [P5: real > real > $o,Xs2: list_real] :
% 0.37/0.65 ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs2 ) )
% 0.37/0.65 => ( P5 @ ( nth_real @ Xs2 @ I3 ) @ ( nth_real @ Xs2 @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_iff_nth_less
% 0.37/0.65 thf(fact_5272_sorted__wrt__iff__nth__less,axiom,
% 0.37/0.65 ( sorted_wrt_o
% 0.37/0.65 = ( ^ [P5: $o > $o > $o,Xs2: list_o] :
% 0.37/0.65 ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs2 ) )
% 0.37/0.65 => ( P5 @ ( nth_o @ Xs2 @ I3 ) @ ( nth_o @ Xs2 @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_iff_nth_less
% 0.37/0.65 thf(fact_5273_sorted__wrt__iff__nth__less,axiom,
% 0.37/0.65 ( sorted_wrt_nat
% 0.37/0.65 = ( ^ [P5: nat > nat > $o,Xs2: list_nat] :
% 0.37/0.65 ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs2 ) )
% 0.37/0.65 => ( P5 @ ( nth_nat @ Xs2 @ I3 ) @ ( nth_nat @ Xs2 @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_iff_nth_less
% 0.37/0.65 thf(fact_5274_sorted__wrt__nth__less,axiom,
% 0.37/0.65 ! [P2: vEBT_VEBTi > vEBT_VEBTi > $o,Xs: list_VEBT_VEBTi,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted9206477368072086664_VEBTi @ P2 @ Xs )
% 0.37/0.65 => ( ( ord_less_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_nth_less
% 0.37/0.65 thf(fact_5275_sorted__wrt__nth__less,axiom,
% 0.37/0.65 ! [P2: int > int > $o,Xs: list_int,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_int @ P2 @ Xs )
% 0.37/0.65 => ( ( ord_less_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( P2 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_nth_less
% 0.37/0.65 thf(fact_5276_sorted__wrt__nth__less,axiom,
% 0.37/0.65 ! [P2: vEBT_VEBT > vEBT_VEBT > $o,Xs: list_VEBT_VEBT,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_VEBT_VEBT @ P2 @ Xs )
% 0.37/0.65 => ( ( ord_less_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_nth_less
% 0.37/0.65 thf(fact_5277_sorted__wrt__nth__less,axiom,
% 0.37/0.65 ! [P2: real > real > $o,Xs: list_real,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_real @ P2 @ Xs )
% 0.37/0.65 => ( ( ord_less_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( P2 @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_nth_less
% 0.37/0.65 thf(fact_5278_sorted__wrt__nth__less,axiom,
% 0.37/0.65 ! [P2: $o > $o > $o,Xs: list_o,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_o @ P2 @ Xs )
% 0.37/0.65 => ( ( ord_less_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( P2 @ ( nth_o @ Xs @ I ) @ ( nth_o @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_nth_less
% 0.37/0.65 thf(fact_5279_sorted__wrt__nth__less,axiom,
% 0.37/0.65 ! [P2: nat > nat > $o,Xs: list_nat,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_nat @ P2 @ Xs )
% 0.37/0.65 => ( ( ord_less_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( P2 @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_nth_less
% 0.37/0.65 thf(fact_5280_sorted__wrt__less__idx,axiom,
% 0.37/0.65 ! [Ns: list_nat,I: nat] :
% 0.37/0.65 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 0.37/0.65 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_wrt_less_idx
% 0.37/0.65 thf(fact_5281_Suc__le__length__iff,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_int] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 = ( ? [X4: int,Ys3: list_int] :
% 0.37/0.65 ( ( Xs
% 0.37/0.65 = ( cons_int @ X4 @ Ys3 ) )
% 0.37/0.65 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Suc_le_length_iff
% 0.37/0.65 thf(fact_5282_Suc__le__length__iff,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 = ( ? [X4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.37/0.65 ( ( Xs
% 0.37/0.65 = ( cons_VEBT_VEBT @ X4 @ Ys3 ) )
% 0.37/0.65 & ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys3 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Suc_le_length_iff
% 0.37/0.65 thf(fact_5283_Suc__le__length__iff,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_real] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 = ( ? [X4: real,Ys3: list_real] :
% 0.37/0.65 ( ( Xs
% 0.37/0.65 = ( cons_real @ X4 @ Ys3 ) )
% 0.37/0.65 & ( ord_less_eq_nat @ N @ ( size_size_list_real @ Ys3 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Suc_le_length_iff
% 0.37/0.65 thf(fact_5284_Suc__le__length__iff,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 = ( ? [X4: $o,Ys3: list_o] :
% 0.37/0.65 ( ( Xs
% 0.37/0.65 = ( cons_o @ X4 @ Ys3 ) )
% 0.37/0.65 & ( ord_less_eq_nat @ N @ ( size_size_list_o @ Ys3 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Suc_le_length_iff
% 0.37/0.65 thf(fact_5285_Suc__le__length__iff,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 = ( ? [X4: nat,Ys3: list_nat] :
% 0.37/0.65 ( ( Xs
% 0.37/0.65 = ( cons_nat @ X4 @ Ys3 ) )
% 0.37/0.65 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Suc_le_length_iff
% 0.37/0.65 thf(fact_5286_sorted01,axiom,
% 0.37/0.65 ! [Xs: list_real] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_real @ ord_less_eq_real @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted01
% 0.37/0.65 thf(fact_5287_sorted01,axiom,
% 0.37/0.65 ! [Xs: list_o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_o @ ord_less_eq_o @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted01
% 0.37/0.65 thf(fact_5288_sorted01,axiom,
% 0.37/0.65 ! [Xs: list_rat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_rat @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted01
% 0.37/0.65 thf(fact_5289_sorted01,axiom,
% 0.37/0.65 ! [Xs: list_num] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_num @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted01
% 0.37/0.65 thf(fact_5290_sorted01,axiom,
% 0.37/0.65 ! [Xs: list_nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted01
% 0.37/0.65 thf(fact_5291_sorted01,axiom,
% 0.37/0.65 ! [Xs: list_int] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 0.37/0.65 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted01
% 0.37/0.65 thf(fact_5292_sorted__iff__nth__mono__less,axiom,
% 0.37/0.65 ! [Xs: list_real] :
% 0.37/0.65 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_real @ ( nth_real @ Xs @ I3 ) @ ( nth_real @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono_less
% 0.37/0.65 thf(fact_5293_sorted__iff__nth__mono__less,axiom,
% 0.37/0.65 ! [Xs: list_o] :
% 0.37/0.65 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_o @ ( nth_o @ Xs @ I3 ) @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono_less
% 0.37/0.65 thf(fact_5294_sorted__iff__nth__mono__less,axiom,
% 0.37/0.65 ! [Xs: list_rat] :
% 0.37/0.65 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_rat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I3 ) @ ( nth_rat @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono_less
% 0.37/0.65 thf(fact_5295_sorted__iff__nth__mono__less,axiom,
% 0.37/0.65 ! [Xs: list_num] :
% 0.37/0.65 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_num @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_num @ ( nth_num @ Xs @ I3 ) @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono_less
% 0.37/0.65 thf(fact_5296_sorted__iff__nth__mono__less,axiom,
% 0.37/0.65 ! [Xs: list_nat] :
% 0.37/0.65 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono_less
% 0.37/0.65 thf(fact_5297_sorted__iff__nth__mono__less,axiom,
% 0.37/0.65 ! [Xs: list_int] :
% 0.37/0.65 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_int @ ( nth_int @ Xs @ I3 ) @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono_less
% 0.37/0.65 thf(fact_5298_list_Osize_I4_J,axiom,
% 0.37/0.65 ! [X21: int,X22: list_int] :
% 0.37/0.65 ( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
% 0.37/0.65 = ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list.size(4)
% 0.37/0.65 thf(fact_5299_list_Osize_I4_J,axiom,
% 0.37/0.65 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 0.37/0.65 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X21 @ X22 ) )
% 0.37/0.65 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list.size(4)
% 0.37/0.65 thf(fact_5300_list_Osize_I4_J,axiom,
% 0.37/0.65 ! [X21: real,X22: list_real] :
% 0.37/0.65 ( ( size_size_list_real @ ( cons_real @ X21 @ X22 ) )
% 0.37/0.65 = ( plus_plus_nat @ ( size_size_list_real @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list.size(4)
% 0.37/0.65 thf(fact_5301_list_Osize_I4_J,axiom,
% 0.37/0.65 ! [X21: $o,X22: list_o] :
% 0.37/0.65 ( ( size_size_list_o @ ( cons_o @ X21 @ X22 ) )
% 0.37/0.65 = ( plus_plus_nat @ ( size_size_list_o @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list.size(4)
% 0.37/0.65 thf(fact_5302_list_Osize_I4_J,axiom,
% 0.37/0.65 ! [X21: nat,X22: list_nat] :
% 0.37/0.65 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X22 ) )
% 0.37/0.65 = ( plus_plus_nat @ ( size_size_list_nat @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list.size(4)
% 0.37/0.65 thf(fact_5303_nth__Cons_H,axiom,
% 0.37/0.65 ! [N: nat,X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.65 ( ( ( N = zero_zero_nat )
% 0.37/0.65 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 0.37/0.65 = X ) )
% 0.37/0.65 & ( ( N != zero_zero_nat )
% 0.37/0.65 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 0.37/0.65 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_Cons'
% 0.37/0.65 thf(fact_5304_nth__Cons_H,axiom,
% 0.37/0.65 ! [N: nat,X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 0.37/0.65 ( ( ( N = zero_zero_nat )
% 0.37/0.65 => ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 0.37/0.65 = X ) )
% 0.37/0.65 & ( ( N != zero_zero_nat )
% 0.37/0.65 => ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_Cons'
% 0.37/0.65 thf(fact_5305_nth__Cons_H,axiom,
% 0.37/0.65 ! [N: nat,X: int,Xs: list_int] :
% 0.37/0.65 ( ( ( N = zero_zero_nat )
% 0.37/0.65 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 0.37/0.65 = X ) )
% 0.37/0.65 & ( ( N != zero_zero_nat )
% 0.37/0.65 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 0.37/0.65 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_Cons'
% 0.37/0.65 thf(fact_5306_nth__Cons_H,axiom,
% 0.37/0.65 ! [N: nat,X: nat,Xs: list_nat] :
% 0.37/0.65 ( ( ( N = zero_zero_nat )
% 0.37/0.65 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 0.37/0.65 = X ) )
% 0.37/0.65 & ( ( N != zero_zero_nat )
% 0.37/0.65 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 0.37/0.65 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_Cons'
% 0.37/0.65 thf(fact_5307_nth__Cons_H,axiom,
% 0.37/0.65 ! [X: $o,Xs: list_o,N: nat] :
% 0.37/0.65 ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 0.37/0.65 = ( ( ( N = zero_zero_nat )
% 0.37/0.65 => X )
% 0.37/0.65 & ( ( N != zero_zero_nat )
% 0.37/0.65 => ( nth_o @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_Cons'
% 0.37/0.65 thf(fact_5308_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L2497118539674116125T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5309_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > nat > assn,Xsi: list_nat] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L2809031099982602151Ti_nat @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5310_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L886525131989349516_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5311_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > int > assn,Xsi: list_int] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L2806540629473551875Ti_int @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5312_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L2018189785592951398T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5313_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > nat > assn,Xsi: list_nat] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L8891422820522952478nt_nat @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5314_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L114188773329725699_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5315_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > int > assn,Xsi: list_int] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L8888932350013902202nt_int @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5316_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L3204528365124325536T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5317_listI__assn__insert,axiom,
% 0.37/0.65 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > nat > assn,Xsi: list_nat] :
% 0.37/0.65 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L8650695023172932196BT_nat @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_insert
% 0.37/0.65 thf(fact_5318_sorted__iff__nth__Suc,axiom,
% 0.37/0.65 ! [Xs: list_real] :
% 0.37/0.65 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 0.37/0.65 = ( ! [I3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_real @ ( nth_real @ Xs @ I3 ) @ ( nth_real @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_Suc
% 0.37/0.65 thf(fact_5319_sorted__iff__nth__Suc,axiom,
% 0.37/0.65 ! [Xs: list_o] :
% 0.37/0.65 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 0.37/0.65 = ( ! [I3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_o @ ( nth_o @ Xs @ I3 ) @ ( nth_o @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_Suc
% 0.37/0.65 thf(fact_5320_sorted__iff__nth__Suc,axiom,
% 0.37/0.65 ! [Xs: list_rat] :
% 0.37/0.65 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.65 = ( ! [I3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_rat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I3 ) @ ( nth_rat @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_Suc
% 0.37/0.65 thf(fact_5321_sorted__iff__nth__Suc,axiom,
% 0.37/0.65 ! [Xs: list_num] :
% 0.37/0.65 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.65 = ( ! [I3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_num @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_num @ ( nth_num @ Xs @ I3 ) @ ( nth_num @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_Suc
% 0.37/0.65 thf(fact_5322_sorted__iff__nth__Suc,axiom,
% 0.37/0.65 ! [Xs: list_nat] :
% 0.37/0.65 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.65 = ( ! [I3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_Suc
% 0.37/0.65 thf(fact_5323_sorted__iff__nth__Suc,axiom,
% 0.37/0.65 ! [Xs: list_int] :
% 0.37/0.65 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.65 = ( ! [I3: nat] :
% 0.37/0.65 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_int @ ( nth_int @ Xs @ I3 ) @ ( nth_int @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_Suc
% 0.37/0.65 thf(fact_5324_sorted__iff__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_real] :
% 0.37/0.65 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_real @ ( nth_real @ Xs @ I3 ) @ ( nth_real @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono
% 0.37/0.65 thf(fact_5325_sorted__iff__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_o] :
% 0.37/0.65 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_o @ ( nth_o @ Xs @ I3 ) @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono
% 0.37/0.65 thf(fact_5326_sorted__iff__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_rat] :
% 0.37/0.65 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_rat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I3 ) @ ( nth_rat @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono
% 0.37/0.65 thf(fact_5327_sorted__iff__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_num] :
% 0.37/0.65 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_num @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_num @ ( nth_num @ Xs @ I3 ) @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono
% 0.37/0.65 thf(fact_5328_sorted__iff__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_nat] :
% 0.37/0.65 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono
% 0.37/0.65 thf(fact_5329_sorted__iff__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_int] :
% 0.37/0.65 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.65 = ( ! [I3: nat,J3: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.37/0.65 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_int @ ( nth_int @ Xs @ I3 ) @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_iff_nth_mono
% 0.37/0.65 thf(fact_5330_sorted__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_real,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 0.37/0.65 => ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_real @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_nth_mono
% 0.37/0.65 thf(fact_5331_sorted__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_o,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 0.37/0.65 => ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_o @ ( nth_o @ Xs @ I ) @ ( nth_o @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_nth_mono
% 0.37/0.65 thf(fact_5332_sorted__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_rat,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.65 => ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I ) @ ( nth_rat @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_nth_mono
% 0.37/0.65 thf(fact_5333_sorted__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_num,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.65 => ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_num @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_num @ ( nth_num @ Xs @ I ) @ ( nth_num @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_nth_mono
% 0.37/0.65 thf(fact_5334_sorted__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_nat,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.65 => ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_nth_mono
% 0.37/0.65 thf(fact_5335_sorted__nth__mono,axiom,
% 0.37/0.65 ! [Xs: list_int,I: nat,J: nat] :
% 0.37/0.65 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.65 => ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ord_less_eq_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_nth_mono
% 0.37/0.65 thf(fact_5336_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_literal] :
% 0.37/0.65 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.65 => ~ ! [L2: list_literal] :
% 0.37/0.65 ( ( sorted_wrt_literal @ ord_less_literal @ L2 )
% 0.37/0.65 => ( ( ( set_literal2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_s2501651207091587910iteral @ L2 )
% 0.37/0.65 != ( finite_card_literal @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5337_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_Code_integer] :
% 0.37/0.65 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.65 => ~ ! [L2: list_Code_integer] :
% 0.37/0.65 ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ L2 )
% 0.37/0.65 => ( ( ( set_Code_integer2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_s3445333598471063425nteger @ L2 )
% 0.37/0.65 != ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5338_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_o] :
% 0.37/0.65 ( ( finite_finite_o @ A4 )
% 0.37/0.65 => ~ ! [L2: list_o] :
% 0.37/0.65 ( ( sorted_wrt_o @ ord_less_o @ L2 )
% 0.37/0.65 => ( ( ( set_o2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_size_list_o @ L2 )
% 0.37/0.65 != ( finite_card_o @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5339_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_real] :
% 0.37/0.65 ( ( finite_finite_real @ A4 )
% 0.37/0.65 => ~ ! [L2: list_real] :
% 0.37/0.65 ( ( sorted_wrt_real @ ord_less_real @ L2 )
% 0.37/0.65 => ( ( ( set_real2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_size_list_real @ L2 )
% 0.37/0.65 != ( finite_card_real @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5340_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_rat] :
% 0.37/0.65 ( ( finite_finite_rat @ A4 )
% 0.37/0.65 => ~ ! [L2: list_rat] :
% 0.37/0.65 ( ( sorted_wrt_rat @ ord_less_rat @ L2 )
% 0.37/0.65 => ( ( ( set_rat2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_size_list_rat @ L2 )
% 0.37/0.65 != ( finite_card_rat @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5341_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_num] :
% 0.37/0.65 ( ( finite_finite_num @ A4 )
% 0.37/0.65 => ~ ! [L2: list_num] :
% 0.37/0.65 ( ( sorted_wrt_num @ ord_less_num @ L2 )
% 0.37/0.65 => ( ( ( set_num2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_size_list_num @ L2 )
% 0.37/0.65 != ( finite_card_num @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5342_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_nat] :
% 0.37/0.65 ( ( finite_finite_nat @ A4 )
% 0.37/0.65 => ~ ! [L2: list_nat] :
% 0.37/0.65 ( ( sorted_wrt_nat @ ord_less_nat @ L2 )
% 0.37/0.65 => ( ( ( set_nat2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_size_list_nat @ L2 )
% 0.37/0.65 != ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5343_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 0.37/0.65 ! [A4: set_int] :
% 0.37/0.65 ( ( finite_finite_int @ A4 )
% 0.37/0.65 => ~ ! [L2: list_int] :
% 0.37/0.65 ( ( sorted_wrt_int @ ord_less_int @ L2 )
% 0.37/0.65 => ( ( ( set_int2 @ L2 )
% 0.37/0.65 = A4 )
% 0.37/0.65 => ( ( size_size_list_int @ L2 )
% 0.37/0.65 != ( finite_card_int @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.finite_set_strict_sorted
% 0.37/0.65 thf(fact_5344_nth__non__equal__first__eq,axiom,
% 0.37/0.65 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 0.37/0.65 ( ( X != Y )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 0.37/0.65 = Y )
% 0.37/0.65 = ( ( ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.65 = Y )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_non_equal_first_eq
% 0.37/0.65 thf(fact_5345_nth__non__equal__first__eq,axiom,
% 0.37/0.65 ! [X: vEBT_VEBTi,Y: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 0.37/0.65 ( ( X != Y )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 0.37/0.65 = Y )
% 0.37/0.65 = ( ( ( nth_VEBT_VEBTi @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.65 = Y )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_non_equal_first_eq
% 0.37/0.65 thf(fact_5346_nth__non__equal__first__eq,axiom,
% 0.37/0.65 ! [X: int,Y: int,Xs: list_int,N: nat] :
% 0.37/0.65 ( ( X != Y )
% 0.37/0.65 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 0.37/0.65 = Y )
% 0.37/0.65 = ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.65 = Y )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_non_equal_first_eq
% 0.37/0.65 thf(fact_5347_nth__non__equal__first__eq,axiom,
% 0.37/0.65 ! [X: nat,Y: nat,Xs: list_nat,N: nat] :
% 0.37/0.65 ( ( X != Y )
% 0.37/0.65 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 0.37/0.65 = Y )
% 0.37/0.65 = ( ( ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.65 = Y )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_non_equal_first_eq
% 0.37/0.65 thf(fact_5348_nth__non__equal__first__eq,axiom,
% 0.37/0.65 ! [X: $o,Y: $o,Xs: list_o,N: nat] :
% 0.37/0.65 ( ( X != Y )
% 0.37/0.65 => ( ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 0.37/0.65 = Y )
% 0.37/0.65 = ( ( ( nth_o @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.37/0.65 = Y )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_non_equal_first_eq
% 0.37/0.65 thf(fact_5349_nth__equal__first__eq,axiom,
% 0.37/0.65 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 0.37/0.65 ( ~ ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 0.37/0.65 = X )
% 0.37/0.65 = ( N = zero_zero_nat ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_equal_first_eq
% 0.37/0.65 thf(fact_5350_nth__equal__first__eq,axiom,
% 0.37/0.65 ! [X: set_nat,Xs: list_set_nat,N: nat] :
% 0.37/0.65 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.65 => ( ( ( nth_set_nat @ ( cons_set_nat @ X @ Xs ) @ N )
% 0.37/0.65 = X )
% 0.37/0.65 = ( N = zero_zero_nat ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_equal_first_eq
% 0.37/0.65 thf(fact_5351_nth__equal__first__eq,axiom,
% 0.37/0.65 ! [X: int,Xs: list_int,N: nat] :
% 0.37/0.65 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 0.37/0.65 = X )
% 0.37/0.65 = ( N = zero_zero_nat ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_equal_first_eq
% 0.37/0.65 thf(fact_5352_nth__equal__first__eq,axiom,
% 0.37/0.65 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 0.37/0.65 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 0.37/0.65 = X )
% 0.37/0.65 = ( N = zero_zero_nat ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_equal_first_eq
% 0.37/0.65 thf(fact_5353_nth__equal__first__eq,axiom,
% 0.37/0.65 ! [X: real,Xs: list_real,N: nat] :
% 0.37/0.65 ( ~ ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ( ( nth_real @ ( cons_real @ X @ Xs ) @ N )
% 0.37/0.65 = X )
% 0.37/0.65 = ( N = zero_zero_nat ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_equal_first_eq
% 0.37/0.65 thf(fact_5354_nth__equal__first__eq,axiom,
% 0.37/0.65 ! [X: $o,Xs: list_o,N: nat] :
% 0.37/0.65 ( ~ ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 0.37/0.65 = X )
% 0.37/0.65 = ( N = zero_zero_nat ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_equal_first_eq
% 0.37/0.65 thf(fact_5355_nth__equal__first__eq,axiom,
% 0.37/0.65 ! [X: nat,Xs: list_nat,N: nat] :
% 0.37/0.65 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 0.37/0.65 = X )
% 0.37/0.65 = ( N = zero_zero_nat ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_equal_first_eq
% 0.37/0.65 thf(fact_5356_slice__Cons,axiom,
% 0.37/0.65 ! [Begin: nat,End: nat,X: int,Xs: list_int] :
% 0.37/0.65 ( ( ( ( Begin = zero_zero_nat )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 0.37/0.65 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 0.37/0.65 = ( cons_int @ X @ ( slice_int @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 0.37/0.65 & ( ~ ( ( Begin = zero_zero_nat )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 0.37/0.65 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 0.37/0.65 = ( slice_int @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % slice_Cons
% 0.37/0.65 thf(fact_5357_slice__Cons,axiom,
% 0.37/0.65 ! [Begin: nat,End: nat,X: nat,Xs: list_nat] :
% 0.37/0.65 ( ( ( ( Begin = zero_zero_nat )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 0.37/0.65 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 0.37/0.65 = ( cons_nat @ X @ ( slice_nat @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 0.37/0.65 & ( ~ ( ( Begin = zero_zero_nat )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 0.37/0.65 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 0.37/0.65 = ( slice_nat @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % slice_Cons
% 0.37/0.65 thf(fact_5358_slice__Cons,axiom,
% 0.37/0.65 ! [Begin: nat,End: nat,X: $o,Xs: list_o] :
% 0.37/0.65 ( ( ( ( Begin = zero_zero_nat )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 0.37/0.65 => ( ( slice_o @ Begin @ End @ ( cons_o @ X @ Xs ) )
% 0.37/0.65 = ( cons_o @ X @ ( slice_o @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 0.37/0.65 & ( ~ ( ( Begin = zero_zero_nat )
% 0.37/0.65 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 0.37/0.65 => ( ( slice_o @ Begin @ End @ ( cons_o @ X @ Xs ) )
% 0.37/0.65 = ( slice_o @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % slice_Cons
% 0.37/0.65 thf(fact_5359_length__Cons,axiom,
% 0.37/0.65 ! [X: int,Xs: list_int] :
% 0.37/0.65 ( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
% 0.37/0.65 = ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % length_Cons
% 0.37/0.65 thf(fact_5360_length__Cons,axiom,
% 0.37/0.65 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.65 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) )
% 0.37/0.65 = ( suc @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % length_Cons
% 0.37/0.65 thf(fact_5361_length__Cons,axiom,
% 0.37/0.65 ! [X: real,Xs: list_real] :
% 0.37/0.65 ( ( size_size_list_real @ ( cons_real @ X @ Xs ) )
% 0.37/0.65 = ( suc @ ( size_size_list_real @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % length_Cons
% 0.37/0.65 thf(fact_5362_length__Cons,axiom,
% 0.37/0.65 ! [X: $o,Xs: list_o] :
% 0.37/0.65 ( ( size_size_list_o @ ( cons_o @ X @ Xs ) )
% 0.37/0.65 = ( suc @ ( size_size_list_o @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % length_Cons
% 0.37/0.65 thf(fact_5363_length__Cons,axiom,
% 0.37/0.65 ! [X: nat,Xs: list_nat] :
% 0.37/0.65 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs ) )
% 0.37/0.65 = ( suc @ ( size_size_list_nat @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % length_Cons
% 0.37/0.65 thf(fact_5364_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5365_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > nat > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5366_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5367_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_int,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5368_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > vEBT_VEBT > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5369_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > nat > assn,Xs: list_int,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5370_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > vEBT_VEBTi > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5371_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > int > assn,Xs: list_int,I: nat,Xsi: list_int,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5372_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5373_listI__assn__reinsert,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert
% 0.37/0.65 thf(fact_5374_sorted__list__of__set__nonempty,axiom,
% 0.37/0.65 ! [A4: set_Code_integer] :
% 0.37/0.65 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.65 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.65 => ( ( linord2324613341767563021nteger @ A4 )
% 0.37/0.65 = ( cons_Code_integer @ ( lattic1063845414844153500nteger @ A4 ) @ ( linord2324613341767563021nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ ( lattic1063845414844153500nteger @ A4 ) @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set_nonempty
% 0.37/0.65 thf(fact_5375_sorted__list__of__set__nonempty,axiom,
% 0.37/0.65 ! [A4: set_int] :
% 0.37/0.65 ( ( finite_finite_int @ A4 )
% 0.37/0.65 => ( ( A4 != bot_bot_set_int )
% 0.37/0.65 => ( ( linord2612477271533052124et_int @ A4 )
% 0.37/0.65 = ( cons_int @ ( lattic8718645017227715691in_int @ A4 ) @ ( linord2612477271533052124et_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ ( lattic8718645017227715691in_int @ A4 ) @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set_nonempty
% 0.37/0.65 thf(fact_5376_sorted__list__of__set__nonempty,axiom,
% 0.37/0.65 ! [A4: set_o] :
% 0.37/0.65 ( ( finite_finite_o @ A4 )
% 0.37/0.65 => ( ( A4 != bot_bot_set_o )
% 0.37/0.65 => ( ( linord3142498349692569832_set_o @ A4 )
% 0.37/0.65 = ( cons_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ ( linord3142498349692569832_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set_nonempty
% 0.37/0.65 thf(fact_5377_sorted__list__of__set__nonempty,axiom,
% 0.37/0.65 ! [A4: set_nat] :
% 0.37/0.65 ( ( finite_finite_nat @ A4 )
% 0.37/0.65 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.65 => ( ( linord2614967742042102400et_nat @ A4 )
% 0.37/0.65 = ( cons_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ ( linord2614967742042102400et_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set_nonempty
% 0.37/0.65 thf(fact_5378_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_literal,L: list_literal] :
% 0.37/0.65 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.65 => ( ( ( sorted_wrt_literal @ ord_less_literal @ L )
% 0.37/0.65 & ( ( set_literal2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_s2501651207091587910iteral @ L )
% 0.37/0.65 = ( finite_card_literal @ A4 ) ) )
% 0.37/0.65 = ( ( linord2913955441264437540iteral @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5379_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_Code_integer,L: list_Code_integer] :
% 0.37/0.65 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.65 => ( ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ L )
% 0.37/0.65 & ( ( set_Code_integer2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_s3445333598471063425nteger @ L )
% 0.37/0.65 = ( finite4902975817058060853nteger @ A4 ) ) )
% 0.37/0.65 = ( ( linord2324613341767563021nteger @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5380_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_o,L: list_o] :
% 0.37/0.65 ( ( finite_finite_o @ A4 )
% 0.37/0.65 => ( ( ( sorted_wrt_o @ ord_less_o @ L )
% 0.37/0.65 & ( ( set_o2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_size_list_o @ L )
% 0.37/0.65 = ( finite_card_o @ A4 ) ) )
% 0.37/0.65 = ( ( linord3142498349692569832_set_o @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5381_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_real,L: list_real] :
% 0.37/0.65 ( ( finite_finite_real @ A4 )
% 0.37/0.65 => ( ( ( sorted_wrt_real @ ord_less_real @ L )
% 0.37/0.65 & ( ( set_real2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_size_list_real @ L )
% 0.37/0.65 = ( finite_card_real @ A4 ) ) )
% 0.37/0.65 = ( ( linord4252657396651189596t_real @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5382_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_rat,L: list_rat] :
% 0.37/0.65 ( ( finite_finite_rat @ A4 )
% 0.37/0.65 => ( ( ( sorted_wrt_rat @ ord_less_rat @ L )
% 0.37/0.65 & ( ( set_rat2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_size_list_rat @ L )
% 0.37/0.65 = ( finite_card_rat @ A4 ) ) )
% 0.37/0.65 = ( ( linord1979837681955606664et_rat @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5383_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_num,L: list_num] :
% 0.37/0.65 ( ( finite_finite_num @ A4 )
% 0.37/0.65 => ( ( ( sorted_wrt_num @ ord_less_num @ L )
% 0.37/0.65 & ( ( set_num2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_size_list_num @ L )
% 0.37/0.65 = ( finite_card_num @ A4 ) ) )
% 0.37/0.65 = ( ( linord8395671565052656842et_num @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5384_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_int,L: list_int] :
% 0.37/0.65 ( ( finite_finite_int @ A4 )
% 0.37/0.65 => ( ( ( sorted_wrt_int @ ord_less_int @ L )
% 0.37/0.65 & ( ( set_int2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_size_list_int @ L )
% 0.37/0.65 = ( finite_card_int @ A4 ) ) )
% 0.37/0.65 = ( ( linord2612477271533052124et_int @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5385_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 0.37/0.65 ! [A4: set_nat,L: list_nat] :
% 0.37/0.65 ( ( finite_finite_nat @ A4 )
% 0.37/0.65 => ( ( ( sorted_wrt_nat @ ord_less_nat @ L )
% 0.37/0.65 & ( ( set_nat2 @ L )
% 0.37/0.65 = A4 )
% 0.37/0.65 & ( ( size_size_list_nat @ L )
% 0.37/0.65 = ( finite_card_nat @ A4 ) ) )
% 0.37/0.65 = ( ( linord2614967742042102400et_nat @ A4 )
% 0.37/0.65 = L ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_unique
% 0.37/0.65 thf(fact_5386_converse__trancl__induct,axiom,
% 0.37/0.65 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,P2: uint32 > $o] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ! [Y3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ B ) @ R )
% 0.37/0.65 => ( P2 @ Y3 ) )
% 0.37/0.65 => ( ! [Y3: uint32,Z3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z3 ) @ R )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Z3 @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ( P2 @ Z3 )
% 0.37/0.65 => ( P2 @ Y3 ) ) ) )
% 0.37/0.65 => ( P2 @ A ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % converse_trancl_induct
% 0.37/0.65 thf(fact_5387_converse__trancl__induct,axiom,
% 0.37/0.65 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,P2: nat > $o] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ! [Y3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ B ) @ R )
% 0.37/0.65 => ( P2 @ Y3 ) )
% 0.37/0.65 => ( ! [Y3: nat,Z3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ R )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z3 @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ( P2 @ Z3 )
% 0.37/0.65 => ( P2 @ Y3 ) ) ) )
% 0.37/0.65 => ( P2 @ A ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % converse_trancl_induct
% 0.37/0.65 thf(fact_5388_converse__trancl__induct,axiom,
% 0.37/0.65 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,P2: int > $o] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ! [Y3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ B ) @ R )
% 0.37/0.65 => ( P2 @ Y3 ) )
% 0.37/0.65 => ( ! [Y3: int,Z3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z3 ) @ R )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z3 @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ( P2 @ Z3 )
% 0.37/0.65 => ( P2 @ Y3 ) ) ) )
% 0.37/0.65 => ( P2 @ A ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % converse_trancl_induct
% 0.37/0.65 thf(fact_5389_trancl__trans__induct,axiom,
% 0.37/0.65 ! [X: uint32,Y: uint32,R: set_Pr1773385645901665561uint32,P2: uint32 > uint32 > $o] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ! [X3: uint32,Y3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ R )
% 0.37/0.65 => ( P2 @ X3 @ Y3 ) )
% 0.37/0.65 => ( ! [X3: uint32,Y3: uint32,Z3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ( P2 @ X3 @ Y3 )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ( P2 @ Y3 @ Z3 )
% 0.37/0.65 => ( P2 @ X3 @ Z3 ) ) ) ) )
% 0.37/0.65 => ( P2 @ X @ Y ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_trans_induct
% 0.37/0.65 thf(fact_5390_trancl__trans__induct,axiom,
% 0.37/0.65 ! [X: nat,Y: nat,R: set_Pr1261947904930325089at_nat,P2: nat > nat > $o] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ! [X3: nat,Y3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 0.37/0.65 => ( P2 @ X3 @ Y3 ) )
% 0.37/0.65 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ( P2 @ X3 @ Y3 )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ( P2 @ Y3 @ Z3 )
% 0.37/0.65 => ( P2 @ X3 @ Z3 ) ) ) ) )
% 0.37/0.65 => ( P2 @ X @ Y ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_trans_induct
% 0.37/0.65 thf(fact_5391_trancl__trans__induct,axiom,
% 0.37/0.65 ! [X: int,Y: int,R: set_Pr958786334691620121nt_int,P2: int > int > $o] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ! [X3: int,Y3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R )
% 0.37/0.65 => ( P2 @ X3 @ Y3 ) )
% 0.37/0.65 => ( ! [X3: int,Y3: int,Z3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ( P2 @ X3 @ Y3 )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ( P2 @ Y3 @ Z3 )
% 0.37/0.65 => ( P2 @ X3 @ Z3 ) ) ) ) )
% 0.37/0.65 => ( P2 @ X @ Y ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_trans_induct
% 0.37/0.65 thf(fact_5392_groupy,axiom,
% 0.37/0.65 ! [A4: assn,B4: assn,C3: assn,D4: assn,X6: assn] :
% 0.37/0.65 ( ( entails @ ( times_times_assn @ ( times_times_assn @ A4 @ B4 ) @ ( times_times_assn @ C3 @ D4 ) ) @ X6 )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ A4 @ B4 ) @ C3 ) @ D4 ) @ X6 ) ) ).
% 0.37/0.65
% 0.37/0.65 % groupy
% 0.37/0.65 thf(fact_5393_midextr,axiom,
% 0.37/0.65 ! [P2: assn,Q2: assn,Q4: assn,R2: assn,X6: assn] :
% 0.37/0.65 ( ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ P2 @ Q2 ) @ Q4 ) @ R2 ) @ X6 )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ P2 @ R2 ) @ Q2 ) @ Q4 ) @ X6 ) ) ).
% 0.37/0.65
% 0.37/0.65 % midextr
% 0.37/0.65 thf(fact_5394_swappa,axiom,
% 0.37/0.65 ! [B4: assn,A4: assn,C3: assn,X6: assn] :
% 0.37/0.65 ( ( entails @ ( times_times_assn @ ( times_times_assn @ B4 @ A4 ) @ C3 ) @ X6 )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ A4 @ B4 ) @ C3 ) @ X6 ) ) ).
% 0.37/0.65
% 0.37/0.65 % swappa
% 0.37/0.65 thf(fact_5395_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_real] :
% 0.37/0.65 ( ( finite_finite_real @ A4 )
% 0.37/0.65 => ( ( set_real2 @ ( linord4252657396651189596t_real @ A4 ) )
% 0.37/0.65 = A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.set_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5396_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_o] :
% 0.37/0.65 ( ( finite_finite_o @ A4 )
% 0.37/0.65 => ( ( set_o2 @ ( linord3142498349692569832_set_o @ A4 ) )
% 0.37/0.65 = A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.set_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5397_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_int] :
% 0.37/0.65 ( ( finite_finite_int @ A4 )
% 0.37/0.65 => ( ( set_int2 @ ( linord2612477271533052124et_int @ A4 ) )
% 0.37/0.65 = A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.set_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5398_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_Code_integer] :
% 0.37/0.65 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.65 => ( ( set_Code_integer2 @ ( linord2324613341767563021nteger @ A4 ) )
% 0.37/0.65 = A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.set_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5399_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_nat] :
% 0.37/0.65 ( ( finite_finite_nat @ A4 )
% 0.37/0.65 => ( ( set_nat2 @ ( linord2614967742042102400et_nat @ A4 ) )
% 0.37/0.65 = A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.set_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5400_ent__false__iff,axiom,
% 0.37/0.65 ! [P2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ bot_bot_assn )
% 0.37/0.65 = ( ! [H4: produc3658429121746597890et_nat] :
% 0.37/0.65 ~ ( rep_assn @ P2 @ H4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ent_false_iff
% 0.37/0.65 thf(fact_5401_ent__trans,axiom,
% 0.37/0.65 ! [P2: assn,Q2: assn,R2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ Q2 )
% 0.37/0.65 => ( ( entails @ Q2 @ R2 )
% 0.37/0.65 => ( entails @ P2 @ R2 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ent_trans
% 0.37/0.65 thf(fact_5402_ent__refl,axiom,
% 0.37/0.65 ! [P2: assn] : ( entails @ P2 @ P2 ) ).
% 0.37/0.65
% 0.37/0.65 % ent_refl
% 0.37/0.65 thf(fact_5403_ent__iffI,axiom,
% 0.37/0.65 ! [A4: assn,B4: assn] :
% 0.37/0.65 ( ( entails @ A4 @ B4 )
% 0.37/0.65 => ( ( entails @ B4 @ A4 )
% 0.37/0.65 => ( A4 = B4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ent_iffI
% 0.37/0.65 thf(fact_5404_ent__star__mono,axiom,
% 0.37/0.65 ! [P2: assn,P6: assn,Q2: assn,Q4: assn] :
% 0.37/0.65 ( ( entails @ P2 @ P6 )
% 0.37/0.65 => ( ( entails @ Q2 @ Q4 )
% 0.37/0.65 => ( entails @ ( times_times_assn @ P2 @ Q2 ) @ ( times_times_assn @ P6 @ Q4 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ent_star_mono
% 0.37/0.65 thf(fact_5405_entails__def,axiom,
% 0.37/0.65 ( entails
% 0.37/0.65 = ( ^ [P5: assn,Q6: assn] :
% 0.37/0.65 ! [H4: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ P5 @ H4 )
% 0.37/0.65 => ( rep_assn @ Q6 @ H4 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % entails_def
% 0.37/0.65 thf(fact_5406_entailsI,axiom,
% 0.37/0.65 ! [P2: assn,Q2: assn] :
% 0.37/0.65 ( ! [H: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ P2 @ H )
% 0.37/0.65 => ( rep_assn @ Q2 @ H ) )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ).
% 0.37/0.65
% 0.37/0.65 % entailsI
% 0.37/0.65 thf(fact_5407_entailsD,axiom,
% 0.37/0.65 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( entails @ P2 @ Q2 )
% 0.37/0.65 => ( ( rep_assn @ P2 @ H2 )
% 0.37/0.65 => ( rep_assn @ Q2 @ H2 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % entailsD
% 0.37/0.65 thf(fact_5408_ent__fwd,axiom,
% 0.37/0.65 ! [P2: assn,H2: produc3658429121746597890et_nat,Q2: assn] :
% 0.37/0.65 ( ( rep_assn @ P2 @ H2 )
% 0.37/0.65 => ( ( entails @ P2 @ Q2 )
% 0.37/0.65 => ( rep_assn @ Q2 @ H2 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ent_fwd
% 0.37/0.65 thf(fact_5409_ent__false,axiom,
% 0.37/0.65 ! [P2: assn] : ( entails @ bot_bot_assn @ P2 ) ).
% 0.37/0.65
% 0.37/0.65 % ent_false
% 0.37/0.65 thf(fact_5410_sorted__list__of__set_Osorted__key__list__of__set__inject,axiom,
% 0.37/0.65 ! [A4: set_int,B4: set_int] :
% 0.37/0.65 ( ( ( linord2612477271533052124et_int @ A4 )
% 0.37/0.65 = ( linord2612477271533052124et_int @ B4 ) )
% 0.37/0.65 => ( ( finite_finite_int @ A4 )
% 0.37/0.65 => ( ( finite_finite_int @ B4 )
% 0.37/0.65 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_inject
% 0.37/0.65 thf(fact_5411_sorted__list__of__set_Osorted__key__list__of__set__inject,axiom,
% 0.37/0.65 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 0.37/0.65 ( ( ( linord2324613341767563021nteger @ A4 )
% 0.37/0.65 = ( linord2324613341767563021nteger @ B4 ) )
% 0.37/0.65 => ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.65 => ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.65 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_inject
% 0.37/0.65 thf(fact_5412_sorted__list__of__set_Osorted__key__list__of__set__inject,axiom,
% 0.37/0.65 ! [A4: set_nat,B4: set_nat] :
% 0.37/0.65 ( ( ( linord2614967742042102400et_nat @ A4 )
% 0.37/0.65 = ( linord2614967742042102400et_nat @ B4 ) )
% 0.37/0.65 => ( ( finite_finite_nat @ A4 )
% 0.37/0.65 => ( ( finite_finite_nat @ B4 )
% 0.37/0.65 => ( A4 = B4 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_key_list_of_set_inject
% 0.37/0.65 thf(fact_5413_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_rat] : ( sorted_wrt_rat @ ord_less_eq_rat @ ( linord1979837681955606664et_rat @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5414_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_num] : ( sorted_wrt_num @ ord_less_eq_num @ ( linord8395671565052656842et_num @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5415_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_int] : ( sorted_wrt_int @ ord_less_eq_int @ ( linord2612477271533052124et_int @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5416_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( linord2614967742042102400et_nat @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.sorted_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5417_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_real] : ( sorted_wrt_real @ ord_less_real @ ( linord4252657396651189596t_real @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.strict_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5418_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_rat] : ( sorted_wrt_rat @ ord_less_rat @ ( linord1979837681955606664et_rat @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.strict_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5419_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_num] : ( sorted_wrt_num @ ord_less_num @ ( linord8395671565052656842et_num @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.strict_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5420_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_int] : ( sorted_wrt_int @ ord_less_int @ ( linord2612477271533052124et_int @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.strict_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5421_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 0.37/0.65 ! [A4: set_nat] : ( sorted_wrt_nat @ ord_less_nat @ ( linord2614967742042102400et_nat @ A4 ) ) ).
% 0.37/0.65
% 0.37/0.65 % sorted_list_of_set.strict_sorted_key_list_of_set
% 0.37/0.65 thf(fact_5422_trancl__induct2,axiom,
% 0.37/0.65 ! [Ax: uint32,Ay: uint32,Bx: uint32,By: uint32,R: set_Pr3773659940955823943uint32,P2: uint32 > uint32 > $o] :
% 0.37/0.65 ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ Ax @ Ay ) @ ( produc1400373151660368625uint32 @ Bx @ By ) ) @ ( transi5456044692924788698uint32 @ R ) )
% 0.37/0.65 => ( ! [A3: uint32,B3: uint32] :
% 0.37/0.65 ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ Ax @ Ay ) @ ( produc1400373151660368625uint32 @ A3 @ B3 ) ) @ R )
% 0.37/0.65 => ( P2 @ A3 @ B3 ) )
% 0.37/0.65 => ( ! [A3: uint32,B3: uint32,Aa: uint32,Ba: uint32] :
% 0.37/0.65 ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ Ax @ Ay ) @ ( produc1400373151660368625uint32 @ A3 @ B3 ) ) @ ( transi5456044692924788698uint32 @ R ) )
% 0.37/0.65 => ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ A3 @ B3 ) @ ( produc1400373151660368625uint32 @ Aa @ Ba ) ) @ R )
% 0.37/0.65 => ( ( P2 @ A3 @ B3 )
% 0.37/0.65 => ( P2 @ Aa @ Ba ) ) ) )
% 0.37/0.65 => ( P2 @ Bx @ By ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct2
% 0.37/0.65 thf(fact_5423_trancl__induct2,axiom,
% 0.37/0.65 ! [Ax: nat,Ay: nat,Bx: nat,By: nat,R: set_Pr8693737435421807431at_nat,P2: nat > nat > $o] :
% 0.37/0.65 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ Bx @ By ) ) @ ( transi243908449541399842at_nat @ R ) )
% 0.37/0.65 => ( ! [A3: nat,B3: nat] :
% 0.37/0.65 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ A3 @ B3 ) ) @ R )
% 0.37/0.65 => ( P2 @ A3 @ B3 ) )
% 0.37/0.65 => ( ! [A3: nat,B3: nat,Aa: nat,Ba: nat] :
% 0.37/0.65 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ A3 @ B3 ) ) @ ( transi243908449541399842at_nat @ R ) )
% 0.37/0.65 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ ( product_Pair_nat_nat @ Aa @ Ba ) ) @ R )
% 0.37/0.65 => ( ( P2 @ A3 @ B3 )
% 0.37/0.65 => ( P2 @ Aa @ Ba ) ) ) )
% 0.37/0.65 => ( P2 @ Bx @ By ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct2
% 0.37/0.65 thf(fact_5424_trancl__induct2,axiom,
% 0.37/0.65 ! [Ax: int,Ay: int,Bx: int,By: int,R: set_Pr2560585780119916871nt_int,P2: int > int > $o] :
% 0.37/0.65 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ Bx @ By ) ) @ ( transi6288783178788033498nt_int @ R ) )
% 0.37/0.65 => ( ! [A3: int,B3: int] :
% 0.37/0.65 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A3 @ B3 ) ) @ R )
% 0.37/0.65 => ( P2 @ A3 @ B3 ) )
% 0.37/0.65 => ( ! [A3: int,B3: int,Aa: int,Ba: int] :
% 0.37/0.65 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A3 @ B3 ) ) @ ( transi6288783178788033498nt_int @ R ) )
% 0.37/0.65 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ ( product_Pair_int_int @ Aa @ Ba ) ) @ R )
% 0.37/0.65 => ( ( P2 @ A3 @ B3 )
% 0.37/0.65 => ( P2 @ Aa @ Ba ) ) ) )
% 0.37/0.65 => ( P2 @ Bx @ By ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct2
% 0.37/0.65 thf(fact_5425_trancl__induct2,axiom,
% 0.37/0.65 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3658429121746597890et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3658429121746597890et_nat,R: set_Pr7928877670098842301et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 0.37/0.65 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi3145040225084697757et_nat @ R ) )
% 0.37/0.65 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A3 @ B3 ) ) @ R )
% 0.37/0.65 => ( P2 @ A3 @ B3 ) )
% 0.37/0.65 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A3 @ B3 ) ) @ ( transi3145040225084697757et_nat @ R ) )
% 0.37/0.65 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A3 @ B3 ) @ ( produc5001842942810119800et_nat @ Aa @ Ba ) ) @ R )
% 0.37/0.65 => ( ( P2 @ A3 @ B3 )
% 0.37/0.65 => ( P2 @ Aa @ Ba ) ) ) )
% 0.37/0.65 => ( P2 @ Bx @ By ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct2
% 0.37/0.65 thf(fact_5426_trancl__induct2,axiom,
% 0.37/0.65 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3925858234332021118et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3925858234332021118et_nat,R: set_Pr3444600963470892981et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 0.37/0.65 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi5221092739591632921et_nat @ R ) )
% 0.37/0.65 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 0.37/0.65 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A3 @ B3 ) ) @ R )
% 0.37/0.65 => ( P2 @ A3 @ B3 ) )
% 0.37/0.65 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3925858234332021118et_nat] :
% 0.37/0.65 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A3 @ B3 ) ) @ ( transi5221092739591632921et_nat @ R ) )
% 0.37/0.65 => ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A3 @ B3 ) @ ( produc2245416461498447860et_nat @ Aa @ Ba ) ) @ R )
% 0.37/0.65 => ( ( P2 @ A3 @ B3 )
% 0.37/0.65 => ( P2 @ Aa @ Ba ) ) ) )
% 0.37/0.65 => ( P2 @ Bx @ By ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct2
% 0.37/0.65 thf(fact_5427_trancl_Ocases,axiom,
% 0.37/0.65 ! [A12: uint32,A23: uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ A23 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ A23 ) @ R )
% 0.37/0.65 => ~ ! [B3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ B3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B3 @ A23 ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.cases
% 0.37/0.65 thf(fact_5428_trancl_Ocases,axiom,
% 0.37/0.65 ! [A12: nat,A23: nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ A23 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ A23 ) @ R )
% 0.37/0.65 => ~ ! [B3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ B3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B3 @ A23 ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.cases
% 0.37/0.65 thf(fact_5429_trancl_Ocases,axiom,
% 0.37/0.65 ! [A12: int,A23: int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ A23 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ A23 ) @ R )
% 0.37/0.65 => ~ ! [B3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ B3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B3 @ A23 ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.cases
% 0.37/0.65 thf(fact_5430_trancl_Osimps,axiom,
% 0.37/0.65 ! [A12: uint32,A23: uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ A23 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 = ( ? [A7: uint32,B7: uint32] :
% 0.37/0.65 ( ( A12 = A7 )
% 0.37/0.65 & ( A23 = B7 )
% 0.37/0.65 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A7 @ B7 ) @ R ) )
% 0.37/0.65 | ? [A7: uint32,B7: uint32,C6: uint32] :
% 0.37/0.65 ( ( A12 = A7 )
% 0.37/0.65 & ( A23 = C6 )
% 0.37/0.65 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A7 @ B7 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B7 @ C6 ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.simps
% 0.37/0.65 thf(fact_5431_trancl_Osimps,axiom,
% 0.37/0.65 ! [A12: nat,A23: nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ A23 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 = ( ? [A7: nat,B7: nat] :
% 0.37/0.65 ( ( A12 = A7 )
% 0.37/0.65 & ( A23 = B7 )
% 0.37/0.65 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A7 @ B7 ) @ R ) )
% 0.37/0.65 | ? [A7: nat,B7: nat,C6: nat] :
% 0.37/0.65 ( ( A12 = A7 )
% 0.37/0.65 & ( A23 = C6 )
% 0.37/0.65 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A7 @ B7 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B7 @ C6 ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.simps
% 0.37/0.65 thf(fact_5432_trancl_Osimps,axiom,
% 0.37/0.65 ! [A12: int,A23: int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ A23 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 = ( ? [A7: int,B7: int] :
% 0.37/0.65 ( ( A12 = A7 )
% 0.37/0.65 & ( A23 = B7 )
% 0.37/0.65 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A7 @ B7 ) @ R ) )
% 0.37/0.65 | ? [A7: int,B7: int,C6: int] :
% 0.37/0.65 ( ( A12 = A7 )
% 0.37/0.65 & ( A23 = C6 )
% 0.37/0.65 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A7 @ B7 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B7 @ C6 ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.simps
% 0.37/0.65 thf(fact_5433_trancl_Or__into__trancl,axiom,
% 0.37/0.65 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R )
% 0.37/0.65 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.r_into_trancl
% 0.37/0.65 thf(fact_5434_trancl_Or__into__trancl,axiom,
% 0.37/0.65 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.37/0.65 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.r_into_trancl
% 0.37/0.65 thf(fact_5435_trancl_Or__into__trancl,axiom,
% 0.37/0.65 ! [A: int,B: int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 0.37/0.65 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl.r_into_trancl
% 0.37/0.65 thf(fact_5436_tranclE,axiom,
% 0.37/0.65 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R )
% 0.37/0.65 => ~ ! [C: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ C @ B ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % tranclE
% 0.37/0.65 thf(fact_5437_tranclE,axiom,
% 0.37/0.65 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.37/0.65 => ~ ! [C: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ C @ B ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % tranclE
% 0.37/0.65 thf(fact_5438_tranclE,axiom,
% 0.37/0.65 ! [A: int,B: int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 0.37/0.65 => ~ ! [C: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ C @ B ) @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % tranclE
% 0.37/0.65 thf(fact_5439_trancl__trans,axiom,
% 0.37/0.65 ! [X: uint32,Y: uint32,R: set_Pr1773385645901665561uint32,Z: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y @ Z ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Z ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_trans
% 0.37/0.65 thf(fact_5440_trancl__trans,axiom,
% 0.37/0.65 ! [X: nat,Y: nat,R: set_Pr1261947904930325089at_nat,Z: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_trans
% 0.37/0.65 thf(fact_5441_trancl__trans,axiom,
% 0.37/0.65 ! [X: int,Y: int,R: set_Pr958786334691620121nt_int,Z: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_trans
% 0.37/0.65 thf(fact_5442_trancl__induct,axiom,
% 0.37/0.65 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,P2: uint32 > $o] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ! [Y3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ Y3 ) @ R )
% 0.37/0.65 => ( P2 @ Y3 ) )
% 0.37/0.65 => ( ! [Y3: uint32,Z3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ Y3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z3 ) @ R )
% 0.37/0.65 => ( ( P2 @ Y3 )
% 0.37/0.65 => ( P2 @ Z3 ) ) ) )
% 0.37/0.65 => ( P2 @ B ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct
% 0.37/0.65 thf(fact_5443_trancl__induct,axiom,
% 0.37/0.65 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,P2: nat > $o] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ! [Y3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ R )
% 0.37/0.65 => ( P2 @ Y3 ) )
% 0.37/0.65 => ( ! [Y3: nat,Z3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ R )
% 0.37/0.65 => ( ( P2 @ Y3 )
% 0.37/0.65 => ( P2 @ Z3 ) ) ) )
% 0.37/0.65 => ( P2 @ B ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct
% 0.37/0.65 thf(fact_5444_trancl__induct,axiom,
% 0.37/0.65 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,P2: int > $o] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ! [Y3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ Y3 ) @ R )
% 0.37/0.65 => ( P2 @ Y3 ) )
% 0.37/0.65 => ( ! [Y3: int,Z3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ Y3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z3 ) @ R )
% 0.37/0.65 => ( ( P2 @ Y3 )
% 0.37/0.65 => ( P2 @ Z3 ) ) ) )
% 0.37/0.65 => ( P2 @ B ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_induct
% 0.37/0.65 thf(fact_5445_r__r__into__trancl,axiom,
% 0.37/0.65 ! [A: uint32,B: uint32,R2: set_Pr1773385645901665561uint32,C2: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R2 )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B @ C2 ) @ R2 )
% 0.37/0.65 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C2 ) @ ( transi3114468042090999947uint32 @ R2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % r_r_into_trancl
% 0.37/0.65 thf(fact_5446_r__r__into__trancl,axiom,
% 0.37/0.65 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C2: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ R2 )
% 0.37/0.65 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % r_r_into_trancl
% 0.37/0.65 thf(fact_5447_r__r__into__trancl,axiom,
% 0.37/0.65 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int,C2: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ R2 )
% 0.37/0.65 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % r_r_into_trancl
% 0.37/0.65 thf(fact_5448_converse__tranclE,axiom,
% 0.37/0.65 ! [X: uint32,Z: uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Z ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Z ) @ R )
% 0.37/0.65 => ~ ! [Y3: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y3 ) @ R )
% 0.37/0.65 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % converse_tranclE
% 0.37/0.65 thf(fact_5449_converse__tranclE,axiom,
% 0.37/0.65 ! [X: nat,Z: nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R )
% 0.37/0.65 => ~ ! [Y3: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) @ R )
% 0.37/0.65 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % converse_tranclE
% 0.37/0.65 thf(fact_5450_converse__tranclE,axiom,
% 0.37/0.65 ! [X: int,Z: int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ R )
% 0.37/0.65 => ~ ! [Y3: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y3 ) @ R )
% 0.37/0.65 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % converse_tranclE
% 0.37/0.65 thf(fact_5451_irrefl__trancl__rD,axiom,
% 0.37/0.65 ! [R: set_Pr1773385645901665561uint32,X: uint32,Y: uint32] :
% 0.37/0.65 ( ! [X3: uint32] :
% 0.37/0.65 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ X3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 0.37/0.65 => ( X != Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % irrefl_trancl_rD
% 0.37/0.65 thf(fact_5452_irrefl__trancl__rD,axiom,
% 0.37/0.65 ! [R: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 0.37/0.65 ( ! [X3: nat] :
% 0.37/0.65 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.37/0.65 => ( X != Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % irrefl_trancl_rD
% 0.37/0.65 thf(fact_5453_irrefl__trancl__rD,axiom,
% 0.37/0.65 ! [R: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 0.37/0.65 ( ! [X3: int] :
% 0.37/0.65 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 0.37/0.65 => ( X != Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % irrefl_trancl_rD
% 0.37/0.65 thf(fact_5454_Transitive__Closure_Otrancl__into__trancl,axiom,
% 0.37/0.65 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,C2: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B @ C2 ) @ R )
% 0.37/0.65 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C2 ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Transitive_Closure.trancl_into_trancl
% 0.37/0.65 thf(fact_5455_Transitive__Closure_Otrancl__into__trancl,axiom,
% 0.37/0.65 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,C2: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ R )
% 0.37/0.65 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Transitive_Closure.trancl_into_trancl
% 0.37/0.65 thf(fact_5456_Transitive__Closure_Otrancl__into__trancl,axiom,
% 0.37/0.65 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,C2: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ R )
% 0.37/0.65 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % Transitive_Closure.trancl_into_trancl
% 0.37/0.65 thf(fact_5457_trancl__into__trancl2,axiom,
% 0.37/0.65 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,C2: uint32] :
% 0.37/0.65 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R )
% 0.37/0.65 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B @ C2 ) @ ( transi3114468042090999947uint32 @ R ) )
% 0.37/0.65 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C2 ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_into_trancl2
% 0.37/0.65 thf(fact_5458_trancl__into__trancl2,axiom,
% 0.37/0.65 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,C2: nat] :
% 0.37/0.65 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.37/0.65 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 0.37/0.65 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_into_trancl2
% 0.37/0.65 thf(fact_5459_trancl__into__trancl2,axiom,
% 0.37/0.65 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,C2: int] :
% 0.37/0.65 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 0.37/0.65 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ ( transi6261509568448316235cl_int @ R ) )
% 0.37/0.65 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % trancl_into_trancl2
% 0.37/0.65 thf(fact_5460_local_Oext,axiom,
% 0.37/0.65 ! [Y: nat,TreeList: list_VEBT_VEBT,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ Y @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % local.ext
% 0.37/0.65 thf(fact_5461_mod__frame__fwd,axiom,
% 0.37/0.65 ! [Ps: assn,H2: produc3658429121746597890et_nat,P2: assn,R2: assn,F2: assn] :
% 0.37/0.65 ( ( rep_assn @ Ps @ H2 )
% 0.37/0.65 => ( ( entails @ P2 @ R2 )
% 0.37/0.65 => ( ( entails @ Ps @ ( times_times_assn @ P2 @ F2 ) )
% 0.37/0.65 => ( rep_assn @ ( times_times_assn @ R2 @ F2 ) @ H2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % mod_frame_fwd
% 0.37/0.65 thf(fact_5462_assnle,axiom,
% 0.37/0.65 ! [TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] : ( entails @ ( times_times_assn @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % assnle
% 0.37/0.65 thf(fact_5463_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5464_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > nat > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5465_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5466_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_int,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5467_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > vEBT_VEBT > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5468_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > nat > assn,Xs: list_int,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5469_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > vEBT_VEBTi > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5470_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: int > int > assn,Xs: list_int,I: nat,Xsi: list_int,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5471_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5472_listI__assn__reinsert_H,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert'
% 0.37/0.65 thf(fact_5473_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X: vEBT_VEBTi,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5474_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,X: vEBT_VEBTi,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5475_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,X: vEBT_VEBT,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5476_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: real > vEBT_VEBTi > assn,X: real,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5477_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: real > vEBT_VEBT > assn,X: real,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5478_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: $o > vEBT_VEBTi > assn,X: $o,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L6286945158656146733_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5479_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: $o > vEBT_VEBT > assn,X: $o,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5480_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: nat > vEBT_VEBTi > assn,X: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7489483478785760935_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5481_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: nat > vEBT_VEBT > assn,X: nat,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L8511957252848910786T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5482_listI__assn__reinsert__upd,axiom,
% 0.37/0.65 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBTi > assn,X: vEBT_VEBT,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 0.37/0.65 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.65 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( member_nat @ I @ I5 )
% 0.37/0.65 => ( ( entails @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 0.37/0.65 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_reinsert_upd
% 0.37/0.65 thf(fact_5483_recomp,axiom,
% 0.37/0.65 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ I ) @ ( nth_VEBT_VEBTi @ Tree_is @ I ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % recomp
% 0.37/0.65 thf(fact_5484_repack,axiom,
% 0.37/0.65 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,Rest: assn,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ I ) @ ( nth_VEBT_VEBTi @ Tree_is @ I ) ) @ Rest ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ Rest @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % repack
% 0.37/0.65 thf(fact_5485_finite__atLeastLessThan,axiom,
% 0.37/0.65 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 0.37/0.65
% 0.37/0.65 % finite_atLeastLessThan
% 0.37/0.65 thf(fact_5486_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: set_nat,L: set_nat,U: set_nat] :
% 0.37/0.65 ( ( member_set_nat @ I @ ( set_or3540276404033026485et_nat @ L @ U ) )
% 0.37/0.65 = ( ( ord_less_eq_set_nat @ L @ I )
% 0.37/0.65 & ( ord_less_set_nat @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5487_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: real,L: real,U: real] :
% 0.37/0.65 ( ( member_real @ I @ ( set_or66887138388493659n_real @ L @ U ) )
% 0.37/0.65 = ( ( ord_less_eq_real @ L @ I )
% 0.37/0.65 & ( ord_less_real @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5488_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: set_int,L: set_int,U: set_int] :
% 0.37/0.65 ( ( member_set_int @ I @ ( set_or8585797421378605585et_int @ L @ U ) )
% 0.37/0.65 = ( ( ord_less_eq_set_int @ L @ I )
% 0.37/0.65 & ( ord_less_set_int @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5489_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: rat,L: rat,U: rat] :
% 0.37/0.65 ( ( member_rat @ I @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 0.37/0.65 = ( ( ord_less_eq_rat @ L @ I )
% 0.37/0.65 & ( ord_less_rat @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5490_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: num,L: num,U: num] :
% 0.37/0.65 ( ( member_num @ I @ ( set_or1222409239386451017an_num @ L @ U ) )
% 0.37/0.65 = ( ( ord_less_eq_num @ L @ I )
% 0.37/0.65 & ( ord_less_num @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5491_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: nat,L: nat,U: nat] :
% 0.37/0.65 ( ( member_nat @ I @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.37/0.65 = ( ( ord_less_eq_nat @ L @ I )
% 0.37/0.65 & ( ord_less_nat @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5492_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: int,L: int,U: int] :
% 0.37/0.65 ( ( member_int @ I @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.37/0.65 = ( ( ord_less_eq_int @ L @ I )
% 0.37/0.65 & ( ord_less_int @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5493_atLeastLessThan__iff,axiom,
% 0.37/0.65 ! [I: code_integer,L: code_integer,U: code_integer] :
% 0.37/0.65 ( ( member_Code_integer @ I @ ( set_or8404916559141939852nteger @ L @ U ) )
% 0.37/0.65 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 0.37/0.65 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_iff
% 0.37/0.65 thf(fact_5494_atLeastLessThan__empty,axiom,
% 0.37/0.65 ! [B: $o,A: $o] :
% 0.37/0.65 ( ( ord_less_eq_o @ B @ A )
% 0.37/0.65 => ( ( set_or7139685690850216873Than_o @ A @ B )
% 0.37/0.65 = bot_bot_set_o ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty
% 0.37/0.65 thf(fact_5495_atLeastLessThan__empty,axiom,
% 0.37/0.65 ! [B: set_int,A: set_int] :
% 0.37/0.65 ( ( ord_less_eq_set_int @ B @ A )
% 0.37/0.65 => ( ( set_or8585797421378605585et_int @ A @ B )
% 0.37/0.65 = bot_bot_set_set_int ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty
% 0.37/0.65 thf(fact_5496_atLeastLessThan__empty,axiom,
% 0.37/0.65 ! [B: rat,A: rat] :
% 0.37/0.65 ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.65 => ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.37/0.65 = bot_bot_set_rat ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty
% 0.37/0.65 thf(fact_5497_atLeastLessThan__empty,axiom,
% 0.37/0.65 ! [B: num,A: num] :
% 0.37/0.65 ( ( ord_less_eq_num @ B @ A )
% 0.37/0.65 => ( ( set_or1222409239386451017an_num @ A @ B )
% 0.37/0.65 = bot_bot_set_num ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty
% 0.37/0.65 thf(fact_5498_atLeastLessThan__empty,axiom,
% 0.37/0.65 ! [B: nat,A: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.65 => ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.37/0.65 = bot_bot_set_nat ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty
% 0.37/0.65 thf(fact_5499_atLeastLessThan__empty,axiom,
% 0.37/0.65 ! [B: int,A: int] :
% 0.37/0.65 ( ( ord_less_eq_int @ B @ A )
% 0.37/0.65 => ( ( set_or4662586982721622107an_int @ A @ B )
% 0.37/0.65 = bot_bot_set_int ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty
% 0.37/0.65 thf(fact_5500_atLeastLessThan__empty,axiom,
% 0.37/0.65 ! [B: code_integer,A: code_integer] :
% 0.37/0.65 ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.37/0.65 => ( ( set_or8404916559141939852nteger @ A @ B )
% 0.37/0.65 = bot_bo3990330152332043303nteger ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty
% 0.37/0.65 thf(fact_5501_atLeastLessThan__empty__iff2,axiom,
% 0.37/0.65 ! [A: $o,B: $o] :
% 0.37/0.65 ( ( bot_bot_set_o
% 0.37/0.65 = ( set_or7139685690850216873Than_o @ A @ B ) )
% 0.37/0.65 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff2
% 0.37/0.65 thf(fact_5502_atLeastLessThan__empty__iff2,axiom,
% 0.37/0.65 ! [A: real,B: real] :
% 0.37/0.65 ( ( bot_bot_set_real
% 0.37/0.65 = ( set_or66887138388493659n_real @ A @ B ) )
% 0.37/0.65 = ( ~ ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff2
% 0.37/0.65 thf(fact_5503_atLeastLessThan__empty__iff2,axiom,
% 0.37/0.65 ! [A: rat,B: rat] :
% 0.37/0.65 ( ( bot_bot_set_rat
% 0.37/0.65 = ( set_or4029947393144176647an_rat @ A @ B ) )
% 0.37/0.65 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff2
% 0.37/0.65 thf(fact_5504_atLeastLessThan__empty__iff2,axiom,
% 0.37/0.65 ! [A: num,B: num] :
% 0.37/0.65 ( ( bot_bot_set_num
% 0.37/0.65 = ( set_or1222409239386451017an_num @ A @ B ) )
% 0.37/0.65 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff2
% 0.37/0.65 thf(fact_5505_atLeastLessThan__empty__iff2,axiom,
% 0.37/0.65 ! [A: nat,B: nat] :
% 0.37/0.65 ( ( bot_bot_set_nat
% 0.37/0.65 = ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.37/0.65 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff2
% 0.37/0.65 thf(fact_5506_atLeastLessThan__empty__iff2,axiom,
% 0.37/0.65 ! [A: int,B: int] :
% 0.37/0.65 ( ( bot_bot_set_int
% 0.37/0.65 = ( set_or4662586982721622107an_int @ A @ B ) )
% 0.37/0.65 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff2
% 0.37/0.65 thf(fact_5507_atLeastLessThan__empty__iff2,axiom,
% 0.37/0.65 ! [A: code_integer,B: code_integer] :
% 0.37/0.65 ( ( bot_bo3990330152332043303nteger
% 0.37/0.65 = ( set_or8404916559141939852nteger @ A @ B ) )
% 0.37/0.65 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff2
% 0.37/0.65 thf(fact_5508_atLeastLessThan__empty__iff,axiom,
% 0.37/0.65 ! [A: $o,B: $o] :
% 0.37/0.65 ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 0.37/0.65 = bot_bot_set_o )
% 0.37/0.65 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff
% 0.37/0.65 thf(fact_5509_atLeastLessThan__empty__iff,axiom,
% 0.37/0.65 ! [A: real,B: real] :
% 0.37/0.65 ( ( ( set_or66887138388493659n_real @ A @ B )
% 0.37/0.65 = bot_bot_set_real )
% 0.37/0.65 = ( ~ ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff
% 0.37/0.65 thf(fact_5510_atLeastLessThan__empty__iff,axiom,
% 0.37/0.65 ! [A: rat,B: rat] :
% 0.37/0.65 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.37/0.65 = bot_bot_set_rat )
% 0.37/0.65 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff
% 0.37/0.65 thf(fact_5511_atLeastLessThan__empty__iff,axiom,
% 0.37/0.65 ! [A: num,B: num] :
% 0.37/0.65 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.37/0.65 = bot_bot_set_num )
% 0.37/0.65 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff
% 0.37/0.65 thf(fact_5512_atLeastLessThan__empty__iff,axiom,
% 0.37/0.65 ! [A: nat,B: nat] :
% 0.37/0.65 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.37/0.65 = bot_bot_set_nat )
% 0.37/0.65 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff
% 0.37/0.65 thf(fact_5513_atLeastLessThan__empty__iff,axiom,
% 0.37/0.65 ! [A: int,B: int] :
% 0.37/0.65 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.37/0.65 = bot_bot_set_int )
% 0.37/0.65 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff
% 0.37/0.65 thf(fact_5514_atLeastLessThan__empty__iff,axiom,
% 0.37/0.65 ! [A: code_integer,B: code_integer] :
% 0.37/0.65 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.37/0.65 = bot_bo3990330152332043303nteger )
% 0.37/0.65 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_empty_iff
% 0.37/0.65 thf(fact_5515_infinite__Ico__iff,axiom,
% 0.37/0.65 ! [A: real,B: real] :
% 0.37/0.65 ( ( ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A @ B ) ) )
% 0.37/0.65 = ( ord_less_real @ A @ B ) ) ).
% 0.37/0.65
% 0.37/0.65 % infinite_Ico_iff
% 0.37/0.65 thf(fact_5516_infinite__Ico__iff,axiom,
% 0.37/0.65 ! [A: rat,B: rat] :
% 0.37/0.65 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) )
% 0.37/0.65 = ( ord_less_rat @ A @ B ) ) ).
% 0.37/0.65
% 0.37/0.65 % infinite_Ico_iff
% 0.37/0.65 thf(fact_5517_ivl__subset,axiom,
% 0.37/0.65 ! [I: rat,J: rat,M: rat,N: rat] :
% 0.37/0.65 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ I @ J ) @ ( set_or4029947393144176647an_rat @ M @ N ) )
% 0.37/0.65 = ( ( ord_less_eq_rat @ J @ I )
% 0.37/0.65 | ( ( ord_less_eq_rat @ M @ I )
% 0.37/0.65 & ( ord_less_eq_rat @ J @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_subset
% 0.37/0.65 thf(fact_5518_ivl__subset,axiom,
% 0.37/0.65 ! [I: num,J: num,M: num,N: num] :
% 0.37/0.65 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I @ J ) @ ( set_or1222409239386451017an_num @ M @ N ) )
% 0.37/0.65 = ( ( ord_less_eq_num @ J @ I )
% 0.37/0.65 | ( ( ord_less_eq_num @ M @ I )
% 0.37/0.65 & ( ord_less_eq_num @ J @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_subset
% 0.37/0.65 thf(fact_5519_ivl__subset,axiom,
% 0.37/0.65 ! [I: nat,J: nat,M: nat,N: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.65 = ( ( ord_less_eq_nat @ J @ I )
% 0.37/0.65 | ( ( ord_less_eq_nat @ M @ I )
% 0.37/0.65 & ( ord_less_eq_nat @ J @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_subset
% 0.37/0.65 thf(fact_5520_ivl__subset,axiom,
% 0.37/0.65 ! [I: int,J: int,M: int,N: int] :
% 0.37/0.65 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I @ J ) @ ( set_or4662586982721622107an_int @ M @ N ) )
% 0.37/0.65 = ( ( ord_less_eq_int @ J @ I )
% 0.37/0.65 | ( ( ord_less_eq_int @ M @ I )
% 0.37/0.65 & ( ord_less_eq_int @ J @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_subset
% 0.37/0.65 thf(fact_5521_ivl__subset,axiom,
% 0.37/0.65 ! [I: code_integer,J: code_integer,M: code_integer,N: code_integer] :
% 0.37/0.65 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ I @ J ) @ ( set_or8404916559141939852nteger @ M @ N ) )
% 0.37/0.65 = ( ( ord_le3102999989581377725nteger @ J @ I )
% 0.37/0.65 | ( ( ord_le3102999989581377725nteger @ M @ I )
% 0.37/0.65 & ( ord_le3102999989581377725nteger @ J @ N ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_subset
% 0.37/0.65 thf(fact_5522_ivl__diff,axiom,
% 0.37/0.65 ! [I: rat,N: rat,M: rat] :
% 0.37/0.65 ( ( ord_less_eq_rat @ I @ N )
% 0.37/0.65 => ( ( minus_minus_set_rat @ ( set_or4029947393144176647an_rat @ I @ M ) @ ( set_or4029947393144176647an_rat @ I @ N ) )
% 0.37/0.65 = ( set_or4029947393144176647an_rat @ N @ M ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_diff
% 0.37/0.65 thf(fact_5523_ivl__diff,axiom,
% 0.37/0.65 ! [I: num,N: num,M: num] :
% 0.37/0.65 ( ( ord_less_eq_num @ I @ N )
% 0.37/0.65 => ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I @ M ) @ ( set_or1222409239386451017an_num @ I @ N ) )
% 0.37/0.65 = ( set_or1222409239386451017an_num @ N @ M ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_diff
% 0.37/0.65 thf(fact_5524_ivl__diff,axiom,
% 0.37/0.65 ! [I: nat,N: nat,M: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ I @ N )
% 0.37/0.65 => ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I @ M ) @ ( set_or4665077453230672383an_nat @ I @ N ) )
% 0.37/0.65 = ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_diff
% 0.37/0.65 thf(fact_5525_ivl__diff,axiom,
% 0.37/0.65 ! [I: int,N: int,M: int] :
% 0.37/0.65 ( ( ord_less_eq_int @ I @ N )
% 0.37/0.65 => ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I @ M ) @ ( set_or4662586982721622107an_int @ I @ N ) )
% 0.37/0.65 = ( set_or4662586982721622107an_int @ N @ M ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_diff
% 0.37/0.65 thf(fact_5526_ivl__diff,axiom,
% 0.37/0.65 ! [I: code_integer,N: code_integer,M: code_integer] :
% 0.37/0.65 ( ( ord_le3102999989581377725nteger @ I @ N )
% 0.37/0.65 => ( ( minus_2355218937544613996nteger @ ( set_or8404916559141939852nteger @ I @ M ) @ ( set_or8404916559141939852nteger @ I @ N ) )
% 0.37/0.65 = ( set_or8404916559141939852nteger @ N @ M ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ivl_diff
% 0.37/0.65 thf(fact_5527_list__update__beyond,axiom,
% 0.37/0.65 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) @ I )
% 0.37/0.65 => ( ( list_u6098035379799741383_VEBTi @ Xs @ I @ X )
% 0.37/0.65 = Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_beyond
% 0.37/0.65 thf(fact_5528_list__update__beyond,axiom,
% 0.37/0.65 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 0.37/0.65 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 0.37/0.65 = Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_beyond
% 0.37/0.65 thf(fact_5529_list__update__beyond,axiom,
% 0.37/0.65 ! [Xs: list_real,I: nat,X: real] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ I )
% 0.37/0.65 => ( ( list_update_real @ Xs @ I @ X )
% 0.37/0.65 = Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_beyond
% 0.37/0.65 thf(fact_5530_list__update__beyond,axiom,
% 0.37/0.65 ! [Xs: list_o,I: nat,X: $o] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 0.37/0.65 => ( ( list_update_o @ Xs @ I @ X )
% 0.37/0.65 = Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_beyond
% 0.37/0.65 thf(fact_5531_list__update__beyond,axiom,
% 0.37/0.65 ! [Xs: list_nat,I: nat,X: nat] :
% 0.37/0.65 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 0.37/0.65 => ( ( list_update_nat @ Xs @ I @ X )
% 0.37/0.65 = Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_beyond
% 0.37/0.65 thf(fact_5532_image__Suc__atLeastLessThan,axiom,
% 0.37/0.65 ! [I: nat,J: nat] :
% 0.37/0.65 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 0.37/0.65 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % image_Suc_atLeastLessThan
% 0.37/0.65 thf(fact_5533_tcd,axiom,
% 0.37/0.65 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_VEBT_VEBT,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % tcd
% 0.37/0.65 thf(fact_5534_tcd,axiom,
% 0.37/0.65 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_real,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.65 = ( size_size_list_real @ TreeList3 ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % tcd
% 0.37/0.65 thf(fact_5535_tcd,axiom,
% 0.37/0.65 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_o,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.65 = ( size_size_list_o @ TreeList3 ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % tcd
% 0.37/0.65 thf(fact_5536_tcd,axiom,
% 0.37/0.65 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_nat,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.65 = ( size_size_list_nat @ TreeList3 ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % tcd
% 0.37/0.65 thf(fact_5537_nth__update__invalid,axiom,
% 0.37/0.65 ! [I: nat,L: list_int,J: nat,X: int] :
% 0.37/0.65 ( ~ ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 0.37/0.65 => ( ( nth_int @ ( list_update_int @ L @ J @ X ) @ I )
% 0.37/0.65 = ( nth_int @ L @ I ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_update_invalid
% 0.37/0.65 thf(fact_5538_nth__update__invalid,axiom,
% 0.37/0.65 ! [I: nat,L: list_VEBT_VEBTi,J: nat,X: vEBT_VEBTi] :
% 0.37/0.65 ( ~ ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.65 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ J @ X ) @ I )
% 0.37/0.65 = ( nth_VEBT_VEBTi @ L @ I ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_update_invalid
% 0.37/0.65 thf(fact_5539_nth__update__invalid,axiom,
% 0.37/0.65 ! [I: nat,L: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 0.37/0.65 ( ~ ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.65 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ J @ X ) @ I )
% 0.37/0.65 = ( nth_VEBT_VEBT @ L @ I ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_update_invalid
% 0.37/0.65 thf(fact_5540_nth__update__invalid,axiom,
% 0.37/0.65 ! [I: nat,L: list_real,J: nat,X: real] :
% 0.37/0.65 ( ~ ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 0.37/0.65 => ( ( nth_real @ ( list_update_real @ L @ J @ X ) @ I )
% 0.37/0.65 = ( nth_real @ L @ I ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_update_invalid
% 0.37/0.65 thf(fact_5541_nth__update__invalid,axiom,
% 0.37/0.65 ! [I: nat,L: list_o,J: nat,X: $o] :
% 0.37/0.65 ( ~ ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 0.37/0.65 => ( ( nth_o @ ( list_update_o @ L @ J @ X ) @ I )
% 0.37/0.65 = ( nth_o @ L @ I ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_update_invalid
% 0.37/0.65 thf(fact_5542_nth__update__invalid,axiom,
% 0.37/0.65 ! [I: nat,L: list_nat,J: nat,X: nat] :
% 0.37/0.65 ( ~ ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 0.37/0.65 => ( ( nth_nat @ ( list_update_nat @ L @ J @ X ) @ I )
% 0.37/0.65 = ( nth_nat @ L @ I ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_update_invalid
% 0.37/0.65 thf(fact_5543_nth__list__update__eq,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_int,X: int] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 0.37/0.65 = X ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_list_update_eq
% 0.37/0.65 thf(fact_5544_nth__list__update__eq,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ I )
% 0.37/0.65 = X ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_list_update_eq
% 0.37/0.65 thf(fact_5545_nth__list__update__eq,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I )
% 0.37/0.65 = X ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_list_update_eq
% 0.37/0.65 thf(fact_5546_nth__list__update__eq,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_real,X: real] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X ) @ I )
% 0.37/0.65 = X ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_list_update_eq
% 0.37/0.65 thf(fact_5547_nth__list__update__eq,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_o,X: $o] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ I )
% 0.37/0.65 = X ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_list_update_eq
% 0.37/0.65 thf(fact_5548_nth__list__update__eq,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_nat,X: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 0.37/0.65 = X ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_list_update_eq
% 0.37/0.65 thf(fact_5549_atLeastLessThan__singleton,axiom,
% 0.37/0.65 ! [M: nat] :
% 0.37/0.65 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 0.37/0.65 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_singleton
% 0.37/0.65 thf(fact_5550_txe,axiom,
% 0.37/0.65 ! [Y: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ Y @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.65 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % txe
% 0.37/0.65 thf(fact_5551_set__swap,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_int,J: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 0.37/0.65 = ( set_int2 @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_swap
% 0.37/0.65 thf(fact_5552_set__swap,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ ( nth_VEBT_VEBTi @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBTi @ Xs @ I ) ) )
% 0.37/0.65 = ( set_VEBT_VEBTi2 @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_swap
% 0.37/0.65 thf(fact_5553_set__swap,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 0.37/0.65 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_swap
% 0.37/0.65 thf(fact_5554_set__swap,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_real,J: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( ( set_real2 @ ( list_update_real @ ( list_update_real @ Xs @ I @ ( nth_real @ Xs @ J ) ) @ J @ ( nth_real @ Xs @ I ) ) )
% 0.37/0.65 = ( set_real2 @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_swap
% 0.37/0.65 thf(fact_5555_set__swap,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_o,J: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 0.37/0.65 = ( set_o2 @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_swap
% 0.37/0.65 thf(fact_5556_set__swap,axiom,
% 0.37/0.65 ! [I: nat,Xs: list_nat,J: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 0.37/0.65 = ( set_nat2 @ Xs ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_swap
% 0.37/0.65 thf(fact_5557_sum_Oop__ivl__Suc,axiom,
% 0.37/0.65 ! [N: nat,M: nat,G: nat > uint32] :
% 0.37/0.65 ( ( ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups833757482993574392uint32 @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = zero_zero_uint32 ) )
% 0.37/0.65 & ( ~ ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups833757482993574392uint32 @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = ( plus_plus_uint32 @ ( groups833757482993574392uint32 @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sum.op_ivl_Suc
% 0.37/0.65 thf(fact_5558_sum_Oop__ivl__Suc,axiom,
% 0.37/0.65 ! [N: nat,M: nat,G: nat > rat] :
% 0.37/0.65 ( ( ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = zero_zero_rat ) )
% 0.37/0.65 & ( ~ ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sum.op_ivl_Suc
% 0.37/0.65 thf(fact_5559_sum_Oop__ivl__Suc,axiom,
% 0.37/0.65 ! [N: nat,M: nat,G: nat > int] :
% 0.37/0.65 ( ( ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = zero_zero_int ) )
% 0.37/0.65 & ( ~ ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sum.op_ivl_Suc
% 0.37/0.65 thf(fact_5560_sum_Oop__ivl__Suc,axiom,
% 0.37/0.65 ! [N: nat,M: nat,G: nat > nat] :
% 0.37/0.65 ( ( ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = zero_zero_nat ) )
% 0.37/0.65 & ( ~ ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sum.op_ivl_Suc
% 0.37/0.65 thf(fact_5561_sum_Oop__ivl__Suc,axiom,
% 0.37/0.65 ! [N: nat,M: nat,G: nat > real] :
% 0.37/0.65 ( ( ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = zero_zero_real ) )
% 0.37/0.65 & ( ~ ( ord_less_nat @ N @ M )
% 0.37/0.65 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.37/0.65 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % sum.op_ivl_Suc
% 0.37/0.65 thf(fact_5562_nth__image__indices,axiom,
% 0.37/0.65 ! [L: list_VEBT_VEBTi] :
% 0.37/0.65 ( ( image_nat_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 0.37/0.65 = ( set_VEBT_VEBTi2 @ L ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_image_indices
% 0.37/0.65 thf(fact_5563_nth__image__indices,axiom,
% 0.37/0.65 ! [L: list_set_nat] :
% 0.37/0.65 ( ( image_nat_set_nat @ ( nth_set_nat @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ L ) ) )
% 0.37/0.65 = ( set_set_nat2 @ L ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_image_indices
% 0.37/0.65 thf(fact_5564_nth__image__indices,axiom,
% 0.37/0.65 ! [L: list_int] :
% 0.37/0.65 ( ( image_nat_int @ ( nth_int @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ L ) ) )
% 0.37/0.65 = ( set_int2 @ L ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_image_indices
% 0.37/0.65 thf(fact_5565_nth__image__indices,axiom,
% 0.37/0.65 ! [L: list_VEBT_VEBT] :
% 0.37/0.65 ( ( image_nat_VEBT_VEBT @ ( nth_VEBT_VEBT @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 0.37/0.65 = ( set_VEBT_VEBT2 @ L ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_image_indices
% 0.37/0.65 thf(fact_5566_nth__image__indices,axiom,
% 0.37/0.65 ! [L: list_real] :
% 0.37/0.65 ( ( image_nat_real @ ( nth_real @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ L ) ) )
% 0.37/0.65 = ( set_real2 @ L ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_image_indices
% 0.37/0.65 thf(fact_5567_nth__image__indices,axiom,
% 0.37/0.65 ! [L: list_o] :
% 0.37/0.65 ( ( image_nat_o @ ( nth_o @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ L ) ) )
% 0.37/0.65 = ( set_o2 @ L ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_image_indices
% 0.37/0.65 thf(fact_5568_nth__image__indices,axiom,
% 0.37/0.65 ! [L: list_nat] :
% 0.37/0.65 ( ( image_nat_nat @ ( nth_nat @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ L ) ) )
% 0.37/0.65 = ( set_nat2 @ L ) ) ).
% 0.37/0.65
% 0.37/0.65 % nth_image_indices
% 0.37/0.65 thf(fact_5569_deleti_H__rf__abstr,axiom,
% 0.37/0.65 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.65 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.65 => ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V1365221501068881998eletei @ T @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ T @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % deleti'_rf_abstr
% 0.37/0.65 thf(fact_5570_atLeastLessThan__eq__iff,axiom,
% 0.37/0.65 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.65 ( ( ord_less_real @ A @ B )
% 0.37/0.65 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.65 => ( ( ( set_or66887138388493659n_real @ A @ B )
% 0.37/0.65 = ( set_or66887138388493659n_real @ C2 @ D ) )
% 0.37/0.65 = ( ( A = C2 )
% 0.37/0.65 & ( B = D ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_eq_iff
% 0.37/0.65 thf(fact_5571_atLeastLessThan__eq__iff,axiom,
% 0.37/0.65 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.65 ( ( ord_less_rat @ A @ B )
% 0.37/0.65 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.65 => ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.37/0.65 = ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 0.37/0.65 = ( ( A = C2 )
% 0.37/0.65 & ( B = D ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_eq_iff
% 0.37/0.65 thf(fact_5572_atLeastLessThan__eq__iff,axiom,
% 0.37/0.65 ! [A: num,B: num,C2: num,D: num] :
% 0.37/0.65 ( ( ord_less_num @ A @ B )
% 0.37/0.65 => ( ( ord_less_num @ C2 @ D )
% 0.37/0.65 => ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.37/0.65 = ( set_or1222409239386451017an_num @ C2 @ D ) )
% 0.37/0.65 = ( ( A = C2 )
% 0.37/0.65 & ( B = D ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_eq_iff
% 0.37/0.65 thf(fact_5573_atLeastLessThan__eq__iff,axiom,
% 0.37/0.65 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.65 ( ( ord_less_nat @ A @ B )
% 0.37/0.65 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.65 => ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.37/0.65 = ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 0.37/0.65 = ( ( A = C2 )
% 0.37/0.65 & ( B = D ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_eq_iff
% 0.37/0.65 thf(fact_5574_atLeastLessThan__eq__iff,axiom,
% 0.37/0.65 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.65 ( ( ord_less_int @ A @ B )
% 0.37/0.65 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.65 => ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.37/0.65 = ( set_or4662586982721622107an_int @ C2 @ D ) )
% 0.37/0.65 = ( ( A = C2 )
% 0.37/0.65 & ( B = D ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_eq_iff
% 0.37/0.65 thf(fact_5575_atLeastLessThan__eq__iff,axiom,
% 0.37/0.65 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 0.37/0.65 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.37/0.65 => ( ( ord_le6747313008572928689nteger @ C2 @ D )
% 0.37/0.65 => ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.37/0.65 = ( set_or8404916559141939852nteger @ C2 @ D ) )
% 0.37/0.65 = ( ( A = C2 )
% 0.37/0.65 & ( B = D ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_eq_iff
% 0.37/0.65 thf(fact_5576_atLeastLessThan__inj_I1_J,axiom,
% 0.37/0.65 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.65 ( ( ( set_or66887138388493659n_real @ A @ B )
% 0.37/0.65 = ( set_or66887138388493659n_real @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_real @ A @ B )
% 0.37/0.65 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.65 => ( A = C2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(1)
% 0.37/0.65 thf(fact_5577_atLeastLessThan__inj_I1_J,axiom,
% 0.37/0.65 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.65 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.37/0.65 = ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_rat @ A @ B )
% 0.37/0.65 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.65 => ( A = C2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(1)
% 0.37/0.65 thf(fact_5578_atLeastLessThan__inj_I1_J,axiom,
% 0.37/0.65 ! [A: num,B: num,C2: num,D: num] :
% 0.37/0.65 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.37/0.65 = ( set_or1222409239386451017an_num @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_num @ A @ B )
% 0.37/0.65 => ( ( ord_less_num @ C2 @ D )
% 0.37/0.65 => ( A = C2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(1)
% 0.37/0.65 thf(fact_5579_atLeastLessThan__inj_I1_J,axiom,
% 0.37/0.65 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.65 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.37/0.65 = ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_nat @ A @ B )
% 0.37/0.65 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.65 => ( A = C2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(1)
% 0.37/0.65 thf(fact_5580_atLeastLessThan__inj_I1_J,axiom,
% 0.37/0.65 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.65 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.37/0.65 = ( set_or4662586982721622107an_int @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_int @ A @ B )
% 0.37/0.65 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.65 => ( A = C2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(1)
% 0.37/0.65 thf(fact_5581_atLeastLessThan__inj_I1_J,axiom,
% 0.37/0.65 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 0.37/0.65 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.37/0.65 = ( set_or8404916559141939852nteger @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.37/0.65 => ( ( ord_le6747313008572928689nteger @ C2 @ D )
% 0.37/0.65 => ( A = C2 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(1)
% 0.37/0.65 thf(fact_5582_atLeastLessThan__inj_I2_J,axiom,
% 0.37/0.65 ! [A: real,B: real,C2: real,D: real] :
% 0.37/0.65 ( ( ( set_or66887138388493659n_real @ A @ B )
% 0.37/0.65 = ( set_or66887138388493659n_real @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_real @ A @ B )
% 0.37/0.65 => ( ( ord_less_real @ C2 @ D )
% 0.37/0.65 => ( B = D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(2)
% 0.37/0.65 thf(fact_5583_atLeastLessThan__inj_I2_J,axiom,
% 0.37/0.65 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.65 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.37/0.65 = ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_rat @ A @ B )
% 0.37/0.65 => ( ( ord_less_rat @ C2 @ D )
% 0.37/0.65 => ( B = D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(2)
% 0.37/0.65 thf(fact_5584_atLeastLessThan__inj_I2_J,axiom,
% 0.37/0.65 ! [A: num,B: num,C2: num,D: num] :
% 0.37/0.65 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 0.37/0.65 = ( set_or1222409239386451017an_num @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_num @ A @ B )
% 0.37/0.65 => ( ( ord_less_num @ C2 @ D )
% 0.37/0.65 => ( B = D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(2)
% 0.37/0.65 thf(fact_5585_atLeastLessThan__inj_I2_J,axiom,
% 0.37/0.65 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.65 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.37/0.65 = ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_nat @ A @ B )
% 0.37/0.65 => ( ( ord_less_nat @ C2 @ D )
% 0.37/0.65 => ( B = D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(2)
% 0.37/0.65 thf(fact_5586_atLeastLessThan__inj_I2_J,axiom,
% 0.37/0.65 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.65 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.37/0.65 = ( set_or4662586982721622107an_int @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_int @ A @ B )
% 0.37/0.65 => ( ( ord_less_int @ C2 @ D )
% 0.37/0.65 => ( B = D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(2)
% 0.37/0.65 thf(fact_5587_atLeastLessThan__inj_I2_J,axiom,
% 0.37/0.65 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 0.37/0.65 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.37/0.65 = ( set_or8404916559141939852nteger @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.37/0.65 => ( ( ord_le6747313008572928689nteger @ C2 @ D )
% 0.37/0.65 => ( B = D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_inj(2)
% 0.37/0.65 thf(fact_5588_listI__assn__conv,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 0.37/0.65 ( ( N
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A4 @ Xs @ Xsi )
% 0.37/0.65 = ( vEBT_L6296928887356842470_VEBTi @ A4 @ Xs @ Xsi ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_conv
% 0.37/0.65 thf(fact_5589_list__assn__conv__idx,axiom,
% 0.37/0.65 ( vEBT_L6296928887356842470_VEBTi
% 0.37/0.65 = ( ^ [A6: vEBT_VEBT > vEBT_VEBTi > assn,Xs2: list_VEBT_VEBT] : ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) @ A6 @ Xs2 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_assn_conv_idx
% 0.37/0.65 thf(fact_5590_list__update__code_I3_J,axiom,
% 0.37/0.65 ! [X: int,Xs: list_int,I: nat,Y: int] :
% 0.37/0.65 ( ( list_update_int @ ( cons_int @ X @ Xs ) @ ( suc @ I ) @ Y )
% 0.37/0.65 = ( cons_int @ X @ ( list_update_int @ Xs @ I @ Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(3)
% 0.37/0.65 thf(fact_5591_list__update__code_I3_J,axiom,
% 0.37/0.65 ! [X: nat,Xs: list_nat,I: nat,Y: nat] :
% 0.37/0.65 ( ( list_update_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ I ) @ Y )
% 0.37/0.65 = ( cons_nat @ X @ ( list_update_nat @ Xs @ I @ Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(3)
% 0.37/0.65 thf(fact_5592_list__update__code_I3_J,axiom,
% 0.37/0.65 ! [X: $o,Xs: list_o,I: nat,Y: $o] :
% 0.37/0.65 ( ( list_update_o @ ( cons_o @ X @ Xs ) @ ( suc @ I ) @ Y )
% 0.37/0.65 = ( cons_o @ X @ ( list_update_o @ Xs @ I @ Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(3)
% 0.37/0.65 thf(fact_5593_list__update__code_I3_J,axiom,
% 0.37/0.65 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,I: nat,Y: vEBT_VEBTi] :
% 0.37/0.65 ( ( list_u6098035379799741383_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ ( suc @ I ) @ Y )
% 0.37/0.65 = ( cons_VEBT_VEBTi @ X @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(3)
% 0.37/0.65 thf(fact_5594_list__update__code_I3_J,axiom,
% 0.37/0.65 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,I: nat,Y: vEBT_VEBT] :
% 0.37/0.65 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( suc @ I ) @ Y )
% 0.37/0.65 = ( cons_VEBT_VEBT @ X @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(3)
% 0.37/0.65 thf(fact_5595_list__update__code_I2_J,axiom,
% 0.37/0.65 ! [X: int,Xs: list_int,Y: int] :
% 0.37/0.65 ( ( list_update_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat @ Y )
% 0.37/0.65 = ( cons_int @ Y @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(2)
% 0.37/0.65 thf(fact_5596_list__update__code_I2_J,axiom,
% 0.37/0.65 ! [X: nat,Xs: list_nat,Y: nat] :
% 0.37/0.65 ( ( list_update_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat @ Y )
% 0.37/0.65 = ( cons_nat @ Y @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(2)
% 0.37/0.65 thf(fact_5597_list__update__code_I2_J,axiom,
% 0.37/0.65 ! [X: $o,Xs: list_o,Y: $o] :
% 0.37/0.65 ( ( list_update_o @ ( cons_o @ X @ Xs ) @ zero_zero_nat @ Y )
% 0.37/0.65 = ( cons_o @ Y @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(2)
% 0.37/0.65 thf(fact_5598_list__update__code_I2_J,axiom,
% 0.37/0.65 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 0.37/0.65 ( ( list_u6098035379799741383_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ zero_zero_nat @ Y )
% 0.37/0.65 = ( cons_VEBT_VEBTi @ Y @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(2)
% 0.37/0.65 thf(fact_5599_list__update__code_I2_J,axiom,
% 0.37/0.65 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.65 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat @ Y )
% 0.37/0.65 = ( cons_VEBT_VEBT @ Y @ Xs ) ) ).
% 0.37/0.65
% 0.37/0.65 % list_update_code(2)
% 0.37/0.65 thf(fact_5600_set__update__subsetI,axiom,
% 0.37/0.65 ! [Xs: list_set_nat,A4: set_set_nat,X: set_nat,I: nat] :
% 0.37/0.65 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 0.37/0.65 => ( ( member_set_nat @ X @ A4 )
% 0.37/0.65 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_subsetI
% 0.37/0.65 thf(fact_5601_set__update__subsetI,axiom,
% 0.37/0.65 ! [Xs: list_nat,A4: set_nat,X: nat,I: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 0.37/0.65 => ( ( member_nat @ X @ A4 )
% 0.37/0.65 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_subsetI
% 0.37/0.65 thf(fact_5602_set__update__subsetI,axiom,
% 0.37/0.65 ! [Xs: list_real,A4: set_real,X: real,I: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A4 )
% 0.37/0.65 => ( ( member_real @ X @ A4 )
% 0.37/0.65 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_subsetI
% 0.37/0.65 thf(fact_5603_set__update__subsetI,axiom,
% 0.37/0.65 ! [Xs: list_o,A4: set_o,X: $o,I: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 0.37/0.65 => ( ( member_o @ X @ A4 )
% 0.37/0.65 => ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_subsetI
% 0.37/0.65 thf(fact_5604_set__update__subsetI,axiom,
% 0.37/0.65 ! [Xs: list_VEBT_VEBTi,A4: set_VEBT_VEBTi,X: vEBT_VEBTi,I: nat] :
% 0.37/0.65 ( ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ Xs ) @ A4 )
% 0.37/0.65 => ( ( member_VEBT_VEBTi @ X @ A4 )
% 0.37/0.65 => ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_subsetI
% 0.37/0.65 thf(fact_5605_set__update__subsetI,axiom,
% 0.37/0.65 ! [Xs: list_VEBT_VEBT,A4: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 0.37/0.65 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 0.37/0.65 => ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.65 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_subsetI
% 0.37/0.65 thf(fact_5606_set__update__subsetI,axiom,
% 0.37/0.65 ! [Xs: list_int,A4: set_int,X: int,I: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 0.37/0.65 => ( ( member_int @ X @ A4 )
% 0.37/0.65 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_subsetI
% 0.37/0.65 thf(fact_5607_infinite__Ico,axiom,
% 0.37/0.65 ! [A: real,B: real] :
% 0.37/0.65 ( ( ord_less_real @ A @ B )
% 0.37/0.65 => ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % infinite_Ico
% 0.37/0.65 thf(fact_5608_infinite__Ico,axiom,
% 0.37/0.65 ! [A: rat,B: rat] :
% 0.37/0.65 ( ( ord_less_rat @ A @ B )
% 0.37/0.65 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % infinite_Ico
% 0.37/0.65 thf(fact_5609_atLeastLessThan__subset__iff,axiom,
% 0.37/0.65 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.37/0.65 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_eq_rat @ B @ A )
% 0.37/0.65 | ( ( ord_less_eq_rat @ C2 @ A )
% 0.37/0.65 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_subset_iff
% 0.37/0.65 thf(fact_5610_atLeastLessThan__subset__iff,axiom,
% 0.37/0.65 ! [A: num,B: num,C2: num,D: num] :
% 0.37/0.65 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_eq_num @ B @ A )
% 0.37/0.65 | ( ( ord_less_eq_num @ C2 @ A )
% 0.37/0.65 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_subset_iff
% 0.37/0.65 thf(fact_5611_atLeastLessThan__subset__iff,axiom,
% 0.37/0.65 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.65 | ( ( ord_less_eq_nat @ C2 @ A )
% 0.37/0.65 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_subset_iff
% 0.37/0.65 thf(fact_5612_atLeastLessThan__subset__iff,axiom,
% 0.37/0.65 ! [A: int,B: int,C2: int,D: int] :
% 0.37/0.65 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_less_eq_int @ B @ A )
% 0.37/0.65 | ( ( ord_less_eq_int @ C2 @ A )
% 0.37/0.65 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_subset_iff
% 0.37/0.65 thf(fact_5613_atLeastLessThan__subset__iff,axiom,
% 0.37/0.65 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 0.37/0.65 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C2 @ D ) )
% 0.37/0.65 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.37/0.65 | ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 0.37/0.65 & ( ord_le3102999989581377725nteger @ B @ D ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan_subset_iff
% 0.37/0.65 thf(fact_5614_ex__nat__less__eq,axiom,
% 0.37/0.65 ! [N: nat,P2: nat > $o] :
% 0.37/0.65 ( ( ? [M5: nat] :
% 0.37/0.65 ( ( ord_less_nat @ M5 @ N )
% 0.37/0.65 & ( P2 @ M5 ) ) )
% 0.37/0.65 = ( ? [X4: nat] :
% 0.37/0.65 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.37/0.65 & ( P2 @ X4 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % ex_nat_less_eq
% 0.37/0.65 thf(fact_5615_all__nat__less__eq,axiom,
% 0.37/0.65 ! [N: nat,P2: nat > $o] :
% 0.37/0.65 ( ( ! [M5: nat] :
% 0.37/0.65 ( ( ord_less_nat @ M5 @ N )
% 0.37/0.65 => ( P2 @ M5 ) ) )
% 0.37/0.65 = ( ! [X4: nat] :
% 0.37/0.65 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.37/0.65 => ( P2 @ X4 ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % all_nat_less_eq
% 0.37/0.65 thf(fact_5616_atLeastLessThan0,axiom,
% 0.37/0.65 ! [M: nat] :
% 0.37/0.65 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 0.37/0.65 = bot_bot_set_nat ) ).
% 0.37/0.65
% 0.37/0.65 % atLeastLessThan0
% 0.37/0.65 thf(fact_5617_listI__assn__conv_H,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi,F2: assn] :
% 0.37/0.65 ( ( N
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A4 @ Xs @ Xsi ) @ F2 )
% 0.37/0.65 = ( times_times_assn @ ( vEBT_L6296928887356842470_VEBTi @ A4 @ Xs @ Xsi ) @ F2 ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % listI_assn_conv'
% 0.37/0.65 thf(fact_5618_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.37/0.65 ! [N8: set_nat,N: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_nat @ N8 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.37/0.65 => ( finite_finite_nat @ N8 ) ) ).
% 0.37/0.65
% 0.37/0.65 % subset_eq_atLeast0_lessThan_finite
% 0.37/0.65 thf(fact_5619_subset__card__intvl__is__intvl,axiom,
% 0.37/0.65 ! [A4: set_nat,K: nat] :
% 0.37/0.65 ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) )
% 0.37/0.65 => ( A4
% 0.37/0.65 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % subset_card_intvl_is_intvl
% 0.37/0.65 thf(fact_5620_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L1279224858307276611T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5621_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: real > vEBT_VEBT > assn,Xs: list_real,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L4595930785310033027T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.65 = ( size_size_list_real @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5622_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: $o > vEBT_VEBT > assn,Xs: list_o,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L1750719106661372127T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.65 = ( size_size_list_o @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5623_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: nat > vEBT_VEBT > assn,Xs: list_nat,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L8158188754432654943T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 0.37/0.65 = ( size_size_list_nat @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5624_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: vEBT_VEBT > real > assn,Xs: list_VEBT_VEBT,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L5781919052683127133T_real @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_size_list_real @ Xsi )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5625_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: real > real > assn,Xs: list_real,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L1930518968523514909l_real @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_size_list_real @ Xsi )
% 0.37/0.65 = ( size_size_list_real @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5626_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: $o > real > assn,Xs: list_o,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L4725278957065240257o_real @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_size_list_real @ Xsi )
% 0.37/0.65 = ( size_size_list_o @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5627_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: nat > real > assn,Xs: list_nat,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L6102073776069194049t_real @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_size_list_real @ Xsi )
% 0.37/0.65 = ( size_size_list_nat @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5628_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: vEBT_VEBT > $o > assn,Xs: list_VEBT_VEBT,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L7489408758114837031VEBT_o @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_size_list_o @ Xsi )
% 0.37/0.65 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5629_extract__pre__list__assn__lengthD,axiom,
% 0.37/0.65 ! [A4: real > $o > assn,Xs: list_real,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 0.37/0.65 ( ( rep_assn @ ( vEBT_L6234343332106409831real_o @ A4 @ Xs @ Xsi ) @ H2 )
% 0.37/0.65 => ( ( size_size_list_o @ Xsi )
% 0.37/0.65 = ( size_size_list_real @ Xs ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % extract_pre_list_assn_lengthD
% 0.37/0.65 thf(fact_5630_set__update__memI,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_int,X: int] :
% 0.37/0.65 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.37/0.65 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_memI
% 0.37/0.65 thf(fact_5631_set__update__memI,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_set_nat,X: set_nat] :
% 0.37/0.65 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.65 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_memI
% 0.37/0.65 thf(fact_5632_set__update__memI,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.65 => ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ N @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_memI
% 0.37/0.65 thf(fact_5633_set__update__memI,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.65 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.65 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_memI
% 0.37/0.65 thf(fact_5634_set__update__memI,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_real,X: real] :
% 0.37/0.65 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.65 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs @ N @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_memI
% 0.37/0.65 thf(fact_5635_set__update__memI,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_o,X: $o] :
% 0.37/0.65 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.65 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs @ N @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_memI
% 0.37/0.65 thf(fact_5636_set__update__memI,axiom,
% 0.37/0.65 ! [N: nat,Xs: list_nat,X: nat] :
% 0.37/0.65 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.65 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % set_update_memI
% 0.37/0.65 thf(fact_5637_in__set__upd__eq,axiom,
% 0.37/0.65 ! [I: nat,L: list_int,X: int,Y: int] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 0.37/0.65 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 0.37/0.65 = ( ( X = Y )
% 0.37/0.65 | ( ( member_int @ X @ ( set_int2 @ L ) )
% 0.37/0.65 & ! [Y4: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % in_set_upd_eq
% 0.37/0.65 thf(fact_5638_in__set__upd__eq,axiom,
% 0.37/0.65 ! [I: nat,L: list_set_nat,X: set_nat,Y: set_nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ L ) )
% 0.37/0.65 => ( ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y ) ) )
% 0.37/0.65 = ( ( X = Y )
% 0.37/0.65 | ( ( member_set_nat @ X @ ( set_set_nat2 @ L ) )
% 0.37/0.65 & ! [Y4: set_nat] : ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % in_set_upd_eq
% 0.37/0.65 thf(fact_5639_in__set__upd__eq,axiom,
% 0.37/0.65 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi,Y: vEBT_VEBTi] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.65 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 0.37/0.65 = ( ( X = Y )
% 0.37/0.65 | ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) )
% 0.37/0.65 & ! [Y4: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % in_set_upd_eq
% 0.37/0.65 thf(fact_5640_in__set__upd__eq,axiom,
% 0.37/0.65 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.65 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 0.37/0.65 = ( ( X = Y )
% 0.37/0.65 | ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) )
% 0.37/0.65 & ! [Y4: vEBT_VEBT] : ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % in_set_upd_eq
% 0.37/0.65 thf(fact_5641_in__set__upd__eq,axiom,
% 0.37/0.65 ! [I: nat,L: list_real,X: real,Y: real] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 0.37/0.65 => ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 0.37/0.65 = ( ( X = Y )
% 0.37/0.65 | ( ( member_real @ X @ ( set_real2 @ L ) )
% 0.37/0.65 & ! [Y4: real] : ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % in_set_upd_eq
% 0.37/0.65 thf(fact_5642_in__set__upd__eq,axiom,
% 0.37/0.65 ! [I: nat,L: list_o,X: $o,Y: $o] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 0.37/0.65 => ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 0.37/0.65 = ( ( X = Y )
% 0.37/0.65 | ( ( member_o @ X @ ( set_o2 @ L ) )
% 0.37/0.65 & ! [Y4: $o] : ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % in_set_upd_eq
% 0.37/0.65 thf(fact_5643_in__set__upd__eq,axiom,
% 0.37/0.65 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 0.37/0.65 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 0.37/0.65 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 0.37/0.65 = ( ( X = Y )
% 0.37/0.65 | ( ( member_nat @ X @ ( set_nat2 @ L ) )
% 0.37/0.65 & ! [Y4: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 0.37/0.65
% 0.37/0.65 % in_set_upd_eq
% 0.37/0.65 thf(fact_5644_in__set__upd__cases,axiom,
% 0.37/0.65 ! [X: int,L: list_int,I: nat,Y: int] :
% 0.37/0.65 ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 0.37/0.65 => ( ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 0.37/0.65 => ( X != Y ) )
% 0.37/0.65 => ( member_int @ X @ ( set_int2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_cases
% 0.37/0.66 thf(fact_5645_in__set__upd__cases,axiom,
% 0.37/0.66 ! [X: set_nat,L: list_set_nat,I: nat,Y: set_nat] :
% 0.37/0.66 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y ) ) )
% 0.37/0.66 => ( ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ L ) )
% 0.37/0.66 => ( X != Y ) )
% 0.37/0.66 => ( member_set_nat @ X @ ( set_set_nat2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_cases
% 0.37/0.66 thf(fact_5646_in__set__upd__cases,axiom,
% 0.37/0.66 ! [X: vEBT_VEBTi,L: list_VEBT_VEBTi,I: nat,Y: vEBT_VEBTi] :
% 0.37/0.66 ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 0.37/0.66 => ( ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.66 => ( X != Y ) )
% 0.37/0.66 => ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_cases
% 0.37/0.66 thf(fact_5647_in__set__upd__cases,axiom,
% 0.37/0.66 ! [X: vEBT_VEBT,L: list_VEBT_VEBT,I: nat,Y: vEBT_VEBT] :
% 0.37/0.66 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 0.37/0.66 => ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.66 => ( X != Y ) )
% 0.37/0.66 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_cases
% 0.37/0.66 thf(fact_5648_in__set__upd__cases,axiom,
% 0.37/0.66 ! [X: real,L: list_real,I: nat,Y: real] :
% 0.37/0.66 ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 0.37/0.66 => ( ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( X != Y ) )
% 0.37/0.66 => ( member_real @ X @ ( set_real2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_cases
% 0.37/0.66 thf(fact_5649_in__set__upd__cases,axiom,
% 0.37/0.66 ! [X: $o,L: list_o,I: nat,Y: $o] :
% 0.37/0.66 ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 0.37/0.66 => ( ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( X = ( ~ Y ) ) )
% 0.37/0.66 => ( member_o @ X @ ( set_o2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_cases
% 0.37/0.66 thf(fact_5650_in__set__upd__cases,axiom,
% 0.37/0.66 ! [X: nat,L: list_nat,I: nat,Y: nat] :
% 0.37/0.66 ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 0.37/0.66 => ( ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( X != Y ) )
% 0.37/0.66 => ( member_nat @ X @ ( set_nat2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_cases
% 0.37/0.66 thf(fact_5651_in__set__upd__eq__aux,axiom,
% 0.37/0.66 ! [I: nat,L: list_int,X: int,Y: int] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 0.37/0.66 = ( ( X = Y )
% 0.37/0.66 | ! [Y4: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y4 ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_eq_aux
% 0.37/0.66 thf(fact_5652_in__set__upd__eq__aux,axiom,
% 0.37/0.66 ! [I: nat,L: list_set_nat,X: set_nat,Y: set_nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ L ) )
% 0.37/0.66 => ( ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y ) ) )
% 0.37/0.66 = ( ( X = Y )
% 0.37/0.66 | ! [Y4: set_nat] : ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y4 ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_eq_aux
% 0.37/0.66 thf(fact_5653_in__set__upd__eq__aux,axiom,
% 0.37/0.66 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi,Y: vEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.66 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 0.37/0.66 = ( ( X = Y )
% 0.37/0.66 | ! [Y4: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y4 ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_eq_aux
% 0.37/0.66 thf(fact_5654_in__set__upd__eq__aux,axiom,
% 0.37/0.66 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.66 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 0.37/0.66 = ( ( X = Y )
% 0.37/0.66 | ! [Y4: vEBT_VEBT] : ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y4 ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_eq_aux
% 0.37/0.66 thf(fact_5655_in__set__upd__eq__aux,axiom,
% 0.37/0.66 ! [I: nat,L: list_real,X: real,Y: real] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 0.37/0.66 = ( ( X = Y )
% 0.37/0.66 | ! [Y4: real] : ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y4 ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_eq_aux
% 0.37/0.66 thf(fact_5656_in__set__upd__eq__aux,axiom,
% 0.37/0.66 ! [I: nat,L: list_o,X: $o,Y: $o] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 0.37/0.66 = ( ( X = Y )
% 0.37/0.66 | ! [Y4: $o] : ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y4 ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_eq_aux
% 0.37/0.66 thf(fact_5657_in__set__upd__eq__aux,axiom,
% 0.37/0.66 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 0.37/0.66 = ( ( X = Y )
% 0.37/0.66 | ! [Y4: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y4 ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % in_set_upd_eq_aux
% 0.37/0.66 thf(fact_5658_nth__list__update_H,axiom,
% 0.37/0.66 ! [I: nat,J: nat,L: list_int,X: int] :
% 0.37/0.66 ( ( ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 0.37/0.66 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ~ ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 0.37/0.66 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 0.37/0.66 = ( nth_int @ L @ J ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update'
% 0.37/0.66 thf(fact_5659_nth__list__update_H,axiom,
% 0.37/0.66 ! [I: nat,J: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ~ ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) @ J )
% 0.37/0.66 = ( nth_VEBT_VEBTi @ L @ J ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update'
% 0.37/0.66 thf(fact_5660_nth__list__update_H,axiom,
% 0.37/0.66 ! [I: nat,J: nat,L: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.66 ( ( ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ~ ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) @ J )
% 0.37/0.66 = ( nth_VEBT_VEBT @ L @ J ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update'
% 0.37/0.66 thf(fact_5661_nth__list__update_H,axiom,
% 0.37/0.66 ! [I: nat,J: nat,L: list_real,X: real] :
% 0.37/0.66 ( ( ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 0.37/0.66 => ( ( nth_real @ ( list_update_real @ L @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ~ ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 0.37/0.66 => ( ( nth_real @ ( list_update_real @ L @ I @ X ) @ J )
% 0.37/0.66 = ( nth_real @ L @ J ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update'
% 0.37/0.66 thf(fact_5662_nth__list__update_H,axiom,
% 0.37/0.66 ! [L: list_o,I: nat,X: $o,J: nat] :
% 0.37/0.66 ( ( nth_o @ ( list_update_o @ L @ I @ X ) @ J )
% 0.37/0.66 = ( ( ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 0.37/0.66 => X )
% 0.37/0.66 & ( ~ ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 0.37/0.66 => ( nth_o @ L @ J ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update'
% 0.37/0.66 thf(fact_5663_nth__list__update_H,axiom,
% 0.37/0.66 ! [I: nat,J: nat,L: list_nat,X: nat] :
% 0.37/0.66 ( ( ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 0.37/0.66 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ~ ( ( I = J )
% 0.37/0.66 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 0.37/0.66 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 0.37/0.66 = ( nth_nat @ L @ J ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update'
% 0.37/0.66 thf(fact_5664_list__update__same__conv,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_int,X: int] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ( list_update_int @ Xs @ I @ X )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ( nth_int @ Xs @ I )
% 0.37/0.66 = X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % list_update_same_conv
% 0.37/0.66 thf(fact_5665_list__update__same__conv,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ( list_u6098035379799741383_VEBTi @ Xs @ I @ X )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ( nth_VEBT_VEBTi @ Xs @ I )
% 0.37/0.66 = X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % list_update_same_conv
% 0.37/0.66 thf(fact_5666_list__update__same__conv,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ( nth_VEBT_VEBT @ Xs @ I )
% 0.37/0.66 = X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % list_update_same_conv
% 0.37/0.66 thf(fact_5667_list__update__same__conv,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_real,X: real] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( ( list_update_real @ Xs @ I @ X )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ( nth_real @ Xs @ I )
% 0.37/0.66 = X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % list_update_same_conv
% 0.37/0.66 thf(fact_5668_list__update__same__conv,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_o,X: $o] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( ( list_update_o @ Xs @ I @ X )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ( nth_o @ Xs @ I )
% 0.37/0.66 = X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % list_update_same_conv
% 0.37/0.66 thf(fact_5669_list__update__same__conv,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_nat,X: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( ( list_update_nat @ Xs @ I @ X )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ( nth_nat @ Xs @ I )
% 0.37/0.66 = X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % list_update_same_conv
% 0.37/0.66 thf(fact_5670_nth__list__update,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_int,J: nat,X: int] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ( I = J )
% 0.37/0.66 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ( I != J )
% 0.37/0.66 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 0.37/0.66 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update
% 0.37/0.66 thf(fact_5671_nth__list__update,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ( I = J )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ( I != J )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ J )
% 0.37/0.66 = ( nth_VEBT_VEBTi @ Xs @ J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update
% 0.37/0.66 thf(fact_5672_nth__list__update,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( ( I = J )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ( I != J )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 0.37/0.66 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update
% 0.37/0.66 thf(fact_5673_nth__list__update,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_real,J: nat,X: real] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( ( I = J )
% 0.37/0.66 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ( I != J )
% 0.37/0.66 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X ) @ J )
% 0.37/0.66 = ( nth_real @ Xs @ J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update
% 0.37/0.66 thf(fact_5674_nth__list__update,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_o,X: $o,J: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ J )
% 0.37/0.66 = ( ( ( I = J )
% 0.37/0.66 => X )
% 0.37/0.66 & ( ( I != J )
% 0.37/0.66 => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update
% 0.37/0.66 thf(fact_5675_nth__list__update,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( ( I = J )
% 0.37/0.66 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 0.37/0.66 = X ) )
% 0.37/0.66 & ( ( I != J )
% 0.37/0.66 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 0.37/0.66 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_list_update
% 0.37/0.66 thf(fact_5676_set__update__subset__insert,axiom,
% 0.37/0.66 ! [Xs: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_subset_insert
% 0.37/0.66 thf(fact_5677_set__update__subset__insert,axiom,
% 0.37/0.66 ! [Xs: list_real,I: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_subset_insert
% 0.37/0.66 thf(fact_5678_set__update__subset__insert,axiom,
% 0.37/0.66 ! [Xs: list_o,I: nat,X: $o] : ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X ) ) @ ( insert_o @ X @ ( set_o2 @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_subset_insert
% 0.37/0.66 thf(fact_5679_set__update__subset__insert,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] : ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_subset_insert
% 0.37/0.66 thf(fact_5680_set__update__subset__insert,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_subset_insert
% 0.37/0.66 thf(fact_5681_set__update__subset__insert,axiom,
% 0.37/0.66 ! [Xs: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_subset_insert
% 0.37/0.66 thf(fact_5682_sum_Oivl__cong,axiom,
% 0.37/0.66 ! [A: nat,C2: nat,B: nat,D: nat,G: nat > nat,H2: nat > nat] :
% 0.37/0.66 ( ( A = C2 )
% 0.37/0.66 => ( ( B = D )
% 0.37/0.66 => ( ! [X3: nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ C2 @ X3 )
% 0.37/0.66 => ( ( ord_less_nat @ X3 @ D )
% 0.37/0.66 => ( ( G @ X3 )
% 0.37/0.66 = ( H2 @ X3 ) ) ) )
% 0.37/0.66 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.37/0.66 = ( groups3542108847815614940at_nat @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.ivl_cong
% 0.37/0.66 thf(fact_5683_sum_Oivl__cong,axiom,
% 0.37/0.66 ! [A: nat,C2: nat,B: nat,D: nat,G: nat > real,H2: nat > real] :
% 0.37/0.66 ( ( A = C2 )
% 0.37/0.66 => ( ( B = D )
% 0.37/0.66 => ( ! [X3: nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ C2 @ X3 )
% 0.37/0.66 => ( ( ord_less_nat @ X3 @ D )
% 0.37/0.66 => ( ( G @ X3 )
% 0.37/0.66 = ( H2 @ X3 ) ) ) )
% 0.37/0.66 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.37/0.66 = ( groups6591440286371151544t_real @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.ivl_cong
% 0.37/0.66 thf(fact_5684_sum_Oivl__cong,axiom,
% 0.37/0.66 ! [A: int,C2: int,B: int,D: int,G: int > int,H2: int > int] :
% 0.37/0.66 ( ( A = C2 )
% 0.37/0.66 => ( ( B = D )
% 0.37/0.66 => ( ! [X3: int] :
% 0.37/0.66 ( ( ord_less_eq_int @ C2 @ X3 )
% 0.37/0.66 => ( ( ord_less_int @ X3 @ D )
% 0.37/0.66 => ( ( G @ X3 )
% 0.37/0.66 = ( H2 @ X3 ) ) ) )
% 0.37/0.66 => ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 0.37/0.66 = ( groups4538972089207619220nt_int @ H2 @ ( set_or4662586982721622107an_int @ C2 @ D ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.ivl_cong
% 0.37/0.66 thf(fact_5685_sum_OatLeastLessThan__concat,axiom,
% 0.37/0.66 ! [M: nat,N: nat,P3: nat,G: nat > rat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( ord_less_eq_nat @ N @ P3 )
% 0.37/0.66 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 0.37/0.66 = ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_concat
% 0.37/0.66 thf(fact_5686_sum_OatLeastLessThan__concat,axiom,
% 0.37/0.66 ! [M: nat,N: nat,P3: nat,G: nat > int] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( ord_less_eq_nat @ N @ P3 )
% 0.37/0.66 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 0.37/0.66 = ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_concat
% 0.37/0.66 thf(fact_5687_sum_OatLeastLessThan__concat,axiom,
% 0.37/0.66 ! [M: nat,N: nat,P3: nat,G: nat > nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( ord_less_eq_nat @ N @ P3 )
% 0.37/0.66 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 0.37/0.66 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_concat
% 0.37/0.66 thf(fact_5688_sum_OatLeastLessThan__concat,axiom,
% 0.37/0.66 ! [M: nat,N: nat,P3: nat,G: nat > real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( ord_less_eq_nat @ N @ P3 )
% 0.37/0.66 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 0.37/0.66 = ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_concat
% 0.37/0.66 thf(fact_5689_sum__diff__nat__ivl,axiom,
% 0.37/0.66 ! [M: nat,N: nat,P3: nat,F: nat > uint32] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( ord_less_eq_nat @ N @ P3 )
% 0.37/0.66 => ( ( minus_minus_uint32 @ ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 0.37/0.66 = ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_diff_nat_ivl
% 0.37/0.66 thf(fact_5690_sum__diff__nat__ivl,axiom,
% 0.37/0.66 ! [M: nat,N: nat,P3: nat,F: nat > int] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( ord_less_eq_nat @ N @ P3 )
% 0.37/0.66 => ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 0.37/0.66 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_diff_nat_ivl
% 0.37/0.66 thf(fact_5691_sum__diff__nat__ivl,axiom,
% 0.37/0.66 ! [M: nat,N: nat,P3: nat,F: nat > real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( ord_less_eq_nat @ N @ P3 )
% 0.37/0.66 => ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 0.37/0.66 = ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_diff_nat_ivl
% 0.37/0.66 thf(fact_5692_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5693_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5694_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5695_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBTi > assn,X1: real,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5696_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBT > assn,X1: real,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5697_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBTi > assn,X1: $o,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5698_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBT > assn,X1: $o,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5699_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBTi > assn,X1: nat,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5700_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBT > assn,X1: nat,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5701_subst__not__in,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subst_not_in
% 0.37/0.66 thf(fact_5702_atLeast0__lessThan__Suc,axiom,
% 0.37/0.66 ! [N: nat] :
% 0.37/0.66 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.37/0.66 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % atLeast0_lessThan_Suc
% 0.37/0.66 thf(fact_5703_subset__eq__atLeast0__lessThan__card,axiom,
% 0.37/0.66 ! [N8: set_nat,N: nat] :
% 0.37/0.66 ( ( ord_less_eq_set_nat @ N8 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.37/0.66 => ( ord_less_eq_nat @ ( finite_card_nat @ N8 ) @ N ) ) ).
% 0.37/0.66
% 0.37/0.66 % subset_eq_atLeast0_lessThan_card
% 0.37/0.66 thf(fact_5704_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X: vEBT_VEBTi,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5705_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,X: vEBT_VEBTi,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5706_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,X: vEBT_VEBT,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5707_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: real > vEBT_VEBTi > assn,X: real,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5708_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: real > vEBT_VEBT > assn,X: real,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5709_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: $o > vEBT_VEBTi > assn,X: $o,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L6286945158656146733_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5710_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: $o > vEBT_VEBT > assn,X: $o,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5711_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: nat > vEBT_VEBTi > assn,X: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7489483478785760935_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5712_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: nat > vEBT_VEBT > assn,X: nat,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L8511957252848910786T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5713_listI__assn__reinsert__upd_H,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X: vEBT_VEBTi,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_Time_Heap_o,Q2: $o > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_hoare_triple_o @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_reinsert_upd'
% 0.37/0.66 thf(fact_5714_sum__shift__lb__Suc0__0__upt,axiom,
% 0.37/0.66 ! [F: nat > uint32,K: nat] :
% 0.37/0.66 ( ( ( F @ zero_zero_nat )
% 0.37/0.66 = zero_zero_uint32 )
% 0.37/0.66 => ( ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.37/0.66 = ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_shift_lb_Suc0_0_upt
% 0.37/0.66 thf(fact_5715_sum__shift__lb__Suc0__0__upt,axiom,
% 0.37/0.66 ! [F: nat > rat,K: nat] :
% 0.37/0.66 ( ( ( F @ zero_zero_nat )
% 0.37/0.66 = zero_zero_rat )
% 0.37/0.66 => ( ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.37/0.66 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_shift_lb_Suc0_0_upt
% 0.37/0.66 thf(fact_5716_sum__shift__lb__Suc0__0__upt,axiom,
% 0.37/0.66 ! [F: nat > int,K: nat] :
% 0.37/0.66 ( ( ( F @ zero_zero_nat )
% 0.37/0.66 = zero_zero_int )
% 0.37/0.66 => ( ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.37/0.66 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_shift_lb_Suc0_0_upt
% 0.37/0.66 thf(fact_5717_sum__shift__lb__Suc0__0__upt,axiom,
% 0.37/0.66 ! [F: nat > nat,K: nat] :
% 0.37/0.66 ( ( ( F @ zero_zero_nat )
% 0.37/0.66 = zero_zero_nat )
% 0.37/0.66 => ( ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.37/0.66 = ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_shift_lb_Suc0_0_upt
% 0.37/0.66 thf(fact_5718_sum__shift__lb__Suc0__0__upt,axiom,
% 0.37/0.66 ! [F: nat > real,K: nat] :
% 0.37/0.66 ( ( ( F @ zero_zero_nat )
% 0.37/0.66 = zero_zero_real )
% 0.37/0.66 => ( ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 0.37/0.66 = ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum_shift_lb_Suc0_0_upt
% 0.37/0.66 thf(fact_5719_sum_OatLeast0__lessThan__Suc,axiom,
% 0.37/0.66 ! [G: nat > rat,N: nat] :
% 0.37/0.66 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.37/0.66 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast0_lessThan_Suc
% 0.37/0.66 thf(fact_5720_sum_OatLeast0__lessThan__Suc,axiom,
% 0.37/0.66 ! [G: nat > int,N: nat] :
% 0.37/0.66 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.37/0.66 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast0_lessThan_Suc
% 0.37/0.66 thf(fact_5721_sum_OatLeast0__lessThan__Suc,axiom,
% 0.37/0.66 ! [G: nat > nat,N: nat] :
% 0.37/0.66 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.37/0.66 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast0_lessThan_Suc
% 0.37/0.66 thf(fact_5722_sum_OatLeast0__lessThan__Suc,axiom,
% 0.37/0.66 ! [G: nat > real,N: nat] :
% 0.37/0.66 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.37/0.66 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast0_lessThan_Suc
% 0.37/0.66 thf(fact_5723_sum_OatLeast__Suc__lessThan,axiom,
% 0.37/0.66 ! [M: nat,N: nat,G: nat > rat] :
% 0.37/0.66 ( ( ord_less_nat @ M @ N )
% 0.37/0.66 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.66 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast_Suc_lessThan
% 0.37/0.66 thf(fact_5724_sum_OatLeast__Suc__lessThan,axiom,
% 0.37/0.66 ! [M: nat,N: nat,G: nat > int] :
% 0.37/0.66 ( ( ord_less_nat @ M @ N )
% 0.37/0.66 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.66 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast_Suc_lessThan
% 0.37/0.66 thf(fact_5725_sum_OatLeast__Suc__lessThan,axiom,
% 0.37/0.66 ! [M: nat,N: nat,G: nat > nat] :
% 0.37/0.66 ( ( ord_less_nat @ M @ N )
% 0.37/0.66 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.66 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast_Suc_lessThan
% 0.37/0.66 thf(fact_5726_sum_OatLeast__Suc__lessThan,axiom,
% 0.37/0.66 ! [M: nat,N: nat,G: nat > real] :
% 0.37/0.66 ( ( ord_less_nat @ M @ N )
% 0.37/0.66 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.66 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeast_Suc_lessThan
% 0.37/0.66 thf(fact_5727_sum_OatLeastLessThan__Suc,axiom,
% 0.37/0.66 ! [A: nat,B: nat,G: nat > rat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.66 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.37/0.66 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_Suc
% 0.37/0.66 thf(fact_5728_sum_OatLeastLessThan__Suc,axiom,
% 0.37/0.66 ! [A: nat,B: nat,G: nat > int] :
% 0.37/0.66 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.66 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.37/0.66 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_Suc
% 0.37/0.66 thf(fact_5729_sum_OatLeastLessThan__Suc,axiom,
% 0.37/0.66 ! [A: nat,B: nat,G: nat > nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.66 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.37/0.66 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_Suc
% 0.37/0.66 thf(fact_5730_sum_OatLeastLessThan__Suc,axiom,
% 0.37/0.66 ! [A: nat,B: nat,G: nat > real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.66 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.37/0.66 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sum.atLeastLessThan_Suc
% 0.37/0.66 thf(fact_5731_atLeastLessThanSuc,axiom,
% 0.37/0.66 ! [M: nat,N: nat] :
% 0.37/0.66 ( ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.37/0.66 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 0.37/0.66 & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.37/0.66 = bot_bot_set_nat ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % atLeastLessThanSuc
% 0.37/0.66 thf(fact_5732_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.37/0.66 ! [N: nat] :
% 0.37/0.66 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.37/0.66 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % atLeast0_lessThan_Suc_eq_insert_0
% 0.37/0.66 thf(fact_5733_insert__swap__set__eq,axiom,
% 0.37/0.66 ! [I: nat,L: list_int,X: int] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ( insert_int @ ( nth_int @ L @ I ) @ ( set_int2 @ ( list_update_int @ L @ I @ X ) ) )
% 0.37/0.66 = ( insert_int @ X @ ( set_int2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % insert_swap_set_eq
% 0.37/0.66 thf(fact_5734_insert__swap__set__eq,axiom,
% 0.37/0.66 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.66 => ( ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ L @ I ) @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) ) )
% 0.37/0.66 = ( insert_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % insert_swap_set_eq
% 0.37/0.66 thf(fact_5735_insert__swap__set__eq,axiom,
% 0.37/0.66 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.66 => ( ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ L @ I ) @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) ) )
% 0.37/0.66 = ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % insert_swap_set_eq
% 0.37/0.66 thf(fact_5736_insert__swap__set__eq,axiom,
% 0.37/0.66 ! [I: nat,L: list_real,X: real] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( insert_real @ ( nth_real @ L @ I ) @ ( set_real2 @ ( list_update_real @ L @ I @ X ) ) )
% 0.37/0.66 = ( insert_real @ X @ ( set_real2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % insert_swap_set_eq
% 0.37/0.66 thf(fact_5737_insert__swap__set__eq,axiom,
% 0.37/0.66 ! [I: nat,L: list_o,X: $o] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( insert_o @ ( nth_o @ L @ I ) @ ( set_o2 @ ( list_update_o @ L @ I @ X ) ) )
% 0.37/0.66 = ( insert_o @ X @ ( set_o2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % insert_swap_set_eq
% 0.37/0.66 thf(fact_5738_insert__swap__set__eq,axiom,
% 0.37/0.66 ! [I: nat,L: list_nat,X: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( insert_nat @ ( nth_nat @ L @ I ) @ ( set_nat2 @ ( list_update_nat @ L @ I @ X ) ) )
% 0.37/0.66 = ( insert_nat @ X @ ( set_nat2 @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % insert_swap_set_eq
% 0.37/0.66 thf(fact_5739_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L886525131989349516_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5740_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L2497118539674116125T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5741_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L3204528365124325536T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5742_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBTi > assn,X1: real,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L7851252805511451907_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5743_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBT > assn,X1: real,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L3095048238742455910T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5744_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBTi > assn,X1: $o,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L6286945158656146733_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5745_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBT > assn,X1: $o,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L1319876754960170684T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5746_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBTi > assn,X1: nat,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L7489483478785760935_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5747_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBT > assn,X1: nat,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L8511957252848910786T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5748_listI__assn__subst,axiom,
% 0.37/0.66 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 0.37/0.66 ( ~ ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( vEBT_L1528199826722428489_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 0.37/0.66 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_subst
% 0.37/0.66 thf(fact_5749_big__assn__simp_H,axiom,
% 0.37/0.66 ! [H2: nat,TreeList: list_VEBT_VEBT,Xaa: vEBT_VEBT,L: nat,X: vEBT_VEBTi,Xb: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.66 => ( ( Xaa
% 0.37/0.66 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.66 => ( entails
% 0.37/0.66 @ ( times_times_assn
% 0.37/0.66 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Xaa @ X )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( Xb
% 0.37/0.66 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 0.37/0.66 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ H2 @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) )
% 0.37/0.66 @ ( times_times_assn
% 0.37/0.66 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( Xb
% 0.37/0.66 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 0.37/0.66 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Xaa ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % big_assn_simp'
% 0.37/0.66 thf(fact_5750_big__assn__simp,axiom,
% 0.37/0.66 ! [H2: nat,TreeList: list_VEBT_VEBT,L: nat,X: vEBT_VEBTi,Xaa: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.66 => ( entails
% 0.37/0.66 @ ( times_times_assn
% 0.37/0.66 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) @ X )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( Xaa
% 0.37/0.66 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 0.37/0.66 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ H2 @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) )
% 0.37/0.66 @ ( times_times_assn
% 0.37/0.66 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( Xaa
% 0.37/0.66 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 0.37/0.66 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % big_assn_simp
% 0.37/0.66 thf(fact_5751_listI__assn__wrap__insert,axiom,
% 0.37/0.66 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_wrap_insert
% 0.37/0.66 thf(fact_5752_listI__assn__wrap__insert,axiom,
% 0.37/0.66 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_Time_Heap_o,Q2: $o > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_hoare_triple_o @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_wrap_insert
% 0.37/0.66 thf(fact_5753_listI__assn__wrap__insert,axiom,
% 0.37/0.66 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T2636463487746394924on_nat,Q2: option_nat > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_7629718768684598413on_nat @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_7629718768684598413on_nat @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_wrap_insert
% 0.37/0.66 thf(fact_5754_listI__assn__wrap__insert,axiom,
% 0.37/0.66 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_Time_Heap_nat,Q2: nat > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( member_nat @ I @ I5 )
% 0.37/0.66 => ( ( hoare_3067605981109127869le_nat @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 0.37/0.66 => ( hoare_3067605981109127869le_nat @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listI_assn_wrap_insert
% 0.37/0.66 thf(fact_5755_set__update__distinct,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBTi,N: nat,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( distinct_VEBT_VEBTi @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ N @ X ) )
% 0.37/0.66 = ( insert_VEBT_VEBTi @ X @ ( minus_3697805406911847364_VEBTi @ ( set_VEBT_VEBTi2 @ Xs ) @ ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N ) @ bot_bo8982466882572371071_VEBTi ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_distinct
% 0.37/0.66 thf(fact_5756_set__update__distinct,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 0.37/0.66 ( ( distinct_VEBT_VEBT @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) )
% 0.37/0.66 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_distinct
% 0.37/0.66 thf(fact_5757_set__update__distinct,axiom,
% 0.37/0.66 ! [Xs: list_real,N: nat,X: real] :
% 0.37/0.66 ( ( distinct_real @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( set_real2 @ ( list_update_real @ Xs @ N @ X ) )
% 0.37/0.66 = ( insert_real @ X @ ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ ( nth_real @ Xs @ N ) @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_distinct
% 0.37/0.66 thf(fact_5758_set__update__distinct,axiom,
% 0.37/0.66 ! [Xs: list_int,N: nat,X: int] :
% 0.37/0.66 ( ( distinct_int @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( set_int2 @ ( list_update_int @ Xs @ N @ X ) )
% 0.37/0.66 = ( insert_int @ X @ ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ ( nth_int @ Xs @ N ) @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_distinct
% 0.37/0.66 thf(fact_5759_set__update__distinct,axiom,
% 0.37/0.66 ! [Xs: list_o,N: nat,X: $o] :
% 0.37/0.66 ( ( distinct_o @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( set_o2 @ ( list_update_o @ Xs @ N @ X ) )
% 0.37/0.66 = ( insert_o @ X @ ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ ( nth_o @ Xs @ N ) @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_distinct
% 0.37/0.66 thf(fact_5760_set__update__distinct,axiom,
% 0.37/0.66 ! [Xs: list_nat,N: nat,X: nat] :
% 0.37/0.66 ( ( distinct_nat @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) )
% 0.37/0.66 = ( insert_nat @ X @ ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ ( nth_nat @ Xs @ N ) @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_update_distinct
% 0.37/0.66 thf(fact_5761_hoare__triple__preI,axiom,
% 0.37/0.66 ! [P2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ! [H: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn @ P2 @ H )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % hoare_triple_preI
% 0.37/0.66 thf(fact_5762_hoare__triple__preI,axiom,
% 0.37/0.66 ! [P2: assn,C2: heap_Time_Heap_o,Q2: $o > assn] :
% 0.37/0.66 ( ! [H: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn @ P2 @ H )
% 0.37/0.66 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) )
% 0.37/0.66 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % hoare_triple_preI
% 0.37/0.66 thf(fact_5763_hoare__triple__preI,axiom,
% 0.37/0.66 ! [P2: assn,C2: heap_T2636463487746394924on_nat,Q2: option_nat > assn] :
% 0.37/0.66 ( ! [H: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn @ P2 @ H )
% 0.37/0.66 => ( hoare_7629718768684598413on_nat @ P2 @ C2 @ Q2 ) )
% 0.37/0.66 => ( hoare_7629718768684598413on_nat @ P2 @ C2 @ Q2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % hoare_triple_preI
% 0.37/0.66 thf(fact_5764_hoare__triple__preI,axiom,
% 0.37/0.66 ! [P2: assn,C2: heap_Time_Heap_nat,Q2: nat > assn] :
% 0.37/0.66 ( ! [H: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn @ P2 @ H )
% 0.37/0.66 => ( hoare_3067605981109127869le_nat @ P2 @ C2 @ Q2 ) )
% 0.37/0.66 => ( hoare_3067605981109127869le_nat @ P2 @ C2 @ Q2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % hoare_triple_preI
% 0.37/0.66 thf(fact_5765_nth__image,axiom,
% 0.37/0.66 ! [L: nat,Xs: list_VEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_eq_nat @ L @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( image_nat_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 0.37/0.66 = ( set_VEBT_VEBTi2 @ ( take_VEBT_VEBTi @ L @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_image
% 0.37/0.66 thf(fact_5766_nth__image,axiom,
% 0.37/0.66 ! [L: nat,Xs: list_set_nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ L @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.66 => ( ( image_nat_set_nat @ ( nth_set_nat @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 0.37/0.66 = ( set_set_nat2 @ ( take_set_nat @ L @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_image
% 0.37/0.66 thf(fact_5767_nth__image,axiom,
% 0.37/0.66 ! [L: nat,Xs: list_int] :
% 0.37/0.66 ( ( ord_less_eq_nat @ L @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( image_nat_int @ ( nth_int @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 0.37/0.66 = ( set_int2 @ ( take_int @ L @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_image
% 0.37/0.66 thf(fact_5768_nth__image,axiom,
% 0.37/0.66 ! [L: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_eq_nat @ L @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( image_nat_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 0.37/0.66 = ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ L @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_image
% 0.37/0.66 thf(fact_5769_nth__image,axiom,
% 0.37/0.66 ! [L: nat,Xs: list_real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ L @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( image_nat_real @ ( nth_real @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 0.37/0.66 = ( set_real2 @ ( take_real @ L @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_image
% 0.37/0.66 thf(fact_5770_nth__image,axiom,
% 0.37/0.66 ! [L: nat,Xs: list_o] :
% 0.37/0.66 ( ( ord_less_eq_nat @ L @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( image_nat_o @ ( nth_o @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 0.37/0.66 = ( set_o2 @ ( take_o @ L @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_image
% 0.37/0.66 thf(fact_5771_nth__image,axiom,
% 0.37/0.66 ! [L: nat,Xs: list_nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ L @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( image_nat_nat @ ( nth_nat @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 0.37/0.66 = ( set_nat2 @ ( take_nat @ L @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_image
% 0.37/0.66 thf(fact_5772_pure__assn__eq__conv,axiom,
% 0.37/0.66 ! [P2: $o,Q2: $o] :
% 0.37/0.66 ( ( ( pure_assn @ P2 )
% 0.37/0.66 = ( pure_assn @ Q2 ) )
% 0.37/0.66 = ( P2 = Q2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % pure_assn_eq_conv
% 0.37/0.66 thf(fact_5773_merge__pure__star,axiom,
% 0.37/0.66 ! [A: $o,B: $o] :
% 0.37/0.66 ( ( times_times_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 0.37/0.66 = ( pure_assn
% 0.37/0.66 @ ( A
% 0.37/0.66 & B ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % merge_pure_star
% 0.37/0.66 thf(fact_5774_take__update,axiom,
% 0.37/0.66 ! [N: nat,L: list_nat,I: nat,X: nat] :
% 0.37/0.66 ( ( take_nat @ N @ ( list_update_nat @ L @ I @ X ) )
% 0.37/0.66 = ( list_update_nat @ ( take_nat @ N @ L ) @ I @ X ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_update
% 0.37/0.66 thf(fact_5775_take__update,axiom,
% 0.37/0.66 ! [N: nat,L: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( take_VEBT_VEBTi @ N @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) )
% 0.37/0.66 = ( list_u6098035379799741383_VEBTi @ ( take_VEBT_VEBTi @ N @ L ) @ I @ X ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_update
% 0.37/0.66 thf(fact_5776_take__update,axiom,
% 0.37/0.66 ! [N: nat,L: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 0.37/0.66 ( ( take_VEBT_VEBT @ N @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) )
% 0.37/0.66 = ( list_u1324408373059187874T_VEBT @ ( take_VEBT_VEBT @ N @ L ) @ I @ X ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_update
% 0.37/0.66 thf(fact_5777_pure__assn__eq__emp__iff,axiom,
% 0.37/0.66 ! [P2: $o] :
% 0.37/0.66 ( ( ( pure_assn @ P2 )
% 0.37/0.66 = one_one_assn )
% 0.37/0.66 = P2 ) ).
% 0.37/0.66
% 0.37/0.66 % pure_assn_eq_emp_iff
% 0.37/0.66 thf(fact_5778_pure__true,axiom,
% 0.37/0.66 ( ( pure_assn @ $true )
% 0.37/0.66 = one_one_assn ) ).
% 0.37/0.66
% 0.37/0.66 % pure_true
% 0.37/0.66 thf(fact_5779_pure__false,axiom,
% 0.37/0.66 ( ( pure_assn @ $false )
% 0.37/0.66 = bot_bot_assn ) ).
% 0.37/0.66
% 0.37/0.66 % pure_false
% 0.37/0.66 thf(fact_5780_pure__assn__eq__false__iff,axiom,
% 0.37/0.66 ! [P2: $o] :
% 0.37/0.66 ( ( ( pure_assn @ P2 )
% 0.37/0.66 = bot_bot_assn )
% 0.37/0.66 = ( ~ P2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % pure_assn_eq_false_iff
% 0.37/0.66 thf(fact_5781_take__Suc__Cons,axiom,
% 0.37/0.66 ! [N: nat,X: int,Xs: list_int] :
% 0.37/0.66 ( ( take_int @ ( suc @ N ) @ ( cons_int @ X @ Xs ) )
% 0.37/0.66 = ( cons_int @ X @ ( take_int @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_Suc_Cons
% 0.37/0.66 thf(fact_5782_take__Suc__Cons,axiom,
% 0.37/0.66 ! [N: nat,X: nat,Xs: list_nat] :
% 0.37/0.66 ( ( take_nat @ ( suc @ N ) @ ( cons_nat @ X @ Xs ) )
% 0.37/0.66 = ( cons_nat @ X @ ( take_nat @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_Suc_Cons
% 0.37/0.66 thf(fact_5783_take__Suc__Cons,axiom,
% 0.37/0.66 ! [N: nat,X: $o,Xs: list_o] :
% 0.37/0.66 ( ( take_o @ ( suc @ N ) @ ( cons_o @ X @ Xs ) )
% 0.37/0.66 = ( cons_o @ X @ ( take_o @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_Suc_Cons
% 0.37/0.66 thf(fact_5784_take__all,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,N: nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N )
% 0.37/0.66 => ( ( take_VEBT_VEBT @ N @ Xs )
% 0.37/0.66 = Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all
% 0.37/0.66 thf(fact_5785_take__all,axiom,
% 0.37/0.66 ! [Xs: list_real,N: nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N )
% 0.37/0.66 => ( ( take_real @ N @ Xs )
% 0.37/0.66 = Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all
% 0.37/0.66 thf(fact_5786_take__all,axiom,
% 0.37/0.66 ! [Xs: list_o,N: nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N )
% 0.37/0.66 => ( ( take_o @ N @ Xs )
% 0.37/0.66 = Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all
% 0.37/0.66 thf(fact_5787_take__all,axiom,
% 0.37/0.66 ! [Xs: list_nat,N: nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N )
% 0.37/0.66 => ( ( take_nat @ N @ Xs )
% 0.37/0.66 = Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all
% 0.37/0.66 thf(fact_5788_take__all__iff,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ( take_VEBT_VEBT @ N @ Xs )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all_iff
% 0.37/0.66 thf(fact_5789_take__all__iff,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_real] :
% 0.37/0.66 ( ( ( take_real @ N @ Xs )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all_iff
% 0.37/0.66 thf(fact_5790_take__all__iff,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_o] :
% 0.37/0.66 ( ( ( take_o @ N @ Xs )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all_iff
% 0.37/0.66 thf(fact_5791_take__all__iff,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_nat] :
% 0.37/0.66 ( ( ( take_nat @ N @ Xs )
% 0.37/0.66 = Xs )
% 0.37/0.66 = ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_all_iff
% 0.37/0.66 thf(fact_5792_nth__take,axiom,
% 0.37/0.66 ! [I: nat,N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ I @ N )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ Xs ) @ I )
% 0.37/0.66 = ( nth_VEBT_VEBT @ Xs @ I ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take
% 0.37/0.66 thf(fact_5793_nth__take,axiom,
% 0.37/0.66 ! [I: nat,N: nat,Xs: list_VEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ I @ N )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ ( take_VEBT_VEBTi @ N @ Xs ) @ I )
% 0.37/0.66 = ( nth_VEBT_VEBTi @ Xs @ I ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take
% 0.37/0.66 thf(fact_5794_nth__take,axiom,
% 0.37/0.66 ! [I: nat,N: nat,Xs: list_int] :
% 0.37/0.66 ( ( ord_less_nat @ I @ N )
% 0.37/0.66 => ( ( nth_int @ ( take_int @ N @ Xs ) @ I )
% 0.37/0.66 = ( nth_int @ Xs @ I ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take
% 0.37/0.66 thf(fact_5795_nth__take,axiom,
% 0.37/0.66 ! [I: nat,N: nat,Xs: list_nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ N )
% 0.37/0.66 => ( ( nth_nat @ ( take_nat @ N @ Xs ) @ I )
% 0.37/0.66 = ( nth_nat @ Xs @ I ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take
% 0.37/0.66 thf(fact_5796_take__update__cancel,axiom,
% 0.37/0.66 ! [N: nat,M: nat,Xs: list_nat,Y: nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.66 => ( ( take_nat @ N @ ( list_update_nat @ Xs @ M @ Y ) )
% 0.37/0.66 = ( take_nat @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_update_cancel
% 0.37/0.66 thf(fact_5797_take__update__cancel,axiom,
% 0.37/0.66 ! [N: nat,M: nat,Xs: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.66 => ( ( take_VEBT_VEBTi @ N @ ( list_u6098035379799741383_VEBTi @ Xs @ M @ Y ) )
% 0.37/0.66 = ( take_VEBT_VEBTi @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_update_cancel
% 0.37/0.66 thf(fact_5798_take__update__cancel,axiom,
% 0.37/0.66 ! [N: nat,M: nat,Xs: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.66 => ( ( take_VEBT_VEBT @ N @ ( list_u1324408373059187874T_VEBT @ Xs @ M @ Y ) )
% 0.37/0.66 = ( take_VEBT_VEBT @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_update_cancel
% 0.37/0.66 thf(fact_5799_ent__pure__pre__iff,axiom,
% 0.37/0.66 ! [P2: assn,B: $o,Q2: assn] :
% 0.37/0.66 ( ( entails @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ Q2 )
% 0.37/0.66 = ( B
% 0.37/0.66 => ( entails @ P2 @ Q2 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % ent_pure_pre_iff
% 0.37/0.66 thf(fact_5800_mod__pure__star__dist,axiom,
% 0.37/0.66 ! [P2: assn,B: $o,H2: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ H2 )
% 0.37/0.66 = ( ( rep_assn @ P2 @ H2 )
% 0.37/0.66 & B ) ) ).
% 0.37/0.66
% 0.37/0.66 % mod_pure_star_dist
% 0.37/0.66 thf(fact_5801_ent__pure__pre__iff__sng,axiom,
% 0.37/0.66 ! [B: $o,Q2: assn] :
% 0.37/0.66 ( ( entails @ ( pure_assn @ B ) @ Q2 )
% 0.37/0.66 = ( B
% 0.37/0.66 => ( entails @ one_one_assn @ Q2 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % ent_pure_pre_iff_sng
% 0.37/0.66 thf(fact_5802_ent__pure__post__iff,axiom,
% 0.37/0.66 ! [P2: assn,Q2: assn,B: $o] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ Q2 @ ( pure_assn @ B ) ) )
% 0.37/0.66 = ( ! [H4: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn @ P2 @ H4 )
% 0.37/0.66 => B )
% 0.37/0.66 & ( entails @ P2 @ Q2 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % ent_pure_post_iff
% 0.37/0.66 thf(fact_5803_mod__h__bot__iff_I1_J,axiom,
% 0.37/0.66 ! [B: $o,H2: heap_e7401611519738050253t_unit] :
% 0.37/0.66 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.37/0.66 = B ) ).
% 0.37/0.66
% 0.37/0.66 % mod_h_bot_iff(1)
% 0.37/0.66 thf(fact_5804_ent__pure__post__iff__sng,axiom,
% 0.37/0.66 ! [P2: assn,B: $o] :
% 0.37/0.66 ( ( entails @ P2 @ ( pure_assn @ B ) )
% 0.37/0.66 = ( ! [H4: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn @ P2 @ H4 )
% 0.37/0.66 => B )
% 0.37/0.66 & ( entails @ P2 @ one_one_assn ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % ent_pure_post_iff_sng
% 0.37/0.66 thf(fact_5805_distinct__swap,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_int,J: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( distinct_int @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 0.37/0.66 = ( distinct_int @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_swap
% 0.37/0.66 thf(fact_5806_distinct__swap,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( distinct_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ ( nth_VEBT_VEBTi @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBTi @ Xs @ I ) ) )
% 0.37/0.66 = ( distinct_VEBT_VEBTi @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_swap
% 0.37/0.66 thf(fact_5807_distinct__swap,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 0.37/0.66 = ( distinct_VEBT_VEBT @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_swap
% 0.37/0.66 thf(fact_5808_distinct__swap,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_real,J: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( distinct_real @ ( list_update_real @ ( list_update_real @ Xs @ I @ ( nth_real @ Xs @ J ) ) @ J @ ( nth_real @ Xs @ I ) ) )
% 0.37/0.66 = ( distinct_real @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_swap
% 0.37/0.66 thf(fact_5809_distinct__swap,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_o,J: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( distinct_o @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 0.37/0.66 = ( distinct_o @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_swap
% 0.37/0.66 thf(fact_5810_distinct__swap,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_nat,J: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 0.37/0.66 = ( distinct_nat @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_swap
% 0.37/0.66 thf(fact_5811_VEBT__internal_OperInsTrans_Ointros_I2_J,axiom,
% 0.37/0.66 ! [T: vEBT_VEBT,S: vEBT_VEBT,X: nat,U: vEBT_VEBT] :
% 0.37/0.66 ( ( T
% 0.37/0.66 = ( vEBT_vebt_insert @ S @ X ) )
% 0.37/0.66 => ( ( vEBT_V6289311342943941716sTrans @ T @ U )
% 0.37/0.66 => ( vEBT_V6289311342943941716sTrans @ S @ U ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % VEBT_internal.perInsTrans.intros(2)
% 0.37/0.66 thf(fact_5812_VEBT__internal_OperInsTrans_Ocases,axiom,
% 0.37/0.66 ! [A12: vEBT_VEBT,A23: vEBT_VEBT] :
% 0.37/0.66 ( ( vEBT_V6289311342943941716sTrans @ A12 @ A23 )
% 0.37/0.66 => ( ( A23 != A12 )
% 0.37/0.66 => ~ ! [T6: vEBT_VEBT] :
% 0.37/0.66 ( ? [X3: nat] :
% 0.37/0.66 ( T6
% 0.37/0.66 = ( vEBT_vebt_insert @ A12 @ X3 ) )
% 0.37/0.66 => ~ ( vEBT_V6289311342943941716sTrans @ T6 @ A23 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % VEBT_internal.perInsTrans.cases
% 0.37/0.66 thf(fact_5813_VEBT__internal_OperInsTrans_Osimps,axiom,
% 0.37/0.66 ( vEBT_V6289311342943941716sTrans
% 0.37/0.66 = ( ^ [A13: vEBT_VEBT,A24: vEBT_VEBT] :
% 0.37/0.66 ( ? [T2: vEBT_VEBT] :
% 0.37/0.66 ( ( A13 = T2 )
% 0.37/0.66 & ( A24 = T2 ) )
% 0.37/0.66 | ? [T2: vEBT_VEBT,S8: vEBT_VEBT,X4: nat,U2: vEBT_VEBT] :
% 0.37/0.66 ( ( A13 = S8 )
% 0.37/0.66 & ( A24 = U2 )
% 0.37/0.66 & ( T2
% 0.37/0.66 = ( vEBT_vebt_insert @ S8 @ X4 ) )
% 0.37/0.66 & ( vEBT_V6289311342943941716sTrans @ T2 @ U2 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % VEBT_internal.perInsTrans.simps
% 0.37/0.66 thf(fact_5814_set__take__subset,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_VEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ N @ Xs ) ) @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset
% 0.37/0.66 thf(fact_5815_set__take__subset,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( take_nat @ N @ Xs ) ) @ ( set_nat2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset
% 0.37/0.66 thf(fact_5816_set__take__subset,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_real] : ( ord_less_eq_set_real @ ( set_real2 @ ( take_real @ N @ Xs ) ) @ ( set_real2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset
% 0.37/0.66 thf(fact_5817_set__take__subset,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_o] : ( ord_less_eq_set_o @ ( set_o2 @ ( take_o @ N @ Xs ) ) @ ( set_o2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset
% 0.37/0.66 thf(fact_5818_set__take__subset,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_int] : ( ord_less_eq_set_int @ ( set_int2 @ ( take_int @ N @ Xs ) ) @ ( set_int2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset
% 0.37/0.66 thf(fact_5819_sorted__take,axiom,
% 0.37/0.66 ! [Xs: list_rat,N: nat] :
% 0.37/0.66 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.66 => ( sorted_wrt_rat @ ord_less_eq_rat @ ( take_rat @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_take
% 0.37/0.66 thf(fact_5820_sorted__take,axiom,
% 0.37/0.66 ! [Xs: list_num,N: nat] :
% 0.37/0.66 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.66 => ( sorted_wrt_num @ ord_less_eq_num @ ( take_num @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_take
% 0.37/0.66 thf(fact_5821_sorted__take,axiom,
% 0.37/0.66 ! [Xs: list_nat,N: nat] :
% 0.37/0.66 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.66 => ( sorted_wrt_nat @ ord_less_eq_nat @ ( take_nat @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_take
% 0.37/0.66 thf(fact_5822_sorted__take,axiom,
% 0.37/0.66 ! [Xs: list_int,N: nat] :
% 0.37/0.66 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.66 => ( sorted_wrt_int @ ord_less_eq_int @ ( take_int @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_take
% 0.37/0.66 thf(fact_5823_finite__distinct__list,axiom,
% 0.37/0.66 ! [A4: set_VEBT_VEBT] :
% 0.37/0.66 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.66 => ? [Xs3: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ( set_VEBT_VEBT2 @ Xs3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( distinct_VEBT_VEBT @ Xs3 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_distinct_list
% 0.37/0.66 thf(fact_5824_finite__distinct__list,axiom,
% 0.37/0.66 ! [A4: set_real] :
% 0.37/0.66 ( ( finite_finite_real @ A4 )
% 0.37/0.66 => ? [Xs3: list_real] :
% 0.37/0.66 ( ( ( set_real2 @ Xs3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( distinct_real @ Xs3 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_distinct_list
% 0.37/0.66 thf(fact_5825_finite__distinct__list,axiom,
% 0.37/0.66 ! [A4: set_o] :
% 0.37/0.66 ( ( finite_finite_o @ A4 )
% 0.37/0.66 => ? [Xs3: list_o] :
% 0.37/0.66 ( ( ( set_o2 @ Xs3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( distinct_o @ Xs3 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_distinct_list
% 0.37/0.66 thf(fact_5826_finite__distinct__list,axiom,
% 0.37/0.66 ! [A4: set_nat] :
% 0.37/0.66 ( ( finite_finite_nat @ A4 )
% 0.37/0.66 => ? [Xs3: list_nat] :
% 0.37/0.66 ( ( ( set_nat2 @ Xs3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( distinct_nat @ Xs3 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_distinct_list
% 0.37/0.66 thf(fact_5827_finite__distinct__list,axiom,
% 0.37/0.66 ! [A4: set_int] :
% 0.37/0.66 ( ( finite_finite_int @ A4 )
% 0.37/0.66 => ? [Xs3: list_int] :
% 0.37/0.66 ( ( ( set_int2 @ Xs3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( distinct_int @ Xs3 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_distinct_list
% 0.37/0.66 thf(fact_5828_finite__distinct__list,axiom,
% 0.37/0.66 ! [A4: set_complex] :
% 0.37/0.66 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.66 => ? [Xs3: list_complex] :
% 0.37/0.66 ( ( ( set_complex2 @ Xs3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( distinct_complex @ Xs3 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_distinct_list
% 0.37/0.66 thf(fact_5829_finite__distinct__list,axiom,
% 0.37/0.66 ! [A4: set_Code_integer] :
% 0.37/0.66 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.66 => ? [Xs3: list_Code_integer] :
% 0.37/0.66 ( ( ( set_Code_integer2 @ Xs3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( distin1543349897113766820nteger @ Xs3 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_distinct_list
% 0.37/0.66 thf(fact_5830_finite__set__image,axiom,
% 0.37/0.66 ! [A4: set_list_VEBT_VEBT] :
% 0.37/0.66 ( ( finite9070685783930458813T_VEBT @ ( image_6463372868993444447T_VEBT @ set_VEBT_VEBT2 @ A4 ) )
% 0.37/0.66 => ( ! [Xs3: list_VEBT_VEBT] :
% 0.37/0.66 ( ( member2936631157270082147T_VEBT @ Xs3 @ A4 )
% 0.37/0.66 => ( distinct_VEBT_VEBT @ Xs3 ) )
% 0.37/0.66 => ( finite3004134309566078307T_VEBT @ A4 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_set_image
% 0.37/0.66 thf(fact_5831_finite__set__image,axiom,
% 0.37/0.66 ! [A4: set_list_nat] :
% 0.37/0.66 ( ( finite1152437895449049373et_nat @ ( image_1775855109352712557et_nat @ set_nat2 @ A4 ) )
% 0.37/0.66 => ( ! [Xs3: list_nat] :
% 0.37/0.66 ( ( member_list_nat @ Xs3 @ A4 )
% 0.37/0.66 => ( distinct_nat @ Xs3 ) )
% 0.37/0.66 => ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_set_image
% 0.37/0.66 thf(fact_5832_finite__set__image,axiom,
% 0.37/0.66 ! [A4: set_list_real] :
% 0.37/0.66 ( ( finite9007344921179782393t_real @ ( image_6239767680843085477t_real @ set_real2 @ A4 ) )
% 0.37/0.66 => ( ! [Xs3: list_real] :
% 0.37/0.66 ( ( member_list_real @ Xs3 @ A4 )
% 0.37/0.66 => ( distinct_real @ Xs3 ) )
% 0.37/0.66 => ( finite306553202115118035t_real @ A4 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_set_image
% 0.37/0.66 thf(fact_5833_finite__set__image,axiom,
% 0.37/0.66 ! [A4: set_list_o] :
% 0.37/0.66 ( ( finite_finite_set_o @ ( image_list_o_set_o @ set_o2 @ A4 ) )
% 0.37/0.66 => ( ! [Xs3: list_o] :
% 0.37/0.66 ( ( member_list_o @ Xs3 @ A4 )
% 0.37/0.66 => ( distinct_o @ Xs3 ) )
% 0.37/0.66 => ( finite_finite_list_o @ A4 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_set_image
% 0.37/0.66 thf(fact_5834_set__take__subset__set__take,axiom,
% 0.37/0.66 ! [M: nat,N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ M @ Xs ) ) @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ N @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset_set_take
% 0.37/0.66 thf(fact_5835_set__take__subset__set__take,axiom,
% 0.37/0.66 ! [M: nat,N: nat,Xs: list_nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( take_nat @ M @ Xs ) ) @ ( set_nat2 @ ( take_nat @ N @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset_set_take
% 0.37/0.66 thf(fact_5836_set__take__subset__set__take,axiom,
% 0.37/0.66 ! [M: nat,N: nat,Xs: list_real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ord_less_eq_set_real @ ( set_real2 @ ( take_real @ M @ Xs ) ) @ ( set_real2 @ ( take_real @ N @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset_set_take
% 0.37/0.66 thf(fact_5837_set__take__subset__set__take,axiom,
% 0.37/0.66 ! [M: nat,N: nat,Xs: list_o] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ord_less_eq_set_o @ ( set_o2 @ ( take_o @ M @ Xs ) ) @ ( set_o2 @ ( take_o @ N @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset_set_take
% 0.37/0.66 thf(fact_5838_set__take__subset__set__take,axiom,
% 0.37/0.66 ! [M: nat,N: nat,Xs: list_int] :
% 0.37/0.66 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.66 => ( ord_less_eq_set_int @ ( set_int2 @ ( take_int @ M @ Xs ) ) @ ( set_int2 @ ( take_int @ N @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_take_subset_set_take
% 0.37/0.66 thf(fact_5839_strict__sorted__iff,axiom,
% 0.37/0.66 ! [L: list_real] :
% 0.37/0.66 ( ( sorted_wrt_real @ ord_less_real @ L )
% 0.37/0.66 = ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 0.37/0.66 & ( distinct_real @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % strict_sorted_iff
% 0.37/0.66 thf(fact_5840_strict__sorted__iff,axiom,
% 0.37/0.66 ! [L: list_rat] :
% 0.37/0.66 ( ( sorted_wrt_rat @ ord_less_rat @ L )
% 0.37/0.66 = ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 0.37/0.66 & ( distinct_rat @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % strict_sorted_iff
% 0.37/0.66 thf(fact_5841_strict__sorted__iff,axiom,
% 0.37/0.66 ! [L: list_num] :
% 0.37/0.66 ( ( sorted_wrt_num @ ord_less_num @ L )
% 0.37/0.66 = ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 0.37/0.66 & ( distinct_num @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % strict_sorted_iff
% 0.37/0.66 thf(fact_5842_strict__sorted__iff,axiom,
% 0.37/0.66 ! [L: list_nat] :
% 0.37/0.66 ( ( sorted_wrt_nat @ ord_less_nat @ L )
% 0.37/0.66 = ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 0.37/0.66 & ( distinct_nat @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % strict_sorted_iff
% 0.37/0.66 thf(fact_5843_strict__sorted__iff,axiom,
% 0.37/0.66 ! [L: list_int] :
% 0.37/0.66 ( ( sorted_wrt_int @ ord_less_int @ L )
% 0.37/0.66 = ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 0.37/0.66 & ( distinct_int @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % strict_sorted_iff
% 0.37/0.66 thf(fact_5844_distinct__conv__nth,axiom,
% 0.37/0.66 ( distinct_VEBT_VEBTi
% 0.37/0.66 = ( ^ [Xs2: list_VEBT_VEBTi] :
% 0.37/0.66 ! [I3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 0.37/0.66 => ! [J3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ J3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 0.37/0.66 => ( ( I3 != J3 )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ Xs2 @ I3 )
% 0.37/0.66 != ( nth_VEBT_VEBTi @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_conv_nth
% 0.37/0.66 thf(fact_5845_distinct__conv__nth,axiom,
% 0.37/0.66 ( distinct_int
% 0.37/0.66 = ( ^ [Xs2: list_int] :
% 0.37/0.66 ! [I3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.37/0.66 => ! [J3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs2 ) )
% 0.37/0.66 => ( ( I3 != J3 )
% 0.37/0.66 => ( ( nth_int @ Xs2 @ I3 )
% 0.37/0.66 != ( nth_int @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_conv_nth
% 0.37/0.66 thf(fact_5846_distinct__conv__nth,axiom,
% 0.37/0.66 ( distinct_VEBT_VEBT
% 0.37/0.66 = ( ^ [Xs2: list_VEBT_VEBT] :
% 0.37/0.66 ! [I3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.37/0.66 => ! [J3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ J3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.37/0.66 => ( ( I3 != J3 )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 0.37/0.66 != ( nth_VEBT_VEBT @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_conv_nth
% 0.37/0.66 thf(fact_5847_distinct__conv__nth,axiom,
% 0.37/0.66 ( distinct_real
% 0.37/0.66 = ( ^ [Xs2: list_real] :
% 0.37/0.66 ! [I3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 0.37/0.66 => ! [J3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs2 ) )
% 0.37/0.66 => ( ( I3 != J3 )
% 0.37/0.66 => ( ( nth_real @ Xs2 @ I3 )
% 0.37/0.66 != ( nth_real @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_conv_nth
% 0.37/0.66 thf(fact_5848_distinct__conv__nth,axiom,
% 0.37/0.66 ( distinct_o
% 0.37/0.66 = ( ^ [Xs2: list_o] :
% 0.37/0.66 ! [I3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.37/0.66 => ! [J3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs2 ) )
% 0.37/0.66 => ( ( I3 != J3 )
% 0.37/0.66 => ( ( nth_o @ Xs2 @ I3 )
% 0.37/0.66 != ( nth_o @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_conv_nth
% 0.37/0.66 thf(fact_5849_distinct__conv__nth,axiom,
% 0.37/0.66 ( distinct_nat
% 0.37/0.66 = ( ^ [Xs2: list_nat] :
% 0.37/0.66 ! [I3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.37/0.66 => ! [J3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs2 ) )
% 0.37/0.66 => ( ( I3 != J3 )
% 0.37/0.66 => ( ( nth_nat @ Xs2 @ I3 )
% 0.37/0.66 != ( nth_nat @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_conv_nth
% 0.37/0.66 thf(fact_5850_nth__eq__iff__index__eq,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBTi,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_VEBT_VEBTi @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ( nth_VEBT_VEBTi @ Xs @ I )
% 0.37/0.66 = ( nth_VEBT_VEBTi @ Xs @ J ) )
% 0.37/0.66 = ( I = J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_eq_iff_index_eq
% 0.37/0.66 thf(fact_5851_nth__eq__iff__index__eq,axiom,
% 0.37/0.66 ! [Xs: list_int,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_int @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ( nth_int @ Xs @ I )
% 0.37/0.66 = ( nth_int @ Xs @ J ) )
% 0.37/0.66 = ( I = J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_eq_iff_index_eq
% 0.37/0.66 thf(fact_5852_nth__eq__iff__index__eq,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_VEBT_VEBT @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( ( nth_VEBT_VEBT @ Xs @ I )
% 0.37/0.66 = ( nth_VEBT_VEBT @ Xs @ J ) )
% 0.37/0.66 = ( I = J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_eq_iff_index_eq
% 0.37/0.66 thf(fact_5853_nth__eq__iff__index__eq,axiom,
% 0.37/0.66 ! [Xs: list_real,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_real @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( ( nth_real @ Xs @ I )
% 0.37/0.66 = ( nth_real @ Xs @ J ) )
% 0.37/0.66 = ( I = J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_eq_iff_index_eq
% 0.37/0.66 thf(fact_5854_nth__eq__iff__index__eq,axiom,
% 0.37/0.66 ! [Xs: list_o,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_o @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( ( nth_o @ Xs @ I )
% 0.37/0.66 = ( nth_o @ Xs @ J ) )
% 0.37/0.66 = ( I = J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_eq_iff_index_eq
% 0.37/0.66 thf(fact_5855_nth__eq__iff__index__eq,axiom,
% 0.37/0.66 ! [Xs: list_nat,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_nat @ Xs )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( ( nth_nat @ Xs @ I )
% 0.37/0.66 = ( nth_nat @ Xs @ J ) )
% 0.37/0.66 = ( I = J ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_eq_iff_index_eq
% 0.37/0.66 thf(fact_5856_distinct__length__le,axiom,
% 0.37/0.66 ! [Ys: list_VEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( distinct_VEBT_VEBT @ Ys )
% 0.37/0.66 => ( ( ( set_VEBT_VEBT2 @ Ys )
% 0.37/0.66 = ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.66 => ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Ys ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_length_le
% 0.37/0.66 thf(fact_5857_distinct__length__le,axiom,
% 0.37/0.66 ! [Ys: list_real,Xs: list_real] :
% 0.37/0.66 ( ( distinct_real @ Ys )
% 0.37/0.66 => ( ( ( set_real2 @ Ys )
% 0.37/0.66 = ( set_real2 @ Xs ) )
% 0.37/0.66 => ( ord_less_eq_nat @ ( size_size_list_real @ Ys ) @ ( size_size_list_real @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_length_le
% 0.37/0.66 thf(fact_5858_distinct__length__le,axiom,
% 0.37/0.66 ! [Ys: list_o,Xs: list_o] :
% 0.37/0.66 ( ( distinct_o @ Ys )
% 0.37/0.66 => ( ( ( set_o2 @ Ys )
% 0.37/0.66 = ( set_o2 @ Xs ) )
% 0.37/0.66 => ( ord_less_eq_nat @ ( size_size_list_o @ Ys ) @ ( size_size_list_o @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_length_le
% 0.37/0.66 thf(fact_5859_distinct__length__le,axiom,
% 0.37/0.66 ! [Ys: list_nat,Xs: list_nat] :
% 0.37/0.66 ( ( distinct_nat @ Ys )
% 0.37/0.66 => ( ( ( set_nat2 @ Ys )
% 0.37/0.66 = ( set_nat2 @ Xs ) )
% 0.37/0.66 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_length_le
% 0.37/0.66 thf(fact_5860_sorted__distinct__set__unique,axiom,
% 0.37/0.66 ! [Xs: list_real,Ys: list_real] :
% 0.37/0.66 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 0.37/0.66 => ( ( distinct_real @ Xs )
% 0.37/0.66 => ( ( sorted_wrt_real @ ord_less_eq_real @ Ys )
% 0.37/0.66 => ( ( distinct_real @ Ys )
% 0.37/0.66 => ( ( ( set_real2 @ Xs )
% 0.37/0.66 = ( set_real2 @ Ys ) )
% 0.37/0.66 => ( Xs = Ys ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_distinct_set_unique
% 0.37/0.66 thf(fact_5861_sorted__distinct__set__unique,axiom,
% 0.37/0.66 ! [Xs: list_o,Ys: list_o] :
% 0.37/0.66 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 0.37/0.66 => ( ( distinct_o @ Xs )
% 0.37/0.66 => ( ( sorted_wrt_o @ ord_less_eq_o @ Ys )
% 0.37/0.66 => ( ( distinct_o @ Ys )
% 0.37/0.66 => ( ( ( set_o2 @ Xs )
% 0.37/0.66 = ( set_o2 @ Ys ) )
% 0.37/0.66 => ( Xs = Ys ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_distinct_set_unique
% 0.37/0.66 thf(fact_5862_sorted__distinct__set__unique,axiom,
% 0.37/0.66 ! [Xs: list_rat,Ys: list_rat] :
% 0.37/0.66 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.66 => ( ( distinct_rat @ Xs )
% 0.37/0.66 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ Ys )
% 0.37/0.66 => ( ( distinct_rat @ Ys )
% 0.37/0.66 => ( ( ( set_rat2 @ Xs )
% 0.37/0.66 = ( set_rat2 @ Ys ) )
% 0.37/0.66 => ( Xs = Ys ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_distinct_set_unique
% 0.37/0.66 thf(fact_5863_sorted__distinct__set__unique,axiom,
% 0.37/0.66 ! [Xs: list_num,Ys: list_num] :
% 0.37/0.66 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.66 => ( ( distinct_num @ Xs )
% 0.37/0.66 => ( ( sorted_wrt_num @ ord_less_eq_num @ Ys )
% 0.37/0.66 => ( ( distinct_num @ Ys )
% 0.37/0.66 => ( ( ( set_num2 @ Xs )
% 0.37/0.66 = ( set_num2 @ Ys ) )
% 0.37/0.66 => ( Xs = Ys ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_distinct_set_unique
% 0.37/0.66 thf(fact_5864_sorted__distinct__set__unique,axiom,
% 0.37/0.66 ! [Xs: list_nat,Ys: list_nat] :
% 0.37/0.66 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.66 => ( ( distinct_nat @ Xs )
% 0.37/0.66 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ Ys )
% 0.37/0.66 => ( ( distinct_nat @ Ys )
% 0.37/0.66 => ( ( ( set_nat2 @ Xs )
% 0.37/0.66 = ( set_nat2 @ Ys ) )
% 0.37/0.66 => ( Xs = Ys ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_distinct_set_unique
% 0.37/0.66 thf(fact_5865_sorted__distinct__set__unique,axiom,
% 0.37/0.66 ! [Xs: list_int,Ys: list_int] :
% 0.37/0.66 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.66 => ( ( distinct_int @ Xs )
% 0.37/0.66 => ( ( sorted_wrt_int @ ord_less_eq_int @ Ys )
% 0.37/0.66 => ( ( distinct_int @ Ys )
% 0.37/0.66 => ( ( ( set_int2 @ Xs )
% 0.37/0.66 = ( set_int2 @ Ys ) )
% 0.37/0.66 => ( Xs = Ys ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_distinct_set_unique
% 0.37/0.66 thf(fact_5866_VEBT__internal_Oinsert_H_Osimps_I1_J,axiom,
% 0.37/0.66 ! [A: $o,B: $o,X: nat] :
% 0.37/0.66 ( ( vEBT_VEBT_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.37/0.66 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X ) ) ).
% 0.37/0.66
% 0.37/0.66 % VEBT_internal.insert'.simps(1)
% 0.37/0.66 thf(fact_5867_vebt__insert__code_I1_J,axiom,
% 0.37/0.66 ! [X: nat,A: $o,B: $o] :
% 0.37/0.66 ( ( ( X = zero_zero_nat )
% 0.37/0.66 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.37/0.66 = ( vEBT_Leaf @ $true @ B ) ) )
% 0.37/0.66 & ( ( X != zero_zero_nat )
% 0.37/0.66 => ( ( ( X = one_one_nat )
% 0.37/0.66 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.37/0.66 = ( vEBT_Leaf @ A @ $true ) ) )
% 0.37/0.66 & ( ( X != one_one_nat )
% 0.37/0.66 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.37/0.66 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % vebt_insert_code(1)
% 0.37/0.66 thf(fact_5868_nth__take__lemma,axiom,
% 0.37/0.66 ! [K: nat,Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_eq_nat @ K @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_eq_nat @ K @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 0.37/0.66 => ( ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ K )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 0.37/0.66 = ( nth_VEBT_VEBTi @ Ys @ I2 ) ) )
% 0.37/0.66 => ( ( take_VEBT_VEBTi @ K @ Xs )
% 0.37/0.66 = ( take_VEBT_VEBTi @ K @ Ys ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take_lemma
% 0.37/0.66 thf(fact_5869_nth__take__lemma,axiom,
% 0.37/0.66 ! [K: nat,Xs: list_int,Ys: list_int] :
% 0.37/0.66 ( ( ord_less_eq_nat @ K @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_eq_nat @ K @ ( size_size_list_int @ Ys ) )
% 0.37/0.66 => ( ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ K )
% 0.37/0.66 => ( ( nth_int @ Xs @ I2 )
% 0.37/0.66 = ( nth_int @ Ys @ I2 ) ) )
% 0.37/0.66 => ( ( take_int @ K @ Xs )
% 0.37/0.66 = ( take_int @ K @ Ys ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take_lemma
% 0.37/0.66 thf(fact_5870_nth__take__lemma,axiom,
% 0.37/0.66 ! [K: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_eq_nat @ K @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( ord_less_eq_nat @ K @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.66 => ( ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ K )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 0.37/0.66 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 0.37/0.66 => ( ( take_VEBT_VEBT @ K @ Xs )
% 0.37/0.66 = ( take_VEBT_VEBT @ K @ Ys ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take_lemma
% 0.37/0.66 thf(fact_5871_nth__take__lemma,axiom,
% 0.37/0.66 ! [K: nat,Xs: list_real,Ys: list_real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ K @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( ord_less_eq_nat @ K @ ( size_size_list_real @ Ys ) )
% 0.37/0.66 => ( ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ K )
% 0.37/0.66 => ( ( nth_real @ Xs @ I2 )
% 0.37/0.66 = ( nth_real @ Ys @ I2 ) ) )
% 0.37/0.66 => ( ( take_real @ K @ Xs )
% 0.37/0.66 = ( take_real @ K @ Ys ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take_lemma
% 0.37/0.66 thf(fact_5872_nth__take__lemma,axiom,
% 0.37/0.66 ! [K: nat,Xs: list_o,Ys: list_o] :
% 0.37/0.66 ( ( ord_less_eq_nat @ K @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( ord_less_eq_nat @ K @ ( size_size_list_o @ Ys ) )
% 0.37/0.66 => ( ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ K )
% 0.37/0.66 => ( ( nth_o @ Xs @ I2 )
% 0.37/0.66 = ( nth_o @ Ys @ I2 ) ) )
% 0.37/0.66 => ( ( take_o @ K @ Xs )
% 0.37/0.66 = ( take_o @ K @ Ys ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take_lemma
% 0.37/0.66 thf(fact_5873_nth__take__lemma,axiom,
% 0.37/0.66 ! [K: nat,Xs: list_nat,Ys: list_nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ K @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( ord_less_eq_nat @ K @ ( size_size_list_nat @ Ys ) )
% 0.37/0.66 => ( ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ K )
% 0.37/0.66 => ( ( nth_nat @ Xs @ I2 )
% 0.37/0.66 = ( nth_nat @ Ys @ I2 ) ) )
% 0.37/0.66 => ( ( take_nat @ K @ Xs )
% 0.37/0.66 = ( take_nat @ K @ Ys ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_take_lemma
% 0.37/0.66 thf(fact_5874_finite__sorted__distinct__unique,axiom,
% 0.37/0.66 ! [A4: set_real] :
% 0.37/0.66 ( ( finite_finite_real @ A4 )
% 0.37/0.66 => ? [X3: list_real] :
% 0.37/0.66 ( ( ( set_real2 @ X3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_real @ ord_less_eq_real @ X3 )
% 0.37/0.66 & ( distinct_real @ X3 )
% 0.37/0.66 & ! [Y5: list_real] :
% 0.37/0.66 ( ( ( ( set_real2 @ Y5 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_real @ ord_less_eq_real @ Y5 )
% 0.37/0.66 & ( distinct_real @ Y5 ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_sorted_distinct_unique
% 0.37/0.66 thf(fact_5875_finite__sorted__distinct__unique,axiom,
% 0.37/0.66 ! [A4: set_o] :
% 0.37/0.66 ( ( finite_finite_o @ A4 )
% 0.37/0.66 => ? [X3: list_o] :
% 0.37/0.66 ( ( ( set_o2 @ X3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_o @ ord_less_eq_o @ X3 )
% 0.37/0.66 & ( distinct_o @ X3 )
% 0.37/0.66 & ! [Y5: list_o] :
% 0.37/0.66 ( ( ( ( set_o2 @ Y5 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_o @ ord_less_eq_o @ Y5 )
% 0.37/0.66 & ( distinct_o @ Y5 ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_sorted_distinct_unique
% 0.37/0.66 thf(fact_5876_finite__sorted__distinct__unique,axiom,
% 0.37/0.66 ! [A4: set_Code_integer] :
% 0.37/0.66 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.66 => ? [X3: list_Code_integer] :
% 0.37/0.66 ( ( ( set_Code_integer2 @ X3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ X3 )
% 0.37/0.66 & ( distin1543349897113766820nteger @ X3 )
% 0.37/0.66 & ! [Y5: list_Code_integer] :
% 0.37/0.66 ( ( ( ( set_Code_integer2 @ Y5 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ Y5 )
% 0.37/0.66 & ( distin1543349897113766820nteger @ Y5 ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_sorted_distinct_unique
% 0.37/0.66 thf(fact_5877_finite__sorted__distinct__unique,axiom,
% 0.37/0.66 ! [A4: set_rat] :
% 0.37/0.66 ( ( finite_finite_rat @ A4 )
% 0.37/0.66 => ? [X3: list_rat] :
% 0.37/0.66 ( ( ( set_rat2 @ X3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_rat @ ord_less_eq_rat @ X3 )
% 0.37/0.66 & ( distinct_rat @ X3 )
% 0.37/0.66 & ! [Y5: list_rat] :
% 0.37/0.66 ( ( ( ( set_rat2 @ Y5 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_rat @ ord_less_eq_rat @ Y5 )
% 0.37/0.66 & ( distinct_rat @ Y5 ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_sorted_distinct_unique
% 0.37/0.66 thf(fact_5878_finite__sorted__distinct__unique,axiom,
% 0.37/0.66 ! [A4: set_num] :
% 0.37/0.66 ( ( finite_finite_num @ A4 )
% 0.37/0.66 => ? [X3: list_num] :
% 0.37/0.66 ( ( ( set_num2 @ X3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_num @ ord_less_eq_num @ X3 )
% 0.37/0.66 & ( distinct_num @ X3 )
% 0.37/0.66 & ! [Y5: list_num] :
% 0.37/0.66 ( ( ( ( set_num2 @ Y5 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_num @ ord_less_eq_num @ Y5 )
% 0.37/0.66 & ( distinct_num @ Y5 ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_sorted_distinct_unique
% 0.37/0.66 thf(fact_5879_finite__sorted__distinct__unique,axiom,
% 0.37/0.66 ! [A4: set_nat] :
% 0.37/0.66 ( ( finite_finite_nat @ A4 )
% 0.37/0.66 => ? [X3: list_nat] :
% 0.37/0.66 ( ( ( set_nat2 @ X3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_nat @ ord_less_eq_nat @ X3 )
% 0.37/0.66 & ( distinct_nat @ X3 )
% 0.37/0.66 & ! [Y5: list_nat] :
% 0.37/0.66 ( ( ( ( set_nat2 @ Y5 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_nat @ ord_less_eq_nat @ Y5 )
% 0.37/0.66 & ( distinct_nat @ Y5 ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_sorted_distinct_unique
% 0.37/0.66 thf(fact_5880_finite__sorted__distinct__unique,axiom,
% 0.37/0.66 ! [A4: set_int] :
% 0.37/0.66 ( ( finite_finite_int @ A4 )
% 0.37/0.66 => ? [X3: list_int] :
% 0.37/0.66 ( ( ( set_int2 @ X3 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_int @ ord_less_eq_int @ X3 )
% 0.37/0.66 & ( distinct_int @ X3 )
% 0.37/0.66 & ! [Y5: list_int] :
% 0.37/0.66 ( ( ( ( set_int2 @ Y5 )
% 0.37/0.66 = A4 )
% 0.37/0.66 & ( sorted_wrt_int @ ord_less_eq_int @ Y5 )
% 0.37/0.66 & ( distinct_int @ Y5 ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % finite_sorted_distinct_unique
% 0.37/0.66 thf(fact_5881_distinct__Ex1,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( distinct_VEBT_VEBTi @ Xs )
% 0.37/0.66 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 0.37/0.66 => ? [X3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ X3 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 & ( ( nth_VEBT_VEBTi @ Xs @ X3 )
% 0.37/0.66 = X )
% 0.37/0.66 & ! [Y5: nat] :
% 0.37/0.66 ( ( ( ord_less_nat @ Y5 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 & ( ( nth_VEBT_VEBTi @ Xs @ Y5 )
% 0.37/0.66 = X ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_Ex1
% 0.37/0.66 thf(fact_5882_distinct__Ex1,axiom,
% 0.37/0.66 ! [Xs: list_int,X: int] :
% 0.37/0.66 ( ( distinct_int @ Xs )
% 0.37/0.66 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.66 => ? [X3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ X3 @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 & ( ( nth_int @ Xs @ X3 )
% 0.37/0.66 = X )
% 0.37/0.66 & ! [Y5: nat] :
% 0.37/0.66 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 & ( ( nth_int @ Xs @ Y5 )
% 0.37/0.66 = X ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_Ex1
% 0.37/0.66 thf(fact_5883_distinct__Ex1,axiom,
% 0.37/0.66 ! [Xs: list_set_nat,X: set_nat] :
% 0.37/0.66 ( ( distinct_set_nat @ Xs )
% 0.37/0.66 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 0.37/0.66 => ? [X3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ X3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.66 & ( ( nth_set_nat @ Xs @ X3 )
% 0.37/0.66 = X )
% 0.37/0.66 & ! [Y5: nat] :
% 0.37/0.66 ( ( ( ord_less_nat @ Y5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 0.37/0.66 & ( ( nth_set_nat @ Xs @ Y5 )
% 0.37/0.66 = X ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_Ex1
% 0.37/0.66 thf(fact_5884_distinct__Ex1,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.66 ( ( distinct_VEBT_VEBT @ Xs )
% 0.37/0.66 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.66 => ? [X3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ X3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 & ( ( nth_VEBT_VEBT @ Xs @ X3 )
% 0.37/0.66 = X )
% 0.37/0.66 & ! [Y5: nat] :
% 0.37/0.66 ( ( ( ord_less_nat @ Y5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 & ( ( nth_VEBT_VEBT @ Xs @ Y5 )
% 0.37/0.66 = X ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_Ex1
% 0.37/0.66 thf(fact_5885_distinct__Ex1,axiom,
% 0.37/0.66 ! [Xs: list_real,X: real] :
% 0.37/0.66 ( ( distinct_real @ Xs )
% 0.37/0.66 => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 0.37/0.66 => ? [X3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ X3 @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 & ( ( nth_real @ Xs @ X3 )
% 0.37/0.66 = X )
% 0.37/0.66 & ! [Y5: nat] :
% 0.37/0.66 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 & ( ( nth_real @ Xs @ Y5 )
% 0.37/0.66 = X ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_Ex1
% 0.37/0.66 thf(fact_5886_distinct__Ex1,axiom,
% 0.37/0.66 ! [Xs: list_o,X: $o] :
% 0.37/0.66 ( ( distinct_o @ Xs )
% 0.37/0.66 => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 0.37/0.66 => ? [X3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ X3 @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 & ( ( nth_o @ Xs @ X3 )
% 0.37/0.66 = X )
% 0.37/0.66 & ! [Y5: nat] :
% 0.37/0.66 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 & ( ( nth_o @ Xs @ Y5 )
% 0.37/0.66 = X ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_Ex1
% 0.37/0.66 thf(fact_5887_distinct__Ex1,axiom,
% 0.37/0.66 ! [Xs: list_nat,X: nat] :
% 0.37/0.66 ( ( distinct_nat @ Xs )
% 0.37/0.66 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.66 => ? [X3: nat] :
% 0.37/0.66 ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 & ( ( nth_nat @ Xs @ X3 )
% 0.37/0.66 = X )
% 0.37/0.66 & ! [Y5: nat] :
% 0.37/0.66 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 & ( ( nth_nat @ Xs @ Y5 )
% 0.37/0.66 = X ) )
% 0.37/0.66 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_Ex1
% 0.37/0.66 thf(fact_5888_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 0.37/0.66 ! [Xs: list_real] :
% 0.37/0.66 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 0.37/0.66 => ( ( distinct_real @ Xs )
% 0.37/0.66 => ( ( linord4252657396651189596t_real @ ( set_real2 @ Xs ) )
% 0.37/0.66 = Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.idem_if_sorted_distinct
% 0.37/0.66 thf(fact_5889_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 0.37/0.66 ! [Xs: list_o] :
% 0.37/0.66 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 0.37/0.66 => ( ( distinct_o @ Xs )
% 0.37/0.66 => ( ( linord3142498349692569832_set_o @ ( set_o2 @ Xs ) )
% 0.37/0.66 = Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.idem_if_sorted_distinct
% 0.37/0.66 thf(fact_5890_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 0.37/0.66 ! [Xs: list_rat] :
% 0.37/0.66 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.66 => ( ( distinct_rat @ Xs )
% 0.37/0.66 => ( ( linord1979837681955606664et_rat @ ( set_rat2 @ Xs ) )
% 0.37/0.66 = Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.idem_if_sorted_distinct
% 0.37/0.66 thf(fact_5891_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 0.37/0.66 ! [Xs: list_num] :
% 0.37/0.66 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.66 => ( ( distinct_num @ Xs )
% 0.37/0.66 => ( ( linord8395671565052656842et_num @ ( set_num2 @ Xs ) )
% 0.37/0.66 = Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.idem_if_sorted_distinct
% 0.37/0.66 thf(fact_5892_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 0.37/0.66 ! [Xs: list_int] :
% 0.37/0.66 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.66 => ( ( distinct_int @ Xs )
% 0.37/0.66 => ( ( linord2612477271533052124et_int @ ( set_int2 @ Xs ) )
% 0.37/0.66 = Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.idem_if_sorted_distinct
% 0.37/0.66 thf(fact_5893_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 0.37/0.66 ! [Xs: list_nat] :
% 0.37/0.66 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.66 => ( ( distinct_nat @ Xs )
% 0.37/0.66 => ( ( linord2614967742042102400et_nat @ ( set_nat2 @ Xs ) )
% 0.37/0.66 = Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.idem_if_sorted_distinct
% 0.37/0.66 thf(fact_5894_distinct__sorted__mono,axiom,
% 0.37/0.66 ! [L: list_o,I: nat,J: nat] :
% 0.37/0.66 ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 0.37/0.66 => ( ( distinct_o @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ J )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ord_less_o @ ( nth_o @ L @ I ) @ ( nth_o @ L @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono
% 0.37/0.66 thf(fact_5895_distinct__sorted__mono,axiom,
% 0.37/0.66 ! [L: list_real,I: nat,J: nat] :
% 0.37/0.66 ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 0.37/0.66 => ( ( distinct_real @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ J )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ord_less_real @ ( nth_real @ L @ I ) @ ( nth_real @ L @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono
% 0.37/0.66 thf(fact_5896_distinct__sorted__mono,axiom,
% 0.37/0.66 ! [L: list_rat,I: nat,J: nat] :
% 0.37/0.66 ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 0.37/0.66 => ( ( distinct_rat @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ J )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 0.37/0.66 => ( ord_less_rat @ ( nth_rat @ L @ I ) @ ( nth_rat @ L @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono
% 0.37/0.66 thf(fact_5897_distinct__sorted__mono,axiom,
% 0.37/0.66 ! [L: list_num,I: nat,J: nat] :
% 0.37/0.66 ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 0.37/0.66 => ( ( distinct_num @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ J )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 0.37/0.66 => ( ord_less_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono
% 0.37/0.66 thf(fact_5898_distinct__sorted__mono,axiom,
% 0.37/0.66 ! [L: list_nat,I: nat,J: nat] :
% 0.37/0.66 ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 0.37/0.66 => ( ( distinct_nat @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ J )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ord_less_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono
% 0.37/0.66 thf(fact_5899_distinct__sorted__mono,axiom,
% 0.37/0.66 ! [L: list_int,I: nat,J: nat] :
% 0.37/0.66 ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 0.37/0.66 => ( ( distinct_int @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ J )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ord_less_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono
% 0.37/0.66 thf(fact_5900_distinct__sorted__strict__mono__iff,axiom,
% 0.37/0.66 ! [L: list_o,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_o @ L )
% 0.37/0.66 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( ord_less_o @ ( nth_o @ L @ I ) @ ( nth_o @ L @ J ) )
% 0.37/0.66 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_strict_mono_iff
% 0.37/0.66 thf(fact_5901_distinct__sorted__strict__mono__iff,axiom,
% 0.37/0.66 ! [L: list_real,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_real @ L )
% 0.37/0.66 => ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( ord_less_real @ ( nth_real @ L @ I ) @ ( nth_real @ L @ J ) )
% 0.37/0.66 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_strict_mono_iff
% 0.37/0.66 thf(fact_5902_distinct__sorted__strict__mono__iff,axiom,
% 0.37/0.66 ! [L: list_rat,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_rat @ L )
% 0.37/0.66 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_rat @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 0.37/0.66 => ( ( ord_less_rat @ ( nth_rat @ L @ I ) @ ( nth_rat @ L @ J ) )
% 0.37/0.66 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_strict_mono_iff
% 0.37/0.66 thf(fact_5903_distinct__sorted__strict__mono__iff,axiom,
% 0.37/0.66 ! [L: list_num,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_num @ L )
% 0.37/0.66 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_num @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 0.37/0.66 => ( ( ord_less_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) )
% 0.37/0.66 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_strict_mono_iff
% 0.37/0.66 thf(fact_5904_distinct__sorted__strict__mono__iff,axiom,
% 0.37/0.66 ! [L: list_nat,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_nat @ L )
% 0.37/0.66 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) )
% 0.37/0.66 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_strict_mono_iff
% 0.37/0.66 thf(fact_5905_distinct__sorted__strict__mono__iff,axiom,
% 0.37/0.66 ! [L: list_int,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_int @ L )
% 0.37/0.66 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ( ord_less_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) )
% 0.37/0.66 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_strict_mono_iff
% 0.37/0.66 thf(fact_5906_distinct__sorted__mono__iff,axiom,
% 0.37/0.66 ! [L: list_real,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_real @ L )
% 0.37/0.66 => ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( ord_less_eq_real @ ( nth_real @ L @ I ) @ ( nth_real @ L @ J ) )
% 0.37/0.66 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono_iff
% 0.37/0.66 thf(fact_5907_distinct__sorted__mono__iff,axiom,
% 0.37/0.66 ! [L: list_o,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_o @ L )
% 0.37/0.66 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( ord_less_eq_o @ ( nth_o @ L @ I ) @ ( nth_o @ L @ J ) )
% 0.37/0.66 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono_iff
% 0.37/0.66 thf(fact_5908_distinct__sorted__mono__iff,axiom,
% 0.37/0.66 ! [L: list_rat,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_rat @ L )
% 0.37/0.66 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_rat @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 0.37/0.66 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I ) @ ( nth_rat @ L @ J ) )
% 0.37/0.66 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono_iff
% 0.37/0.66 thf(fact_5909_distinct__sorted__mono__iff,axiom,
% 0.37/0.66 ! [L: list_num,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_num @ L )
% 0.37/0.66 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_num @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 0.37/0.66 => ( ( ord_less_eq_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) )
% 0.37/0.66 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono_iff
% 0.37/0.66 thf(fact_5910_distinct__sorted__mono__iff,axiom,
% 0.37/0.66 ! [L: list_nat,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_nat @ L )
% 0.37/0.66 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) )
% 0.37/0.66 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono_iff
% 0.37/0.66 thf(fact_5911_distinct__sorted__mono__iff,axiom,
% 0.37/0.66 ! [L: list_int,I: nat,J: nat] :
% 0.37/0.66 ( ( distinct_int @ L )
% 0.37/0.66 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) )
% 0.37/0.66 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_sorted_mono_iff
% 0.37/0.66 thf(fact_5912_distinct__list__update,axiom,
% 0.37/0.66 ! [Xs: list_set_nat,A: set_nat,I: nat] :
% 0.37/0.66 ( ( distinct_set_nat @ Xs )
% 0.37/0.66 => ( ~ ( member_set_nat @ A @ ( minus_2163939370556025621et_nat @ ( set_set_nat2 @ Xs ) @ ( insert_set_nat @ ( nth_set_nat @ Xs @ I ) @ bot_bot_set_set_nat ) ) )
% 0.37/0.66 => ( distinct_set_nat @ ( list_update_set_nat @ Xs @ I @ A ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_list_update
% 0.37/0.66 thf(fact_5913_distinct__list__update,axiom,
% 0.37/0.66 ! [Xs: list_real,A: real,I: nat] :
% 0.37/0.66 ( ( distinct_real @ Xs )
% 0.37/0.66 => ( ~ ( member_real @ A @ ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ ( nth_real @ Xs @ I ) @ bot_bot_set_real ) ) )
% 0.37/0.66 => ( distinct_real @ ( list_update_real @ Xs @ I @ A ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_list_update
% 0.37/0.66 thf(fact_5914_distinct__list__update,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBTi,A: vEBT_VEBTi,I: nat] :
% 0.37/0.66 ( ( distinct_VEBT_VEBTi @ Xs )
% 0.37/0.66 => ( ~ ( member_VEBT_VEBTi @ A @ ( minus_3697805406911847364_VEBTi @ ( set_VEBT_VEBTi2 @ Xs ) @ ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ I ) @ bot_bo8982466882572371071_VEBTi ) ) )
% 0.37/0.66 => ( distinct_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ A ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_list_update
% 0.37/0.66 thf(fact_5915_distinct__list__update,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,A: vEBT_VEBT,I: nat] :
% 0.37/0.66 ( ( distinct_VEBT_VEBT @ Xs )
% 0.37/0.66 => ( ~ ( member_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ I ) @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.66 => ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ A ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_list_update
% 0.37/0.66 thf(fact_5916_distinct__list__update,axiom,
% 0.37/0.66 ! [Xs: list_int,A: int,I: nat] :
% 0.37/0.66 ( ( distinct_int @ Xs )
% 0.37/0.66 => ( ~ ( member_int @ A @ ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ ( nth_int @ Xs @ I ) @ bot_bot_set_int ) ) )
% 0.37/0.66 => ( distinct_int @ ( list_update_int @ Xs @ I @ A ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_list_update
% 0.37/0.66 thf(fact_5917_distinct__list__update,axiom,
% 0.37/0.66 ! [Xs: list_o,A: $o,I: nat] :
% 0.37/0.66 ( ( distinct_o @ Xs )
% 0.37/0.66 => ( ~ ( member_o @ A @ ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ ( nth_o @ Xs @ I ) @ bot_bot_set_o ) ) )
% 0.37/0.66 => ( distinct_o @ ( list_update_o @ Xs @ I @ A ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_list_update
% 0.37/0.66 thf(fact_5918_distinct__list__update,axiom,
% 0.37/0.66 ! [Xs: list_nat,A: nat,I: nat] :
% 0.37/0.66 ( ( distinct_nat @ Xs )
% 0.37/0.66 => ( ~ ( member_nat @ A @ ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ ( nth_nat @ Xs @ I ) @ bot_bot_set_nat ) ) )
% 0.37/0.66 => ( distinct_nat @ ( list_update_nat @ Xs @ I @ A ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_list_update
% 0.37/0.66 thf(fact_5919_vebt__insert_Osimps_I4_J,axiom,
% 0.37/0.66 ! [V2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.66 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) ) ).
% 0.37/0.66
% 0.37/0.66 % vebt_insert.simps(4)
% 0.37/0.66 thf(fact_5920_heaphelp,axiom,
% 0.37/0.66 ! [Xa2: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn
% 0.37/0.66 @ ( times_times_assn
% 0.37/0.66 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa2 @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb ) )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( ( none_P5556105721700978146at_nat = none_P5556105721700978146at_nat )
% 0.37/0.66 & ( N = N ) ) ) )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( Xc
% 0.37/0.66 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa2 @ Xb ) ) ) )
% 0.37/0.66 @ H2 )
% 0.37/0.66 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % heaphelp
% 0.37/0.66 thf(fact_5921_heaphelp,axiom,
% 0.37/0.66 ! [Xa2: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 0.37/0.66 ( ( rep_assn
% 0.37/0.66 @ ( times_times_assn
% 0.37/0.66 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa2 @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb ) )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( ( none_nat = none_nat )
% 0.37/0.66 & ( N = N ) ) ) )
% 0.37/0.66 @ ( pure_assn
% 0.37/0.66 @ ( Xc
% 0.37/0.66 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa2 @ Xb ) ) ) )
% 0.37/0.66 @ H2 )
% 0.37/0.66 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 0.37/0.66
% 0.37/0.66 % heaphelp
% 0.37/0.66 thf(fact_5922_vebt__insert_Osimps_I3_J,axiom,
% 0.37/0.66 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.37/0.66 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X )
% 0.37/0.66 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) ).
% 0.37/0.66
% 0.37/0.66 % vebt_insert.simps(3)
% 0.37/0.66 thf(fact_5923_vebt__insert_Osimps_I2_J,axiom,
% 0.37/0.66 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.37/0.66 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X )
% 0.37/0.66 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) ) ).
% 0.37/0.66
% 0.37/0.66 % vebt_insert.simps(2)
% 0.37/0.66 thf(fact_5924_mergesort__remdups__correct,axiom,
% 0.37/0.66 ! [L: list_real] :
% 0.37/0.66 ( ( distinct_real @ ( merges7559785487730971421s_real @ L ) )
% 0.37/0.66 & ( sorted_wrt_real @ ord_less_eq_real @ ( merges7559785487730971421s_real @ L ) )
% 0.37/0.66 & ( ( set_real2 @ ( merges7559785487730971421s_real @ L ) )
% 0.37/0.66 = ( set_real2 @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % mergesort_remdups_correct
% 0.37/0.66 thf(fact_5925_mergesort__remdups__correct,axiom,
% 0.37/0.66 ! [L: list_o] :
% 0.37/0.66 ( ( distinct_o @ ( mergesort_remdups_o @ L ) )
% 0.37/0.66 & ( sorted_wrt_o @ ord_less_eq_o @ ( mergesort_remdups_o @ L ) )
% 0.37/0.66 & ( ( set_o2 @ ( mergesort_remdups_o @ L ) )
% 0.37/0.66 = ( set_o2 @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % mergesort_remdups_correct
% 0.37/0.66 thf(fact_5926_mergesort__remdups__correct,axiom,
% 0.37/0.66 ! [L: list_rat] :
% 0.37/0.66 ( ( distinct_rat @ ( merges1021483306759835337ps_rat @ L ) )
% 0.37/0.66 & ( sorted_wrt_rat @ ord_less_eq_rat @ ( merges1021483306759835337ps_rat @ L ) )
% 0.37/0.66 & ( ( set_rat2 @ ( merges1021483306759835337ps_rat @ L ) )
% 0.37/0.66 = ( set_rat2 @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % mergesort_remdups_correct
% 0.37/0.66 thf(fact_5927_mergesort__remdups__correct,axiom,
% 0.37/0.66 ! [L: list_num] :
% 0.37/0.66 ( ( distinct_num @ ( merges7437317189856885515ps_num @ L ) )
% 0.37/0.66 & ( sorted_wrt_num @ ord_less_eq_num @ ( merges7437317189856885515ps_num @ L ) )
% 0.37/0.66 & ( ( set_num2 @ ( merges7437317189856885515ps_num @ L ) )
% 0.37/0.66 = ( set_num2 @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % mergesort_remdups_correct
% 0.37/0.66 thf(fact_5928_mergesort__remdups__correct,axiom,
% 0.37/0.66 ! [L: list_nat] :
% 0.37/0.66 ( ( distinct_nat @ ( merges1656613366846331073ps_nat @ L ) )
% 0.37/0.66 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( merges1656613366846331073ps_nat @ L ) )
% 0.37/0.66 & ( ( set_nat2 @ ( merges1656613366846331073ps_nat @ L ) )
% 0.37/0.66 = ( set_nat2 @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % mergesort_remdups_correct
% 0.37/0.66 thf(fact_5929_mergesort__remdups__correct,axiom,
% 0.37/0.66 ! [L: list_int] :
% 0.37/0.66 ( ( distinct_int @ ( merges1654122896337280797ps_int @ L ) )
% 0.37/0.66 & ( sorted_wrt_int @ ord_less_eq_int @ ( merges1654122896337280797ps_int @ L ) )
% 0.37/0.66 & ( ( set_int2 @ ( merges1654122896337280797ps_int @ L ) )
% 0.37/0.66 = ( set_int2 @ L ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % mergesort_remdups_correct
% 0.37/0.66 thf(fact_5930_last__take__nth__conv,axiom,
% 0.37/0.66 ! [N: nat,L: list_VEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_s7982070591426661849_VEBTi @ L ) )
% 0.37/0.66 => ( ( N != zero_zero_nat )
% 0.37/0.66 => ( ( last_VEBT_VEBTi @ ( take_VEBT_VEBTi @ N @ L ) )
% 0.37/0.66 = ( nth_VEBT_VEBTi @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % last_take_nth_conv
% 0.37/0.66 thf(fact_5931_last__take__nth__conv,axiom,
% 0.37/0.66 ! [N: nat,L: list_int] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ L ) )
% 0.37/0.66 => ( ( N != zero_zero_nat )
% 0.37/0.66 => ( ( last_int @ ( take_int @ N @ L ) )
% 0.37/0.66 = ( nth_int @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % last_take_nth_conv
% 0.37/0.66 thf(fact_5932_last__take__nth__conv,axiom,
% 0.37/0.66 ! [N: nat,L: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.66 => ( ( N != zero_zero_nat )
% 0.37/0.66 => ( ( last_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ L ) )
% 0.37/0.66 = ( nth_VEBT_VEBT @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % last_take_nth_conv
% 0.37/0.66 thf(fact_5933_last__take__nth__conv,axiom,
% 0.37/0.66 ! [N: nat,L: list_real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( N != zero_zero_nat )
% 0.37/0.66 => ( ( last_real @ ( take_real @ N @ L ) )
% 0.37/0.66 = ( nth_real @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % last_take_nth_conv
% 0.37/0.66 thf(fact_5934_last__take__nth__conv,axiom,
% 0.37/0.66 ! [N: nat,L: list_o] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( N != zero_zero_nat )
% 0.37/0.66 => ( ( last_o @ ( take_o @ N @ L ) )
% 0.37/0.66 = ( nth_o @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % last_take_nth_conv
% 0.37/0.66 thf(fact_5935_last__take__nth__conv,axiom,
% 0.37/0.66 ! [N: nat,L: list_nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( N != zero_zero_nat )
% 0.37/0.66 => ( ( last_nat @ ( take_nat @ N @ L ) )
% 0.37/0.66 = ( nth_nat @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % last_take_nth_conv
% 0.37/0.66 thf(fact_5936_VEBTi_Oinject_I1_J,axiom,
% 0.37/0.66 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,Y11: option4927543243414619207at_nat,Y12: nat,Y13: array_VEBT_VEBTi,Y14: vEBT_VEBTi] :
% 0.37/0.66 ( ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 0.37/0.66 = ( vEBT_Nodei @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 0.37/0.66 = ( ( X11 = Y11 )
% 0.37/0.66 & ( X12 = Y12 )
% 0.37/0.66 & ( X13 = Y13 )
% 0.37/0.66 & ( X14 = Y14 ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % VEBTi.inject(1)
% 0.37/0.66 thf(fact_5937_vebt__assn__raw_Osimps_I4_J,axiom,
% 0.37/0.66 ! [Vd2: $o,Ve2: $o,V2: option4927543243414619207at_nat,Va2: nat,Vb: array_VEBT_VEBTi,Vc: vEBT_VEBTi] :
% 0.37/0.66 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ Vd2 @ Ve2 ) @ ( vEBT_Nodei @ V2 @ Va2 @ Vb @ Vc ) )
% 0.37/0.66 = bot_bot_assn ) ).
% 0.37/0.66
% 0.37/0.66 % vebt_assn_raw.simps(4)
% 0.37/0.66 thf(fact_5938_subset__subseqs,axiom,
% 0.37/0.66 ! [X6: set_VEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_le4337996190870823476T_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.66 => ( member_set_VEBT_VEBT @ X6 @ ( image_6463372868993444447T_VEBT @ set_VEBT_VEBT2 @ ( set_list_VEBT_VEBT2 @ ( subseqs_VEBT_VEBT @ Xs ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subset_subseqs
% 0.37/0.66 thf(fact_5939_subset__subseqs,axiom,
% 0.37/0.66 ! [X6: set_nat,Xs: list_nat] :
% 0.37/0.66 ( ( ord_less_eq_set_nat @ X6 @ ( set_nat2 @ Xs ) )
% 0.37/0.66 => ( member_set_nat @ X6 @ ( image_1775855109352712557et_nat @ set_nat2 @ ( set_list_nat2 @ ( subseqs_nat @ Xs ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subset_subseqs
% 0.37/0.66 thf(fact_5940_subset__subseqs,axiom,
% 0.37/0.66 ! [X6: set_real,Xs: list_real] :
% 0.37/0.66 ( ( ord_less_eq_set_real @ X6 @ ( set_real2 @ Xs ) )
% 0.37/0.66 => ( member_set_real @ X6 @ ( image_6239767680843085477t_real @ set_real2 @ ( set_list_real2 @ ( subseqs_real @ Xs ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subset_subseqs
% 0.37/0.66 thf(fact_5941_subset__subseqs,axiom,
% 0.37/0.66 ! [X6: set_o,Xs: list_o] :
% 0.37/0.66 ( ( ord_less_eq_set_o @ X6 @ ( set_o2 @ Xs ) )
% 0.37/0.66 => ( member_set_o @ X6 @ ( image_list_o_set_o @ set_o2 @ ( set_list_o2 @ ( subseqs_o @ Xs ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subset_subseqs
% 0.37/0.66 thf(fact_5942_subset__subseqs,axiom,
% 0.37/0.66 ! [X6: set_int,Xs: list_int] :
% 0.37/0.66 ( ( ord_less_eq_set_int @ X6 @ ( set_int2 @ Xs ) )
% 0.37/0.66 => ( member_set_int @ X6 @ ( image_3606813740839090725et_int @ set_int2 @ ( set_list_int2 @ ( subseqs_int @ Xs ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % subset_subseqs
% 0.37/0.66 thf(fact_5943_set__remove1__eq,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.66 ( ( distinct_VEBT_VEBT @ Xs )
% 0.37/0.66 => ( ( set_VEBT_VEBT2 @ ( remove1_VEBT_VEBT @ X @ Xs ) )
% 0.37/0.66 = ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_eq
% 0.37/0.66 thf(fact_5944_set__remove1__eq,axiom,
% 0.37/0.66 ! [Xs: list_real,X: real] :
% 0.37/0.66 ( ( distinct_real @ Xs )
% 0.37/0.66 => ( ( set_real2 @ ( remove1_real @ X @ Xs ) )
% 0.37/0.66 = ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_eq
% 0.37/0.66 thf(fact_5945_set__remove1__eq,axiom,
% 0.37/0.66 ! [Xs: list_int,X: int] :
% 0.37/0.66 ( ( distinct_int @ Xs )
% 0.37/0.66 => ( ( set_int2 @ ( remove1_int @ X @ Xs ) )
% 0.37/0.66 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_eq
% 0.37/0.66 thf(fact_5946_set__remove1__eq,axiom,
% 0.37/0.66 ! [Xs: list_o,X: $o] :
% 0.37/0.66 ( ( distinct_o @ Xs )
% 0.37/0.66 => ( ( set_o2 @ ( remove1_o @ X @ Xs ) )
% 0.37/0.66 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_eq
% 0.37/0.66 thf(fact_5947_set__remove1__eq,axiom,
% 0.37/0.66 ! [Xs: list_nat,X: nat] :
% 0.37/0.66 ( ( distinct_nat @ Xs )
% 0.37/0.66 => ( ( set_nat2 @ ( remove1_nat @ X @ Xs ) )
% 0.37/0.66 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_eq
% 0.37/0.66 thf(fact_5948_lex__take__index,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi,R: set_Pr2227491710730465451_VEBTi] :
% 0.37/0.66 ( ( member4173000155140927252_VEBTi @ ( produc4384243565435462691_VEBTi @ Xs @ Ys ) @ ( lex_VEBT_VEBTi @ R ) )
% 0.37/0.66 => ~ ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 0.37/0.66 => ( ( ( take_VEBT_VEBTi @ I2 @ Xs )
% 0.37/0.66 = ( take_VEBT_VEBTi @ I2 @ Ys ) )
% 0.37/0.66 => ~ ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_VEBT_VEBTi @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % lex_take_index
% 0.37/0.66 thf(fact_5949_lex__take__index,axiom,
% 0.37/0.66 ! [Xs: list_uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.66 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( lex_uint32 @ R ) )
% 0.37/0.66 => ~ ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ ( size_s4844771616002835472uint32 @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I2 @ ( size_s4844771616002835472uint32 @ Ys ) )
% 0.37/0.66 => ( ( ( take_uint32 @ I2 @ Xs )
% 0.37/0.66 = ( take_uint32 @ I2 @ Ys ) )
% 0.37/0.66 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ I2 ) @ ( nth_uint32 @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % lex_take_index
% 0.37/0.66 thf(fact_5950_lex__take__index,axiom,
% 0.37/0.66 ! [Xs: list_int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.66 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( lex_int @ R ) )
% 0.37/0.66 => ~ ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 0.37/0.66 => ( ( ( take_int @ I2 @ Xs )
% 0.37/0.66 = ( take_int @ I2 @ Ys ) )
% 0.37/0.66 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % lex_take_index
% 0.37/0.66 thf(fact_5951_lex__take__index,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 0.37/0.66 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( lex_VEBT_VEBT @ R ) )
% 0.37/0.66 => ~ ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.66 => ( ( ( take_VEBT_VEBT @ I2 @ Xs )
% 0.37/0.66 = ( take_VEBT_VEBT @ I2 @ Ys ) )
% 0.37/0.66 => ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % lex_take_index
% 0.37/0.66 thf(fact_5952_lex__take__index,axiom,
% 0.37/0.66 ! [Xs: list_real,Ys: list_real,R: set_Pr6218003697084177305l_real] :
% 0.37/0.66 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Xs @ Ys ) @ ( lex_real @ R ) )
% 0.37/0.66 => ~ ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Ys ) )
% 0.37/0.66 => ( ( ( take_real @ I2 @ Xs )
% 0.37/0.66 = ( take_real @ I2 @ Ys ) )
% 0.37/0.66 => ~ ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ I2 ) @ ( nth_real @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % lex_take_index
% 0.37/0.66 thf(fact_5953_lex__take__index,axiom,
% 0.37/0.66 ! [Xs: list_o,Ys: list_o,R: set_Product_prod_o_o] :
% 0.37/0.66 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( lex_o @ R ) )
% 0.37/0.66 => ~ ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 0.37/0.66 => ( ( ( take_o @ I2 @ Xs )
% 0.37/0.66 = ( take_o @ I2 @ Ys ) )
% 0.37/0.66 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ I2 ) @ ( nth_o @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % lex_take_index
% 0.37/0.66 thf(fact_5954_lex__take__index,axiom,
% 0.37/0.66 ! [Xs: list_nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.66 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( lex_nat @ R ) )
% 0.37/0.66 => ~ ! [I2: nat] :
% 0.37/0.66 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 0.37/0.66 => ( ( ( take_nat @ I2 @ Xs )
% 0.37/0.66 = ( take_nat @ I2 @ Ys ) )
% 0.37/0.66 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % lex_take_index
% 0.37/0.66 thf(fact_5955_take__butlast__conv,axiom,
% 0.37/0.66 ! [L: list_VEBT_VEBT] :
% 0.37/0.66 ( ( take_VEBT_VEBT @ ( minus_minus_nat @ ( size_s6755466524823107622T_VEBT @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_VEBT_VEBT @ L ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast_conv
% 0.37/0.66 thf(fact_5956_take__butlast__conv,axiom,
% 0.37/0.66 ! [L: list_real] :
% 0.37/0.66 ( ( take_real @ ( minus_minus_nat @ ( size_size_list_real @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_real @ L ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast_conv
% 0.37/0.66 thf(fact_5957_take__butlast__conv,axiom,
% 0.37/0.66 ! [L: list_o] :
% 0.37/0.66 ( ( take_o @ ( minus_minus_nat @ ( size_size_list_o @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_o @ L ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast_conv
% 0.37/0.66 thf(fact_5958_take__butlast__conv,axiom,
% 0.37/0.66 ! [L: list_nat] :
% 0.37/0.66 ( ( take_nat @ ( minus_minus_nat @ ( size_size_list_nat @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_nat @ L ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast_conv
% 0.37/0.66 thf(fact_5959_take__minus__one__conv__butlast,axiom,
% 0.37/0.66 ! [N: nat,L: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ L ) )
% 0.37/0.66 => ( ( take_VEBT_VEBT @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_minus_one_conv_butlast
% 0.37/0.66 thf(fact_5960_take__minus__one__conv__butlast,axiom,
% 0.37/0.66 ! [N: nat,L: list_real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ L ) )
% 0.37/0.66 => ( ( take_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_real @ ( take_real @ N @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_minus_one_conv_butlast
% 0.37/0.66 thf(fact_5961_take__minus__one__conv__butlast,axiom,
% 0.37/0.66 ! [N: nat,L: list_o] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ L ) )
% 0.37/0.66 => ( ( take_o @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_o @ ( take_o @ N @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_minus_one_conv_butlast
% 0.37/0.66 thf(fact_5962_take__minus__one__conv__butlast,axiom,
% 0.37/0.66 ! [N: nat,L: list_nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ L ) )
% 0.37/0.66 => ( ( take_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 0.37/0.66 = ( butlast_nat @ ( take_nat @ N @ L ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_minus_one_conv_butlast
% 0.37/0.66 thf(fact_5963_Cons__in__lex,axiom,
% 0.37/0.66 ! [X: uint32,Xs: list_uint32,Y: uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.66 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Ys ) ) @ ( lex_uint32 @ R ) )
% 0.37/0.66 = ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 0.37/0.66 & ( ( size_s4844771616002835472uint32 @ Xs )
% 0.37/0.66 = ( size_s4844771616002835472uint32 @ Ys ) ) )
% 0.37/0.66 | ( ( X = Y )
% 0.37/0.66 & ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( lex_uint32 @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_in_lex
% 0.37/0.66 thf(fact_5964_Cons__in__lex,axiom,
% 0.37/0.66 ! [X: int,Xs: list_int,Y: int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.66 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( lex_int @ R ) )
% 0.37/0.66 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 0.37/0.66 & ( ( size_size_list_int @ Xs )
% 0.37/0.66 = ( size_size_list_int @ Ys ) ) )
% 0.37/0.66 | ( ( X = Y )
% 0.37/0.66 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( lex_int @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_in_lex
% 0.37/0.66 thf(fact_5965_Cons__in__lex,axiom,
% 0.37/0.66 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,Y: vEBT_VEBT,Ys: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 0.37/0.66 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( cons_VEBT_VEBT @ Y @ Ys ) ) @ ( lex_VEBT_VEBT @ R ) )
% 0.37/0.66 = ( ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y ) @ R )
% 0.37/0.66 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.66 = ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.37/0.66 | ( ( X = Y )
% 0.37/0.66 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( lex_VEBT_VEBT @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_in_lex
% 0.37/0.66 thf(fact_5966_Cons__in__lex,axiom,
% 0.37/0.66 ! [X: real,Xs: list_real,Y: real,Ys: list_real,R: set_Pr6218003697084177305l_real] :
% 0.37/0.66 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ ( cons_real @ X @ Xs ) @ ( cons_real @ Y @ Ys ) ) @ ( lex_real @ R ) )
% 0.37/0.66 = ( ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X @ Y ) @ R )
% 0.37/0.66 & ( ( size_size_list_real @ Xs )
% 0.37/0.66 = ( size_size_list_real @ Ys ) ) )
% 0.37/0.66 | ( ( X = Y )
% 0.37/0.66 & ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Xs @ Ys ) @ ( lex_real @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_in_lex
% 0.37/0.66 thf(fact_5967_Cons__in__lex,axiom,
% 0.37/0.66 ! [X: $o,Xs: list_o,Y: $o,Ys: list_o,R: set_Product_prod_o_o] :
% 0.37/0.66 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Ys ) ) @ ( lex_o @ R ) )
% 0.37/0.66 = ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 0.37/0.66 & ( ( size_size_list_o @ Xs )
% 0.37/0.66 = ( size_size_list_o @ Ys ) ) )
% 0.37/0.66 | ( ( X = Y )
% 0.37/0.66 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( lex_o @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_in_lex
% 0.37/0.66 thf(fact_5968_Cons__in__lex,axiom,
% 0.37/0.66 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.66 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( lex_nat @ R ) )
% 0.37/0.66 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.37/0.66 & ( ( size_size_list_nat @ Xs )
% 0.37/0.66 = ( size_size_list_nat @ Ys ) ) )
% 0.37/0.66 | ( ( X = Y )
% 0.37/0.66 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( lex_nat @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_in_lex
% 0.37/0.66 thf(fact_5969_butlast__update_H,axiom,
% 0.37/0.66 ! [L: list_nat,I: nat,X: nat] :
% 0.37/0.66 ( ( list_update_nat @ ( butlast_nat @ L ) @ I @ X )
% 0.37/0.66 = ( butlast_nat @ ( list_update_nat @ L @ I @ X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % butlast_update'
% 0.37/0.66 thf(fact_5970_butlast__update_H,axiom,
% 0.37/0.66 ! [L: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 0.37/0.66 ( ( list_u6098035379799741383_VEBTi @ ( butlast_VEBT_VEBTi @ L ) @ I @ X )
% 0.37/0.66 = ( butlast_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % butlast_update'
% 0.37/0.66 thf(fact_5971_butlast__update_H,axiom,
% 0.37/0.66 ! [L: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 0.37/0.66 ( ( list_u1324408373059187874T_VEBT @ ( butlast_VEBT_VEBT @ L ) @ I @ X )
% 0.37/0.66 = ( butlast_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % butlast_update'
% 0.37/0.66 thf(fact_5972_foldl__absorb1,axiom,
% 0.37/0.66 ! [X: rat,Zs: list_rat] :
% 0.37/0.66 ( ( times_times_rat @ X @ ( foldl_rat_rat @ times_times_rat @ one_one_rat @ Zs ) )
% 0.37/0.66 = ( foldl_rat_rat @ times_times_rat @ X @ Zs ) ) ).
% 0.37/0.66
% 0.37/0.66 % foldl_absorb1
% 0.37/0.66 thf(fact_5973_foldl__absorb1,axiom,
% 0.37/0.66 ! [X: assn,Zs: list_assn] :
% 0.37/0.66 ( ( times_times_assn @ X @ ( foldl_assn_assn @ times_times_assn @ one_one_assn @ Zs ) )
% 0.37/0.66 = ( foldl_assn_assn @ times_times_assn @ X @ Zs ) ) ).
% 0.37/0.66
% 0.37/0.66 % foldl_absorb1
% 0.37/0.66 thf(fact_5974_foldl__absorb1,axiom,
% 0.37/0.66 ! [X: uint32,Zs: list_uint32] :
% 0.37/0.66 ( ( times_times_uint32 @ X @ ( foldl_uint32_uint32 @ times_times_uint32 @ one_one_uint32 @ Zs ) )
% 0.37/0.66 = ( foldl_uint32_uint32 @ times_times_uint32 @ X @ Zs ) ) ).
% 0.37/0.66
% 0.37/0.66 % foldl_absorb1
% 0.37/0.66 thf(fact_5975_foldl__absorb1,axiom,
% 0.37/0.66 ! [X: real,Zs: list_real] :
% 0.37/0.66 ( ( times_times_real @ X @ ( foldl_real_real @ times_times_real @ one_one_real @ Zs ) )
% 0.37/0.66 = ( foldl_real_real @ times_times_real @ X @ Zs ) ) ).
% 0.37/0.66
% 0.37/0.66 % foldl_absorb1
% 0.37/0.66 thf(fact_5976_foldl__absorb1,axiom,
% 0.37/0.66 ! [X: nat,Zs: list_nat] :
% 0.37/0.66 ( ( times_times_nat @ X @ ( foldl_nat_nat @ times_times_nat @ one_one_nat @ Zs ) )
% 0.37/0.66 = ( foldl_nat_nat @ times_times_nat @ X @ Zs ) ) ).
% 0.37/0.66
% 0.37/0.66 % foldl_absorb1
% 0.37/0.66 thf(fact_5977_foldl__absorb1,axiom,
% 0.37/0.66 ! [X: int,Zs: list_int] :
% 0.37/0.66 ( ( times_times_int @ X @ ( foldl_int_int @ times_times_int @ one_one_int @ Zs ) )
% 0.37/0.66 = ( foldl_int_int @ times_times_int @ X @ Zs ) ) ).
% 0.37/0.66
% 0.37/0.66 % foldl_absorb1
% 0.37/0.66 thf(fact_5978_set__remove1__subset,axiom,
% 0.37/0.66 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( remove1_VEBT_VEBT @ X @ Xs ) ) @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_subset
% 0.37/0.66 thf(fact_5979_set__remove1__subset,axiom,
% 0.37/0.66 ! [X: nat,Xs: list_nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( remove1_nat @ X @ Xs ) ) @ ( set_nat2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_subset
% 0.37/0.66 thf(fact_5980_set__remove1__subset,axiom,
% 0.37/0.66 ! [X: real,Xs: list_real] : ( ord_less_eq_set_real @ ( set_real2 @ ( remove1_real @ X @ Xs ) ) @ ( set_real2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_subset
% 0.37/0.66 thf(fact_5981_set__remove1__subset,axiom,
% 0.37/0.66 ! [X: $o,Xs: list_o] : ( ord_less_eq_set_o @ ( set_o2 @ ( remove1_o @ X @ Xs ) ) @ ( set_o2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_subset
% 0.37/0.66 thf(fact_5982_set__remove1__subset,axiom,
% 0.37/0.66 ! [X: int,Xs: list_int] : ( ord_less_eq_set_int @ ( set_int2 @ ( remove1_int @ X @ Xs ) ) @ ( set_int2 @ Xs ) ) ).
% 0.37/0.66
% 0.37/0.66 % set_remove1_subset
% 0.37/0.66 thf(fact_5983_sorted__remove1,axiom,
% 0.37/0.66 ! [Xs: list_rat,A: rat] :
% 0.37/0.66 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 0.37/0.66 => ( sorted_wrt_rat @ ord_less_eq_rat @ ( remove1_rat @ A @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_remove1
% 0.37/0.66 thf(fact_5984_sorted__remove1,axiom,
% 0.37/0.66 ! [Xs: list_num,A: num] :
% 0.37/0.66 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 0.37/0.66 => ( sorted_wrt_num @ ord_less_eq_num @ ( remove1_num @ A @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_remove1
% 0.37/0.66 thf(fact_5985_sorted__remove1,axiom,
% 0.37/0.66 ! [Xs: list_nat,A: nat] :
% 0.37/0.66 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 0.37/0.66 => ( sorted_wrt_nat @ ord_less_eq_nat @ ( remove1_nat @ A @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_remove1
% 0.37/0.66 thf(fact_5986_sorted__remove1,axiom,
% 0.37/0.66 ! [Xs: list_int,A: int] :
% 0.37/0.66 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 0.37/0.66 => ( sorted_wrt_int @ ord_less_eq_int @ ( remove1_int @ A @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_remove1
% 0.37/0.66 thf(fact_5987_nth__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_VEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ ( butlast_VEBT_VEBTi @ Xs ) ) )
% 0.37/0.66 => ( ( nth_VEBT_VEBTi @ ( butlast_VEBT_VEBTi @ Xs ) @ N )
% 0.37/0.66 = ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_butlast
% 0.37/0.66 thf(fact_5988_nth__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_int] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_size_list_int @ ( butlast_int @ Xs ) ) )
% 0.37/0.66 => ( ( nth_int @ ( butlast_int @ Xs ) @ N )
% 0.37/0.66 = ( nth_int @ Xs @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_butlast
% 0.37/0.66 thf(fact_5989_nth__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ ( butlast_VEBT_VEBT @ Xs ) ) )
% 0.37/0.66 => ( ( nth_VEBT_VEBT @ ( butlast_VEBT_VEBT @ Xs ) @ N )
% 0.37/0.66 = ( nth_VEBT_VEBT @ Xs @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_butlast
% 0.37/0.66 thf(fact_5990_nth__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_real] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_size_list_real @ ( butlast_real @ Xs ) ) )
% 0.37/0.66 => ( ( nth_real @ ( butlast_real @ Xs ) @ N )
% 0.37/0.66 = ( nth_real @ Xs @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_butlast
% 0.37/0.66 thf(fact_5991_nth__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_o] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_size_list_o @ ( butlast_o @ Xs ) ) )
% 0.37/0.66 => ( ( nth_o @ ( butlast_o @ Xs ) @ N )
% 0.37/0.66 = ( nth_o @ Xs @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_butlast
% 0.37/0.66 thf(fact_5992_nth__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_nat] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_size_list_nat @ ( butlast_nat @ Xs ) ) )
% 0.37/0.66 => ( ( nth_nat @ ( butlast_nat @ Xs ) @ N )
% 0.37/0.66 = ( nth_nat @ Xs @ N ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_butlast
% 0.37/0.66 thf(fact_5993_take__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( take_VEBT_VEBT @ N @ ( butlast_VEBT_VEBT @ Xs ) )
% 0.37/0.66 = ( take_VEBT_VEBT @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast
% 0.37/0.66 thf(fact_5994_take__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_real] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( take_real @ N @ ( butlast_real @ Xs ) )
% 0.37/0.66 = ( take_real @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast
% 0.37/0.66 thf(fact_5995_take__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_o] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( take_o @ N @ ( butlast_o @ Xs ) )
% 0.37/0.66 = ( take_o @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast
% 0.37/0.66 thf(fact_5996_take__butlast,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_nat] :
% 0.37/0.66 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( take_nat @ N @ ( butlast_nat @ Xs ) )
% 0.37/0.66 = ( take_nat @ N @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % take_butlast
% 0.37/0.66 thf(fact_5997_distinct__butlast__swap,axiom,
% 0.37/0.66 ! [Pq: list_nat,I: nat] :
% 0.37/0.66 ( ( distinct_nat @ Pq )
% 0.37/0.66 => ( distinct_nat @ ( butlast_nat @ ( list_update_nat @ Pq @ I @ ( last_nat @ Pq ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_butlast_swap
% 0.37/0.66 thf(fact_5998_distinct__butlast__swap,axiom,
% 0.37/0.66 ! [Pq: list_VEBT_VEBTi,I: nat] :
% 0.37/0.66 ( ( distinct_VEBT_VEBTi @ Pq )
% 0.37/0.66 => ( distinct_VEBT_VEBTi @ ( butlast_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Pq @ I @ ( last_VEBT_VEBTi @ Pq ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_butlast_swap
% 0.37/0.66 thf(fact_5999_distinct__butlast__swap,axiom,
% 0.37/0.66 ! [Pq: list_VEBT_VEBT,I: nat] :
% 0.37/0.66 ( ( distinct_VEBT_VEBT @ Pq )
% 0.37/0.66 => ( distinct_VEBT_VEBT @ ( butlast_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Pq @ I @ ( last_VEBT_VEBT @ Pq ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % distinct_butlast_swap
% 0.37/0.66 thf(fact_6000_butlast__take,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( butlast_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ Xs ) )
% 0.37/0.66 = ( take_VEBT_VEBT @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % butlast_take
% 0.37/0.66 thf(fact_6001_butlast__take,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_real] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 => ( ( butlast_real @ ( take_real @ N @ Xs ) )
% 0.37/0.66 = ( take_real @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % butlast_take
% 0.37/0.66 thf(fact_6002_butlast__take,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_o] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 => ( ( butlast_o @ ( take_o @ N @ Xs ) )
% 0.37/0.66 = ( take_o @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % butlast_take
% 0.37/0.66 thf(fact_6003_butlast__take,axiom,
% 0.37/0.66 ! [N: nat,Xs: list_nat] :
% 0.37/0.66 ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 => ( ( butlast_nat @ ( take_nat @ N @ Xs ) )
% 0.37/0.66 = ( take_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % butlast_take
% 0.37/0.66 thf(fact_6004_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 0.37/0.66 ! [A4: set_Code_integer,X: code_integer] :
% 0.37/0.66 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.66 => ( ( linord2324613341767563021nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) )
% 0.37/0.66 = ( remove1_Code_integer @ X @ ( linord2324613341767563021nteger @ A4 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.sorted_key_list_of_set_remove
% 0.37/0.66 thf(fact_6005_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 0.37/0.66 ! [A4: set_int,X: int] :
% 0.37/0.66 ( ( finite_finite_int @ A4 )
% 0.37/0.66 => ( ( linord2612477271533052124et_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.37/0.66 = ( remove1_int @ X @ ( linord2612477271533052124et_int @ A4 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.sorted_key_list_of_set_remove
% 0.37/0.66 thf(fact_6006_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 0.37/0.66 ! [A4: set_o,X: $o] :
% 0.37/0.66 ( ( finite_finite_o @ A4 )
% 0.37/0.66 => ( ( linord3142498349692569832_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.37/0.66 = ( remove1_o @ X @ ( linord3142498349692569832_set_o @ A4 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.sorted_key_list_of_set_remove
% 0.37/0.66 thf(fact_6007_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 0.37/0.66 ! [A4: set_nat,X: nat] :
% 0.37/0.66 ( ( finite_finite_nat @ A4 )
% 0.37/0.66 => ( ( linord2614967742042102400et_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.37/0.66 = ( remove1_nat @ X @ ( linord2614967742042102400et_nat @ A4 ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % sorted_list_of_set.sorted_key_list_of_set_remove
% 0.37/0.66 thf(fact_6008_Cons__lenlex__iff,axiom,
% 0.37/0.66 ! [M: uint32,Ms: list_uint32,N: uint32,Ns: list_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.66 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ M @ Ms ) @ ( cons_uint32 @ N @ Ns ) ) @ ( lenlex_uint32 @ R ) )
% 0.37/0.66 = ( ( ord_less_nat @ ( size_s4844771616002835472uint32 @ Ms ) @ ( size_s4844771616002835472uint32 @ Ns ) )
% 0.37/0.66 | ( ( ( size_s4844771616002835472uint32 @ Ms )
% 0.37/0.66 = ( size_s4844771616002835472uint32 @ Ns ) )
% 0.37/0.66 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ M @ N ) @ R ) )
% 0.37/0.66 | ( ( M = N )
% 0.37/0.66 & ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Ms @ Ns ) @ ( lenlex_uint32 @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_lenlex_iff
% 0.37/0.66 thf(fact_6009_Cons__lenlex__iff,axiom,
% 0.37/0.66 ! [M: int,Ms: list_int,N: int,Ns: list_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.66 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ M @ Ms ) @ ( cons_int @ N @ Ns ) ) @ ( lenlex_int @ R ) )
% 0.37/0.66 = ( ( ord_less_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) )
% 0.37/0.66 | ( ( ( size_size_list_int @ Ms )
% 0.37/0.66 = ( size_size_list_int @ Ns ) )
% 0.37/0.66 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ M @ N ) @ R ) )
% 0.37/0.66 | ( ( M = N )
% 0.37/0.66 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_lenlex_iff
% 0.37/0.66 thf(fact_6010_Cons__lenlex__iff,axiom,
% 0.37/0.66 ! [M: vEBT_VEBT,Ms: list_VEBT_VEBT,N: vEBT_VEBT,Ns: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 0.37/0.66 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ M @ Ms ) @ ( cons_VEBT_VEBT @ N @ Ns ) ) @ ( lenlex_VEBT_VEBT @ R ) )
% 0.37/0.66 = ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) )
% 0.37/0.66 | ( ( ( size_s6755466524823107622T_VEBT @ Ms )
% 0.37/0.66 = ( size_s6755466524823107622T_VEBT @ Ns ) )
% 0.37/0.66 & ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ M @ N ) @ R ) )
% 0.37/0.66 | ( ( M = N )
% 0.37/0.66 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_lenlex_iff
% 0.37/0.66 thf(fact_6011_Cons__lenlex__iff,axiom,
% 0.37/0.66 ! [M: real,Ms: list_real,N: real,Ns: list_real,R: set_Pr6218003697084177305l_real] :
% 0.37/0.66 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ ( cons_real @ M @ Ms ) @ ( cons_real @ N @ Ns ) ) @ ( lenlex_real @ R ) )
% 0.37/0.66 = ( ( ord_less_nat @ ( size_size_list_real @ Ms ) @ ( size_size_list_real @ Ns ) )
% 0.37/0.66 | ( ( ( size_size_list_real @ Ms )
% 0.37/0.66 = ( size_size_list_real @ Ns ) )
% 0.37/0.66 & ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ M @ N ) @ R ) )
% 0.37/0.66 | ( ( M = N )
% 0.37/0.66 & ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Ms @ Ns ) @ ( lenlex_real @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_lenlex_iff
% 0.37/0.66 thf(fact_6012_Cons__lenlex__iff,axiom,
% 0.37/0.66 ! [M: $o,Ms: list_o,N: $o,Ns: list_o,R: set_Product_prod_o_o] :
% 0.37/0.66 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ M @ Ms ) @ ( cons_o @ N @ Ns ) ) @ ( lenlex_o @ R ) )
% 0.37/0.66 = ( ( ord_less_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) )
% 0.37/0.66 | ( ( ( size_size_list_o @ Ms )
% 0.37/0.66 = ( size_size_list_o @ Ns ) )
% 0.37/0.66 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ M @ N ) @ R ) )
% 0.37/0.66 | ( ( M = N )
% 0.37/0.66 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_lenlex_iff
% 0.37/0.66 thf(fact_6013_Cons__lenlex__iff,axiom,
% 0.37/0.66 ! [M: nat,Ms: list_nat,N: nat,Ns: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.66 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ M @ Ms ) @ ( cons_nat @ N @ Ns ) ) @ ( lenlex_nat @ R ) )
% 0.37/0.66 = ( ( ord_less_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) )
% 0.37/0.66 | ( ( ( size_size_list_nat @ Ms )
% 0.37/0.66 = ( size_size_list_nat @ Ns ) )
% 0.37/0.66 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ R ) )
% 0.37/0.66 | ( ( M = N )
% 0.37/0.66 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % Cons_lenlex_iff
% 0.37/0.66 thf(fact_6014_listrel1__iff__update,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi,R: set_Pr2227491710730465451_VEBTi] :
% 0.37/0.66 ( ( member4173000155140927252_VEBTi @ ( produc4384243565435462691_VEBTi @ Xs @ Ys ) @ ( listrel1_VEBT_VEBTi @ R ) )
% 0.37/0.66 = ( ? [Y4: vEBT_VEBTi,N6: nat] :
% 0.37/0.66 ( ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N6 ) @ Y4 ) @ R )
% 0.37/0.66 & ( ord_less_nat @ N6 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 & ( Ys
% 0.37/0.66 = ( list_u6098035379799741383_VEBTi @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listrel1_iff_update
% 0.37/0.66 thf(fact_6015_listrel1__iff__update,axiom,
% 0.37/0.66 ! [Xs: list_uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.66 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( listrel1_uint32 @ R ) )
% 0.37/0.66 = ( ? [Y4: uint32,N6: nat] :
% 0.37/0.66 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ N6 ) @ Y4 ) @ R )
% 0.37/0.66 & ( ord_less_nat @ N6 @ ( size_s4844771616002835472uint32 @ Xs ) )
% 0.37/0.66 & ( Ys
% 0.37/0.66 = ( list_update_uint32 @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listrel1_iff_update
% 0.37/0.66 thf(fact_6016_listrel1__iff__update,axiom,
% 0.37/0.66 ! [Xs: list_int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.66 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R ) )
% 0.37/0.66 = ( ? [Y4: int,N6: nat] :
% 0.37/0.66 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N6 ) @ Y4 ) @ R )
% 0.37/0.66 & ( ord_less_nat @ N6 @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 & ( Ys
% 0.37/0.66 = ( list_update_int @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listrel1_iff_update
% 0.37/0.66 thf(fact_6017_listrel1__iff__update,axiom,
% 0.37/0.66 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 0.37/0.66 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( listrel1_VEBT_VEBT @ R ) )
% 0.37/0.66 = ( ? [Y4: vEBT_VEBT,N6: nat] :
% 0.37/0.66 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ N6 ) @ Y4 ) @ R )
% 0.37/0.66 & ( ord_less_nat @ N6 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 & ( Ys
% 0.37/0.66 = ( list_u1324408373059187874T_VEBT @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listrel1_iff_update
% 0.37/0.66 thf(fact_6018_listrel1__iff__update,axiom,
% 0.37/0.66 ! [Xs: list_real,Ys: list_real,R: set_Pr6218003697084177305l_real] :
% 0.37/0.66 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Xs @ Ys ) @ ( listrel1_real @ R ) )
% 0.37/0.66 = ( ? [Y4: real,N6: nat] :
% 0.37/0.66 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ N6 ) @ Y4 ) @ R )
% 0.37/0.66 & ( ord_less_nat @ N6 @ ( size_size_list_real @ Xs ) )
% 0.37/0.66 & ( Ys
% 0.37/0.66 = ( list_update_real @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listrel1_iff_update
% 0.37/0.66 thf(fact_6019_listrel1__iff__update,axiom,
% 0.37/0.66 ! [Xs: list_o,Ys: list_o,R: set_Product_prod_o_o] :
% 0.37/0.66 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( listrel1_o @ R ) )
% 0.37/0.66 = ( ? [Y4: $o,N6: nat] :
% 0.37/0.66 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ N6 ) @ Y4 ) @ R )
% 0.37/0.66 & ( ord_less_nat @ N6 @ ( size_size_list_o @ Xs ) )
% 0.37/0.66 & ( Ys
% 0.37/0.66 = ( list_update_o @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listrel1_iff_update
% 0.37/0.66 thf(fact_6020_listrel1__iff__update,axiom,
% 0.37/0.66 ! [Xs: list_nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.66 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.37/0.66 = ( ? [Y4: nat,N6: nat] :
% 0.37/0.66 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N6 ) @ Y4 ) @ R )
% 0.37/0.66 & ( ord_less_nat @ N6 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.66 & ( Ys
% 0.37/0.66 = ( list_update_nat @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % listrel1_iff_update
% 0.37/0.66 thf(fact_6021_total__on__singleton,axiom,
% 0.37/0.66 ! [X: vEBT_VEBT] : ( total_on_VEBT_VEBT @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) @ ( insert494605675473494903T_VEBT @ ( produc537772716801021591T_VEBT @ X @ X ) @ bot_bo5088076668136028147T_VEBT ) ) ).
% 0.37/0.66
% 0.37/0.66 % total_on_singleton
% 0.37/0.66 thf(fact_6022_total__on__singleton,axiom,
% 0.37/0.66 ! [X: uint32] : ( total_on_uint32 @ ( insert_uint32 @ X @ bot_bot_set_uint32 ) @ ( insert4454361187789264009uint32 @ ( produc1400373151660368625uint32 @ X @ X ) @ bot_bo8438649754162204037uint32 ) ) ).
% 0.37/0.66
% 0.37/0.66 % total_on_singleton
% 0.37/0.66 thf(fact_6023_total__on__singleton,axiom,
% 0.37/0.66 ! [X: nat] : ( total_on_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 0.37/0.66
% 0.37/0.66 % total_on_singleton
% 0.37/0.66 thf(fact_6024_total__on__singleton,axiom,
% 0.37/0.66 ! [X: int] : ( total_on_int @ ( insert_int @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 0.37/0.66
% 0.37/0.66 % total_on_singleton
% 0.37/0.66 thf(fact_6025_total__on__singleton,axiom,
% 0.37/0.66 ! [X: $o] : ( total_on_o @ ( insert_o @ X @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X @ X ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 0.37/0.66
% 0.37/0.66 % total_on_singleton
% 0.37/0.66 thf(fact_6026_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr6329974346453275474_VEBTi @ ( zip_VE793581609497812771_VEBTi @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6027_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_int] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr2733638074192486473Ti_int @ ( zip_VEBT_VEBTi_int @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc7190175284220460154Ti_int @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6028_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_int,Ys: list_VEBT_VEBTi] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr5092243222550848201_VEBTi @ ( zip_int_VEBT_VEBTi @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc4497823428076633978_VEBTi @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6029_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_uint32,Ys: list_uint32] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s4844771616002835472uint32 @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s4844771616002835472uint32 @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr6139322253122866368uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ I ) @ ( nth_uint32 @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6030_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_int,Ys: list_int] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr4439495888332055232nt_int @ ( zip_int_int @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( product_Pair_int_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6031_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr8725177398587324397T_VEBT @ ( zip_VE7413257051550508102T_VEBT @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc7053807326796202854T_VEBT @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6032_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_int,Ys: list_VEBT_VEBT] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr3474266648193625910T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc3329399203697025711T_VEBT @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6033_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_real] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr3433448822664029129i_real @ ( zip_VEBT_VEBTi_real @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc8457151488442208762i_real @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_real @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6034_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_int,Ys: list_real] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr731366597535767232t_real @ ( zip_int_real @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc801115645435158769t_real @ ( nth_int @ Xs @ I ) @ ( nth_real @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6035_nth__zip,axiom,
% 0.37/0.66 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_o] :
% 0.37/0.66 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Ys ) )
% 0.37/0.66 => ( ( nth_Pr3306050735993963089EBTi_o @ ( zip_VEBT_VEBTi_o @ Xs @ Ys ) @ I )
% 0.37/0.66 = ( produc8194178580519725514EBTi_o @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_o @ Ys @ I ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % nth_zip
% 0.37/0.66 thf(fact_6036_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L7265847600308530106T_VEBT @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L7265847600308530106T_VEBT @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6037_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBTi > nat > assn,Xs: list_VEBT_VEBTi,Xsi: list_nat,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L8930081998596925642Ti_nat @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L8930081998596925642Ti_nat @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6038_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L1891944875198410415_VEBTi @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1891944875198410415_VEBTi @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6039_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,Xsi: list_int,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L8927591528087875366Ti_int @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L8927591528087875366Ti_int @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6040_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: int > vEBT_VEBT > assn,Xs: list_int,Xsi: list_VEBT_VEBT,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L1664421287176695555T_VEBT @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1664421287176695555T_VEBT @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6041_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: int > nat > assn,Xs: list_int,Xsi: list_nat,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L77084186935402305nt_nat @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L77084186935402305nt_nat @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6042_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: int > vEBT_VEBTi > assn,Xs: list_int,Xsi: list_VEBT_VEBTi,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L6235239671944049190_VEBTi @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L6235239671944049190_VEBTi @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6043_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: int > int > assn,Xs: list_int,Xsi: list_int,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L74593716426352029nt_int @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L74593716426352029nt_int @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6044_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L1279224858307276611T_VEBT @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.66 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.66 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.66 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1279224858307276611T_VEBT @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.66
% 0.37/0.66 % rule_at_index
% 0.37/0.66 thf(fact_6045_rule__at__index,axiom,
% 0.37/0.66 ! [P2: assn,A4: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,Xsi: list_nat,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 0.37/0.66 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L8296926524756676353BT_nat @ A4 @ Xs @ Xsi ) @ F2 ) )
% 0.37/0.66 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.37/0.66 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 0.37/0.67 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 0.37/0.67 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 0.37/0.67 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L8296926524756676353BT_nat @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % rule_at_index
% 0.37/0.67 thf(fact_6046_atLeast1__lessThan__eq__remove0,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.67 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % atLeast1_lessThan_eq_remove0
% 0.37/0.67 thf(fact_6047_Bernoulli__inequality,axiom,
% 0.37/0.67 ! [X: real,N: nat] :
% 0.37/0.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.67 => ( 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 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Bernoulli_inequality
% 0.37/0.67 thf(fact_6048_set__vebt_H__def,axiom,
% 0.37/0.67 ( vEBT_VEBT_set_vebt
% 0.37/0.67 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_vebt'_def
% 0.37/0.67 thf(fact_6049_of__nat__eq__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ( semiri5074537144036343181t_real @ M )
% 0.37/0.67 = ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.67 = ( M = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_iff
% 0.37/0.67 thf(fact_6050_of__nat__eq__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ( semiri1314217659103216013at_int @ M )
% 0.37/0.67 = ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.67 = ( M = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_iff
% 0.37/0.67 thf(fact_6051_of__nat__eq__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ( semiri4939895301339042750nteger @ M )
% 0.37/0.67 = ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.67 = ( M = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_iff
% 0.37/0.67 thf(fact_6052_image__ident,axiom,
% 0.37/0.67 ! [Y7: set_nat] :
% 0.37/0.67 ( ( image_nat_nat
% 0.37/0.67 @ ^ [X4: nat] : X4
% 0.37/0.67 @ Y7 )
% 0.37/0.67 = Y7 ) ).
% 0.37/0.67
% 0.37/0.67 % image_ident
% 0.37/0.67 thf(fact_6053_image__ident,axiom,
% 0.37/0.67 ! [Y7: set_int] :
% 0.37/0.67 ( ( image_int_int
% 0.37/0.67 @ ^ [X4: int] : X4
% 0.37/0.67 @ Y7 )
% 0.37/0.67 = Y7 ) ).
% 0.37/0.67
% 0.37/0.67 % image_ident
% 0.37/0.67 thf(fact_6054_finite__Collect__disjI,axiom,
% 0.37/0.67 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 0.37/0.67 ( ( finite8100373058378681591st_nat
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 | ( Q2 @ X4 ) ) ) )
% 0.37/0.67 = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 0.37/0.67 & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_disjI
% 0.37/0.67 thf(fact_6055_finite__Collect__disjI,axiom,
% 0.37/0.67 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 0.37/0.67 ( ( finite1152437895449049373et_nat
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 | ( Q2 @ X4 ) ) ) )
% 0.37/0.67 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 0.37/0.67 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_disjI
% 0.37/0.67 thf(fact_6056_finite__Collect__disjI,axiom,
% 0.37/0.67 ! [P2: nat > $o,Q2: nat > $o] :
% 0.37/0.67 ( ( finite_finite_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 | ( Q2 @ X4 ) ) ) )
% 0.37/0.67 = ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.37/0.67 & ( finite_finite_nat @ ( collect_nat @ Q2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_disjI
% 0.37/0.67 thf(fact_6057_finite__Collect__disjI,axiom,
% 0.37/0.67 ! [P2: int > $o,Q2: int > $o] :
% 0.37/0.67 ( ( finite_finite_int
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 | ( Q2 @ X4 ) ) ) )
% 0.37/0.67 = ( ( finite_finite_int @ ( collect_int @ P2 ) )
% 0.37/0.67 & ( finite_finite_int @ ( collect_int @ Q2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_disjI
% 0.37/0.67 thf(fact_6058_finite__Collect__disjI,axiom,
% 0.37/0.67 ! [P2: complex > $o,Q2: complex > $o] :
% 0.37/0.67 ( ( finite3207457112153483333omplex
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 | ( Q2 @ X4 ) ) ) )
% 0.37/0.67 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P2 ) )
% 0.37/0.67 & ( finite3207457112153483333omplex @ ( collect_complex @ Q2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_disjI
% 0.37/0.67 thf(fact_6059_finite__Collect__disjI,axiom,
% 0.37/0.67 ! [P2: code_integer > $o,Q2: code_integer > $o] :
% 0.37/0.67 ( ( finite6017078050557962740nteger
% 0.37/0.67 @ ( collect_Code_integer
% 0.37/0.67 @ ^ [X4: code_integer] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 | ( Q2 @ X4 ) ) ) )
% 0.37/0.67 = ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 0.37/0.67 & ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_disjI
% 0.37/0.67 thf(fact_6060_finite__Collect__conjI,axiom,
% 0.37/0.67 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 0.37/0.67 ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 0.37/0.67 | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q2 ) ) )
% 0.37/0.67 => ( finite8100373058378681591st_nat
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_conjI
% 0.37/0.67 thf(fact_6061_finite__Collect__conjI,axiom,
% 0.37/0.67 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 0.37/0.67 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 0.37/0.67 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) )
% 0.37/0.67 => ( finite1152437895449049373et_nat
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_conjI
% 0.37/0.67 thf(fact_6062_finite__Collect__conjI,axiom,
% 0.37/0.67 ! [P2: nat > $o,Q2: nat > $o] :
% 0.37/0.67 ( ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.37/0.67 | ( finite_finite_nat @ ( collect_nat @ Q2 ) ) )
% 0.37/0.67 => ( finite_finite_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_conjI
% 0.37/0.67 thf(fact_6063_finite__Collect__conjI,axiom,
% 0.37/0.67 ! [P2: int > $o,Q2: int > $o] :
% 0.37/0.67 ( ( ( finite_finite_int @ ( collect_int @ P2 ) )
% 0.37/0.67 | ( finite_finite_int @ ( collect_int @ Q2 ) ) )
% 0.37/0.67 => ( finite_finite_int
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_conjI
% 0.37/0.67 thf(fact_6064_finite__Collect__conjI,axiom,
% 0.37/0.67 ! [P2: complex > $o,Q2: complex > $o] :
% 0.37/0.67 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P2 ) )
% 0.37/0.67 | ( finite3207457112153483333omplex @ ( collect_complex @ Q2 ) ) )
% 0.37/0.67 => ( finite3207457112153483333omplex
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_conjI
% 0.37/0.67 thf(fact_6065_finite__Collect__conjI,axiom,
% 0.37/0.67 ! [P2: code_integer > $o,Q2: code_integer > $o] :
% 0.37/0.67 ( ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 0.37/0.67 | ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q2 ) ) )
% 0.37/0.67 => ( finite6017078050557962740nteger
% 0.37/0.67 @ ( collect_Code_integer
% 0.37/0.67 @ ^ [X4: code_integer] :
% 0.37/0.67 ( ( P2 @ X4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_conjI
% 0.37/0.67 thf(fact_6066_succ__empty,axiom,
% 0.37/0.67 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.67 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.67 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.37/0.67 = none_nat )
% 0.37/0.67 = ( ( collect_nat
% 0.37/0.67 @ ^ [Y4: nat] :
% 0.37/0.67 ( ( vEBT_vebt_member @ T @ Y4 )
% 0.37/0.67 & ( ord_less_nat @ X @ Y4 ) ) )
% 0.37/0.67 = bot_bot_set_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % succ_empty
% 0.37/0.67 thf(fact_6067_pred__empty,axiom,
% 0.37/0.67 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.67 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.67 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.37/0.67 = none_nat )
% 0.37/0.67 = ( ( collect_nat
% 0.37/0.67 @ ^ [Y4: nat] :
% 0.37/0.67 ( ( vEBT_vebt_member @ T @ Y4 )
% 0.37/0.67 & ( ord_less_nat @ Y4 @ X ) ) )
% 0.37/0.67 = bot_bot_set_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_empty
% 0.37/0.67 thf(fact_6068_foldr__mono,axiom,
% 0.37/0.67 ! [Xs: list_nat,Ys: list_nat,C2: nat,D: nat] :
% 0.37/0.67 ( ( ( size_size_list_nat @ Xs )
% 0.37/0.67 = ( size_size_list_nat @ Ys ) )
% 0.37/0.67 => ( ! [I2: nat] :
% 0.37/0.67 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.67 => ( ord_less_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) )
% 0.37/0.67 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.37/0.67 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ C2 ) @ ( size_size_list_nat @ Ys ) ) @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldr_mono
% 0.37/0.67 thf(fact_6069_lessThan__iff,axiom,
% 0.37/0.67 ! [I: set_nat,K: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 0.37/0.67 = ( ord_less_set_nat @ I @ K ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_iff
% 0.37/0.67 thf(fact_6070_lessThan__iff,axiom,
% 0.37/0.67 ! [I: rat,K: rat] :
% 0.37/0.67 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 0.37/0.67 = ( ord_less_rat @ I @ K ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_iff
% 0.37/0.67 thf(fact_6071_lessThan__iff,axiom,
% 0.37/0.67 ! [I: num,K: num] :
% 0.37/0.67 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 0.37/0.67 = ( ord_less_num @ I @ K ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_iff
% 0.37/0.67 thf(fact_6072_lessThan__iff,axiom,
% 0.37/0.67 ! [I: nat,K: nat] :
% 0.37/0.67 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 0.37/0.67 = ( ord_less_nat @ I @ K ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_iff
% 0.37/0.67 thf(fact_6073_lessThan__iff,axiom,
% 0.37/0.67 ! [I: int,K: int] :
% 0.37/0.67 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 0.37/0.67 = ( ord_less_int @ I @ K ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_iff
% 0.37/0.67 thf(fact_6074_lessThan__iff,axiom,
% 0.37/0.67 ! [I: real,K: real] :
% 0.37/0.67 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 0.37/0.67 = ( ord_less_real @ I @ K ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_iff
% 0.37/0.67 thf(fact_6075_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,A2: list_VEBT_VEBT,B2: list_VEBT_VEBT] :
% 0.37/0.67 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ B ) )
% 0.37/0.67 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 0.37/0.67 => ( ( ( zip_VE537291747668921783T_VEBT @ A @ B )
% 0.37/0.67 = ( zip_VE537291747668921783T_VEBT @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6076_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_VEBT_VEBT,B: list_real,A2: list_VEBT_VEBT,B2: list_real] :
% 0.37/0.67 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.67 = ( size_size_list_real @ B ) )
% 0.37/0.67 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.67 = ( size_size_list_real @ B2 ) )
% 0.37/0.67 => ( ( ( zip_VEBT_VEBT_real @ A @ B )
% 0.37/0.67 = ( zip_VEBT_VEBT_real @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6077_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_VEBT_VEBT,B: list_o,A2: list_VEBT_VEBT,B2: list_o] :
% 0.37/0.67 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.67 = ( size_size_list_o @ B ) )
% 0.37/0.67 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.67 = ( size_size_list_o @ B2 ) )
% 0.37/0.67 => ( ( ( zip_VEBT_VEBT_o @ A @ B )
% 0.37/0.67 = ( zip_VEBT_VEBT_o @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6078_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_VEBT_VEBT,B: list_nat,A2: list_VEBT_VEBT,B2: list_nat] :
% 0.37/0.67 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.67 = ( size_size_list_nat @ B ) )
% 0.37/0.67 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.67 = ( size_size_list_nat @ B2 ) )
% 0.37/0.67 => ( ( ( zip_VEBT_VEBT_nat @ A @ B )
% 0.37/0.67 = ( zip_VEBT_VEBT_nat @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6079_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_real,B: list_VEBT_VEBT,A2: list_real,B2: list_VEBT_VEBT] :
% 0.37/0.67 ( ( ( size_size_list_real @ A )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ B ) )
% 0.37/0.67 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 0.37/0.67 => ( ( ( zip_real_VEBT_VEBT @ A @ B )
% 0.37/0.67 = ( zip_real_VEBT_VEBT @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6080_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_real,B: list_real,A2: list_real,B2: list_real] :
% 0.37/0.67 ( ( ( size_size_list_real @ A )
% 0.37/0.67 = ( size_size_list_real @ B ) )
% 0.37/0.67 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.67 = ( size_size_list_real @ B2 ) )
% 0.37/0.67 => ( ( ( zip_real_real @ A @ B )
% 0.37/0.67 = ( zip_real_real @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6081_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_real,B: list_o,A2: list_real,B2: list_o] :
% 0.37/0.67 ( ( ( size_size_list_real @ A )
% 0.37/0.67 = ( size_size_list_o @ B ) )
% 0.37/0.67 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.67 = ( size_size_list_o @ B2 ) )
% 0.37/0.67 => ( ( ( zip_real_o @ A @ B )
% 0.37/0.67 = ( zip_real_o @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6082_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_real,B: list_nat,A2: list_real,B2: list_nat] :
% 0.37/0.67 ( ( ( size_size_list_real @ A )
% 0.37/0.67 = ( size_size_list_nat @ B ) )
% 0.37/0.67 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.67 = ( size_size_list_nat @ B2 ) )
% 0.37/0.67 => ( ( ( zip_real_nat @ A @ B )
% 0.37/0.67 = ( zip_real_nat @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6083_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_o,B: list_VEBT_VEBT,A2: list_o,B2: list_VEBT_VEBT] :
% 0.37/0.67 ( ( ( size_size_list_o @ A )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ B ) )
% 0.37/0.67 => ( ( ( size_size_list_o @ A2 )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 0.37/0.67 => ( ( ( zip_o_VEBT_VEBT @ A @ B )
% 0.37/0.67 = ( zip_o_VEBT_VEBT @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6084_zip__eq__zip__same__len,axiom,
% 0.37/0.67 ! [A: list_o,B: list_real,A2: list_o,B2: list_real] :
% 0.37/0.67 ( ( ( size_size_list_o @ A )
% 0.37/0.67 = ( size_size_list_real @ B ) )
% 0.37/0.67 => ( ( ( size_size_list_o @ A2 )
% 0.37/0.67 = ( size_size_list_real @ B2 ) )
% 0.37/0.67 => ( ( ( zip_o_real @ A @ B )
% 0.37/0.67 = ( zip_o_real @ A2 @ B2 ) )
% 0.37/0.67 = ( ( A = A2 )
% 0.37/0.67 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_eq_zip_same_len
% 0.37/0.67 thf(fact_6085_finite__lessThan,axiom,
% 0.37/0.67 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lessThan
% 0.37/0.67 thf(fact_6086_foldr__zero,axiom,
% 0.37/0.67 ! [Xs: list_nat,D: nat] :
% 0.37/0.67 ( ! [I2: nat] :
% 0.37/0.67 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 0.37/0.67 => ( ord_less_nat @ zero_zero_nat @ ( nth_nat @ Xs @ I2 ) ) )
% 0.37/0.67 => ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( minus_minus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ D ) @ D ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldr_zero
% 0.37/0.67 thf(fact_6087_sum_Oneutral__const,axiom,
% 0.37/0.67 ! [A4: set_nat] :
% 0.37/0.67 ( ( groups3542108847815614940at_nat
% 0.37/0.67 @ ^ [Uu3: nat] : zero_zero_nat
% 0.37/0.67 @ A4 )
% 0.37/0.67 = zero_zero_nat ) ).
% 0.37/0.67
% 0.37/0.67 % sum.neutral_const
% 0.37/0.67 thf(fact_6088_sum_Oneutral__const,axiom,
% 0.37/0.67 ! [A4: set_complex] :
% 0.37/0.67 ( ( groups7754918857620584856omplex
% 0.37/0.67 @ ^ [Uu3: complex] : zero_zero_complex
% 0.37/0.67 @ A4 )
% 0.37/0.67 = zero_zero_complex ) ).
% 0.37/0.67
% 0.37/0.67 % sum.neutral_const
% 0.37/0.67 thf(fact_6089_sum_Oneutral__const,axiom,
% 0.37/0.67 ! [A4: set_nat] :
% 0.37/0.67 ( ( groups6591440286371151544t_real
% 0.37/0.67 @ ^ [Uu3: nat] : zero_zero_real
% 0.37/0.67 @ A4 )
% 0.37/0.67 = zero_zero_real ) ).
% 0.37/0.67
% 0.37/0.67 % sum.neutral_const
% 0.37/0.67 thf(fact_6090_sum_Oneutral__const,axiom,
% 0.37/0.67 ! [A4: set_int] :
% 0.37/0.67 ( ( groups4538972089207619220nt_int
% 0.37/0.67 @ ^ [Uu3: int] : zero_zero_int
% 0.37/0.67 @ A4 )
% 0.37/0.67 = zero_zero_int ) ).
% 0.37/0.67
% 0.37/0.67 % sum.neutral_const
% 0.37/0.67 thf(fact_6091_singleton__conv2,axiom,
% 0.37/0.67 ! [A: vEBT_VEBT] :
% 0.37/0.67 ( ( collect_VEBT_VEBT
% 0.37/0.67 @ ( ^ [Y6: vEBT_VEBT,Z4: vEBT_VEBT] : ( Y6 = Z4 )
% 0.37/0.67 @ A ) )
% 0.37/0.67 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv2
% 0.37/0.67 thf(fact_6092_singleton__conv2,axiom,
% 0.37/0.67 ! [A: complex] :
% 0.37/0.67 ( ( collect_complex
% 0.37/0.67 @ ( ^ [Y6: complex,Z4: complex] : ( Y6 = Z4 )
% 0.37/0.67 @ A ) )
% 0.37/0.67 = ( insert_complex @ A @ bot_bot_set_complex ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv2
% 0.37/0.67 thf(fact_6093_singleton__conv2,axiom,
% 0.37/0.67 ! [A: list_nat] :
% 0.37/0.67 ( ( collect_list_nat
% 0.37/0.67 @ ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 )
% 0.37/0.67 @ A ) )
% 0.37/0.67 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv2
% 0.37/0.67 thf(fact_6094_singleton__conv2,axiom,
% 0.37/0.67 ! [A: set_nat] :
% 0.37/0.67 ( ( collect_set_nat
% 0.37/0.67 @ ( ^ [Y6: set_nat,Z4: set_nat] : ( Y6 = Z4 )
% 0.37/0.67 @ A ) )
% 0.37/0.67 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv2
% 0.37/0.67 thf(fact_6095_singleton__conv2,axiom,
% 0.37/0.67 ! [A: nat] :
% 0.37/0.67 ( ( collect_nat
% 0.37/0.67 @ ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.67 @ A ) )
% 0.37/0.67 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv2
% 0.37/0.67 thf(fact_6096_singleton__conv2,axiom,
% 0.37/0.67 ! [A: int] :
% 0.37/0.67 ( ( collect_int
% 0.37/0.67 @ ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.67 @ A ) )
% 0.37/0.67 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv2
% 0.37/0.67 thf(fact_6097_singleton__conv2,axiom,
% 0.37/0.67 ! [A: $o] :
% 0.37/0.67 ( ( collect_o
% 0.37/0.67 @ ( ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 0.37/0.67 @ A ) )
% 0.37/0.67 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv2
% 0.37/0.67 thf(fact_6098_singleton__conv,axiom,
% 0.37/0.67 ! [A: vEBT_VEBT] :
% 0.37/0.67 ( ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( X4 = A ) )
% 0.37/0.67 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv
% 0.37/0.67 thf(fact_6099_singleton__conv,axiom,
% 0.37/0.67 ! [A: complex] :
% 0.37/0.67 ( ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] : ( X4 = A ) )
% 0.37/0.67 = ( insert_complex @ A @ bot_bot_set_complex ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv
% 0.37/0.67 thf(fact_6100_singleton__conv,axiom,
% 0.37/0.67 ! [A: list_nat] :
% 0.37/0.67 ( ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] : ( X4 = A ) )
% 0.37/0.67 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv
% 0.37/0.67 thf(fact_6101_singleton__conv,axiom,
% 0.37/0.67 ! [A: set_nat] :
% 0.37/0.67 ( ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] : ( X4 = A ) )
% 0.37/0.67 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv
% 0.37/0.67 thf(fact_6102_singleton__conv,axiom,
% 0.37/0.67 ! [A: nat] :
% 0.37/0.67 ( ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] : ( X4 = A ) )
% 0.37/0.67 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv
% 0.37/0.67 thf(fact_6103_singleton__conv,axiom,
% 0.37/0.67 ! [A: int] :
% 0.37/0.67 ( ( collect_int
% 0.37/0.67 @ ^ [X4: int] : ( X4 = A ) )
% 0.37/0.67 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv
% 0.37/0.67 thf(fact_6104_singleton__conv,axiom,
% 0.37/0.67 ! [A: $o] :
% 0.37/0.67 ( ( collect_o
% 0.37/0.67 @ ^ [X4: $o] : ( X4 = A ) )
% 0.37/0.67 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.37/0.67
% 0.37/0.67 % singleton_conv
% 0.37/0.67 thf(fact_6105_finite__Collect__less__nat,axiom,
% 0.37/0.67 ! [K: nat] :
% 0.37/0.67 ( finite_finite_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [N6: nat] : ( ord_less_nat @ N6 @ K ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_less_nat
% 0.37/0.67 thf(fact_6106_finite__Collect__le__nat,axiom,
% 0.37/0.67 ! [K: nat] :
% 0.37/0.67 ( finite_finite_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [N6: nat] : ( ord_less_eq_nat @ N6 @ K ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_le_nat
% 0.37/0.67 thf(fact_6107_card__Collect__less__nat,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( finite_card_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 0.37/0.67 = N ) ).
% 0.37/0.67
% 0.37/0.67 % card_Collect_less_nat
% 0.37/0.67 thf(fact_6108_of__nat__eq__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ( semiri681578069525770553at_rat @ M )
% 0.37/0.67 = zero_zero_rat )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_0_iff
% 0.37/0.67 thf(fact_6109_of__nat__eq__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ( semiri1316708129612266289at_nat @ M )
% 0.37/0.67 = zero_zero_nat )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_0_iff
% 0.37/0.67 thf(fact_6110_of__nat__eq__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ( semiri5074537144036343181t_real @ M )
% 0.37/0.67 = zero_zero_real )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_0_iff
% 0.37/0.67 thf(fact_6111_of__nat__eq__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ( semiri1314217659103216013at_int @ M )
% 0.37/0.67 = zero_zero_int )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_0_iff
% 0.37/0.67 thf(fact_6112_of__nat__eq__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ( semiri4939895301339042750nteger @ M )
% 0.37/0.67 = zero_z3403309356797280102nteger )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_0_iff
% 0.37/0.67 thf(fact_6113_of__nat__0__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( zero_zero_rat
% 0.37/0.67 = ( semiri681578069525770553at_rat @ N ) )
% 0.37/0.67 = ( zero_zero_nat = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_eq_iff
% 0.37/0.67 thf(fact_6114_of__nat__0__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( zero_zero_nat
% 0.37/0.67 = ( semiri1316708129612266289at_nat @ N ) )
% 0.37/0.67 = ( zero_zero_nat = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_eq_iff
% 0.37/0.67 thf(fact_6115_of__nat__0__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( zero_zero_real
% 0.37/0.67 = ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.67 = ( zero_zero_nat = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_eq_iff
% 0.37/0.67 thf(fact_6116_of__nat__0__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( zero_zero_int
% 0.37/0.67 = ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.67 = ( zero_zero_nat = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_eq_iff
% 0.37/0.67 thf(fact_6117_of__nat__0__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( zero_z3403309356797280102nteger
% 0.37/0.67 = ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.67 = ( zero_zero_nat = N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_eq_iff
% 0.37/0.67 thf(fact_6118_semiring__1__class_Oof__nat__0,axiom,
% 0.37/0.67 ( ( semiri2565882477558803405uint32 @ zero_zero_nat )
% 0.37/0.67 = zero_zero_uint32 ) ).
% 0.37/0.67
% 0.37/0.67 % semiring_1_class.of_nat_0
% 0.37/0.67 thf(fact_6119_semiring__1__class_Oof__nat__0,axiom,
% 0.37/0.67 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.37/0.67 = zero_zero_rat ) ).
% 0.37/0.67
% 0.37/0.67 % semiring_1_class.of_nat_0
% 0.37/0.67 thf(fact_6120_semiring__1__class_Oof__nat__0,axiom,
% 0.37/0.67 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.37/0.67 = zero_zero_nat ) ).
% 0.37/0.67
% 0.37/0.67 % semiring_1_class.of_nat_0
% 0.37/0.67 thf(fact_6121_semiring__1__class_Oof__nat__0,axiom,
% 0.37/0.67 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 0.37/0.67 = zero_zero_real ) ).
% 0.37/0.67
% 0.37/0.67 % semiring_1_class.of_nat_0
% 0.37/0.67 thf(fact_6122_semiring__1__class_Oof__nat__0,axiom,
% 0.37/0.67 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.37/0.67 = zero_zero_int ) ).
% 0.37/0.67
% 0.37/0.67 % semiring_1_class.of_nat_0
% 0.37/0.67 thf(fact_6123_semiring__1__class_Oof__nat__0,axiom,
% 0.37/0.67 ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 0.37/0.67 = zero_z3403309356797280102nteger ) ).
% 0.37/0.67
% 0.37/0.67 % semiring_1_class.of_nat_0
% 0.37/0.67 thf(fact_6124_of__nat__less__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.37/0.67 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_iff
% 0.37/0.67 thf(fact_6125_of__nat__less__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.37/0.67 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_iff
% 0.37/0.67 thf(fact_6126_of__nat__less__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.67 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_iff
% 0.37/0.67 thf(fact_6127_of__nat__less__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.67 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_iff
% 0.37/0.67 thf(fact_6128_of__nat__less__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.67 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_iff
% 0.37/0.67 thf(fact_6129_of__nat__le__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_iff
% 0.37/0.67 thf(fact_6130_of__nat__le__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_iff
% 0.37/0.67 thf(fact_6131_of__nat__le__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.37/0.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_iff
% 0.37/0.67 thf(fact_6132_of__nat__le__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.37/0.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_iff
% 0.37/0.67 thf(fact_6133_of__nat__le__iff,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_iff
% 0.37/0.67 thf(fact_6134_of__nat__add,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 0.37/0.67 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_add
% 0.37/0.67 thf(fact_6135_of__nat__add,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.37/0.67 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_add
% 0.37/0.67 thf(fact_6136_of__nat__add,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 0.37/0.67 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_add
% 0.37/0.67 thf(fact_6137_of__nat__add,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 0.37/0.67 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_add
% 0.37/0.67 thf(fact_6138_of__nat__add,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N ) )
% 0.37/0.67 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_add
% 0.37/0.67 thf(fact_6139_of__nat__1,axiom,
% 0.37/0.67 ( ( semiri2565882477558803405uint32 @ one_one_nat )
% 0.37/0.67 = one_one_uint32 ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1
% 0.37/0.67 thf(fact_6140_of__nat__1,axiom,
% 0.37/0.67 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.37/0.67 = one_one_rat ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1
% 0.37/0.67 thf(fact_6141_of__nat__1,axiom,
% 0.37/0.67 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.37/0.67 = one_one_nat ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1
% 0.37/0.67 thf(fact_6142_of__nat__1,axiom,
% 0.37/0.67 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 0.37/0.67 = one_one_real ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1
% 0.37/0.67 thf(fact_6143_of__nat__1,axiom,
% 0.37/0.67 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.37/0.67 = one_one_int ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1
% 0.37/0.67 thf(fact_6144_of__nat__1,axiom,
% 0.37/0.67 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 0.37/0.67 = one_one_Code_integer ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1
% 0.37/0.67 thf(fact_6145_of__nat__1__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( one_one_rat
% 0.37/0.67 = ( semiri681578069525770553at_rat @ N ) )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1_eq_iff
% 0.37/0.67 thf(fact_6146_of__nat__1__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( one_one_nat
% 0.37/0.67 = ( semiri1316708129612266289at_nat @ N ) )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1_eq_iff
% 0.37/0.67 thf(fact_6147_of__nat__1__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( one_one_real
% 0.37/0.67 = ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1_eq_iff
% 0.37/0.67 thf(fact_6148_of__nat__1__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( one_one_int
% 0.37/0.67 = ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1_eq_iff
% 0.37/0.67 thf(fact_6149_of__nat__1__eq__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( one_one_Code_integer
% 0.37/0.67 = ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_1_eq_iff
% 0.37/0.67 thf(fact_6150_of__nat__eq__1__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ( semiri681578069525770553at_rat @ N )
% 0.37/0.67 = one_one_rat )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_1_iff
% 0.37/0.67 thf(fact_6151_of__nat__eq__1__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ( semiri1316708129612266289at_nat @ N )
% 0.37/0.67 = one_one_nat )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_1_iff
% 0.37/0.67 thf(fact_6152_of__nat__eq__1__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ( semiri5074537144036343181t_real @ N )
% 0.37/0.67 = one_one_real )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_1_iff
% 0.37/0.67 thf(fact_6153_of__nat__eq__1__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ( semiri1314217659103216013at_int @ N )
% 0.37/0.67 = one_one_int )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_1_iff
% 0.37/0.67 thf(fact_6154_of__nat__eq__1__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ( semiri4939895301339042750nteger @ N )
% 0.37/0.67 = one_one_Code_integer )
% 0.37/0.67 = ( N = one_one_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_eq_1_iff
% 0.37/0.67 thf(fact_6155_of__nat__mult,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri2565882477558803405uint32 @ ( times_times_nat @ M @ N ) )
% 0.37/0.67 = ( times_times_uint32 @ ( semiri2565882477558803405uint32 @ M ) @ ( semiri2565882477558803405uint32 @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_mult
% 0.37/0.67 thf(fact_6156_of__nat__mult,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 0.37/0.67 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_mult
% 0.37/0.67 thf(fact_6157_of__nat__mult,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 0.37/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_mult
% 0.37/0.67 thf(fact_6158_of__nat__mult,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 0.37/0.67 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_mult
% 0.37/0.67 thf(fact_6159_of__nat__mult,axiom,
% 0.37/0.67 ! [M: nat,N: nat] :
% 0.37/0.67 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 0.37/0.67 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_mult
% 0.37/0.67 thf(fact_6160_lessThan__subset__iff,axiom,
% 0.37/0.67 ! [X: rat,Y: rat] :
% 0.37/0.67 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 0.37/0.67 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_subset_iff
% 0.37/0.67 thf(fact_6161_lessThan__subset__iff,axiom,
% 0.37/0.67 ! [X: num,Y: num] :
% 0.37/0.67 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 0.37/0.67 = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_subset_iff
% 0.37/0.67 thf(fact_6162_lessThan__subset__iff,axiom,
% 0.37/0.67 ! [X: nat,Y: nat] :
% 0.37/0.67 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 0.37/0.67 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_subset_iff
% 0.37/0.67 thf(fact_6163_lessThan__subset__iff,axiom,
% 0.37/0.67 ! [X: int,Y: int] :
% 0.37/0.67 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 0.37/0.67 = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_subset_iff
% 0.37/0.67 thf(fact_6164_lessThan__subset__iff,axiom,
% 0.37/0.67 ! [X: real,Y: real] :
% 0.37/0.67 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 0.37/0.67 = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_subset_iff
% 0.37/0.67 thf(fact_6165_lessThan__0,axiom,
% 0.37/0.67 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.37/0.67 = bot_bot_set_nat ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_0
% 0.37/0.67 thf(fact_6166_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > uint32] :
% 0.37/0.67 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.67 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups8325533452322294502uint32
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups8325533452322294502uint32
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6167_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_real,A: real,B: real > uint32] :
% 0.37/0.67 ( ( finite_finite_real @ S3 )
% 0.37/0.67 => ( ( ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups5944083974425963860uint32
% 0.37/0.67 @ ^ [K3: real] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups5944083974425963860uint32
% 0.37/0.67 @ ^ [K3: real] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6168_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_nat,A: nat,B: nat > uint32] :
% 0.37/0.67 ( ( finite_finite_nat @ S3 )
% 0.37/0.67 => ( ( ( member_nat @ A @ S3 )
% 0.37/0.67 => ( ( groups833757482993574392uint32
% 0.37/0.67 @ ^ [K3: nat] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_nat @ A @ S3 )
% 0.37/0.67 => ( ( groups833757482993574392uint32
% 0.37/0.67 @ ^ [K3: nat] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6169_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_int,A: int,B: int > uint32] :
% 0.37/0.67 ( ( finite_finite_int @ S3 )
% 0.37/0.67 => ( ( ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups5712668689793887828uint32
% 0.37/0.67 @ ^ [K3: int] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups5712668689793887828uint32
% 0.37/0.67 @ ^ [K3: int] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6170_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_complex,A: complex,B: complex > uint32] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.67 => ( ( ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups8736914816313324502uint32
% 0.37/0.67 @ ^ [K3: complex] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups8736914816313324502uint32
% 0.37/0.67 @ ^ [K3: complex] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6171_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_Code_integer,A: code_integer,B: code_integer > uint32] :
% 0.37/0.67 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.67 => ( ( ( member_Code_integer @ A @ S3 )
% 0.37/0.67 => ( ( groups8847630953604152069uint32
% 0.37/0.67 @ ^ [K3: code_integer] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_Code_integer @ A @ S3 )
% 0.37/0.67 => ( ( groups8847630953604152069uint32
% 0.37/0.67 @ ^ [K3: code_integer] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6172_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 0.37/0.67 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.67 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups2240296850493347238T_real
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups2240296850493347238T_real
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6173_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_real,A: real,B: real > real] :
% 0.37/0.67 ( ( finite_finite_real @ S3 )
% 0.37/0.67 => ( ( ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups8097168146408367636l_real
% 0.37/0.67 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups8097168146408367636l_real
% 0.37/0.67 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6174_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_int,A: int,B: int > real] :
% 0.37/0.67 ( ( finite_finite_int @ S3 )
% 0.37/0.67 => ( ( ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups8778361861064173332t_real
% 0.37/0.67 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups8778361861064173332t_real
% 0.37/0.67 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6175_sum_Odelta_H,axiom,
% 0.37/0.67 ! [S3: set_complex,A: complex,B: complex > real] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.67 => ( ( ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups5808333547571424918x_real
% 0.37/0.67 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups5808333547571424918x_real
% 0.37/0.67 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta'
% 0.37/0.67 thf(fact_6176_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > uint32] :
% 0.37/0.67 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.67 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups8325533452322294502uint32
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups8325533452322294502uint32
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6177_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_real,A: real,B: real > uint32] :
% 0.37/0.67 ( ( finite_finite_real @ S3 )
% 0.37/0.67 => ( ( ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups5944083974425963860uint32
% 0.37/0.67 @ ^ [K3: real] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups5944083974425963860uint32
% 0.37/0.67 @ ^ [K3: real] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6178_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_nat,A: nat,B: nat > uint32] :
% 0.37/0.67 ( ( finite_finite_nat @ S3 )
% 0.37/0.67 => ( ( ( member_nat @ A @ S3 )
% 0.37/0.67 => ( ( groups833757482993574392uint32
% 0.37/0.67 @ ^ [K3: nat] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_nat @ A @ S3 )
% 0.37/0.67 => ( ( groups833757482993574392uint32
% 0.37/0.67 @ ^ [K3: nat] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6179_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_int,A: int,B: int > uint32] :
% 0.37/0.67 ( ( finite_finite_int @ S3 )
% 0.37/0.67 => ( ( ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups5712668689793887828uint32
% 0.37/0.67 @ ^ [K3: int] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups5712668689793887828uint32
% 0.37/0.67 @ ^ [K3: int] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6180_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_complex,A: complex,B: complex > uint32] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.67 => ( ( ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups8736914816313324502uint32
% 0.37/0.67 @ ^ [K3: complex] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups8736914816313324502uint32
% 0.37/0.67 @ ^ [K3: complex] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6181_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_Code_integer,A: code_integer,B: code_integer > uint32] :
% 0.37/0.67 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.67 => ( ( ( member_Code_integer @ A @ S3 )
% 0.37/0.67 => ( ( groups8847630953604152069uint32
% 0.37/0.67 @ ^ [K3: code_integer] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_Code_integer @ A @ S3 )
% 0.37/0.67 => ( ( groups8847630953604152069uint32
% 0.37/0.67 @ ^ [K3: code_integer] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_uint32 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6182_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 0.37/0.67 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.67 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups2240296850493347238T_real
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.67 => ( ( groups2240296850493347238T_real
% 0.37/0.67 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6183_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_real,A: real,B: real > real] :
% 0.37/0.67 ( ( finite_finite_real @ S3 )
% 0.37/0.67 => ( ( ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups8097168146408367636l_real
% 0.37/0.67 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_real @ A @ S3 )
% 0.37/0.67 => ( ( groups8097168146408367636l_real
% 0.37/0.67 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6184_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_int,A: int,B: int > real] :
% 0.37/0.67 ( ( finite_finite_int @ S3 )
% 0.37/0.67 => ( ( ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups8778361861064173332t_real
% 0.37/0.67 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_int @ A @ S3 )
% 0.37/0.67 => ( ( groups8778361861064173332t_real
% 0.37/0.67 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6185_sum_Odelta,axiom,
% 0.37/0.67 ! [S3: set_complex,A: complex,B: complex > real] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.67 => ( ( ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups5808333547571424918x_real
% 0.37/0.67 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = ( B @ A ) ) )
% 0.37/0.67 & ( ~ ( member_complex @ A @ S3 )
% 0.37/0.67 => ( ( groups5808333547571424918x_real
% 0.37/0.67 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.37/0.67 @ S3 )
% 0.37/0.67 = zero_zero_real ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.delta
% 0.37/0.67 thf(fact_6186_foldl__length,axiom,
% 0.37/0.67 ! [L: list_VEBT_VEBT] :
% 0.37/0.67 ( ( foldl_nat_VEBT_VEBT
% 0.37/0.67 @ ^ [I3: nat,X4: vEBT_VEBT] : ( suc @ I3 )
% 0.37/0.67 @ zero_zero_nat
% 0.37/0.67 @ L )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldl_length
% 0.37/0.67 thf(fact_6187_foldl__length,axiom,
% 0.37/0.67 ! [L: list_real] :
% 0.37/0.67 ( ( foldl_nat_real
% 0.37/0.67 @ ^ [I3: nat,X4: real] : ( suc @ I3 )
% 0.37/0.67 @ zero_zero_nat
% 0.37/0.67 @ L )
% 0.37/0.67 = ( size_size_list_real @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldl_length
% 0.37/0.67 thf(fact_6188_foldl__length,axiom,
% 0.37/0.67 ! [L: list_o] :
% 0.37/0.67 ( ( foldl_nat_o
% 0.37/0.67 @ ^ [I3: nat,X4: $o] : ( suc @ I3 )
% 0.37/0.67 @ zero_zero_nat
% 0.37/0.67 @ L )
% 0.37/0.67 = ( size_size_list_o @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldl_length
% 0.37/0.67 thf(fact_6189_foldl__length,axiom,
% 0.37/0.67 ! [L: list_nat] :
% 0.37/0.67 ( ( foldl_nat_nat
% 0.37/0.67 @ ^ [I3: nat,X4: nat] : ( suc @ I3 )
% 0.37/0.67 @ zero_zero_nat
% 0.37/0.67 @ L )
% 0.37/0.67 = ( size_size_list_nat @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldl_length
% 0.37/0.67 thf(fact_6190_card__Collect__le__nat,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( finite_card_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 0.37/0.67 = ( suc @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % card_Collect_le_nat
% 0.37/0.67 thf(fact_6191_finite__Collect__subsets,axiom,
% 0.37/0.67 ! [A4: set_nat] :
% 0.37/0.67 ( ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( finite1152437895449049373et_nat
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A4 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_subsets
% 0.37/0.67 thf(fact_6192_finite__Collect__subsets,axiom,
% 0.37/0.67 ! [A4: set_complex] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.67 => ( finite6551019134538273531omplex
% 0.37/0.67 @ ( collect_set_complex
% 0.37/0.67 @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A4 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_subsets
% 0.37/0.67 thf(fact_6193_finite__Collect__subsets,axiom,
% 0.37/0.67 ! [A4: set_Code_integer] :
% 0.37/0.67 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.67 => ( finite6931041176100689706nteger
% 0.37/0.67 @ ( collec574505750873337192nteger
% 0.37/0.67 @ ^ [B6: set_Code_integer] : ( ord_le7084787975880047091nteger @ B6 @ A4 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_subsets
% 0.37/0.67 thf(fact_6194_finite__Collect__subsets,axiom,
% 0.37/0.67 ! [A4: set_int] :
% 0.37/0.67 ( ( finite_finite_int @ A4 )
% 0.37/0.67 => ( finite6197958912794628473et_int
% 0.37/0.67 @ ( collect_set_int
% 0.37/0.67 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A4 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_Collect_subsets
% 0.37/0.67 thf(fact_6195_of__nat__le__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_0_iff
% 0.37/0.67 thf(fact_6196_of__nat__le__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_0_iff
% 0.37/0.67 thf(fact_6197_of__nat__le__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_0_iff
% 0.37/0.67 thf(fact_6198_of__nat__le__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_0_iff
% 0.37/0.67 thf(fact_6199_of__nat__le__0__iff,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 0.37/0.67 = ( M = zero_zero_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_0_iff
% 0.37/0.67 thf(fact_6200_of__nat__Suc,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( semiri2565882477558803405uint32 @ ( suc @ M ) )
% 0.37/0.67 = ( plus_plus_uint32 @ one_one_uint32 @ ( semiri2565882477558803405uint32 @ M ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_Suc
% 0.37/0.67 thf(fact_6201_of__nat__Suc,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.37/0.67 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_Suc
% 0.37/0.67 thf(fact_6202_of__nat__Suc,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.37/0.67 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_Suc
% 0.37/0.67 thf(fact_6203_of__nat__Suc,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 0.37/0.67 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_Suc
% 0.37/0.67 thf(fact_6204_of__nat__Suc,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.37/0.67 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_Suc
% 0.37/0.67 thf(fact_6205_of__nat__Suc,axiom,
% 0.37/0.67 ! [M: nat] :
% 0.37/0.67 ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 0.37/0.67 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_Suc
% 0.37/0.67 thf(fact_6206_sum_OlessThan__Suc,axiom,
% 0.37/0.67 ! [G: nat > rat,N: nat] :
% 0.37/0.67 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.67 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.lessThan_Suc
% 0.37/0.67 thf(fact_6207_sum_OlessThan__Suc,axiom,
% 0.37/0.67 ! [G: nat > int,N: nat] :
% 0.37/0.67 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.67 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.lessThan_Suc
% 0.37/0.67 thf(fact_6208_sum_OlessThan__Suc,axiom,
% 0.37/0.67 ! [G: nat > nat,N: nat] :
% 0.37/0.67 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.67 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.lessThan_Suc
% 0.37/0.67 thf(fact_6209_sum_OlessThan__Suc,axiom,
% 0.37/0.67 ! [G: nat > real,N: nat] :
% 0.37/0.67 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.67 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum.lessThan_Suc
% 0.37/0.67 thf(fact_6210_single__Diff__lessThan,axiom,
% 0.37/0.67 ! [K: $o] :
% 0.37/0.67 ( ( minus_minus_set_o @ ( insert_o @ K @ bot_bot_set_o ) @ ( set_ord_lessThan_o @ K ) )
% 0.37/0.67 = ( insert_o @ K @ bot_bot_set_o ) ) ).
% 0.37/0.67
% 0.37/0.67 % single_Diff_lessThan
% 0.37/0.67 thf(fact_6211_single__Diff__lessThan,axiom,
% 0.37/0.67 ! [K: nat] :
% 0.37/0.67 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 0.37/0.67 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 0.37/0.67
% 0.37/0.67 % single_Diff_lessThan
% 0.37/0.67 thf(fact_6212_single__Diff__lessThan,axiom,
% 0.37/0.67 ! [K: int] :
% 0.37/0.67 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 0.37/0.67 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 0.37/0.67
% 0.37/0.67 % single_Diff_lessThan
% 0.37/0.67 thf(fact_6213_single__Diff__lessThan,axiom,
% 0.37/0.67 ! [K: real] :
% 0.37/0.67 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 0.37/0.67 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 0.37/0.67
% 0.37/0.67 % single_Diff_lessThan
% 0.37/0.67 thf(fact_6214_Cons__listrel1__Cons,axiom,
% 0.37/0.67 ! [X: $o,Xs: list_o,Y: $o,Ys: list_o,R: set_Product_prod_o_o] :
% 0.37/0.67 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Ys ) ) @ ( listrel1_o @ R ) )
% 0.37/0.67 = ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 0.37/0.67 & ( Xs = Ys ) )
% 0.37/0.67 | ( ( X = Y )
% 0.37/0.67 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( listrel1_o @ R ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Cons_listrel1_Cons
% 0.37/0.67 thf(fact_6215_Cons__listrel1__Cons,axiom,
% 0.37/0.67 ! [X: uint32,Xs: list_uint32,Y: uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.67 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Ys ) ) @ ( listrel1_uint32 @ R ) )
% 0.37/0.67 = ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 0.37/0.67 & ( Xs = Ys ) )
% 0.37/0.67 | ( ( X = Y )
% 0.37/0.67 & ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( listrel1_uint32 @ R ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Cons_listrel1_Cons
% 0.37/0.67 thf(fact_6216_Cons__listrel1__Cons,axiom,
% 0.37/0.67 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.67 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 0.37/0.67 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.37/0.67 & ( Xs = Ys ) )
% 0.37/0.67 | ( ( X = Y )
% 0.37/0.67 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Cons_listrel1_Cons
% 0.37/0.67 thf(fact_6217_Cons__listrel1__Cons,axiom,
% 0.37/0.67 ! [X: int,Xs: list_int,Y: int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.67 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel1_int @ R ) )
% 0.37/0.67 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 0.37/0.67 & ( Xs = Ys ) )
% 0.37/0.67 | ( ( X = Y )
% 0.37/0.67 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Cons_listrel1_Cons
% 0.37/0.67 thf(fact_6218_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: int,Xs: list_int,Y: nat,Ys: list_nat] :
% 0.37/0.67 ( ( zip_int_nat @ ( cons_int @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P7512249878480867347nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( zip_int_nat @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6219_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: int,Xs: list_int,Y: $o,Ys: list_o] :
% 0.37/0.67 ( ( zip_int_o @ ( cons_int @ X @ Xs ) @ ( cons_o @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P7321330006258091179_int_o @ ( product_Pair_int_o @ X @ Y ) @ ( zip_int_o @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6220_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: nat,Xs: list_nat,Y: int,Ys: list_int] :
% 0.37/0.67 ( ( zip_nat_int @ ( cons_nat @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( zip_nat_int @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6221_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: nat,Xs: list_nat,Y: $o,Ys: list_o] :
% 0.37/0.67 ( ( zip_nat_o @ ( cons_nat @ X @ Xs ) @ ( cons_o @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P9142372351690779143_nat_o @ ( product_Pair_nat_o @ X @ Y ) @ ( zip_nat_o @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6222_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: $o,Xs: list_o,Y: int,Ys: list_int] :
% 0.37/0.67 ( ( zip_o_int @ ( cons_o @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P1455986808126089405_o_int @ ( product_Pair_o_int @ X @ Y ) @ ( zip_o_int @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6223_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: $o,Xs: list_o,Y: nat,Ys: list_nat] :
% 0.37/0.67 ( ( zip_o_nat @ ( cons_o @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P5633837827635286113_o_nat @ ( product_Pair_o_nat @ X @ Y ) @ ( zip_o_nat @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6224_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: $o,Xs: list_o,Y: $o,Ys: list_o] :
% 0.37/0.67 ( ( zip_o_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P8766293264717362397od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( zip_o_o @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6225_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: uint32,Xs: list_uint32,Y: uint32,Ys: list_uint32] :
% 0.37/0.67 ( ( zip_uint32_uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P3149448846263281007uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( zip_uint32_uint32 @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6226_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 0.37/0.67 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6227_zip__Cons__Cons,axiom,
% 0.37/0.67 ! [X: int,Xs: list_int,Y: int,Ys: list_int] :
% 0.37/0.67 ( ( zip_int_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 0.37/0.67 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs @ Ys ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % zip_Cons_Cons
% 0.37/0.67 thf(fact_6228_Max__const,axiom,
% 0.37/0.67 ! [A4: set_nat,C2: int] :
% 0.37/0.67 ( ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.67 => ( ( lattic8263393255366662781ax_int
% 0.37/0.67 @ ( image_nat_int
% 0.37/0.67 @ ^ [Uu3: nat] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Max_const
% 0.37/0.67 thf(fact_6229_Max__const,axiom,
% 0.37/0.67 ! [A4: set_int,C2: int] :
% 0.37/0.67 ( ( finite_finite_int @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_int )
% 0.37/0.67 => ( ( lattic8263393255366662781ax_int
% 0.37/0.67 @ ( image_int_int
% 0.37/0.67 @ ^ [Uu3: int] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Max_const
% 0.37/0.67 thf(fact_6230_Max__const,axiom,
% 0.37/0.67 ! [A4: set_complex,C2: nat] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_complex )
% 0.37/0.67 => ( ( lattic8265883725875713057ax_nat
% 0.37/0.67 @ ( image_complex_nat
% 0.37/0.67 @ ^ [Uu3: complex] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Max_const
% 0.37/0.67 thf(fact_6231_Max__const,axiom,
% 0.37/0.67 ! [A4: set_Code_integer,C2: nat] :
% 0.37/0.67 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.67 => ( ( lattic8265883725875713057ax_nat
% 0.37/0.67 @ ( image_951025933927791156er_nat
% 0.37/0.67 @ ^ [Uu3: code_integer] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Max_const
% 0.37/0.67 thf(fact_6232_Max__const,axiom,
% 0.37/0.67 ! [A4: set_nat,C2: nat] :
% 0.37/0.67 ( ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.67 => ( ( lattic8265883725875713057ax_nat
% 0.37/0.67 @ ( image_nat_nat
% 0.37/0.67 @ ^ [Uu3: nat] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Max_const
% 0.37/0.67 thf(fact_6233_Max__const,axiom,
% 0.37/0.67 ! [A4: set_int,C2: nat] :
% 0.37/0.67 ( ( finite_finite_int @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_int )
% 0.37/0.67 => ( ( lattic8265883725875713057ax_nat
% 0.37/0.67 @ ( image_int_nat
% 0.37/0.67 @ ^ [Uu3: int] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Max_const
% 0.37/0.67 thf(fact_6234_Max__const,axiom,
% 0.37/0.67 ! [A4: set_o,C2: nat] :
% 0.37/0.67 ( ( finite_finite_o @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_o )
% 0.37/0.67 => ( ( lattic8265883725875713057ax_nat
% 0.37/0.67 @ ( image_o_nat
% 0.37/0.67 @ ^ [Uu3: $o] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Max_const
% 0.37/0.67 thf(fact_6235_Min__const,axiom,
% 0.37/0.67 ! [A4: set_nat,C2: int] :
% 0.37/0.67 ( ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.67 => ( ( lattic8718645017227715691in_int
% 0.37/0.67 @ ( image_nat_int
% 0.37/0.67 @ ^ [Uu3: nat] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Min_const
% 0.37/0.67 thf(fact_6236_Min__const,axiom,
% 0.37/0.67 ! [A4: set_int,C2: int] :
% 0.37/0.67 ( ( finite_finite_int @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_int )
% 0.37/0.67 => ( ( lattic8718645017227715691in_int
% 0.37/0.67 @ ( image_int_int
% 0.37/0.67 @ ^ [Uu3: int] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Min_const
% 0.37/0.67 thf(fact_6237_Min__const,axiom,
% 0.37/0.67 ! [A4: set_complex,C2: nat] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_complex )
% 0.37/0.67 => ( ( lattic8721135487736765967in_nat
% 0.37/0.67 @ ( image_complex_nat
% 0.37/0.67 @ ^ [Uu3: complex] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Min_const
% 0.37/0.67 thf(fact_6238_Min__const,axiom,
% 0.37/0.67 ! [A4: set_Code_integer,C2: nat] :
% 0.37/0.67 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bo3990330152332043303nteger )
% 0.37/0.67 => ( ( lattic8721135487736765967in_nat
% 0.37/0.67 @ ( image_951025933927791156er_nat
% 0.37/0.67 @ ^ [Uu3: code_integer] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Min_const
% 0.37/0.67 thf(fact_6239_Min__const,axiom,
% 0.37/0.67 ! [A4: set_nat,C2: nat] :
% 0.37/0.67 ( ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.67 => ( ( lattic8721135487736765967in_nat
% 0.37/0.67 @ ( image_nat_nat
% 0.37/0.67 @ ^ [Uu3: nat] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Min_const
% 0.37/0.67 thf(fact_6240_Min__const,axiom,
% 0.37/0.67 ! [A4: set_int,C2: nat] :
% 0.37/0.67 ( ( finite_finite_int @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_int )
% 0.37/0.67 => ( ( lattic8721135487736765967in_nat
% 0.37/0.67 @ ( image_int_nat
% 0.37/0.67 @ ^ [Uu3: int] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Min_const
% 0.37/0.67 thf(fact_6241_Min__const,axiom,
% 0.37/0.67 ! [A4: set_o,C2: nat] :
% 0.37/0.67 ( ( finite_finite_o @ A4 )
% 0.37/0.67 => ( ( A4 != bot_bot_set_o )
% 0.37/0.67 => ( ( lattic8721135487736765967in_nat
% 0.37/0.67 @ ( image_o_nat
% 0.37/0.67 @ ^ [Uu3: $o] : C2
% 0.37/0.67 @ A4 ) )
% 0.37/0.67 = C2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Min_const
% 0.37/0.67 thf(fact_6242_foldr__length,axiom,
% 0.37/0.67 ! [L: list_VEBT_VEBT] :
% 0.37/0.67 ( ( foldr_VEBT_VEBT_nat
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : suc
% 0.37/0.67 @ L
% 0.37/0.67 @ zero_zero_nat )
% 0.37/0.67 = ( size_s6755466524823107622T_VEBT @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldr_length
% 0.37/0.67 thf(fact_6243_foldr__length,axiom,
% 0.37/0.67 ! [L: list_real] :
% 0.37/0.67 ( ( foldr_real_nat
% 0.37/0.67 @ ^ [X4: real] : suc
% 0.37/0.67 @ L
% 0.37/0.67 @ zero_zero_nat )
% 0.37/0.67 = ( size_size_list_real @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldr_length
% 0.37/0.67 thf(fact_6244_foldr__length,axiom,
% 0.37/0.67 ! [L: list_o] :
% 0.37/0.67 ( ( foldr_o_nat
% 0.37/0.67 @ ^ [X4: $o] : suc
% 0.37/0.67 @ L
% 0.37/0.67 @ zero_zero_nat )
% 0.37/0.67 = ( size_size_list_o @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldr_length
% 0.37/0.67 thf(fact_6245_foldr__length,axiom,
% 0.37/0.67 ! [L: list_nat] :
% 0.37/0.67 ( ( foldr_nat_nat
% 0.37/0.67 @ ^ [X4: nat] : suc
% 0.37/0.67 @ L
% 0.37/0.67 @ zero_zero_nat )
% 0.37/0.67 = ( size_size_list_nat @ L ) ) ).
% 0.37/0.67
% 0.37/0.67 % foldr_length
% 0.37/0.67 thf(fact_6246_of__nat__0__less__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.37/0.67 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_less_iff
% 0.37/0.67 thf(fact_6247_of__nat__0__less__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 0.37/0.67 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_less_iff
% 0.37/0.67 thf(fact_6248_of__nat__0__less__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.67 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_less_iff
% 0.37/0.67 thf(fact_6249_of__nat__0__less__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.67 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_less_iff
% 0.37/0.67 thf(fact_6250_of__nat__0__less__iff,axiom,
% 0.37/0.67 ! [N: nat] :
% 0.37/0.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.67 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_0_less_iff
% 0.37/0.67 thf(fact_6251_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_less_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6252_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_less_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6253_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_less_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6254_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_less_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6255_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_less_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6256_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.37/0.67 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6257_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.37/0.67 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6258_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.37/0.67 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6259_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.37/0.67 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6260_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 0.37/0.67 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_less_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6261_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.37/0.67 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6262_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 0.37/0.67 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6263_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.37/0.67 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6264_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.37/0.67 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6265_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.37/0.67 ! [B: nat,W2: nat,X: nat] :
% 0.37/0.67 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.37/0.67 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_le_of_nat_power_cancel_iff
% 0.37/0.67 thf(fact_6266_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_le_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6267_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_le_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6268_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_le_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6269_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_le_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6270_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.37/0.67 ! [X: nat,B: nat,W2: nat] :
% 0.37/0.67 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.37/0.67 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_power_le_of_nat_cancel_iff
% 0.37/0.67 thf(fact_6271_of__nat__zero__less__power__iff,axiom,
% 0.37/0.67 ! [X: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 0.37/0.67 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.37/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_zero_less_power_iff
% 0.37/0.67 thf(fact_6272_of__nat__zero__less__power__iff,axiom,
% 0.37/0.67 ! [X: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 0.37/0.67 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.37/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_zero_less_power_iff
% 0.37/0.67 thf(fact_6273_of__nat__zero__less__power__iff,axiom,
% 0.37/0.67 ! [X: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 0.37/0.67 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.37/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_zero_less_power_iff
% 0.37/0.67 thf(fact_6274_of__nat__zero__less__power__iff,axiom,
% 0.37/0.67 ! [X: nat,N: nat] :
% 0.37/0.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 0.37/0.67 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.37/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_zero_less_power_iff
% 0.37/0.67 thf(fact_6275_of__nat__zero__less__power__iff,axiom,
% 0.37/0.67 ! [X: nat,N: nat] :
% 0.37/0.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X ) @ N ) )
% 0.37/0.67 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.37/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % of_nat_zero_less_power_iff
% 0.37/0.67 thf(fact_6276_sum__zero__power,axiom,
% 0.37/0.67 ! [A4: set_nat,C2: nat > rat] :
% 0.37/0.67 ( ( ( ( finite_finite_nat @ A4 )
% 0.37/0.67 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.37/0.67 => ( ( groups2906978787729119204at_rat
% 0.37/0.67 @ ^ [I3: nat] : ( times_times_rat @ ( C2 @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 0.37/0.67 @ A4 )
% 0.37/0.67 = ( C2 @ zero_zero_nat ) ) )
% 0.37/0.67 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.37/0.67 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.37/0.67 => ( ( groups2906978787729119204at_rat
% 0.37/0.67 @ ^ [I3: nat] : ( times_times_rat @ ( C2 @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 0.37/0.67 @ A4 )
% 0.37/0.67 = zero_zero_rat ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum_zero_power
% 0.37/0.67 thf(fact_6277_sum__zero__power,axiom,
% 0.37/0.67 ! [A4: set_nat,C2: nat > complex] :
% 0.37/0.67 ( ( ( ( finite_finite_nat @ A4 )
% 0.37/0.67 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.37/0.67 => ( ( groups2073611262835488442omplex
% 0.37/0.67 @ ^ [I3: nat] : ( times_times_complex @ ( C2 @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 0.37/0.67 @ A4 )
% 0.37/0.67 = ( C2 @ zero_zero_nat ) ) )
% 0.37/0.67 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.37/0.67 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.37/0.67 => ( ( groups2073611262835488442omplex
% 0.37/0.67 @ ^ [I3: nat] : ( times_times_complex @ ( C2 @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 0.37/0.67 @ A4 )
% 0.37/0.67 = zero_zero_complex ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum_zero_power
% 0.37/0.67 thf(fact_6278_sum__zero__power,axiom,
% 0.37/0.67 ! [A4: set_nat,C2: nat > real] :
% 0.37/0.67 ( ( ( ( finite_finite_nat @ A4 )
% 0.37/0.67 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.37/0.67 => ( ( groups6591440286371151544t_real
% 0.37/0.67 @ ^ [I3: nat] : ( times_times_real @ ( C2 @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 0.37/0.67 @ A4 )
% 0.37/0.67 = ( C2 @ zero_zero_nat ) ) )
% 0.37/0.67 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.37/0.67 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.37/0.67 => ( ( groups6591440286371151544t_real
% 0.37/0.67 @ ^ [I3: nat] : ( times_times_real @ ( C2 @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 0.37/0.67 @ A4 )
% 0.37/0.67 = zero_zero_real ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % sum_zero_power
% 0.37/0.67 thf(fact_6279_finite__lists__distinct__length__eq,axiom,
% 0.37/0.67 ! [A4: set_complex,N: nat] :
% 0.37/0.67 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.67 => ( finite8712137658972009173omplex
% 0.37/0.67 @ ( collect_list_complex
% 0.37/0.67 @ ^ [Xs2: list_complex] :
% 0.37/0.67 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.37/0.67 = N )
% 0.37/0.67 & ( distinct_complex @ Xs2 )
% 0.37/0.67 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lists_distinct_length_eq
% 0.37/0.67 thf(fact_6280_finite__lists__distinct__length__eq,axiom,
% 0.37/0.67 ! [A4: set_Code_integer,N: nat] :
% 0.37/0.67 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.67 => ( finite1283093830868386564nteger
% 0.37/0.67 @ ( collec3483841146883906114nteger
% 0.37/0.67 @ ^ [Xs2: list_Code_integer] :
% 0.37/0.67 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 0.37/0.67 = N )
% 0.37/0.67 & ( distin1543349897113766820nteger @ Xs2 )
% 0.37/0.67 & ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lists_distinct_length_eq
% 0.37/0.67 thf(fact_6281_finite__lists__distinct__length__eq,axiom,
% 0.37/0.67 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.37/0.67 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.67 => ( finite3004134309566078307T_VEBT
% 0.37/0.67 @ ( collec5608196760682091941T_VEBT
% 0.37/0.67 @ ^ [Xs2: list_VEBT_VEBT] :
% 0.37/0.67 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.37/0.67 = N )
% 0.37/0.67 & ( distinct_VEBT_VEBT @ Xs2 )
% 0.37/0.67 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lists_distinct_length_eq
% 0.37/0.67 thf(fact_6282_finite__lists__distinct__length__eq,axiom,
% 0.37/0.67 ! [A4: set_real,N: nat] :
% 0.37/0.67 ( ( finite_finite_real @ A4 )
% 0.37/0.67 => ( finite306553202115118035t_real
% 0.37/0.67 @ ( collect_list_real
% 0.37/0.67 @ ^ [Xs2: list_real] :
% 0.37/0.67 ( ( ( size_size_list_real @ Xs2 )
% 0.37/0.67 = N )
% 0.37/0.67 & ( distinct_real @ Xs2 )
% 0.37/0.67 & ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lists_distinct_length_eq
% 0.37/0.67 thf(fact_6283_finite__lists__distinct__length__eq,axiom,
% 0.37/0.67 ! [A4: set_o,N: nat] :
% 0.37/0.67 ( ( finite_finite_o @ A4 )
% 0.37/0.67 => ( finite_finite_list_o
% 0.37/0.67 @ ( collect_list_o
% 0.37/0.67 @ ^ [Xs2: list_o] :
% 0.37/0.67 ( ( ( size_size_list_o @ Xs2 )
% 0.37/0.67 = N )
% 0.37/0.67 & ( distinct_o @ Xs2 )
% 0.37/0.67 & ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lists_distinct_length_eq
% 0.37/0.67 thf(fact_6284_finite__lists__distinct__length__eq,axiom,
% 0.37/0.67 ! [A4: set_nat,N: nat] :
% 0.37/0.67 ( ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( finite8100373058378681591st_nat
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [Xs2: list_nat] :
% 0.37/0.67 ( ( ( size_size_list_nat @ Xs2 )
% 0.37/0.67 = N )
% 0.37/0.67 & ( distinct_nat @ Xs2 )
% 0.37/0.67 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lists_distinct_length_eq
% 0.37/0.67 thf(fact_6285_finite__lists__distinct__length__eq,axiom,
% 0.37/0.67 ! [A4: set_int,N: nat] :
% 0.37/0.67 ( ( finite_finite_int @ A4 )
% 0.37/0.67 => ( finite3922522038869484883st_int
% 0.37/0.67 @ ( collect_list_int
% 0.37/0.67 @ ^ [Xs2: list_int] :
% 0.37/0.67 ( ( ( size_size_list_int @ Xs2 )
% 0.37/0.67 = N )
% 0.37/0.67 & ( distinct_int @ Xs2 )
% 0.37/0.67 & ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % finite_lists_distinct_length_eq
% 0.37/0.67 thf(fact_6286_vebt__memberi_H__rf__abstr,axiom,
% 0.37/0.67 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.67 ( hoare_hoare_triple_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X )
% 0.37/0.67 @ ^ [R5: $o] :
% 0.37/0.67 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.67 @ ( pure_assn
% 0.37/0.67 @ ( R5
% 0.37/0.67 = ( vEBT_vebt_member @ T @ X ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % vebt_memberi'_rf_abstr
% 0.37/0.67 thf(fact_6287_vebt__succi_H__rf__abstr,axiom,
% 0.37/0.67 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.67 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.67 => ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X )
% 0.37/0.67 @ ^ [R5: option_nat] :
% 0.37/0.67 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.67 @ ( pure_assn
% 0.37/0.67 @ ( R5
% 0.37/0.67 = ( vEBT_vebt_succ @ T @ X ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % vebt_succi'_rf_abstr
% 0.37/0.67 thf(fact_6288_vebt__pred_H__rf__abstr,axiom,
% 0.37/0.67 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.67 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.67 => ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X )
% 0.37/0.67 @ ^ [R5: option_nat] :
% 0.37/0.67 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.67 @ ( pure_assn
% 0.37/0.67 @ ( R5
% 0.37/0.67 = ( vEBT_vebt_pred @ T @ X ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % vebt_pred'_rf_abstr
% 0.37/0.67 thf(fact_6289_vebt__inserti_H__rf__abstr,axiom,
% 0.37/0.67 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % vebt_inserti'_rf_abstr
% 0.37/0.67 thf(fact_6290_pred__equals__eq2,axiom,
% 0.37/0.67 ! [R2: set_Pr1773385645901665561uint32,S3: set_Pr1773385645901665561uint32] :
% 0.37/0.67 ( ( ( ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R2 ) )
% 0.37/0.67 = ( ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ S3 ) ) )
% 0.37/0.67 = ( R2 = S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_equals_eq2
% 0.37/0.67 thf(fact_6291_pred__equals__eq2,axiom,
% 0.37/0.67 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 0.37/0.67 ( ( ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R2 ) )
% 0.37/0.67 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S3 ) ) )
% 0.37/0.67 = ( R2 = S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_equals_eq2
% 0.37/0.67 thf(fact_6292_pred__equals__eq2,axiom,
% 0.37/0.67 ! [R2: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 0.37/0.67 ( ( ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R2 ) )
% 0.37/0.67 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S3 ) ) )
% 0.37/0.67 = ( R2 = S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_equals_eq2
% 0.37/0.67 thf(fact_6293_pred__equals__eq2,axiom,
% 0.37/0.67 ! [R2: set_Pr3286484037609594932et_nat,S3: set_Pr3286484037609594932et_nat] :
% 0.37/0.67 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R2 ) )
% 0.37/0.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S3 ) ) )
% 0.37/0.67 = ( R2 = S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_equals_eq2
% 0.37/0.67 thf(fact_6294_pred__equals__eq2,axiom,
% 0.37/0.67 ! [R2: set_Pr8536935166611901872et_nat,S3: set_Pr8536935166611901872et_nat] :
% 0.37/0.67 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R2 ) )
% 0.37/0.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S3 ) ) )
% 0.37/0.67 = ( R2 = S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_equals_eq2
% 0.37/0.67 thf(fact_6295_pred__subset__eq,axiom,
% 0.37/0.67 ! [R2: set_nat,S3: set_nat] :
% 0.37/0.67 ( ( ord_less_eq_nat_o
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ R2 )
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ S3 ) )
% 0.37/0.67 = ( ord_less_eq_set_nat @ R2 @ S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_subset_eq
% 0.37/0.67 thf(fact_6296_pred__subset__eq,axiom,
% 0.37/0.67 ! [R2: set_VEBT_VEBT,S3: set_VEBT_VEBT] :
% 0.37/0.67 ( ( ord_le418104280809901481VEBT_o
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ R2 )
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ S3 ) )
% 0.37/0.67 = ( ord_le4337996190870823476T_VEBT @ R2 @ S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_subset_eq
% 0.37/0.67 thf(fact_6297_pred__subset__eq,axiom,
% 0.37/0.67 ! [R2: set_real,S3: set_real] :
% 0.37/0.67 ( ( ord_less_eq_real_o
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ R2 )
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ S3 ) )
% 0.37/0.67 = ( ord_less_eq_set_real @ R2 @ S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_subset_eq
% 0.37/0.67 thf(fact_6298_pred__subset__eq,axiom,
% 0.37/0.67 ! [R2: set_set_nat,S3: set_set_nat] :
% 0.37/0.67 ( ( ord_le3964352015994296041_nat_o
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R2 )
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S3 ) )
% 0.37/0.67 = ( ord_le6893508408891458716et_nat @ R2 @ S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_subset_eq
% 0.37/0.67 thf(fact_6299_pred__subset__eq,axiom,
% 0.37/0.67 ! [R2: set_int,S3: set_int] :
% 0.37/0.67 ( ( ord_less_eq_int_o
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ R2 )
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ S3 ) )
% 0.37/0.67 = ( ord_less_eq_set_int @ R2 @ S3 ) ) ).
% 0.37/0.67
% 0.37/0.67 % pred_subset_eq
% 0.37/0.67 thf(fact_6300_less__eq__set__def,axiom,
% 0.37/0.67 ( ord_less_eq_set_nat
% 0.37/0.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.37/0.67 ( ord_less_eq_nat_o
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_eq_set_def
% 0.37/0.67 thf(fact_6301_less__eq__set__def,axiom,
% 0.37/0.67 ( ord_le4337996190870823476T_VEBT
% 0.37/0.67 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.67 ( ord_le418104280809901481VEBT_o
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_eq_set_def
% 0.37/0.67 thf(fact_6302_less__eq__set__def,axiom,
% 0.37/0.67 ( ord_less_eq_set_real
% 0.37/0.67 = ( ^ [A6: set_real,B6: set_real] :
% 0.37/0.67 ( ord_less_eq_real_o
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_eq_set_def
% 0.37/0.67 thf(fact_6303_less__eq__set__def,axiom,
% 0.37/0.67 ( ord_le6893508408891458716et_nat
% 0.37/0.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.37/0.67 ( ord_le3964352015994296041_nat_o
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_eq_set_def
% 0.37/0.67 thf(fact_6304_less__eq__set__def,axiom,
% 0.37/0.67 ( ord_less_eq_set_int
% 0.37/0.67 = ( ^ [A6: set_int,B6: set_int] :
% 0.37/0.67 ( ord_less_eq_int_o
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_eq_set_def
% 0.37/0.67 thf(fact_6305_Collect__subset,axiom,
% 0.37/0.67 ! [A4: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ord_le4337996190870823476T_VEBT
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ A4 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_subset
% 0.37/0.67 thf(fact_6306_Collect__subset,axiom,
% 0.37/0.67 ! [A4: set_real,P2: real > $o] :
% 0.37/0.67 ( ord_less_eq_set_real
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ A4 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_subset
% 0.37/0.67 thf(fact_6307_Collect__subset,axiom,
% 0.37/0.67 ! [A4: set_complex,P2: complex > $o] :
% 0.37/0.67 ( ord_le211207098394363844omplex
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ A4 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_subset
% 0.37/0.67 thf(fact_6308_Collect__subset,axiom,
% 0.37/0.67 ! [A4: set_list_nat,P2: list_nat > $o] :
% 0.37/0.67 ( ord_le6045566169113846134st_nat
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ A4 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_subset
% 0.37/0.67 thf(fact_6309_Collect__subset,axiom,
% 0.37/0.67 ! [A4: set_set_nat,P2: set_nat > $o] :
% 0.37/0.67 ( ord_le6893508408891458716et_nat
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ A4 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_subset
% 0.37/0.67 thf(fact_6310_Collect__subset,axiom,
% 0.37/0.67 ! [A4: set_nat,P2: nat > $o] :
% 0.37/0.67 ( ord_less_eq_set_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ A4 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_subset
% 0.37/0.67 thf(fact_6311_Collect__subset,axiom,
% 0.37/0.67 ! [A4: set_int,P2: int > $o] :
% 0.37/0.67 ( ord_less_eq_set_int
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ A4 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_subset
% 0.37/0.67 thf(fact_6312_prop__restrict,axiom,
% 0.37/0.67 ! [X: vEBT_VEBT,Z6: set_VEBT_VEBT,X6: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X @ Z6 )
% 0.37/0.67 => ( ( ord_le4337996190870823476T_VEBT @ Z6
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 => ( P2 @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % prop_restrict
% 0.37/0.67 thf(fact_6313_prop__restrict,axiom,
% 0.37/0.67 ! [X: real,Z6: set_real,X6: set_real,P2: real > $o] :
% 0.37/0.67 ( ( member_real @ X @ Z6 )
% 0.37/0.67 => ( ( ord_less_eq_set_real @ Z6
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 => ( P2 @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % prop_restrict
% 0.37/0.67 thf(fact_6314_prop__restrict,axiom,
% 0.37/0.67 ! [X: complex,Z6: set_complex,X6: set_complex,P2: complex > $o] :
% 0.37/0.67 ( ( member_complex @ X @ Z6 )
% 0.37/0.67 => ( ( ord_le211207098394363844omplex @ Z6
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 => ( P2 @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % prop_restrict
% 0.37/0.67 thf(fact_6315_prop__restrict,axiom,
% 0.37/0.67 ! [X: list_nat,Z6: set_list_nat,X6: set_list_nat,P2: list_nat > $o] :
% 0.37/0.67 ( ( member_list_nat @ X @ Z6 )
% 0.37/0.67 => ( ( ord_le6045566169113846134st_nat @ Z6
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 => ( P2 @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % prop_restrict
% 0.37/0.67 thf(fact_6316_prop__restrict,axiom,
% 0.37/0.67 ! [X: set_nat,Z6: set_set_nat,X6: set_set_nat,P2: set_nat > $o] :
% 0.37/0.67 ( ( member_set_nat @ X @ Z6 )
% 0.37/0.67 => ( ( ord_le6893508408891458716et_nat @ Z6
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 => ( P2 @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % prop_restrict
% 0.37/0.67 thf(fact_6317_prop__restrict,axiom,
% 0.37/0.67 ! [X: nat,Z6: set_nat,X6: set_nat,P2: nat > $o] :
% 0.37/0.67 ( ( member_nat @ X @ Z6 )
% 0.37/0.67 => ( ( ord_less_eq_set_nat @ Z6
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 => ( P2 @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % prop_restrict
% 0.37/0.67 thf(fact_6318_prop__restrict,axiom,
% 0.37/0.67 ! [X: int,Z6: set_int,X6: set_int,P2: int > $o] :
% 0.37/0.67 ( ( member_int @ X @ Z6 )
% 0.37/0.67 => ( ( ord_less_eq_set_int @ Z6
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 => ( P2 @ X ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % prop_restrict
% 0.37/0.67 thf(fact_6319_Collect__restrict,axiom,
% 0.37/0.67 ! [X6: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ord_le4337996190870823476T_VEBT
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ X6 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_restrict
% 0.37/0.67 thf(fact_6320_Collect__restrict,axiom,
% 0.37/0.67 ! [X6: set_real,P2: real > $o] :
% 0.37/0.67 ( ord_less_eq_set_real
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ X6 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_restrict
% 0.37/0.67 thf(fact_6321_Collect__restrict,axiom,
% 0.37/0.67 ! [X6: set_complex,P2: complex > $o] :
% 0.37/0.67 ( ord_le211207098394363844omplex
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ X6 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_restrict
% 0.37/0.67 thf(fact_6322_Collect__restrict,axiom,
% 0.37/0.67 ! [X6: set_list_nat,P2: list_nat > $o] :
% 0.37/0.67 ( ord_le6045566169113846134st_nat
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ X6 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_restrict
% 0.37/0.67 thf(fact_6323_Collect__restrict,axiom,
% 0.37/0.67 ! [X6: set_set_nat,P2: set_nat > $o] :
% 0.37/0.67 ( ord_le6893508408891458716et_nat
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ X6 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_restrict
% 0.37/0.67 thf(fact_6324_Collect__restrict,axiom,
% 0.37/0.67 ! [X6: set_nat,P2: nat > $o] :
% 0.37/0.67 ( ord_less_eq_set_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ X6 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_restrict
% 0.37/0.67 thf(fact_6325_Collect__restrict,axiom,
% 0.37/0.67 ! [X6: set_int,P2: int > $o] :
% 0.37/0.67 ( ord_less_eq_set_int
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ X6 )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 @ X6 ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_restrict
% 0.37/0.67 thf(fact_6326_subset__CollectI,axiom,
% 0.37/0.67 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,Q2: vEBT_VEBT > $o,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ( ord_le4337996190870823476T_VEBT @ B4 @ A4 )
% 0.37/0.67 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 0.37/0.67 => ( ( Q2 @ X3 )
% 0.37/0.67 => ( P2 @ X3 ) ) )
% 0.37/0.67 => ( ord_le4337996190870823476T_VEBT
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ B4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) )
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_CollectI
% 0.37/0.67 thf(fact_6327_subset__CollectI,axiom,
% 0.37/0.67 ! [B4: set_real,A4: set_real,Q2: real > $o,P2: real > $o] :
% 0.37/0.67 ( ( ord_less_eq_set_real @ B4 @ A4 )
% 0.37/0.67 => ( ! [X3: real] :
% 0.37/0.67 ( ( member_real @ X3 @ B4 )
% 0.37/0.67 => ( ( Q2 @ X3 )
% 0.37/0.67 => ( P2 @ X3 ) ) )
% 0.37/0.67 => ( ord_less_eq_set_real
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ B4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) )
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_CollectI
% 0.37/0.67 thf(fact_6328_subset__CollectI,axiom,
% 0.37/0.67 ! [B4: set_complex,A4: set_complex,Q2: complex > $o,P2: complex > $o] :
% 0.37/0.67 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.67 => ( ! [X3: complex] :
% 0.37/0.67 ( ( member_complex @ X3 @ B4 )
% 0.37/0.67 => ( ( Q2 @ X3 )
% 0.37/0.67 => ( P2 @ X3 ) ) )
% 0.37/0.67 => ( ord_le211207098394363844omplex
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ B4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) )
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_CollectI
% 0.37/0.67 thf(fact_6329_subset__CollectI,axiom,
% 0.37/0.67 ! [B4: set_list_nat,A4: set_list_nat,Q2: list_nat > $o,P2: list_nat > $o] :
% 0.37/0.67 ( ( ord_le6045566169113846134st_nat @ B4 @ A4 )
% 0.37/0.67 => ( ! [X3: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X3 @ B4 )
% 0.37/0.67 => ( ( Q2 @ X3 )
% 0.37/0.67 => ( P2 @ X3 ) ) )
% 0.37/0.67 => ( ord_le6045566169113846134st_nat
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ B4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) )
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_CollectI
% 0.37/0.67 thf(fact_6330_subset__CollectI,axiom,
% 0.37/0.67 ! [B4: set_set_nat,A4: set_set_nat,Q2: set_nat > $o,P2: set_nat > $o] :
% 0.37/0.67 ( ( ord_le6893508408891458716et_nat @ B4 @ A4 )
% 0.37/0.67 => ( ! [X3: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X3 @ B4 )
% 0.37/0.67 => ( ( Q2 @ X3 )
% 0.37/0.67 => ( P2 @ X3 ) ) )
% 0.37/0.67 => ( ord_le6893508408891458716et_nat
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ B4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) )
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_CollectI
% 0.37/0.67 thf(fact_6331_subset__CollectI,axiom,
% 0.37/0.67 ! [B4: set_nat,A4: set_nat,Q2: nat > $o,P2: nat > $o] :
% 0.37/0.67 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.67 => ( ! [X3: nat] :
% 0.37/0.67 ( ( member_nat @ X3 @ B4 )
% 0.37/0.67 => ( ( Q2 @ X3 )
% 0.37/0.67 => ( P2 @ X3 ) ) )
% 0.37/0.67 => ( ord_less_eq_set_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ B4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) )
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_CollectI
% 0.37/0.67 thf(fact_6332_subset__CollectI,axiom,
% 0.37/0.67 ! [B4: set_int,A4: set_int,Q2: int > $o,P2: int > $o] :
% 0.37/0.67 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.37/0.67 => ( ! [X3: int] :
% 0.37/0.67 ( ( member_int @ X3 @ B4 )
% 0.37/0.67 => ( ( Q2 @ X3 )
% 0.37/0.67 => ( P2 @ X3 ) ) )
% 0.37/0.67 => ( ord_less_eq_set_int
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ B4 )
% 0.37/0.67 & ( Q2 @ X4 ) ) )
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_CollectI
% 0.37/0.67 thf(fact_6333_subset__Collect__iff,axiom,
% 0.37/0.67 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ( ord_le4337996190870823476T_VEBT @ B4 @ A4 )
% 0.37/0.67 => ( ( ord_le4337996190870823476T_VEBT @ B4
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 = ( ! [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ B4 )
% 0.37/0.67 => ( P2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_Collect_iff
% 0.37/0.67 thf(fact_6334_subset__Collect__iff,axiom,
% 0.37/0.67 ! [B4: set_real,A4: set_real,P2: real > $o] :
% 0.37/0.67 ( ( ord_less_eq_set_real @ B4 @ A4 )
% 0.37/0.67 => ( ( ord_less_eq_set_real @ B4
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 = ( ! [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ B4 )
% 0.37/0.67 => ( P2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_Collect_iff
% 0.37/0.67 thf(fact_6335_subset__Collect__iff,axiom,
% 0.37/0.67 ! [B4: set_complex,A4: set_complex,P2: complex > $o] :
% 0.37/0.67 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 0.37/0.67 => ( ( ord_le211207098394363844omplex @ B4
% 0.37/0.67 @ ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 = ( ! [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ B4 )
% 0.37/0.67 => ( P2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_Collect_iff
% 0.37/0.67 thf(fact_6336_subset__Collect__iff,axiom,
% 0.37/0.67 ! [B4: set_list_nat,A4: set_list_nat,P2: list_nat > $o] :
% 0.37/0.67 ( ( ord_le6045566169113846134st_nat @ B4 @ A4 )
% 0.37/0.67 => ( ( ord_le6045566169113846134st_nat @ B4
% 0.37/0.67 @ ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 = ( ! [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ B4 )
% 0.37/0.67 => ( P2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_Collect_iff
% 0.37/0.67 thf(fact_6337_subset__Collect__iff,axiom,
% 0.37/0.67 ! [B4: set_set_nat,A4: set_set_nat,P2: set_nat > $o] :
% 0.37/0.67 ( ( ord_le6893508408891458716et_nat @ B4 @ A4 )
% 0.37/0.67 => ( ( ord_le6893508408891458716et_nat @ B4
% 0.37/0.67 @ ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 = ( ! [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ B4 )
% 0.37/0.67 => ( P2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_Collect_iff
% 0.37/0.67 thf(fact_6338_subset__Collect__iff,axiom,
% 0.37/0.67 ! [B4: set_nat,A4: set_nat,P2: nat > $o] :
% 0.37/0.67 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 0.37/0.67 => ( ( ord_less_eq_set_nat @ B4
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 = ( ! [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ B4 )
% 0.37/0.67 => ( P2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_Collect_iff
% 0.37/0.67 thf(fact_6339_subset__Collect__iff,axiom,
% 0.37/0.67 ! [B4: set_int,A4: set_int,P2: int > $o] :
% 0.37/0.67 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 0.37/0.67 => ( ( ord_less_eq_set_int @ B4
% 0.37/0.67 @ ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ X4 ) ) ) )
% 0.37/0.67 = ( ! [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ B4 )
% 0.37/0.67 => ( P2 @ X4 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % subset_Collect_iff
% 0.37/0.67 thf(fact_6340_insert__compr,axiom,
% 0.37/0.67 ( insert_o
% 0.37/0.67 = ( ^ [A7: $o,B6: set_o] :
% 0.37/0.67 ( collect_o
% 0.37/0.67 @ ^ [X4: $o] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6341_insert__compr,axiom,
% 0.37/0.67 ( insert_VEBT_VEBT
% 0.37/0.67 = ( ^ [A7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.67 ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6342_insert__compr,axiom,
% 0.37/0.67 ( insert_real
% 0.37/0.67 = ( ^ [A7: real,B6: set_real] :
% 0.37/0.67 ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_real @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6343_insert__compr,axiom,
% 0.37/0.67 ( insert_complex
% 0.37/0.67 = ( ^ [A7: complex,B6: set_complex] :
% 0.37/0.67 ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_complex @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6344_insert__compr,axiom,
% 0.37/0.67 ( insert_list_nat
% 0.37/0.67 = ( ^ [A7: list_nat,B6: set_list_nat] :
% 0.37/0.67 ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6345_insert__compr,axiom,
% 0.37/0.67 ( insert_set_nat
% 0.37/0.67 = ( ^ [A7: set_nat,B6: set_set_nat] :
% 0.37/0.67 ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6346_insert__compr,axiom,
% 0.37/0.67 ( insert_nat
% 0.37/0.67 = ( ^ [A7: nat,B6: set_nat] :
% 0.37/0.67 ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6347_insert__compr,axiom,
% 0.37/0.67 ( insert_int
% 0.37/0.67 = ( ^ [A7: int,B6: set_int] :
% 0.37/0.67 ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( X4 = A7 )
% 0.37/0.67 | ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_compr
% 0.37/0.67 thf(fact_6348_insert__Collect,axiom,
% 0.37/0.67 ! [A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ( insert_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P2 ) )
% 0.37/0.67 = ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [U2: vEBT_VEBT] :
% 0.37/0.67 ( ( U2 != A )
% 0.37/0.67 => ( P2 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_Collect
% 0.37/0.67 thf(fact_6349_insert__Collect,axiom,
% 0.37/0.67 ! [A: $o,P2: $o > $o] :
% 0.37/0.67 ( ( insert_o @ A @ ( collect_o @ P2 ) )
% 0.37/0.67 = ( collect_o
% 0.37/0.67 @ ^ [U2: $o] :
% 0.37/0.67 ( ( U2 != A )
% 0.37/0.67 => ( P2 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_Collect
% 0.37/0.67 thf(fact_6350_insert__Collect,axiom,
% 0.37/0.67 ! [A: complex,P2: complex > $o] :
% 0.37/0.67 ( ( insert_complex @ A @ ( collect_complex @ P2 ) )
% 0.37/0.67 = ( collect_complex
% 0.37/0.67 @ ^ [U2: complex] :
% 0.37/0.67 ( ( U2 != A )
% 0.37/0.67 => ( P2 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_Collect
% 0.37/0.67 thf(fact_6351_insert__Collect,axiom,
% 0.37/0.67 ! [A: list_nat,P2: list_nat > $o] :
% 0.37/0.67 ( ( insert_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 0.37/0.67 = ( collect_list_nat
% 0.37/0.67 @ ^ [U2: list_nat] :
% 0.37/0.67 ( ( U2 != A )
% 0.37/0.67 => ( P2 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_Collect
% 0.37/0.67 thf(fact_6352_insert__Collect,axiom,
% 0.37/0.67 ! [A: set_nat,P2: set_nat > $o] :
% 0.37/0.67 ( ( insert_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 0.37/0.67 = ( collect_set_nat
% 0.37/0.67 @ ^ [U2: set_nat] :
% 0.37/0.67 ( ( U2 != A )
% 0.37/0.67 => ( P2 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_Collect
% 0.37/0.67 thf(fact_6353_insert__Collect,axiom,
% 0.37/0.67 ! [A: nat,P2: nat > $o] :
% 0.37/0.67 ( ( insert_nat @ A @ ( collect_nat @ P2 ) )
% 0.37/0.67 = ( collect_nat
% 0.37/0.67 @ ^ [U2: nat] :
% 0.37/0.67 ( ( U2 != A )
% 0.37/0.67 => ( P2 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_Collect
% 0.37/0.67 thf(fact_6354_insert__Collect,axiom,
% 0.37/0.67 ! [A: int,P2: int > $o] :
% 0.37/0.67 ( ( insert_int @ A @ ( collect_int @ P2 ) )
% 0.37/0.67 = ( collect_int
% 0.37/0.67 @ ^ [U2: int] :
% 0.37/0.67 ( ( U2 != A )
% 0.37/0.67 => ( P2 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % insert_Collect
% 0.37/0.67 thf(fact_6355_Compl__eq,axiom,
% 0.37/0.67 ( uminus8041839845116263051T_VEBT
% 0.37/0.67 = ( ^ [A6: set_VEBT_VEBT] :
% 0.37/0.67 ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ~ ( member_VEBT_VEBT @ X4 @ A6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compl_eq
% 0.37/0.67 thf(fact_6356_Compl__eq,axiom,
% 0.37/0.67 ( uminus612125837232591019t_real
% 0.37/0.67 = ( ^ [A6: set_real] :
% 0.37/0.67 ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ~ ( member_real @ X4 @ A6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compl_eq
% 0.37/0.67 thf(fact_6357_Compl__eq,axiom,
% 0.37/0.67 ( uminus8566677241136511917omplex
% 0.37/0.67 = ( ^ [A6: set_complex] :
% 0.37/0.67 ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ~ ( member_complex @ X4 @ A6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compl_eq
% 0.37/0.67 thf(fact_6358_Compl__eq,axiom,
% 0.37/0.67 ( uminus3195874150345416415st_nat
% 0.37/0.67 = ( ^ [A6: set_list_nat] :
% 0.37/0.67 ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ~ ( member_list_nat @ X4 @ A6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compl_eq
% 0.37/0.67 thf(fact_6359_Compl__eq,axiom,
% 0.37/0.67 ( uminus613421341184616069et_nat
% 0.37/0.67 = ( ^ [A6: set_set_nat] :
% 0.37/0.67 ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ~ ( member_set_nat @ X4 @ A6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compl_eq
% 0.37/0.67 thf(fact_6360_Compl__eq,axiom,
% 0.37/0.67 ( uminus5710092332889474511et_nat
% 0.37/0.67 = ( ^ [A6: set_nat] :
% 0.37/0.67 ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ~ ( member_nat @ X4 @ A6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compl_eq
% 0.37/0.67 thf(fact_6361_Compl__eq,axiom,
% 0.37/0.67 ( uminus1532241313380277803et_int
% 0.37/0.67 = ( ^ [A6: set_int] :
% 0.37/0.67 ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ~ ( member_int @ X4 @ A6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compl_eq
% 0.37/0.67 thf(fact_6362_Collect__neg__eq,axiom,
% 0.37/0.67 ! [P2: complex > $o] :
% 0.37/0.67 ( ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ~ ( P2 @ X4 ) )
% 0.37/0.67 = ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_neg_eq
% 0.37/0.67 thf(fact_6363_Collect__neg__eq,axiom,
% 0.37/0.67 ! [P2: list_nat > $o] :
% 0.37/0.67 ( ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ~ ( P2 @ X4 ) )
% 0.37/0.67 = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_neg_eq
% 0.37/0.67 thf(fact_6364_Collect__neg__eq,axiom,
% 0.37/0.67 ! [P2: set_nat > $o] :
% 0.37/0.67 ( ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ~ ( P2 @ X4 ) )
% 0.37/0.67 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_neg_eq
% 0.37/0.67 thf(fact_6365_Collect__neg__eq,axiom,
% 0.37/0.67 ! [P2: nat > $o] :
% 0.37/0.67 ( ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ~ ( P2 @ X4 ) )
% 0.37/0.67 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_neg_eq
% 0.37/0.67 thf(fact_6366_Collect__neg__eq,axiom,
% 0.37/0.67 ! [P2: int > $o] :
% 0.37/0.67 ( ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ~ ( P2 @ X4 ) )
% 0.37/0.67 = ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Collect_neg_eq
% 0.37/0.67 thf(fact_6367_uminus__set__def,axiom,
% 0.37/0.67 ( uminus8041839845116263051T_VEBT
% 0.37/0.67 = ( ^ [A6: set_VEBT_VEBT] :
% 0.37/0.67 ( collect_VEBT_VEBT
% 0.37/0.67 @ ( uminus2746543603091002386VEBT_o
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % uminus_set_def
% 0.37/0.67 thf(fact_6368_uminus__set__def,axiom,
% 0.37/0.67 ( uminus612125837232591019t_real
% 0.37/0.67 = ( ^ [A6: set_real] :
% 0.37/0.67 ( collect_real
% 0.37/0.67 @ ( uminus_uminus_real_o
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ A6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % uminus_set_def
% 0.37/0.67 thf(fact_6369_uminus__set__def,axiom,
% 0.37/0.67 ( uminus8566677241136511917omplex
% 0.37/0.67 = ( ^ [A6: set_complex] :
% 0.37/0.67 ( collect_complex
% 0.37/0.67 @ ( uminus1680532995456772888plex_o
% 0.37/0.67 @ ^ [X4: complex] : ( member_complex @ X4 @ A6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % uminus_set_def
% 0.37/0.67 thf(fact_6370_uminus__set__def,axiom,
% 0.37/0.67 ( uminus3195874150345416415st_nat
% 0.37/0.67 = ( ^ [A6: set_list_nat] :
% 0.37/0.67 ( collect_list_nat
% 0.37/0.67 @ ( uminus5770388063884162150_nat_o
% 0.37/0.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % uminus_set_def
% 0.37/0.67 thf(fact_6371_uminus__set__def,axiom,
% 0.37/0.67 ( uminus613421341184616069et_nat
% 0.37/0.67 = ( ^ [A6: set_set_nat] :
% 0.37/0.67 ( collect_set_nat
% 0.37/0.67 @ ( uminus6401447641752708672_nat_o
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % uminus_set_def
% 0.37/0.67 thf(fact_6372_uminus__set__def,axiom,
% 0.37/0.67 ( uminus5710092332889474511et_nat
% 0.37/0.67 = ( ^ [A6: set_nat] :
% 0.37/0.67 ( collect_nat
% 0.37/0.67 @ ( uminus_uminus_nat_o
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % uminus_set_def
% 0.37/0.67 thf(fact_6373_uminus__set__def,axiom,
% 0.37/0.67 ( uminus1532241313380277803et_int
% 0.37/0.67 = ( ^ [A6: set_int] :
% 0.37/0.67 ( collect_int
% 0.37/0.67 @ ( uminus_uminus_int_o
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ A6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % uminus_set_def
% 0.37/0.67 thf(fact_6374_lessThan__def,axiom,
% 0.37/0.67 ( set_or890127255671739683et_nat
% 0.37/0.67 = ( ^ [U2: set_nat] :
% 0.37/0.67 ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_def
% 0.37/0.67 thf(fact_6375_lessThan__def,axiom,
% 0.37/0.67 ( set_ord_lessThan_rat
% 0.37/0.67 = ( ^ [U2: rat] :
% 0.37/0.67 ( collect_rat
% 0.37/0.67 @ ^ [X4: rat] : ( ord_less_rat @ X4 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_def
% 0.37/0.67 thf(fact_6376_lessThan__def,axiom,
% 0.37/0.67 ( set_ord_lessThan_num
% 0.37/0.67 = ( ^ [U2: num] :
% 0.37/0.67 ( collect_num
% 0.37/0.67 @ ^ [X4: num] : ( ord_less_num @ X4 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_def
% 0.37/0.67 thf(fact_6377_lessThan__def,axiom,
% 0.37/0.67 ( set_ord_lessThan_nat
% 0.37/0.67 = ( ^ [U2: nat] :
% 0.37/0.67 ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_def
% 0.37/0.67 thf(fact_6378_lessThan__def,axiom,
% 0.37/0.67 ( set_ord_lessThan_int
% 0.37/0.67 = ( ^ [U2: int] :
% 0.37/0.67 ( collect_int
% 0.37/0.67 @ ^ [X4: int] : ( ord_less_int @ X4 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_def
% 0.37/0.67 thf(fact_6379_lessThan__def,axiom,
% 0.37/0.67 ( set_or5984915006950818249n_real
% 0.37/0.67 = ( ^ [U2: real] :
% 0.37/0.67 ( collect_real
% 0.37/0.67 @ ^ [X4: real] : ( ord_less_real @ X4 @ U2 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % lessThan_def
% 0.37/0.67 thf(fact_6380_less__set__def,axiom,
% 0.37/0.67 ( ord_less_set_nat
% 0.37/0.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.37/0.67 ( ord_less_nat_o
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_set_def
% 0.37/0.67 thf(fact_6381_less__set__def,axiom,
% 0.37/0.67 ( ord_le3480810397992357184T_VEBT
% 0.37/0.67 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.67 ( ord_less_VEBT_VEBT_o
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_set_def
% 0.37/0.67 thf(fact_6382_less__set__def,axiom,
% 0.37/0.67 ( ord_less_set_real
% 0.37/0.67 = ( ^ [A6: set_real,B6: set_real] :
% 0.37/0.67 ( ord_less_real_o
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_set_def
% 0.37/0.67 thf(fact_6383_less__set__def,axiom,
% 0.37/0.67 ( ord_less_set_int
% 0.37/0.67 = ( ^ [A6: set_int,B6: set_int] :
% 0.37/0.67 ( ord_less_int_o
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_set_def
% 0.37/0.67 thf(fact_6384_less__set__def,axiom,
% 0.37/0.67 ( ord_less_set_set_nat
% 0.37/0.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.37/0.67 ( ord_less_set_nat_o
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % less_set_def
% 0.37/0.67 thf(fact_6385_Set_Oempty__def,axiom,
% 0.37/0.67 ( bot_bot_set_complex
% 0.37/0.67 = ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] : $false ) ) ).
% 0.37/0.67
% 0.37/0.67 % Set.empty_def
% 0.37/0.67 thf(fact_6386_Set_Oempty__def,axiom,
% 0.37/0.67 ( bot_bot_set_list_nat
% 0.37/0.67 = ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] : $false ) ) ).
% 0.37/0.67
% 0.37/0.67 % Set.empty_def
% 0.37/0.67 thf(fact_6387_Set_Oempty__def,axiom,
% 0.37/0.67 ( bot_bot_set_set_nat
% 0.37/0.67 = ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] : $false ) ) ).
% 0.37/0.67
% 0.37/0.67 % Set.empty_def
% 0.37/0.67 thf(fact_6388_Set_Oempty__def,axiom,
% 0.37/0.67 ( bot_bot_set_nat
% 0.37/0.67 = ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] : $false ) ) ).
% 0.37/0.67
% 0.37/0.67 % Set.empty_def
% 0.37/0.67 thf(fact_6389_Set_Oempty__def,axiom,
% 0.37/0.67 ( bot_bot_set_int
% 0.37/0.67 = ( collect_int
% 0.37/0.67 @ ^ [X4: int] : $false ) ) ).
% 0.37/0.67
% 0.37/0.67 % Set.empty_def
% 0.37/0.67 thf(fact_6390_Set_Oempty__def,axiom,
% 0.37/0.67 ( bot_bot_set_o
% 0.37/0.67 = ( collect_o
% 0.37/0.67 @ ^ [X4: $o] : $false ) ) ).
% 0.37/0.67
% 0.37/0.67 % Set.empty_def
% 0.37/0.67 thf(fact_6391_minus__set__def,axiom,
% 0.37/0.67 ( minus_5127226145743854075T_VEBT
% 0.37/0.67 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.67 ( collect_VEBT_VEBT
% 0.37/0.67 @ ( minus_2794559001203777698VEBT_o
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % minus_set_def
% 0.37/0.67 thf(fact_6392_minus__set__def,axiom,
% 0.37/0.67 ( minus_minus_set_real
% 0.37/0.67 = ( ^ [A6: set_real,B6: set_real] :
% 0.37/0.67 ( collect_real
% 0.37/0.67 @ ( minus_minus_real_o
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: real] : ( member_real @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % minus_set_def
% 0.37/0.67 thf(fact_6393_minus__set__def,axiom,
% 0.37/0.67 ( minus_811609699411566653omplex
% 0.37/0.67 = ( ^ [A6: set_complex,B6: set_complex] :
% 0.37/0.67 ( collect_complex
% 0.37/0.67 @ ( minus_8727706125548526216plex_o
% 0.37/0.67 @ ^ [X4: complex] : ( member_complex @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: complex] : ( member_complex @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % minus_set_def
% 0.37/0.67 thf(fact_6394_minus__set__def,axiom,
% 0.37/0.67 ( minus_7954133019191499631st_nat
% 0.37/0.67 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 0.37/0.67 ( collect_list_nat
% 0.37/0.67 @ ( minus_1139252259498527702_nat_o
% 0.37/0.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % minus_set_def
% 0.37/0.67 thf(fact_6395_minus__set__def,axiom,
% 0.37/0.67 ( minus_2163939370556025621et_nat
% 0.37/0.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.37/0.67 ( collect_set_nat
% 0.37/0.67 @ ( minus_6910147592129066416_nat_o
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % minus_set_def
% 0.37/0.67 thf(fact_6396_minus__set__def,axiom,
% 0.37/0.67 ( minus_minus_set_int
% 0.37/0.67 = ( ^ [A6: set_int,B6: set_int] :
% 0.37/0.67 ( collect_int
% 0.37/0.67 @ ( minus_minus_int_o
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % minus_set_def
% 0.37/0.67 thf(fact_6397_minus__set__def,axiom,
% 0.37/0.67 ( minus_minus_set_nat
% 0.37/0.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.37/0.67 ( collect_nat
% 0.37/0.67 @ ( minus_minus_nat_o
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 0.37/0.67 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % minus_set_def
% 0.37/0.67 thf(fact_6398_set__diff__eq,axiom,
% 0.37/0.67 ( minus_5127226145743854075T_VEBT
% 0.37/0.67 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 0.37/0.67 ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ A6 )
% 0.37/0.67 & ~ ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_diff_eq
% 0.37/0.67 thf(fact_6399_set__diff__eq,axiom,
% 0.37/0.67 ( minus_minus_set_real
% 0.37/0.67 = ( ^ [A6: set_real,B6: set_real] :
% 0.37/0.67 ( collect_real
% 0.37/0.67 @ ^ [X4: real] :
% 0.37/0.67 ( ( member_real @ X4 @ A6 )
% 0.37/0.67 & ~ ( member_real @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_diff_eq
% 0.37/0.67 thf(fact_6400_set__diff__eq,axiom,
% 0.37/0.67 ( minus_811609699411566653omplex
% 0.37/0.67 = ( ^ [A6: set_complex,B6: set_complex] :
% 0.37/0.67 ( collect_complex
% 0.37/0.67 @ ^ [X4: complex] :
% 0.37/0.67 ( ( member_complex @ X4 @ A6 )
% 0.37/0.67 & ~ ( member_complex @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_diff_eq
% 0.37/0.67 thf(fact_6401_set__diff__eq,axiom,
% 0.37/0.67 ( minus_7954133019191499631st_nat
% 0.37/0.67 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 0.37/0.67 ( collect_list_nat
% 0.37/0.67 @ ^ [X4: list_nat] :
% 0.37/0.67 ( ( member_list_nat @ X4 @ A6 )
% 0.37/0.67 & ~ ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_diff_eq
% 0.37/0.67 thf(fact_6402_set__diff__eq,axiom,
% 0.37/0.67 ( minus_2163939370556025621et_nat
% 0.37/0.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 0.37/0.67 ( collect_set_nat
% 0.37/0.67 @ ^ [X4: set_nat] :
% 0.37/0.67 ( ( member_set_nat @ X4 @ A6 )
% 0.37/0.67 & ~ ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_diff_eq
% 0.37/0.67 thf(fact_6403_set__diff__eq,axiom,
% 0.37/0.67 ( minus_minus_set_int
% 0.37/0.67 = ( ^ [A6: set_int,B6: set_int] :
% 0.37/0.67 ( collect_int
% 0.37/0.67 @ ^ [X4: int] :
% 0.37/0.67 ( ( member_int @ X4 @ A6 )
% 0.37/0.67 & ~ ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_diff_eq
% 0.37/0.67 thf(fact_6404_set__diff__eq,axiom,
% 0.37/0.67 ( minus_minus_set_nat
% 0.37/0.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 0.37/0.67 ( collect_nat
% 0.37/0.67 @ ^ [X4: nat] :
% 0.37/0.67 ( ( member_nat @ X4 @ A6 )
% 0.37/0.67 & ~ ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % set_diff_eq
% 0.37/0.67 thf(fact_6405_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_VEBT_VEBT,B4: set_nat,R2: vEBT_VEBT > nat > $o] :
% 0.37/0.67 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.67 => ( ( finite_finite_nat @ B4 )
% 0.37/0.67 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: nat] :
% 0.37/0.67 ( ( member_nat @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: nat] :
% 0.37/0.67 ( ( member_nat @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6406_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_real,B4: set_nat,R2: real > nat > $o] :
% 0.37/0.67 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.67 => ( ( finite_finite_nat @ B4 )
% 0.37/0.67 => ( ! [X3: real] :
% 0.37/0.67 ( ( member_real @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: nat] :
% 0.37/0.67 ( ( member_nat @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: nat] :
% 0.37/0.67 ( ( member_nat @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite_finite_real
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [A7: real] :
% 0.37/0.67 ( ( member_real @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6407_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_VEBT_VEBT,B4: set_int,R2: vEBT_VEBT > int > $o] :
% 0.37/0.67 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.67 => ( ( finite_finite_int @ B4 )
% 0.37/0.67 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: int] :
% 0.37/0.67 ( ( member_int @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: int] :
% 0.37/0.67 ( ( member_int @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6408_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_real,B4: set_int,R2: real > int > $o] :
% 0.37/0.67 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.67 => ( ( finite_finite_int @ B4 )
% 0.37/0.67 => ( ! [X3: real] :
% 0.37/0.67 ( ( member_real @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: int] :
% 0.37/0.67 ( ( member_int @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: int] :
% 0.37/0.67 ( ( member_int @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite_finite_real
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [A7: real] :
% 0.37/0.67 ( ( member_real @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6409_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_VEBT_VEBT,B4: set_complex,R2: vEBT_VEBT > complex > $o] :
% 0.37/0.67 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.67 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.67 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: complex] :
% 0.37/0.67 ( ( member_complex @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: complex] :
% 0.37/0.67 ( ( member_complex @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6410_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_real,B4: set_complex,R2: real > complex > $o] :
% 0.37/0.67 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.67 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.67 => ( ! [X3: real] :
% 0.37/0.67 ( ( member_real @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: complex] :
% 0.37/0.67 ( ( member_complex @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: complex] :
% 0.37/0.67 ( ( member_complex @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite_finite_real
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [A7: real] :
% 0.37/0.67 ( ( member_real @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6411_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_VEBT_VEBT,B4: set_Code_integer,R2: vEBT_VEBT > code_integer > $o] :
% 0.37/0.67 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.67 => ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.67 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: code_integer] :
% 0.37/0.67 ( ( member_Code_integer @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: code_integer] :
% 0.37/0.67 ( ( member_Code_integer @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6412_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_real,B4: set_Code_integer,R2: real > code_integer > $o] :
% 0.37/0.67 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.67 => ( ( finite6017078050557962740nteger @ B4 )
% 0.37/0.67 => ( ! [X3: real] :
% 0.37/0.67 ( ( member_real @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: code_integer] :
% 0.37/0.67 ( ( member_Code_integer @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: code_integer] :
% 0.37/0.67 ( ( member_Code_integer @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite_finite_real
% 0.37/0.67 @ ( collect_real
% 0.37/0.67 @ ^ [A7: real] :
% 0.37/0.67 ( ( member_real @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6413_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_nat,B4: set_nat,R2: nat > nat > $o] :
% 0.37/0.67 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( ( finite_finite_nat @ B4 )
% 0.37/0.67 => ( ! [X3: nat] :
% 0.37/0.67 ( ( member_nat @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: nat] :
% 0.37/0.67 ( ( member_nat @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: nat] :
% 0.37/0.67 ( ( member_nat @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite_finite_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [A7: nat] :
% 0.37/0.67 ( ( member_nat @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6414_pigeonhole__infinite__rel,axiom,
% 0.37/0.67 ! [A4: set_nat,B4: set_int,R2: nat > int > $o] :
% 0.37/0.67 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.67 => ( ( finite_finite_int @ B4 )
% 0.37/0.67 => ( ! [X3: nat] :
% 0.37/0.67 ( ( member_nat @ X3 @ A4 )
% 0.37/0.67 => ? [Xa: int] :
% 0.37/0.67 ( ( member_int @ Xa @ B4 )
% 0.37/0.67 & ( R2 @ X3 @ Xa ) ) )
% 0.37/0.67 => ? [X3: int] :
% 0.37/0.67 ( ( member_int @ X3 @ B4 )
% 0.37/0.67 & ~ ( finite_finite_nat
% 0.37/0.67 @ ( collect_nat
% 0.37/0.67 @ ^ [A7: nat] :
% 0.37/0.67 ( ( member_nat @ A7 @ A4 )
% 0.37/0.67 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % pigeonhole_infinite_rel
% 0.37/0.67 thf(fact_6415_not__finite__existsD,axiom,
% 0.37/0.67 ! [P2: list_nat > $o] :
% 0.37/0.67 ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 0.37/0.67 => ? [X_1: list_nat] : ( P2 @ X_1 ) ) ).
% 0.37/0.67
% 0.37/0.67 % not_finite_existsD
% 0.37/0.67 thf(fact_6416_not__finite__existsD,axiom,
% 0.37/0.67 ! [P2: set_nat > $o] :
% 0.37/0.67 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 0.37/0.67 => ? [X_1: set_nat] : ( P2 @ X_1 ) ) ).
% 0.37/0.67
% 0.37/0.67 % not_finite_existsD
% 0.37/0.67 thf(fact_6417_not__finite__existsD,axiom,
% 0.37/0.67 ! [P2: nat > $o] :
% 0.37/0.67 ( ~ ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.37/0.67 => ? [X_1: nat] : ( P2 @ X_1 ) ) ).
% 0.37/0.67
% 0.37/0.67 % not_finite_existsD
% 0.37/0.67 thf(fact_6418_not__finite__existsD,axiom,
% 0.37/0.67 ! [P2: int > $o] :
% 0.37/0.67 ( ~ ( finite_finite_int @ ( collect_int @ P2 ) )
% 0.37/0.67 => ? [X_1: int] : ( P2 @ X_1 ) ) ).
% 0.37/0.67
% 0.37/0.67 % not_finite_existsD
% 0.37/0.67 thf(fact_6419_not__finite__existsD,axiom,
% 0.37/0.67 ! [P2: complex > $o] :
% 0.37/0.67 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P2 ) )
% 0.37/0.67 => ? [X_1: complex] : ( P2 @ X_1 ) ) ).
% 0.37/0.67
% 0.37/0.67 % not_finite_existsD
% 0.37/0.67 thf(fact_6420_not__finite__existsD,axiom,
% 0.37/0.67 ! [P2: code_integer > $o] :
% 0.37/0.67 ( ~ ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 0.37/0.67 => ? [X_1: code_integer] : ( P2 @ X_1 ) ) ).
% 0.37/0.67
% 0.37/0.67 % not_finite_existsD
% 0.37/0.67 thf(fact_6421_imageE,axiom,
% 0.37/0.67 ! [B: nat,F: nat > nat,A4: set_nat] :
% 0.37/0.67 ( ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: nat] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_nat @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6422_imageE,axiom,
% 0.37/0.67 ! [B: nat,F: vEBT_VEBT > nat,A4: set_VEBT_VEBT] :
% 0.37/0.67 ( ( member_nat @ B @ ( image_VEBT_VEBT_nat @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_VEBT_VEBT @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6423_imageE,axiom,
% 0.37/0.67 ! [B: nat,F: real > nat,A4: set_real] :
% 0.37/0.67 ( ( member_nat @ B @ ( image_real_nat @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: real] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_real @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6424_imageE,axiom,
% 0.37/0.67 ! [B: nat,F: int > nat,A4: set_int] :
% 0.37/0.67 ( ( member_nat @ B @ ( image_int_nat @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: int] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_int @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6425_imageE,axiom,
% 0.37/0.67 ! [B: vEBT_VEBT,F: nat > vEBT_VEBT,A4: set_nat] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ B @ ( image_nat_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: nat] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_nat @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6426_imageE,axiom,
% 0.37/0.67 ! [B: vEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT,A4: set_VEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ B @ ( image_3375948659692109573T_VEBT @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_VEBT_VEBT @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6427_imageE,axiom,
% 0.37/0.67 ! [B: vEBT_VEBT,F: real > vEBT_VEBT,A4: set_real] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ B @ ( image_real_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: real] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_real @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6428_imageE,axiom,
% 0.37/0.67 ! [B: vEBT_VEBT,F: int > vEBT_VEBT,A4: set_int] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ B @ ( image_int_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: int] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_int @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6429_imageE,axiom,
% 0.37/0.67 ! [B: real,F: nat > real,A4: set_nat] :
% 0.37/0.67 ( ( member_real @ B @ ( image_nat_real @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: nat] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_nat @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6430_imageE,axiom,
% 0.37/0.67 ! [B: real,F: vEBT_VEBT > real,A4: set_VEBT_VEBT] :
% 0.37/0.67 ( ( member_real @ B @ ( image_VEBT_VEBT_real @ F @ A4 ) )
% 0.37/0.67 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.67 ( ( B
% 0.37/0.67 = ( F @ X3 ) )
% 0.37/0.67 => ~ ( member_VEBT_VEBT @ X3 @ A4 ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % imageE
% 0.37/0.67 thf(fact_6431_image__image,axiom,
% 0.37/0.67 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 0.37/0.67 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ A4 ) )
% 0.37/0.67 = ( image_nat_nat
% 0.37/0.67 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6432_image__image,axiom,
% 0.37/0.67 ! [F: nat > nat,G: int > nat,A4: set_int] :
% 0.37/0.67 ( ( image_nat_nat @ F @ ( image_int_nat @ G @ A4 ) )
% 0.37/0.67 = ( image_int_nat
% 0.37/0.67 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6433_image__image,axiom,
% 0.37/0.67 ! [F: nat > int,G: nat > nat,A4: set_nat] :
% 0.37/0.67 ( ( image_nat_int @ F @ ( image_nat_nat @ G @ A4 ) )
% 0.37/0.67 = ( image_nat_int
% 0.37/0.67 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6434_image__image,axiom,
% 0.37/0.67 ! [F: nat > int,G: int > nat,A4: set_int] :
% 0.37/0.67 ( ( image_nat_int @ F @ ( image_int_nat @ G @ A4 ) )
% 0.37/0.67 = ( image_int_int
% 0.37/0.67 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6435_image__image,axiom,
% 0.37/0.67 ! [F: int > nat,G: nat > int,A4: set_nat] :
% 0.37/0.67 ( ( image_int_nat @ F @ ( image_nat_int @ G @ A4 ) )
% 0.37/0.67 = ( image_nat_nat
% 0.37/0.67 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6436_image__image,axiom,
% 0.37/0.67 ! [F: int > nat,G: int > int,A4: set_int] :
% 0.37/0.67 ( ( image_int_nat @ F @ ( image_int_int @ G @ A4 ) )
% 0.37/0.67 = ( image_int_nat
% 0.37/0.67 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6437_image__image,axiom,
% 0.37/0.67 ! [F: int > int,G: nat > int,A4: set_nat] :
% 0.37/0.67 ( ( image_int_int @ F @ ( image_nat_int @ G @ A4 ) )
% 0.37/0.67 = ( image_nat_int
% 0.37/0.67 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6438_image__image,axiom,
% 0.37/0.67 ! [F: int > int,G: int > int,A4: set_int] :
% 0.37/0.67 ( ( image_int_int @ F @ ( image_int_int @ G @ A4 ) )
% 0.37/0.67 = ( image_int_int
% 0.37/0.67 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6439_image__image,axiom,
% 0.37/0.67 ! [F: set_nat > nat,G: nat > set_nat,A4: set_nat] :
% 0.37/0.67 ( ( image_set_nat_nat @ F @ ( image_nat_set_nat @ G @ A4 ) )
% 0.37/0.67 = ( image_nat_nat
% 0.37/0.67 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6440_image__image,axiom,
% 0.37/0.67 ! [F: set_nat > int,G: nat > set_nat,A4: set_nat] :
% 0.37/0.67 ( ( image_set_nat_int @ F @ ( image_nat_set_nat @ G @ A4 ) )
% 0.37/0.67 = ( image_nat_int
% 0.37/0.67 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.37/0.67 @ A4 ) ) ).
% 0.37/0.67
% 0.37/0.67 % image_image
% 0.37/0.67 thf(fact_6441_Compr__image__eq,axiom,
% 0.37/0.67 ! [F: vEBT_VEBT > vEBT_VEBT,A4: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ ( image_3375948659692109573T_VEBT @ F @ A4 ) )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 = ( image_3375948659692109573T_VEBT @ F
% 0.37/0.67 @ ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.67 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.67
% 0.37/0.67 % Compr_image_eq
% 0.37/0.67 thf(fact_6442_Compr__image__eq,axiom,
% 0.37/0.67 ! [F: real > vEBT_VEBT,A4: set_real,P2: vEBT_VEBT > $o] :
% 0.37/0.67 ( ( collect_VEBT_VEBT
% 0.37/0.67 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.67 ( ( member_VEBT_VEBT @ X4 @ ( image_real_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.67 & ( P2 @ X4 ) ) )
% 0.37/0.67 = ( image_real_VEBT_VEBT @ F
% 0.37/0.67 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6443_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: vEBT_VEBT > real,A4: set_VEBT_VEBT,P2: real > $o] :
% 0.37/0.68 ( ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ ( image_VEBT_VEBT_real @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_VEBT_VEBT_real @ F
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6444_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: real > real,A4: set_real,P2: real > $o] :
% 0.37/0.68 ( ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ ( image_real_real @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_real_real @ F
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6445_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: complex > vEBT_VEBT,A4: set_complex,P2: vEBT_VEBT > $o] :
% 0.37/0.68 ( ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ ( image_932796090930683071T_VEBT @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_932796090930683071T_VEBT @ F
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( member_complex @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6446_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: complex > real,A4: set_complex,P2: real > $o] :
% 0.37/0.68 ( ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ ( image_complex_real @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_complex_real @ F
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( member_complex @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6447_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: nat > vEBT_VEBT,A4: set_nat,P2: vEBT_VEBT > $o] :
% 0.37/0.68 ( ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ ( image_nat_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_nat_VEBT_VEBT @ F
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( member_nat @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6448_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: nat > real,A4: set_nat,P2: real > $o] :
% 0.37/0.68 ( ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ ( image_nat_real @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_nat_real @ F
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( member_nat @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6449_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: int > vEBT_VEBT,A4: set_int,P2: vEBT_VEBT > $o] :
% 0.37/0.68 ( ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ ( image_int_VEBT_VEBT @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_int_VEBT_VEBT @ F
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6450_Compr__image__eq,axiom,
% 0.37/0.68 ! [F: int > real,A4: set_int,P2: real > $o] :
% 0.37/0.68 ( ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ ( image_int_real @ F @ A4 ) )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( image_int_real @ F
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Compr_image_eq
% 0.37/0.68 thf(fact_6451_lambda__zero,axiom,
% 0.37/0.68 ( ( ^ [H4: rat] : zero_zero_rat )
% 0.37/0.68 = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.37/0.68
% 0.37/0.68 % lambda_zero
% 0.37/0.68 thf(fact_6452_lambda__zero,axiom,
% 0.37/0.68 ( ( ^ [H4: uint32] : zero_zero_uint32 )
% 0.37/0.68 = ( times_times_uint32 @ zero_zero_uint32 ) ) ).
% 0.37/0.68
% 0.37/0.68 % lambda_zero
% 0.37/0.68 thf(fact_6453_lambda__zero,axiom,
% 0.37/0.68 ( ( ^ [H4: real] : zero_zero_real )
% 0.37/0.68 = ( times_times_real @ zero_zero_real ) ) ).
% 0.37/0.68
% 0.37/0.68 % lambda_zero
% 0.37/0.68 thf(fact_6454_lambda__zero,axiom,
% 0.37/0.68 ( ( ^ [H4: nat] : zero_zero_nat )
% 0.37/0.68 = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.37/0.68
% 0.37/0.68 % lambda_zero
% 0.37/0.68 thf(fact_6455_lambda__zero,axiom,
% 0.37/0.68 ( ( ^ [H4: int] : zero_zero_int )
% 0.37/0.68 = ( times_times_int @ zero_zero_int ) ) ).
% 0.37/0.68
% 0.37/0.68 % lambda_zero
% 0.37/0.68 thf(fact_6456_sum_Onat__diff__reindex,axiom,
% 0.37/0.68 ! [G: nat > nat,N: nat] :
% 0.37/0.68 ( ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.68 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.nat_diff_reindex
% 0.37/0.68 thf(fact_6457_sum_Onat__diff__reindex,axiom,
% 0.37/0.68 ! [G: nat > real,N: nat] :
% 0.37/0.68 ( ( groups6591440286371151544t_real
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.68 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.nat_diff_reindex
% 0.37/0.68 thf(fact_6458_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_nat,F: nat > rat,G: nat > rat] :
% 0.37/0.68 ( ! [I2: nat] :
% 0.37/0.68 ( ( member_nat @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K4 ) @ ( groups2906978787729119204at_rat @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6459_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 0.37/0.68 ( ! [I2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ K4 ) @ ( groups136491112297645522BT_rat @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6460_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_real,F: real > rat,G: real > rat] :
% 0.37/0.68 ( ! [I2: real] :
% 0.37/0.68 ( ( member_real @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K4 ) @ ( groups1300246762558778688al_rat @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6461_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_int,F: int > rat,G: int > rat] :
% 0.37/0.68 ( ! [I2: int] :
% 0.37/0.68 ( ( member_int @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K4 ) @ ( groups3906332499630173760nt_rat @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6462_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.37/0.68 ( ! [I2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ K4 ) @ ( groups771621172384141258BT_nat @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6463_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_real,F: real > nat,G: real > nat] :
% 0.37/0.68 ( ! [I2: real] :
% 0.37/0.68 ( ( member_real @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K4 ) @ ( groups1935376822645274424al_nat @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6464_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_int,F: int > nat,G: int > nat] :
% 0.37/0.68 ( ! [I2: int] :
% 0.37/0.68 ( ( member_int @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K4 ) @ ( groups4541462559716669496nt_nat @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6465_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_nat,F: nat > int,G: nat > int] :
% 0.37/0.68 ( ! [I2: nat] :
% 0.37/0.68 ( ( member_nat @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K4 ) @ ( groups3539618377306564664at_int @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6466_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 0.37/0.68 ( ! [I2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_int @ ( groups769130701875090982BT_int @ F @ K4 ) @ ( groups769130701875090982BT_int @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6467_sum__mono,axiom,
% 0.37/0.68 ! [K4: set_real,F: real > int,G: real > int] :
% 0.37/0.68 ( ! [I2: real] :
% 0.37/0.68 ( ( member_real @ I2 @ K4 )
% 0.37/0.68 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 0.37/0.68 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K4 ) @ ( groups1932886352136224148al_int @ G @ K4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_mono
% 0.37/0.68 thf(fact_6468_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 0.37/0.68 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ ( image_VEBT_VEBT_nat @ F @ A4 ) )
% 0.37/0.68 => ? [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6469_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_real,F: real > nat] :
% 0.37/0.68 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ ( image_real_nat @ F @ A4 ) )
% 0.37/0.68 => ? [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [A7: real] :
% 0.37/0.68 ( ( member_real @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6470_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 0.37/0.68 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( finite_finite_int @ ( image_VEBT_VEBT_int @ F @ A4 ) )
% 0.37/0.68 => ? [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6471_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_real,F: real > int] :
% 0.37/0.68 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( finite_finite_int @ ( image_real_int @ F @ A4 ) )
% 0.37/0.68 => ? [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [A7: real] :
% 0.37/0.68 ( ( member_real @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6472_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > complex] :
% 0.37/0.68 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( finite3207457112153483333omplex @ ( image_3793382806556112285omplex @ F @ A4 ) )
% 0.37/0.68 => ? [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6473_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_real,F: real > complex] :
% 0.37/0.68 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( finite3207457112153483333omplex @ ( image_real_complex @ F @ A4 ) )
% 0.37/0.68 => ? [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [A7: real] :
% 0.37/0.68 ( ( member_real @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6474_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > code_integer] :
% 0.37/0.68 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( finite6017078050557962740nteger @ ( image_2092689629700589388nteger @ F @ A4 ) )
% 0.37/0.68 => ? [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [A7: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6475_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_real,F: real > code_integer] :
% 0.37/0.68 ( ~ ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( finite6017078050557962740nteger @ ( image_4958697645175560720nteger @ F @ A4 ) )
% 0.37/0.68 => ? [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [A7: real] :
% 0.37/0.68 ( ( member_real @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6476_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_nat,F: nat > nat] :
% 0.37/0.68 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 0.37/0.68 => ? [X3: nat] :
% 0.37/0.68 ( ( member_nat @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [A7: nat] :
% 0.37/0.68 ( ( member_nat @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6477_pigeonhole__infinite,axiom,
% 0.37/0.68 ! [A4: set_nat,F: nat > int] :
% 0.37/0.68 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.68 => ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 0.37/0.68 => ? [X3: nat] :
% 0.37/0.68 ( ( member_nat @ X3 @ A4 )
% 0.37/0.68 & ~ ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [A7: nat] :
% 0.37/0.68 ( ( member_nat @ A7 @ A4 )
% 0.37/0.68 & ( ( F @ A7 )
% 0.37/0.68 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pigeonhole_infinite
% 0.37/0.68 thf(fact_6478_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: complex > $o,F: complex > nat,B4: set_nat] :
% 0.37/0.68 ( ! [X3: complex] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_less_eq_set_nat @ ( image_complex_nat @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6479_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: complex > $o,F: complex > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.68 ( ! [X3: complex] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_le4337996190870823476T_VEBT @ ( image_932796090930683071T_VEBT @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6480_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: complex > $o,F: complex > real,B4: set_real] :
% 0.37/0.68 ( ! [X3: complex] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_less_eq_set_real @ ( image_complex_real @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6481_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: nat > $o,F: nat > nat,B4: set_nat] :
% 0.37/0.68 ( ! [X3: nat] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( collect_nat @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6482_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: nat > $o,F: nat > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.68 ( ! [X3: nat] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_le4337996190870823476T_VEBT @ ( image_nat_VEBT_VEBT @ F @ ( collect_nat @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6483_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: nat > $o,F: nat > real,B4: set_real] :
% 0.37/0.68 ( ! [X3: nat] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_less_eq_set_real @ ( image_nat_real @ F @ ( collect_nat @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6484_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: int > $o,F: int > nat,B4: set_nat] :
% 0.37/0.68 ( ! [X3: int] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( collect_int @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6485_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: int > $o,F: int > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 0.37/0.68 ( ! [X3: int] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_le4337996190870823476T_VEBT @ ( image_int_VEBT_VEBT @ F @ ( collect_int @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6486_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: int > $o,F: int > real,B4: set_real] :
% 0.37/0.68 ( ! [X3: int] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_less_eq_set_real @ ( image_int_real @ F @ ( collect_int @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6487_image__Collect__subsetI,axiom,
% 0.37/0.68 ! [P2: complex > $o,F: complex > int,B4: set_int] :
% 0.37/0.68 ( ! [X3: complex] :
% 0.37/0.68 ( ( P2 @ X3 )
% 0.37/0.68 => ( member_int @ ( F @ X3 ) @ B4 ) )
% 0.37/0.68 => ( ord_less_eq_set_int @ ( image_complex_int @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_Collect_subsetI
% 0.37/0.68 thf(fact_6488_Collect__conv__if2,axiom,
% 0.37/0.68 ! [P2: vEBT_VEBT > $o,A: vEBT_VEBT] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if2
% 0.37/0.68 thf(fact_6489_Collect__conv__if2,axiom,
% 0.37/0.68 ! [P2: complex > $o,A: complex] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_complex ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if2
% 0.37/0.68 thf(fact_6490_Collect__conv__if2,axiom,
% 0.37/0.68 ! [P2: list_nat > $o,A: list_nat] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_list_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if2
% 0.37/0.68 thf(fact_6491_Collect__conv__if2,axiom,
% 0.37/0.68 ! [P2: set_nat > $o,A: set_nat] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if2
% 0.37/0.68 thf(fact_6492_Collect__conv__if2,axiom,
% 0.37/0.68 ! [P2: nat > $o,A: nat] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if2
% 0.37/0.68 thf(fact_6493_Collect__conv__if2,axiom,
% 0.37/0.68 ! [P2: int > $o,A: int] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_int ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if2
% 0.37/0.68 thf(fact_6494_Collect__conv__if2,axiom,
% 0.37/0.68 ! [P2: $o > $o,A: $o] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_o
% 0.37/0.68 @ ^ [X4: $o] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_o
% 0.37/0.68 @ ^ [X4: $o] :
% 0.37/0.68 ( ( A = X4 )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_o ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if2
% 0.37/0.68 thf(fact_6495_Collect__conv__if,axiom,
% 0.37/0.68 ! [P2: vEBT_VEBT > $o,A: vEBT_VEBT] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if
% 0.37/0.68 thf(fact_6496_Collect__conv__if,axiom,
% 0.37/0.68 ! [P2: complex > $o,A: complex] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_complex ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if
% 0.37/0.68 thf(fact_6497_Collect__conv__if,axiom,
% 0.37/0.68 ! [P2: list_nat > $o,A: list_nat] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_list_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if
% 0.37/0.68 thf(fact_6498_Collect__conv__if,axiom,
% 0.37/0.68 ! [P2: set_nat > $o,A: set_nat] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if
% 0.37/0.68 thf(fact_6499_Collect__conv__if,axiom,
% 0.37/0.68 ! [P2: nat > $o,A: nat] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if
% 0.37/0.68 thf(fact_6500_Collect__conv__if,axiom,
% 0.37/0.68 ! [P2: int > $o,A: int] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_int ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if
% 0.37/0.68 thf(fact_6501_Collect__conv__if,axiom,
% 0.37/0.68 ! [P2: $o > $o,A: $o] :
% 0.37/0.68 ( ( ( P2 @ A )
% 0.37/0.68 => ( ( collect_o
% 0.37/0.68 @ ^ [X4: $o] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.37/0.68 & ( ~ ( P2 @ A )
% 0.37/0.68 => ( ( collect_o
% 0.37/0.68 @ ^ [X4: $o] :
% 0.37/0.68 ( ( X4 = A )
% 0.37/0.68 & ( P2 @ X4 ) ) )
% 0.37/0.68 = bot_bot_set_o ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Collect_conv_if
% 0.37/0.68 thf(fact_6502_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,B4: set_nat,G: vEBT_VEBT > nat > nat,R2: vEBT_VEBT > nat > $o] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ B4 )
% 0.37/0.68 => ( ( groups771621172384141258BT_nat
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( ( member_nat @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups771621172384141258BT_nat
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6503_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_real,B4: set_nat,G: real > nat > nat,R2: real > nat > $o] :
% 0.37/0.68 ( ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ B4 )
% 0.37/0.68 => ( ( groups1935376822645274424al_nat
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( ( member_nat @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups1935376822645274424al_nat
% 0.37/0.68 @ ^ [X4: real] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6504_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_int,B4: set_nat,G: int > nat > nat,R2: int > nat > $o] :
% 0.37/0.68 ( ( finite_finite_int @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ B4 )
% 0.37/0.68 => ( ( groups4541462559716669496nt_nat
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( ( member_nat @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups4541462559716669496nt_nat
% 0.37/0.68 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6505_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_complex,B4: set_nat,G: complex > nat > nat,R2: complex > nat > $o] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ B4 )
% 0.37/0.68 => ( ( groups5693394587270226106ex_nat
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( ( member_nat @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups5693394587270226106ex_nat
% 0.37/0.68 @ ^ [X4: complex] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( member_complex @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6506_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_Code_integer,B4: set_nat,G: code_integer > nat > nat,R2: code_integer > nat > $o] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.68 => ( ( finite_finite_nat @ B4 )
% 0.37/0.68 => ( ( groups7237345082560585321er_nat
% 0.37/0.68 @ ^ [X4: code_integer] :
% 0.37/0.68 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( ( member_nat @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups7237345082560585321er_nat
% 0.37/0.68 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [X4: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6507_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,B4: set_complex,G: vEBT_VEBT > complex > complex,R2: vEBT_VEBT > complex > $o] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.68 => ( ( groups1794756597179926696omplex
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( groups7754918857620584856omplex @ ( G @ X4 )
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( ( member_complex @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups1794756597179926696omplex
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6508_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_real,B4: set_complex,G: real > complex > complex,R2: real > complex > $o] :
% 0.37/0.68 ( ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.68 => ( ( groups5754745047067104278omplex
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( groups7754918857620584856omplex @ ( G @ X4 )
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( ( member_complex @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups5754745047067104278omplex
% 0.37/0.68 @ ^ [X4: real] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6509_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_nat,B4: set_complex,G: nat > complex > complex,R2: nat > complex > $o] :
% 0.37/0.68 ( ( finite_finite_nat @ A4 )
% 0.37/0.68 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.68 => ( ( groups2073611262835488442omplex
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( groups7754918857620584856omplex @ ( G @ X4 )
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( ( member_complex @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups2073611262835488442omplex
% 0.37/0.68 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( member_nat @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6510_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_int,B4: set_complex,G: int > complex > complex,R2: int > complex > $o] :
% 0.37/0.68 ( ( finite_finite_int @ A4 )
% 0.37/0.68 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.68 => ( ( groups3049146728041665814omplex
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( groups7754918857620584856omplex @ ( G @ X4 )
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( ( member_complex @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups3049146728041665814omplex
% 0.37/0.68 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6511_sum_Oswap__restrict,axiom,
% 0.37/0.68 ! [A4: set_Code_integer,B4: set_complex,G: code_integer > complex > complex,R2: code_integer > complex > $o] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.68 => ( ( finite3207457112153483333omplex @ B4 )
% 0.37/0.68 => ( ( groups8024822376189712711omplex
% 0.37/0.68 @ ^ [X4: code_integer] :
% 0.37/0.68 ( groups7754918857620584856omplex @ ( G @ X4 )
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( ( member_complex @ Y4 @ B4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups8024822376189712711omplex
% 0.37/0.68 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [X4: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ X4 @ A4 )
% 0.37/0.68 & ( R2 @ X4 @ Y4 ) ) ) )
% 0.37/0.68 @ B4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.swap_restrict
% 0.37/0.68 thf(fact_6512_sum__diff__distrib,axiom,
% 0.37/0.68 ! [Q2: int > nat,P2: int > nat,N: int] :
% 0.37/0.68 ( ! [X3: int] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 0.37/0.68 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P2 @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q2 @ ( set_ord_lessThan_int @ N ) ) )
% 0.37/0.68 = ( groups4541462559716669496nt_nat
% 0.37/0.68 @ ^ [X4: int] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 0.37/0.68 @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_diff_distrib
% 0.37/0.68 thf(fact_6513_sum__diff__distrib,axiom,
% 0.37/0.68 ! [Q2: real > nat,P2: real > nat,N: real] :
% 0.37/0.68 ( ! [X3: real] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 0.37/0.68 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P2 @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q2 @ ( set_or5984915006950818249n_real @ N ) ) )
% 0.37/0.68 = ( groups1935376822645274424al_nat
% 0.37/0.68 @ ^ [X4: real] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 0.37/0.68 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_diff_distrib
% 0.37/0.68 thf(fact_6514_sum__diff__distrib,axiom,
% 0.37/0.68 ! [Q2: nat > nat,P2: nat > nat,N: nat] :
% 0.37/0.68 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 0.37/0.68 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P2 @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q2 @ ( set_ord_lessThan_nat @ N ) ) )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [X4: nat] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_diff_distrib
% 0.37/0.68 thf(fact_6515_max__def__raw,axiom,
% 0.37/0.68 ( ord_max_Code_integer
% 0.37/0.68 = ( ^ [A7: code_integer,B7: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % max_def_raw
% 0.37/0.68 thf(fact_6516_max__def__raw,axiom,
% 0.37/0.68 ( ord_max_set_int
% 0.37/0.68 = ( ^ [A7: set_int,B7: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % max_def_raw
% 0.37/0.68 thf(fact_6517_max__def__raw,axiom,
% 0.37/0.68 ( ord_max_rat
% 0.37/0.68 = ( ^ [A7: rat,B7: rat] : ( if_rat @ ( ord_less_eq_rat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % max_def_raw
% 0.37/0.68 thf(fact_6518_max__def__raw,axiom,
% 0.37/0.68 ( ord_max_num
% 0.37/0.68 = ( ^ [A7: num,B7: num] : ( if_num @ ( ord_less_eq_num @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % max_def_raw
% 0.37/0.68 thf(fact_6519_max__def__raw,axiom,
% 0.37/0.68 ( ord_max_nat
% 0.37/0.68 = ( ^ [A7: nat,B7: nat] : ( if_nat @ ( ord_less_eq_nat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % max_def_raw
% 0.37/0.68 thf(fact_6520_max__def__raw,axiom,
% 0.37/0.68 ( ord_max_int
% 0.37/0.68 = ( ^ [A7: int,B7: int] : ( if_int @ ( ord_less_eq_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % max_def_raw
% 0.37/0.68 thf(fact_6521_pred__subset__eq2,axiom,
% 0.37/0.68 ! [R2: set_Pr1773385645901665561uint32,S3: set_Pr1773385645901665561uint32] :
% 0.37/0.68 ( ( ord_le5999336846926846542nt32_o
% 0.37/0.68 @ ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R2 )
% 0.37/0.68 @ ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ S3 ) )
% 0.37/0.68 = ( ord_le6429528607962791097uint32 @ R2 @ S3 ) ) ).
% 0.37/0.68
% 0.37/0.68 % pred_subset_eq2
% 0.37/0.68 thf(fact_6522_pred__subset__eq2,axiom,
% 0.37/0.68 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 0.37/0.68 ( ( ord_le2646555220125990790_nat_o
% 0.37/0.68 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R2 )
% 0.37/0.68 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S3 ) )
% 0.37/0.68 = ( ord_le3146513528884898305at_nat @ R2 @ S3 ) ) ).
% 0.37/0.68
% 0.37/0.68 % pred_subset_eq2
% 0.37/0.68 thf(fact_6523_pred__subset__eq2,axiom,
% 0.37/0.68 ! [R2: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 0.37/0.68 ( ( ord_le6741204236512500942_int_o
% 0.37/0.68 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R2 )
% 0.37/0.68 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S3 ) )
% 0.37/0.68 = ( ord_le2843351958646193337nt_int @ R2 @ S3 ) ) ).
% 0.37/0.68
% 0.37/0.68 % pred_subset_eq2
% 0.37/0.68 thf(fact_6524_pred__subset__eq2,axiom,
% 0.37/0.68 ! [R2: set_Pr3286484037609594932et_nat,S3: set_Pr3286484037609594932et_nat] :
% 0.37/0.68 ( ( ord_le8000401564054156549_nat_o
% 0.37/0.68 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R2 )
% 0.37/0.68 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S3 ) )
% 0.37/0.68 = ( ord_le5966269811547037844et_nat @ R2 @ S3 ) ) ).
% 0.37/0.68
% 0.37/0.68 % pred_subset_eq2
% 0.37/0.68 thf(fact_6525_pred__subset__eq2,axiom,
% 0.37/0.68 ! [R2: set_Pr8536935166611901872et_nat,S3: set_Pr8536935166611901872et_nat] :
% 0.37/0.68 ( ( ord_le6753239538765779593_nat_o
% 0.37/0.68 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R2 )
% 0.37/0.68 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S3 ) )
% 0.37/0.68 = ( ord_le4763372923235995152et_nat @ R2 @ S3 ) ) ).
% 0.37/0.68
% 0.37/0.68 % pred_subset_eq2
% 0.37/0.68 thf(fact_6526_bot__empty__eq2,axiom,
% 0.37/0.68 ( bot_bo8112279147790955290nt32_o
% 0.37/0.68 = ( ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ bot_bo8438649754162204037uint32 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % bot_empty_eq2
% 0.37/0.68 thf(fact_6527_bot__empty__eq2,axiom,
% 0.37/0.68 ( bot_bot_nat_nat_o
% 0.37/0.68 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % bot_empty_eq2
% 0.37/0.68 thf(fact_6528_bot__empty__eq2,axiom,
% 0.37/0.68 ( bot_bot_int_int_o
% 0.37/0.68 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % bot_empty_eq2
% 0.37/0.68 thf(fact_6529_bot__empty__eq2,axiom,
% 0.37/0.68 ( bot_bo5580076615179976505_nat_o
% 0.37/0.68 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % bot_empty_eq2
% 0.37/0.68 thf(fact_6530_bot__empty__eq2,axiom,
% 0.37/0.68 ( bot_bo3790638025767943357_nat_o
% 0.37/0.68 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % bot_empty_eq2
% 0.37/0.68 thf(fact_6531_finite__M__bounded__by__nat,axiom,
% 0.37/0.68 ! [P2: nat > $o,I: nat] :
% 0.37/0.68 ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [K3: nat] :
% 0.37/0.68 ( ( P2 @ K3 )
% 0.37/0.68 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_M_bounded_by_nat
% 0.37/0.68 thf(fact_6532_finite__less__ub,axiom,
% 0.37/0.68 ! [F: nat > nat,U: nat] :
% 0.37/0.68 ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 0.37/0.68 => ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [N6: nat] : ( ord_less_eq_nat @ ( F @ N6 ) @ U ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_less_ub
% 0.37/0.68 thf(fact_6533_set__vebt__def,axiom,
% 0.37/0.68 ( vEBT_set_vebt
% 0.37/0.68 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % set_vebt_def
% 0.37/0.68 thf(fact_6534_zip__inj,axiom,
% 0.37/0.68 ! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,A2: list_VEBT_VEBT,B2: list_VEBT_VEBT] :
% 0.37/0.68 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ B ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 0.37/0.68 => ( ( ( zip_VE537291747668921783T_VEBT @ A @ B )
% 0.37/0.68 = ( zip_VE537291747668921783T_VEBT @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6535_zip__inj,axiom,
% 0.37/0.68 ! [A: list_VEBT_VEBT,B: list_real,A2: list_VEBT_VEBT,B2: list_real] :
% 0.37/0.68 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.68 = ( size_size_list_real @ B ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.68 = ( size_size_list_real @ B2 ) )
% 0.37/0.68 => ( ( ( zip_VEBT_VEBT_real @ A @ B )
% 0.37/0.68 = ( zip_VEBT_VEBT_real @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6536_zip__inj,axiom,
% 0.37/0.68 ! [A: list_VEBT_VEBT,B: list_o,A2: list_VEBT_VEBT,B2: list_o] :
% 0.37/0.68 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.68 = ( size_size_list_o @ B ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.68 = ( size_size_list_o @ B2 ) )
% 0.37/0.68 => ( ( ( zip_VEBT_VEBT_o @ A @ B )
% 0.37/0.68 = ( zip_VEBT_VEBT_o @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6537_zip__inj,axiom,
% 0.37/0.68 ! [A: list_VEBT_VEBT,B: list_nat,A2: list_VEBT_VEBT,B2: list_nat] :
% 0.37/0.68 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 0.37/0.68 = ( size_size_list_nat @ B ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 0.37/0.68 = ( size_size_list_nat @ B2 ) )
% 0.37/0.68 => ( ( ( zip_VEBT_VEBT_nat @ A @ B )
% 0.37/0.68 = ( zip_VEBT_VEBT_nat @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6538_zip__inj,axiom,
% 0.37/0.68 ! [A: list_real,B: list_VEBT_VEBT,A2: list_real,B2: list_VEBT_VEBT] :
% 0.37/0.68 ( ( ( size_size_list_real @ A )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ B ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 0.37/0.68 => ( ( ( zip_real_VEBT_VEBT @ A @ B )
% 0.37/0.68 = ( zip_real_VEBT_VEBT @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6539_zip__inj,axiom,
% 0.37/0.68 ! [A: list_real,B: list_real,A2: list_real,B2: list_real] :
% 0.37/0.68 ( ( ( size_size_list_real @ A )
% 0.37/0.68 = ( size_size_list_real @ B ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.68 = ( size_size_list_real @ B2 ) )
% 0.37/0.68 => ( ( ( zip_real_real @ A @ B )
% 0.37/0.68 = ( zip_real_real @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6540_zip__inj,axiom,
% 0.37/0.68 ! [A: list_real,B: list_o,A2: list_real,B2: list_o] :
% 0.37/0.68 ( ( ( size_size_list_real @ A )
% 0.37/0.68 = ( size_size_list_o @ B ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.68 = ( size_size_list_o @ B2 ) )
% 0.37/0.68 => ( ( ( zip_real_o @ A @ B )
% 0.37/0.68 = ( zip_real_o @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6541_zip__inj,axiom,
% 0.37/0.68 ! [A: list_real,B: list_nat,A2: list_real,B2: list_nat] :
% 0.37/0.68 ( ( ( size_size_list_real @ A )
% 0.37/0.68 = ( size_size_list_nat @ B ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ A2 )
% 0.37/0.68 = ( size_size_list_nat @ B2 ) )
% 0.37/0.68 => ( ( ( zip_real_nat @ A @ B )
% 0.37/0.68 = ( zip_real_nat @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6542_zip__inj,axiom,
% 0.37/0.68 ! [A: list_o,B: list_VEBT_VEBT,A2: list_o,B2: list_VEBT_VEBT] :
% 0.37/0.68 ( ( ( size_size_list_o @ A )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ B ) )
% 0.37/0.68 => ( ( ( size_size_list_o @ A2 )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 0.37/0.68 => ( ( ( zip_o_VEBT_VEBT @ A @ B )
% 0.37/0.68 = ( zip_o_VEBT_VEBT @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6543_zip__inj,axiom,
% 0.37/0.68 ! [A: list_o,B: list_real,A2: list_o,B2: list_real] :
% 0.37/0.68 ( ( ( size_size_list_o @ A )
% 0.37/0.68 = ( size_size_list_real @ B ) )
% 0.37/0.68 => ( ( ( size_size_list_o @ A2 )
% 0.37/0.68 = ( size_size_list_real @ B2 ) )
% 0.37/0.68 => ( ( ( zip_o_real @ A @ B )
% 0.37/0.68 = ( zip_o_real @ A2 @ B2 ) )
% 0.37/0.68 => ( ( A = A2 )
% 0.37/0.68 & ( B = B2 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % zip_inj
% 0.37/0.68 thf(fact_6544_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P7413028617227757229T_VEBT] :
% 0.37/0.68 ~ ! [L1: list_VEBT_VEBT,L22: list_VEBT_VEBT] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_VE537291747668921783T_VEBT @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ L22 ) )
% 0.37/0.68 => ( ( size_s7466405169056248089T_VEBT @ L )
% 0.37/0.68 != ( size_s6755466524823107622T_VEBT @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6545_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P2623026923184700063T_real] :
% 0.37/0.68 ~ ! [L1: list_VEBT_VEBT,L22: list_real] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_VEBT_VEBT_real @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 0.37/0.68 = ( size_size_list_real @ L22 ) )
% 0.37/0.68 => ( ( size_s5035110155006384947T_real @ L )
% 0.37/0.68 != ( size_size_list_real @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6546_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P3126845725202233233VEBT_o] :
% 0.37/0.68 ~ ! [L1: list_VEBT_VEBT,L22: list_o] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_VEBT_VEBT_o @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 0.37/0.68 = ( size_size_list_o @ L22 ) )
% 0.37/0.68 => ( ( size_s9168528473962070013VEBT_o @ L )
% 0.37/0.68 != ( size_size_list_o @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6547_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P7037539587688870467BT_nat] :
% 0.37/0.68 ~ ! [L1: list_VEBT_VEBT,L22: list_nat] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_VEBT_VEBT_nat @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 0.37/0.68 = ( size_size_list_nat @ L22 ) )
% 0.37/0.68 => ( ( size_s6152045936467909847BT_nat @ L )
% 0.37/0.68 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6548_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P877281246627933069T_VEBT] :
% 0.37/0.68 ~ ! [L1: list_real,L22: list_VEBT_VEBT] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_real_VEBT_VEBT @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ L1 )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ L22 ) )
% 0.37/0.68 => ( ( size_s3289364478449617953T_VEBT @ L )
% 0.37/0.68 != ( size_s6755466524823107622T_VEBT @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6549_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P8689742595348180415l_real] :
% 0.37/0.68 ~ ! [L1: list_real,L22: list_real] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_real_real @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ L1 )
% 0.37/0.68 = ( size_size_list_real @ L22 ) )
% 0.37/0.68 => ( ( size_s3932428310213730859l_real @ L )
% 0.37/0.68 != ( size_size_list_real @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6550_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P3595434254542482545real_o] :
% 0.37/0.68 ~ ! [L1: list_real,L22: list_o] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_real_o @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ L1 )
% 0.37/0.68 = ( size_size_list_o @ L22 ) )
% 0.37/0.68 => ( ( size_s987546567493390085real_o @ L )
% 0.37/0.68 != ( size_size_list_o @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6551_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P6834414599653733731al_nat] :
% 0.37/0.68 ~ ! [L1: list_real,L22: list_nat] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_real_nat @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_size_list_real @ L1 )
% 0.37/0.68 = ( size_size_list_nat @ L22 ) )
% 0.37/0.68 => ( ( size_s1877336372972134351al_nat @ L )
% 0.37/0.68 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6552_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P7495141550334521929T_VEBT] :
% 0.37/0.68 ~ ! [L1: list_o,L22: list_VEBT_VEBT] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_o_VEBT_VEBT @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_size_list_o @ L1 )
% 0.37/0.68 = ( size_s6755466524823107622T_VEBT @ L22 ) )
% 0.37/0.68 => ( ( size_s4313452262239582901T_VEBT @ L )
% 0.37/0.68 != ( size_s6755466524823107622T_VEBT @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6553_pair__list__split,axiom,
% 0.37/0.68 ! [L: list_P5232166724548748803o_real] :
% 0.37/0.68 ~ ! [L1: list_o,L22: list_real] :
% 0.37/0.68 ( ( L
% 0.37/0.68 = ( zip_o_real @ L1 @ L22 ) )
% 0.37/0.68 => ( ( ( size_size_list_o @ L1 )
% 0.37/0.68 = ( size_size_list_real @ L22 ) )
% 0.37/0.68 => ( ( size_s2624279037499656343o_real @ L )
% 0.37/0.68 != ( size_size_list_real @ L22 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % pair_list_split
% 0.37/0.68 thf(fact_6554_real__arch__simple,axiom,
% 0.37/0.68 ! [X: real] :
% 0.37/0.68 ? [N2: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.37/0.68
% 0.37/0.68 % real_arch_simple
% 0.37/0.68 thf(fact_6555_real__arch__simple,axiom,
% 0.37/0.68 ! [X: rat] :
% 0.37/0.68 ? [N2: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.37/0.68
% 0.37/0.68 % real_arch_simple
% 0.37/0.68 thf(fact_6556_reals__Archimedean2,axiom,
% 0.37/0.68 ! [X: rat] :
% 0.37/0.68 ? [N2: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 0.37/0.68
% 0.37/0.68 % reals_Archimedean2
% 0.37/0.68 thf(fact_6557_reals__Archimedean2,axiom,
% 0.37/0.68 ! [X: real] :
% 0.37/0.68 ? [N2: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 0.37/0.68
% 0.37/0.68 % reals_Archimedean2
% 0.37/0.68 thf(fact_6558_mult__of__nat__commute,axiom,
% 0.37/0.68 ! [X: nat,Y: uint32] :
% 0.37/0.68 ( ( times_times_uint32 @ ( semiri2565882477558803405uint32 @ X ) @ Y )
% 0.37/0.68 = ( times_times_uint32 @ Y @ ( semiri2565882477558803405uint32 @ X ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % mult_of_nat_commute
% 0.37/0.68 thf(fact_6559_mult__of__nat__commute,axiom,
% 0.37/0.68 ! [X: nat,Y: nat] :
% 0.37/0.68 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 0.37/0.68 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % mult_of_nat_commute
% 0.37/0.68 thf(fact_6560_mult__of__nat__commute,axiom,
% 0.37/0.68 ! [X: nat,Y: real] :
% 0.37/0.68 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 0.37/0.68 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % mult_of_nat_commute
% 0.37/0.68 thf(fact_6561_mult__of__nat__commute,axiom,
% 0.37/0.68 ! [X: nat,Y: int] :
% 0.37/0.68 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 0.37/0.68 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % mult_of_nat_commute
% 0.37/0.68 thf(fact_6562_mult__of__nat__commute,axiom,
% 0.37/0.68 ! [X: nat,Y: code_integer] :
% 0.37/0.68 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 0.37/0.68 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % mult_of_nat_commute
% 0.37/0.68 thf(fact_6563_lessThan__non__empty,axiom,
% 0.37/0.68 ! [X: int] :
% 0.37/0.68 ( ( set_ord_lessThan_int @ X )
% 0.37/0.68 != bot_bot_set_int ) ).
% 0.37/0.68
% 0.37/0.68 % lessThan_non_empty
% 0.37/0.68 thf(fact_6564_lessThan__non__empty,axiom,
% 0.37/0.68 ! [X: real] :
% 0.37/0.68 ( ( set_or5984915006950818249n_real @ X )
% 0.37/0.68 != bot_bot_set_real ) ).
% 0.37/0.68
% 0.37/0.68 % lessThan_non_empty
% 0.37/0.68 thf(fact_6565_infinite__Iio,axiom,
% 0.37/0.68 ! [A: int] :
% 0.37/0.68 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 0.37/0.68
% 0.37/0.68 % infinite_Iio
% 0.37/0.68 thf(fact_6566_infinite__Iio,axiom,
% 0.37/0.68 ! [A: real] :
% 0.37/0.68 ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A ) ) ).
% 0.37/0.68
% 0.37/0.68 % infinite_Iio
% 0.37/0.68 thf(fact_6567_sum_OlessThan__Suc__shift,axiom,
% 0.37/0.68 ! [G: nat > rat,N: nat] :
% 0.37/0.68 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.68 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 0.37/0.68 @ ( groups2906978787729119204at_rat
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.lessThan_Suc_shift
% 0.37/0.68 thf(fact_6568_sum_OlessThan__Suc__shift,axiom,
% 0.37/0.68 ! [G: nat > int,N: nat] :
% 0.37/0.68 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.68 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 0.37/0.68 @ ( groups3539618377306564664at_int
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.lessThan_Suc_shift
% 0.37/0.68 thf(fact_6569_sum_OlessThan__Suc__shift,axiom,
% 0.37/0.68 ! [G: nat > nat,N: nat] :
% 0.37/0.68 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.68 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 0.37/0.68 @ ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.lessThan_Suc_shift
% 0.37/0.68 thf(fact_6570_sum_OlessThan__Suc__shift,axiom,
% 0.37/0.68 ! [G: nat > real,N: nat] :
% 0.37/0.68 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.68 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 0.37/0.68 @ ( groups6591440286371151544t_real
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.lessThan_Suc_shift
% 0.37/0.68 thf(fact_6571_sum__lessThan__telescope,axiom,
% 0.37/0.68 ! [F: nat > uint32,M: nat] :
% 0.37/0.68 ( ( groups833757482993574392uint32
% 0.37/0.68 @ ^ [N6: nat] : ( minus_minus_uint32 @ ( F @ ( suc @ N6 ) ) @ ( F @ N6 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ M ) )
% 0.37/0.68 = ( minus_minus_uint32 @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_lessThan_telescope
% 0.37/0.68 thf(fact_6572_sum__lessThan__telescope,axiom,
% 0.37/0.68 ! [F: nat > int,M: nat] :
% 0.37/0.68 ( ( groups3539618377306564664at_int
% 0.37/0.68 @ ^ [N6: nat] : ( minus_minus_int @ ( F @ ( suc @ N6 ) ) @ ( F @ N6 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ M ) )
% 0.37/0.68 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_lessThan_telescope
% 0.37/0.68 thf(fact_6573_sum__lessThan__telescope,axiom,
% 0.37/0.68 ! [F: nat > real,M: nat] :
% 0.37/0.68 ( ( groups6591440286371151544t_real
% 0.37/0.68 @ ^ [N6: nat] : ( minus_minus_real @ ( F @ ( suc @ N6 ) ) @ ( F @ N6 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ M ) )
% 0.37/0.68 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_lessThan_telescope
% 0.37/0.68 thf(fact_6574_sum__lessThan__telescope_H,axiom,
% 0.37/0.68 ! [F: nat > uint32,M: nat] :
% 0.37/0.68 ( ( groups833757482993574392uint32
% 0.37/0.68 @ ^ [N6: nat] : ( minus_minus_uint32 @ ( F @ N6 ) @ ( F @ ( suc @ N6 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ M ) )
% 0.37/0.68 = ( minus_minus_uint32 @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_lessThan_telescope'
% 0.37/0.68 thf(fact_6575_sum__lessThan__telescope_H,axiom,
% 0.37/0.68 ! [F: nat > int,M: nat] :
% 0.37/0.68 ( ( groups3539618377306564664at_int
% 0.37/0.68 @ ^ [N6: nat] : ( minus_minus_int @ ( F @ N6 ) @ ( F @ ( suc @ N6 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ M ) )
% 0.37/0.68 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_lessThan_telescope'
% 0.37/0.68 thf(fact_6576_sum__lessThan__telescope_H,axiom,
% 0.37/0.68 ! [F: nat > real,M: nat] :
% 0.37/0.68 ( ( groups6591440286371151544t_real
% 0.37/0.68 @ ^ [N6: nat] : ( minus_minus_real @ ( F @ N6 ) @ ( F @ ( suc @ N6 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ M ) )
% 0.37/0.68 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_lessThan_telescope'
% 0.37/0.68 thf(fact_6577_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > uint32,Y: vEBT_VEBT > uint32] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_uint32 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6578_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_real,X: real > uint32,Y: real > uint32] :
% 0.37/0.68 ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_uint32 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6579_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_nat,X: nat > uint32,Y: nat > uint32] :
% 0.37/0.68 ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_uint32 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6580_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_int,X: int > uint32,Y: int > uint32] :
% 0.37/0.68 ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_uint32 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6581_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_complex,X: complex > uint32,Y: complex > uint32] :
% 0.37/0.68 ( ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [I3: complex] :
% 0.37/0.68 ( ( member_complex @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [I3: complex] :
% 0.37/0.68 ( ( member_complex @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [I3: complex] :
% 0.37/0.68 ( ( member_complex @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_uint32 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6582_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_Code_integer,X: code_integer > uint32,Y: code_integer > uint32] :
% 0.37/0.68 ( ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [I3: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [I3: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_uint32 ) ) ) )
% 0.37/0.68 => ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [I3: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_uint32 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6583_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > real,Y: vEBT_VEBT > real] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6584_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_real,X: real > real,Y: real > real] :
% 0.37/0.68 ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6585_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 0.37/0.68 ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6586_sum_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_int,X: int > real,Y: int > real] :
% 0.37/0.68 ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != zero_zero_real ) ) ) )
% 0.37/0.68 => ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.finite_Collect_op
% 0.37/0.68 thf(fact_6587_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > rat,Y: vEBT_VEBT > rat] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_rat ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6588_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_real,X: real > rat,Y: real > rat] :
% 0.37/0.68 ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_rat ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6589_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 0.37/0.68 ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_rat ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6590_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_int,X: int > rat,Y: int > rat] :
% 0.37/0.68 ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_rat ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6591_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_complex,X: complex > rat,Y: complex > rat] :
% 0.37/0.68 ( ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [I3: complex] :
% 0.37/0.68 ( ( member_complex @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [I3: complex] :
% 0.37/0.68 ( ( member_complex @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [I3: complex] :
% 0.37/0.68 ( ( member_complex @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_rat ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6592_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_Code_integer,X: code_integer > rat,Y: code_integer > rat] :
% 0.37/0.68 ( ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [I3: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [I3: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_rat ) ) ) )
% 0.37/0.68 => ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [I3: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_rat ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6593_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > assn,Y: vEBT_VEBT > assn] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( finite5795047828879050333T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_assn ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6594_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_real,X: real > assn,Y: real > assn] :
% 0.37/0.68 ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_assn ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6595_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_nat,X: nat > assn,Y: nat > assn] :
% 0.37/0.68 ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] :
% 0.37/0.68 ( ( member_nat @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_assn ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6596_prod_Ofinite__Collect__op,axiom,
% 0.37/0.68 ! [I5: set_int,X: int > assn,Y: int > assn] :
% 0.37/0.68 ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( X @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( Y @ I3 )
% 0.37/0.68 != one_one_assn ) ) ) )
% 0.37/0.68 => ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [I3: int] :
% 0.37/0.68 ( ( member_int @ I3 @ I5 )
% 0.37/0.68 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.37/0.68 != one_one_assn ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % prod.finite_Collect_op
% 0.37/0.68 thf(fact_6597_filter__preserves__multiset,axiom,
% 0.37/0.68 ! [M7: list_nat > nat,P2: list_nat > $o] :
% 0.37/0.68 ( ( finite8100373058378681591st_nat
% 0.37/0.68 @ ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite8100373058378681591st_nat
% 0.37/0.68 @ ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % filter_preserves_multiset
% 0.37/0.68 thf(fact_6598_filter__preserves__multiset,axiom,
% 0.37/0.68 ! [M7: set_nat > nat,P2: set_nat > $o] :
% 0.37/0.68 ( ( finite1152437895449049373et_nat
% 0.37/0.68 @ ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite1152437895449049373et_nat
% 0.37/0.68 @ ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % filter_preserves_multiset
% 0.37/0.68 thf(fact_6599_filter__preserves__multiset,axiom,
% 0.37/0.68 ! [M7: nat > nat,P2: nat > $o] :
% 0.37/0.68 ( ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite_finite_nat
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % filter_preserves_multiset
% 0.37/0.68 thf(fact_6600_filter__preserves__multiset,axiom,
% 0.37/0.68 ! [M7: int > nat,P2: int > $o] :
% 0.37/0.68 ( ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite_finite_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % filter_preserves_multiset
% 0.37/0.68 thf(fact_6601_filter__preserves__multiset,axiom,
% 0.37/0.68 ! [M7: complex > nat,P2: complex > $o] :
% 0.37/0.68 ( ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite3207457112153483333omplex
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % filter_preserves_multiset
% 0.37/0.68 thf(fact_6602_filter__preserves__multiset,axiom,
% 0.37/0.68 ! [M7: code_integer > nat,P2: code_integer > $o] :
% 0.37/0.68 ( ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite6017078050557962740nteger
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % filter_preserves_multiset
% 0.37/0.68 thf(fact_6603_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > uint32,P2: vEBT_VEBT > $o] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( groups8325533452322294502uint32 @ G
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups8325533452322294502uint32
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6604_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_real,G: real > uint32,P2: real > $o] :
% 0.37/0.68 ( ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( groups5944083974425963860uint32 @ G
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups5944083974425963860uint32
% 0.37/0.68 @ ^ [X4: real] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6605_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_nat,G: nat > uint32,P2: nat > $o] :
% 0.37/0.68 ( ( finite_finite_nat @ A4 )
% 0.37/0.68 => ( ( groups833757482993574392uint32 @ G
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( member_nat @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups833757482993574392uint32
% 0.37/0.68 @ ^ [X4: nat] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6606_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_int,G: int > uint32,P2: int > $o] :
% 0.37/0.68 ( ( finite_finite_int @ A4 )
% 0.37/0.68 => ( ( groups5712668689793887828uint32 @ G
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups5712668689793887828uint32
% 0.37/0.68 @ ^ [X4: int] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6607_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_complex,G: complex > uint32,P2: complex > $o] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.68 => ( ( groups8736914816313324502uint32 @ G
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( member_complex @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups8736914816313324502uint32
% 0.37/0.68 @ ^ [X4: complex] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6608_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_Code_integer,G: code_integer > uint32,P2: code_integer > $o] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.68 => ( ( groups8847630953604152069uint32 @ G
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [X4: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups8847630953604152069uint32
% 0.37/0.68 @ ^ [X4: code_integer] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6609_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > real,P2: vEBT_VEBT > $o] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.68 => ( ( groups2240296850493347238T_real @ G
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups2240296850493347238T_real
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6610_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_real,G: real > real,P2: real > $o] :
% 0.37/0.68 ( ( finite_finite_real @ A4 )
% 0.37/0.68 => ( ( groups8097168146408367636l_real @ G
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups8097168146408367636l_real
% 0.37/0.68 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6611_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_int,G: int > real,P2: int > $o] :
% 0.37/0.68 ( ( finite_finite_int @ A4 )
% 0.37/0.68 => ( ( groups8778361861064173332t_real @ G
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups8778361861064173332t_real
% 0.37/0.68 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6612_sum_Ointer__filter,axiom,
% 0.37/0.68 ! [A4: set_complex,G: complex > real,P2: complex > $o] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.68 => ( ( groups5808333547571424918x_real @ G
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( member_complex @ X4 @ A4 )
% 0.37/0.68 & ( P2 @ X4 ) ) ) )
% 0.37/0.68 = ( groups5808333547571424918x_real
% 0.37/0.68 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 0.37/0.68 @ A4 ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.inter_filter
% 0.37/0.68 thf(fact_6613_image__constant,axiom,
% 0.37/0.68 ! [X: nat,A4: set_nat,C2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_nat @ X @ A4 )
% 0.37/0.68 => ( ( image_nat_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6614_image__constant,axiom,
% 0.37/0.68 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,C2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.68 => ( ( image_3375948659692109573T_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6615_image__constant,axiom,
% 0.37/0.68 ! [X: real,A4: set_real,C2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_real @ X @ A4 )
% 0.37/0.68 => ( ( image_real_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: real] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6616_image__constant,axiom,
% 0.37/0.68 ! [X: int,A4: set_int,C2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_int @ X @ A4 )
% 0.37/0.68 => ( ( image_int_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6617_image__constant,axiom,
% 0.37/0.68 ! [X: nat,A4: set_nat,C2: nat] :
% 0.37/0.68 ( ( member_nat @ X @ A4 )
% 0.37/0.68 => ( ( image_nat_nat
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6618_image__constant,axiom,
% 0.37/0.68 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,C2: nat] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.68 => ( ( image_VEBT_VEBT_nat
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6619_image__constant,axiom,
% 0.37/0.68 ! [X: real,A4: set_real,C2: nat] :
% 0.37/0.68 ( ( member_real @ X @ A4 )
% 0.37/0.68 => ( ( image_real_nat
% 0.37/0.68 @ ^ [X4: real] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6620_image__constant,axiom,
% 0.37/0.68 ! [X: int,A4: set_int,C2: nat] :
% 0.37/0.68 ( ( member_int @ X @ A4 )
% 0.37/0.68 => ( ( image_int_nat
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6621_image__constant,axiom,
% 0.37/0.68 ! [X: nat,A4: set_nat,C2: int] :
% 0.37/0.68 ( ( member_nat @ X @ A4 )
% 0.37/0.68 => ( ( image_nat_int
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6622_image__constant,axiom,
% 0.37/0.68 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,C2: int] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X @ A4 )
% 0.37/0.68 => ( ( image_VEBT_VEBT_int
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant
% 0.37/0.68 thf(fact_6623_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_nat,C2: vEBT_VEBT] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bo8194388402131092736T_VEBT ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6624_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_nat,C2: nat] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_nat
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bot_set_nat ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_nat
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6625_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_nat,C2: int] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_int
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bot_set_int ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_int
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6626_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_nat,C2: $o] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_o
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bot_set_o ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_nat )
% 0.37/0.68 => ( ( image_nat_o
% 0.37/0.68 @ ^ [X4: nat] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_o @ C2 @ bot_bot_set_o ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6627_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_int,C2: vEBT_VEBT] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bo8194388402131092736T_VEBT ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6628_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_int,C2: nat] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_nat
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bot_set_nat ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_nat
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6629_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_int,C2: int] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_int
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bot_set_int ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_int
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6630_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_int,C2: $o] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_o
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bot_set_o ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_int )
% 0.37/0.68 => ( ( image_int_o
% 0.37/0.68 @ ^ [X4: int] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_o @ C2 @ bot_bot_set_o ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6631_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_o,C2: vEBT_VEBT] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_o )
% 0.37/0.68 => ( ( image_o_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: $o] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bo8194388402131092736T_VEBT ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_o )
% 0.37/0.68 => ( ( image_o_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: $o] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6632_image__constant__conv,axiom,
% 0.37/0.68 ! [A4: set_o,C2: nat] :
% 0.37/0.68 ( ( ( A4 = bot_bot_set_o )
% 0.37/0.68 => ( ( image_o_nat
% 0.37/0.68 @ ^ [X4: $o] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = bot_bot_set_nat ) )
% 0.37/0.68 & ( ( A4 != bot_bot_set_o )
% 0.37/0.68 => ( ( image_o_nat
% 0.37/0.68 @ ^ [X4: $o] : C2
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % image_constant_conv
% 0.37/0.68 thf(fact_6633_foldl__length__aux,axiom,
% 0.37/0.68 ! [A: nat,L: list_VEBT_VEBT] :
% 0.37/0.68 ( ( foldl_nat_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: nat,X4: vEBT_VEBT] : ( suc @ I3 )
% 0.37/0.68 @ A
% 0.37/0.68 @ L )
% 0.37/0.68 = ( plus_plus_nat @ A @ ( size_s6755466524823107622T_VEBT @ L ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % foldl_length_aux
% 0.37/0.68 thf(fact_6634_foldl__length__aux,axiom,
% 0.37/0.68 ! [A: nat,L: list_real] :
% 0.37/0.68 ( ( foldl_nat_real
% 0.37/0.68 @ ^ [I3: nat,X4: real] : ( suc @ I3 )
% 0.37/0.68 @ A
% 0.37/0.68 @ L )
% 0.37/0.68 = ( plus_plus_nat @ A @ ( size_size_list_real @ L ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % foldl_length_aux
% 0.37/0.68 thf(fact_6635_foldl__length__aux,axiom,
% 0.37/0.68 ! [A: nat,L: list_o] :
% 0.37/0.68 ( ( foldl_nat_o
% 0.37/0.68 @ ^ [I3: nat,X4: $o] : ( suc @ I3 )
% 0.37/0.68 @ A
% 0.37/0.68 @ L )
% 0.37/0.68 = ( plus_plus_nat @ A @ ( size_size_list_o @ L ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % foldl_length_aux
% 0.37/0.68 thf(fact_6636_foldl__length__aux,axiom,
% 0.37/0.68 ! [A: nat,L: list_nat] :
% 0.37/0.68 ( ( foldl_nat_nat
% 0.37/0.68 @ ^ [I3: nat,X4: nat] : ( suc @ I3 )
% 0.37/0.68 @ A
% 0.37/0.68 @ L )
% 0.37/0.68 = ( plus_plus_nat @ A @ ( size_size_list_nat @ L ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % foldl_length_aux
% 0.37/0.68 thf(fact_6637_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_VEBT_VEBT,H2: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.68 => ( ( groups771621172384141258BT_nat @ H2 @ S3 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups771621172384141258BT_nat @ H2
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_VEBT_VEBT_nat @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6638_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_real,H2: real > nat,G: real > nat] :
% 0.37/0.68 ( ( finite_finite_real @ S3 )
% 0.37/0.68 => ( ( groups1935376822645274424al_nat @ H2 @ S3 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups1935376822645274424al_nat @ H2
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_real_nat @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6639_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_int,H2: int > nat,G: int > nat] :
% 0.37/0.68 ( ( finite_finite_int @ S3 )
% 0.37/0.68 => ( ( groups4541462559716669496nt_nat @ H2 @ S3 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups4541462559716669496nt_nat @ H2
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_int_nat @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6640_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_complex,H2: complex > nat,G: complex > nat] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.68 => ( ( groups5693394587270226106ex_nat @ H2 @ S3 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups5693394587270226106ex_nat @ H2
% 0.37/0.68 @ ( collect_complex
% 0.37/0.68 @ ^ [X4: complex] :
% 0.37/0.68 ( ( member_complex @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_complex_nat @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6641_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_Code_integer,H2: code_integer > nat,G: code_integer > nat] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.68 => ( ( groups7237345082560585321er_nat @ H2 @ S3 )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [Y4: nat] :
% 0.37/0.68 ( groups7237345082560585321er_nat @ H2
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [X4: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_951025933927791156er_nat @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6642_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_VEBT_VEBT,H2: vEBT_VEBT > complex,G: vEBT_VEBT > complex] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.68 => ( ( groups1794756597179926696omplex @ H2 @ S3 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups1794756597179926696omplex @ H2
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_3793382806556112285omplex @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6643_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_real,H2: real > complex,G: real > complex] :
% 0.37/0.68 ( ( finite_finite_real @ S3 )
% 0.37/0.68 => ( ( groups5754745047067104278omplex @ H2 @ S3 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups5754745047067104278omplex @ H2
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_real_complex @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6644_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_nat,H2: nat > complex,G: nat > complex] :
% 0.37/0.68 ( ( finite_finite_nat @ S3 )
% 0.37/0.68 => ( ( groups2073611262835488442omplex @ H2 @ S3 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups2073611262835488442omplex @ H2
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [X4: nat] :
% 0.37/0.68 ( ( member_nat @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_nat_complex @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6645_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_int,H2: int > complex,G: int > complex] :
% 0.37/0.68 ( ( finite_finite_int @ S3 )
% 0.37/0.68 => ( ( groups3049146728041665814omplex @ H2 @ S3 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups3049146728041665814omplex @ H2
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_int_complex @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6646_sum_Oimage__gen,axiom,
% 0.37/0.68 ! [S3: set_Code_integer,H2: code_integer > complex,G: code_integer > complex] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.68 => ( ( groups8024822376189712711omplex @ H2 @ S3 )
% 0.37/0.68 = ( groups7754918857620584856omplex
% 0.37/0.68 @ ^ [Y4: complex] :
% 0.37/0.68 ( groups8024822376189712711omplex @ H2
% 0.37/0.68 @ ( collect_Code_integer
% 0.37/0.68 @ ^ [X4: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ X4 @ S3 )
% 0.37/0.68 & ( ( G @ X4 )
% 0.37/0.68 = Y4 ) ) ) )
% 0.37/0.68 @ ( image_3397630267976458002omplex @ G @ S3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.image_gen
% 0.37/0.68 thf(fact_6647_nat__seg__image__imp__finite,axiom,
% 0.37/0.68 ! [A4: set_set_nat,F: nat > set_nat,N: nat] :
% 0.37/0.68 ( ( A4
% 0.37/0.68 = ( image_nat_set_nat @ F
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 0.37/0.68 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % nat_seg_image_imp_finite
% 0.37/0.68 thf(fact_6648_nat__seg__image__imp__finite,axiom,
% 0.37/0.68 ! [A4: set_nat,F: nat > nat,N: nat] :
% 0.37/0.68 ( ( A4
% 0.37/0.68 = ( image_nat_nat @ F
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 0.37/0.68 => ( finite_finite_nat @ A4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % nat_seg_image_imp_finite
% 0.37/0.68 thf(fact_6649_nat__seg__image__imp__finite,axiom,
% 0.37/0.68 ! [A4: set_int,F: nat > int,N: nat] :
% 0.37/0.68 ( ( A4
% 0.37/0.68 = ( image_nat_int @ F
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 0.37/0.68 => ( finite_finite_int @ A4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % nat_seg_image_imp_finite
% 0.37/0.68 thf(fact_6650_nat__seg__image__imp__finite,axiom,
% 0.37/0.68 ! [A4: set_complex,F: nat > complex,N: nat] :
% 0.37/0.68 ( ( A4
% 0.37/0.68 = ( image_nat_complex @ F
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 0.37/0.68 => ( finite3207457112153483333omplex @ A4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % nat_seg_image_imp_finite
% 0.37/0.68 thf(fact_6651_nat__seg__image__imp__finite,axiom,
% 0.37/0.68 ! [A4: set_Code_integer,F: nat > code_integer,N: nat] :
% 0.37/0.68 ( ( A4
% 0.37/0.68 = ( image_1215581382706833972nteger @ F
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 0.37/0.68 => ( finite6017078050557962740nteger @ A4 ) ) ).
% 0.37/0.68
% 0.37/0.68 % nat_seg_image_imp_finite
% 0.37/0.68 thf(fact_6652_finite__conv__nat__seg__image,axiom,
% 0.37/0.68 ( finite1152437895449049373et_nat
% 0.37/0.68 = ( ^ [A6: set_set_nat] :
% 0.37/0.68 ? [N6: nat,F5: nat > set_nat] :
% 0.37/0.68 ( A6
% 0.37/0.68 = ( image_nat_set_nat @ F5
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_conv_nat_seg_image
% 0.37/0.68 thf(fact_6653_finite__conv__nat__seg__image,axiom,
% 0.37/0.68 ( finite_finite_nat
% 0.37/0.68 = ( ^ [A6: set_nat] :
% 0.37/0.68 ? [N6: nat,F5: nat > nat] :
% 0.37/0.68 ( A6
% 0.37/0.68 = ( image_nat_nat @ F5
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_conv_nat_seg_image
% 0.37/0.68 thf(fact_6654_finite__conv__nat__seg__image,axiom,
% 0.37/0.68 ( finite_finite_int
% 0.37/0.68 = ( ^ [A6: set_int] :
% 0.37/0.68 ? [N6: nat,F5: nat > int] :
% 0.37/0.68 ( A6
% 0.37/0.68 = ( image_nat_int @ F5
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_conv_nat_seg_image
% 0.37/0.68 thf(fact_6655_finite__conv__nat__seg__image,axiom,
% 0.37/0.68 ( finite3207457112153483333omplex
% 0.37/0.68 = ( ^ [A6: set_complex] :
% 0.37/0.68 ? [N6: nat,F5: nat > complex] :
% 0.37/0.68 ( A6
% 0.37/0.68 = ( image_nat_complex @ F5
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_conv_nat_seg_image
% 0.37/0.68 thf(fact_6656_finite__conv__nat__seg__image,axiom,
% 0.37/0.68 ( finite6017078050557962740nteger
% 0.37/0.68 = ( ^ [A6: set_Code_integer] :
% 0.37/0.68 ? [N6: nat,F5: nat > code_integer] :
% 0.37/0.68 ( A6
% 0.37/0.68 = ( image_1215581382706833972nteger @ F5
% 0.37/0.68 @ ( collect_nat
% 0.37/0.68 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_conv_nat_seg_image
% 0.37/0.68 thf(fact_6657_finite__int__segment,axiom,
% 0.37/0.68 ! [A: real,B: real] :
% 0.37/0.68 ( finite_finite_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [X4: real] :
% 0.37/0.68 ( ( member_real @ X4 @ ring_1_Ints_real )
% 0.37/0.68 & ( ord_less_eq_real @ A @ X4 )
% 0.37/0.68 & ( ord_less_eq_real @ X4 @ B ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_int_segment
% 0.37/0.68 thf(fact_6658_finite__int__segment,axiom,
% 0.37/0.68 ! [A: rat,B: rat] :
% 0.37/0.68 ( finite_finite_rat
% 0.37/0.68 @ ( collect_rat
% 0.37/0.68 @ ^ [X4: rat] :
% 0.37/0.68 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 0.37/0.68 & ( ord_less_eq_rat @ A @ X4 )
% 0.37/0.68 & ( ord_less_eq_rat @ X4 @ B ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_int_segment
% 0.37/0.68 thf(fact_6659_sum_Oshift__bounds__Suc__ivl,axiom,
% 0.37/0.68 ! [G: nat > nat,M: nat,N: nat] :
% 0.37/0.68 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.37/0.68 = ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.37/0.68 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.shift_bounds_Suc_ivl
% 0.37/0.68 thf(fact_6660_sum_Oshift__bounds__Suc__ivl,axiom,
% 0.37/0.68 ! [G: nat > real,M: nat,N: nat] :
% 0.37/0.68 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.37/0.68 = ( groups6591440286371151544t_real
% 0.37/0.68 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 0.37/0.68 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum.shift_bounds_Suc_ivl
% 0.37/0.68 thf(fact_6661_sum__subtractf__nat,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > nat,F: vEBT_VEBT > nat] :
% 0.37/0.68 ( ! [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.37/0.68 => ( ( groups771621172384141258BT_nat
% 0.37/0.68 @ ^ [X4: vEBT_VEBT] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( groups771621172384141258BT_nat @ G @ A4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_subtractf_nat
% 0.37/0.68 thf(fact_6662_sum__subtractf__nat,axiom,
% 0.37/0.68 ! [A4: set_real,G: real > nat,F: real > nat] :
% 0.37/0.68 ( ! [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ A4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.37/0.68 => ( ( groups1935376822645274424al_nat
% 0.37/0.68 @ ^ [X4: real] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( groups1935376822645274424al_nat @ G @ A4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_subtractf_nat
% 0.37/0.68 thf(fact_6663_sum__subtractf__nat,axiom,
% 0.37/0.68 ! [A4: set_int,G: int > nat,F: int > nat] :
% 0.37/0.68 ( ! [X3: int] :
% 0.37/0.68 ( ( member_int @ X3 @ A4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.37/0.68 => ( ( groups4541462559716669496nt_nat
% 0.37/0.68 @ ^ [X4: int] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_subtractf_nat
% 0.37/0.68 thf(fact_6664_sum__subtractf__nat,axiom,
% 0.37/0.68 ! [A4: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 0.37/0.68 ( ! [X3: set_nat] :
% 0.37/0.68 ( ( member_set_nat @ X3 @ A4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.37/0.68 => ( ( groups8294997508430121362at_nat
% 0.37/0.68 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( groups8294997508430121362at_nat @ G @ A4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_subtractf_nat
% 0.37/0.68 thf(fact_6665_sum__subtractf__nat,axiom,
% 0.37/0.68 ! [A4: set_nat,G: nat > nat,F: nat > nat] :
% 0.37/0.68 ( ! [X3: nat] :
% 0.37/0.68 ( ( member_nat @ X3 @ A4 )
% 0.37/0.68 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 0.37/0.68 => ( ( groups3542108847815614940at_nat
% 0.37/0.68 @ ^ [X4: nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.37/0.68 @ A4 )
% 0.37/0.68 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_subtractf_nat
% 0.37/0.68 thf(fact_6666_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,T: set_VEBT_VEBT,R2: vEBT_VEBT > vEBT_VEBT > $o,K: vEBT_VEBT > nat] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ( finite5795047828879050333T_VEBT @ T )
% 0.37/0.68 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ T )
% 0.37/0.68 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups771621172384141258BT_nat
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( finite7802652506058667612T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [J3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups771621172384141258BT_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6667_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,T: set_real,R2: vEBT_VEBT > real > $o,K: real > nat] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ( finite_finite_real @ T )
% 0.37/0.68 => ( ! [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ T )
% 0.37/0.68 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups771621172384141258BT_nat
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( finite_card_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [J3: real] :
% 0.37/0.68 ( ( member_real @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6668_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_real,T: set_VEBT_VEBT,R2: real > vEBT_VEBT > $o,K: vEBT_VEBT > nat] :
% 0.37/0.68 ( ( finite_finite_real @ S )
% 0.37/0.68 => ( ( finite5795047828879050333T_VEBT @ T )
% 0.37/0.68 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ T )
% 0.37/0.68 => ( ( finite_card_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups1935376822645274424al_nat
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( finite7802652506058667612T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [J3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups771621172384141258BT_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6669_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_real,T: set_real,R2: real > real > $o,K: real > nat] :
% 0.37/0.68 ( ( finite_finite_real @ S )
% 0.37/0.68 => ( ( finite_finite_real @ T )
% 0.37/0.68 => ( ! [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ T )
% 0.37/0.68 => ( ( finite_card_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups1935376822645274424al_nat
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( finite_card_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [J3: real] :
% 0.37/0.68 ( ( member_real @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6670_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,T: set_literal,R2: vEBT_VEBT > literal > $o,K: literal > nat] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ( finite5847741373460823677iteral @ T )
% 0.37/0.68 => ( ! [X3: literal] :
% 0.37/0.68 ( ( member_literal @ X3 @ T )
% 0.37/0.68 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups771621172384141258BT_nat
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( finite_card_literal
% 0.37/0.68 @ ( collect_literal
% 0.37/0.68 @ ^ [J3: literal] :
% 0.37/0.68 ( ( member_literal @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups8652099787943017962al_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6671_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_real,T: set_literal,R2: real > literal > $o,K: literal > nat] :
% 0.37/0.68 ( ( finite_finite_real @ S )
% 0.37/0.68 => ( ( finite5847741373460823677iteral @ T )
% 0.37/0.68 => ( ! [X3: literal] :
% 0.37/0.68 ( ( member_literal @ X3 @ T )
% 0.37/0.68 => ( ( finite_card_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( ( member_real @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups1935376822645274424al_nat
% 0.37/0.68 @ ^ [I3: real] :
% 0.37/0.68 ( finite_card_literal
% 0.37/0.68 @ ( collect_literal
% 0.37/0.68 @ ^ [J3: literal] :
% 0.37/0.68 ( ( member_literal @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups8652099787943017962al_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6672_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_literal,T: set_VEBT_VEBT,R2: literal > vEBT_VEBT > $o,K: vEBT_VEBT > nat] :
% 0.37/0.68 ( ( finite5847741373460823677iteral @ S )
% 0.37/0.68 => ( ( finite5795047828879050333T_VEBT @ T )
% 0.37/0.68 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ T )
% 0.37/0.68 => ( ( finite_card_literal
% 0.37/0.68 @ ( collect_literal
% 0.37/0.68 @ ^ [I3: literal] :
% 0.37/0.68 ( ( member_literal @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups8652099787943017962al_nat
% 0.37/0.68 @ ^ [I3: literal] :
% 0.37/0.68 ( finite7802652506058667612T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [J3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups771621172384141258BT_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6673_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_literal,T: set_real,R2: literal > real > $o,K: real > nat] :
% 0.37/0.68 ( ( finite5847741373460823677iteral @ S )
% 0.37/0.68 => ( ( finite_finite_real @ T )
% 0.37/0.68 => ( ! [X3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ T )
% 0.37/0.68 => ( ( finite_card_literal
% 0.37/0.68 @ ( collect_literal
% 0.37/0.68 @ ^ [I3: literal] :
% 0.37/0.68 ( ( member_literal @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups8652099787943017962al_nat
% 0.37/0.68 @ ^ [I3: literal] :
% 0.37/0.68 ( finite_card_real
% 0.37/0.68 @ ( collect_real
% 0.37/0.68 @ ^ [J3: real] :
% 0.37/0.68 ( ( member_real @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6674_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_literal,T: set_literal,R2: literal > literal > $o,K: literal > nat] :
% 0.37/0.68 ( ( finite5847741373460823677iteral @ S )
% 0.37/0.68 => ( ( finite5847741373460823677iteral @ T )
% 0.37/0.68 => ( ! [X3: literal] :
% 0.37/0.68 ( ( member_literal @ X3 @ T )
% 0.37/0.68 => ( ( finite_card_literal
% 0.37/0.68 @ ( collect_literal
% 0.37/0.68 @ ^ [I3: literal] :
% 0.37/0.68 ( ( member_literal @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups8652099787943017962al_nat
% 0.37/0.68 @ ^ [I3: literal] :
% 0.37/0.68 ( finite_card_literal
% 0.37/0.68 @ ( collect_literal
% 0.37/0.68 @ ^ [J3: literal] :
% 0.37/0.68 ( ( member_literal @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups8652099787943017962al_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6675_sum__multicount__gen,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,T: set_int,R2: vEBT_VEBT > int > $o,K: int > nat] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ( finite_finite_int @ T )
% 0.37/0.68 => ( ! [X3: int] :
% 0.37/0.68 ( ( member_int @ X3 @ T )
% 0.37/0.68 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.68 @ ( collect_VEBT_VEBT
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I3 @ S )
% 0.37/0.68 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.68 = ( K @ X3 ) ) )
% 0.37/0.68 => ( ( groups771621172384141258BT_nat
% 0.37/0.68 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.68 ( finite_card_int
% 0.37/0.68 @ ( collect_int
% 0.37/0.68 @ ^ [J3: int] :
% 0.37/0.68 ( ( member_int @ J3 @ T )
% 0.37/0.68 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.68 @ S )
% 0.37/0.68 = ( groups4541462559716669496nt_nat @ K @ T ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_multicount_gen
% 0.37/0.68 thf(fact_6676_total__onI,axiom,
% 0.37/0.68 ! [A4: set_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 0.37/0.68 ( ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 0.37/0.68 => ( ( member_VEBT_VEBT @ Y3 @ A4 )
% 0.37/0.68 => ( ( X3 != Y3 )
% 0.37/0.68 => ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X3 @ Y3 ) @ R )
% 0.37/0.68 | ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ Y3 @ X3 ) @ R ) ) ) ) )
% 0.37/0.68 => ( total_on_VEBT_VEBT @ A4 @ R ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_onI
% 0.37/0.68 thf(fact_6677_total__onI,axiom,
% 0.37/0.68 ! [A4: set_real,R: set_Pr6218003697084177305l_real] :
% 0.37/0.68 ( ! [X3: real,Y3: real] :
% 0.37/0.68 ( ( member_real @ X3 @ A4 )
% 0.37/0.68 => ( ( member_real @ Y3 @ A4 )
% 0.37/0.68 => ( ( X3 != Y3 )
% 0.37/0.68 => ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X3 @ Y3 ) @ R )
% 0.37/0.68 | ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ Y3 @ X3 ) @ R ) ) ) ) )
% 0.37/0.68 => ( total_on_real @ A4 @ R ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_onI
% 0.37/0.68 thf(fact_6678_total__onI,axiom,
% 0.37/0.68 ! [A4: set_set_nat,R: set_Pr5488025237498180813et_nat] :
% 0.37/0.68 ( ! [X3: set_nat,Y3: set_nat] :
% 0.37/0.68 ( ( member_set_nat @ X3 @ A4 )
% 0.37/0.68 => ( ( member_set_nat @ Y3 @ A4 )
% 0.37/0.68 => ( ( X3 != Y3 )
% 0.37/0.68 => ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X3 @ Y3 ) @ R )
% 0.37/0.68 | ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ Y3 @ X3 ) @ R ) ) ) ) )
% 0.37/0.68 => ( total_on_set_nat @ A4 @ R ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_onI
% 0.37/0.68 thf(fact_6679_total__onI,axiom,
% 0.37/0.68 ! [A4: set_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.68 ( ! [X3: uint32,Y3: uint32] :
% 0.37/0.68 ( ( member_uint32 @ X3 @ A4 )
% 0.37/0.68 => ( ( member_uint32 @ Y3 @ A4 )
% 0.37/0.68 => ( ( X3 != Y3 )
% 0.37/0.68 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ R )
% 0.37/0.68 | ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ X3 ) @ R ) ) ) ) )
% 0.37/0.68 => ( total_on_uint32 @ A4 @ R ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_onI
% 0.37/0.68 thf(fact_6680_total__onI,axiom,
% 0.37/0.68 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.68 ( ! [X3: nat,Y3: nat] :
% 0.37/0.68 ( ( member_nat @ X3 @ A4 )
% 0.37/0.68 => ( ( member_nat @ Y3 @ A4 )
% 0.37/0.68 => ( ( X3 != Y3 )
% 0.37/0.68 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 0.37/0.68 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X3 ) @ R ) ) ) ) )
% 0.37/0.68 => ( total_on_nat @ A4 @ R ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_onI
% 0.37/0.68 thf(fact_6681_total__onI,axiom,
% 0.37/0.68 ! [A4: set_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.68 ( ! [X3: int,Y3: int] :
% 0.37/0.68 ( ( member_int @ X3 @ A4 )
% 0.37/0.68 => ( ( member_int @ Y3 @ A4 )
% 0.37/0.68 => ( ( X3 != Y3 )
% 0.37/0.68 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R )
% 0.37/0.68 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X3 ) @ R ) ) ) ) )
% 0.37/0.68 => ( total_on_int @ A4 @ R ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_onI
% 0.37/0.68 thf(fact_6682_total__on__def,axiom,
% 0.37/0.68 ( total_on_uint32
% 0.37/0.68 = ( ^ [A6: set_uint32,R5: set_Pr1773385645901665561uint32] :
% 0.37/0.68 ! [X4: uint32] :
% 0.37/0.68 ( ( member_uint32 @ X4 @ A6 )
% 0.37/0.68 => ! [Y4: uint32] :
% 0.37/0.68 ( ( member_uint32 @ Y4 @ A6 )
% 0.37/0.68 => ( ( X4 != Y4 )
% 0.37/0.68 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R5 )
% 0.37/0.68 | ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y4 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_on_def
% 0.37/0.68 thf(fact_6683_total__on__def,axiom,
% 0.37/0.68 ( total_on_nat
% 0.37/0.68 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 0.37/0.68 ! [X4: nat] :
% 0.37/0.68 ( ( member_nat @ X4 @ A6 )
% 0.37/0.68 => ! [Y4: nat] :
% 0.37/0.68 ( ( member_nat @ Y4 @ A6 )
% 0.37/0.68 => ( ( X4 != Y4 )
% 0.37/0.68 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R5 )
% 0.37/0.68 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y4 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_on_def
% 0.37/0.68 thf(fact_6684_total__on__def,axiom,
% 0.37/0.68 ( total_on_int
% 0.37/0.68 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 0.37/0.68 ! [X4: int] :
% 0.37/0.68 ( ( member_int @ X4 @ A6 )
% 0.37/0.68 => ! [Y4: int] :
% 0.37/0.68 ( ( member_int @ Y4 @ A6 )
% 0.37/0.68 => ( ( X4 != Y4 )
% 0.37/0.68 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R5 )
% 0.37/0.68 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y4 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % total_on_def
% 0.37/0.68 thf(fact_6685_finite__if__eq__beyond__finite,axiom,
% 0.37/0.68 ! [S3: set_int,S2: set_int] :
% 0.37/0.68 ( ( finite_finite_int @ S3 )
% 0.37/0.68 => ( finite6197958912794628473et_int
% 0.37/0.68 @ ( collect_set_int
% 0.37/0.68 @ ^ [S8: set_int] :
% 0.37/0.68 ( ( minus_minus_set_int @ S8 @ S3 )
% 0.37/0.68 = ( minus_minus_set_int @ S2 @ S3 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_if_eq_beyond_finite
% 0.37/0.68 thf(fact_6686_finite__if__eq__beyond__finite,axiom,
% 0.37/0.68 ! [S3: set_complex,S2: set_complex] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.68 => ( finite6551019134538273531omplex
% 0.37/0.68 @ ( collect_set_complex
% 0.37/0.68 @ ^ [S8: set_complex] :
% 0.37/0.68 ( ( minus_811609699411566653omplex @ S8 @ S3 )
% 0.37/0.68 = ( minus_811609699411566653omplex @ S2 @ S3 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_if_eq_beyond_finite
% 0.37/0.68 thf(fact_6687_finite__if__eq__beyond__finite,axiom,
% 0.37/0.68 ! [S3: set_Code_integer,S2: set_Code_integer] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.68 => ( finite6931041176100689706nteger
% 0.37/0.68 @ ( collec574505750873337192nteger
% 0.37/0.68 @ ^ [S8: set_Code_integer] :
% 0.37/0.68 ( ( minus_2355218937544613996nteger @ S8 @ S3 )
% 0.37/0.68 = ( minus_2355218937544613996nteger @ S2 @ S3 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_if_eq_beyond_finite
% 0.37/0.68 thf(fact_6688_finite__if__eq__beyond__finite,axiom,
% 0.37/0.68 ! [S3: set_nat,S2: set_nat] :
% 0.37/0.68 ( ( finite_finite_nat @ S3 )
% 0.37/0.68 => ( finite1152437895449049373et_nat
% 0.37/0.68 @ ( collect_set_nat
% 0.37/0.68 @ ^ [S8: set_nat] :
% 0.37/0.68 ( ( minus_minus_set_nat @ S8 @ S3 )
% 0.37/0.68 = ( minus_minus_set_nat @ S2 @ S3 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % finite_if_eq_beyond_finite
% 0.37/0.68 thf(fact_6689_total__on__empty,axiom,
% 0.37/0.68 ! [R: set_Pr1261947904930325089at_nat] : ( total_on_nat @ bot_bot_set_nat @ R ) ).
% 0.37/0.68
% 0.37/0.68 % total_on_empty
% 0.37/0.68 thf(fact_6690_total__on__empty,axiom,
% 0.37/0.68 ! [R: set_Pr958786334691620121nt_int] : ( total_on_int @ bot_bot_set_int @ R ) ).
% 0.37/0.68
% 0.37/0.68 % total_on_empty
% 0.37/0.68 thf(fact_6691_total__on__empty,axiom,
% 0.37/0.68 ! [R: set_Product_prod_o_o] : ( total_on_o @ bot_bot_set_o @ R ) ).
% 0.37/0.68
% 0.37/0.68 % total_on_empty
% 0.37/0.68 thf(fact_6692_Fpow__def,axiom,
% 0.37/0.68 ( finite_Fpow_nat
% 0.37/0.68 = ( ^ [A6: set_nat] :
% 0.37/0.68 ( collect_set_nat
% 0.37/0.68 @ ^ [X8: set_nat] :
% 0.37/0.68 ( ( ord_less_eq_set_nat @ X8 @ A6 )
% 0.37/0.68 & ( finite_finite_nat @ X8 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Fpow_def
% 0.37/0.68 thf(fact_6693_Fpow__def,axiom,
% 0.37/0.68 ( finite_Fpow_complex
% 0.37/0.68 = ( ^ [A6: set_complex] :
% 0.37/0.68 ( collect_set_complex
% 0.37/0.68 @ ^ [X8: set_complex] :
% 0.37/0.68 ( ( ord_le211207098394363844omplex @ X8 @ A6 )
% 0.37/0.68 & ( finite3207457112153483333omplex @ X8 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Fpow_def
% 0.37/0.68 thf(fact_6694_Fpow__def,axiom,
% 0.37/0.68 ( finite1532502677820914807nteger
% 0.37/0.68 = ( ^ [A6: set_Code_integer] :
% 0.37/0.68 ( collec574505750873337192nteger
% 0.37/0.68 @ ^ [X8: set_Code_integer] :
% 0.37/0.68 ( ( ord_le7084787975880047091nteger @ X8 @ A6 )
% 0.37/0.68 & ( finite6017078050557962740nteger @ X8 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Fpow_def
% 0.37/0.68 thf(fact_6695_Fpow__def,axiom,
% 0.37/0.68 ( finite_Fpow_int
% 0.37/0.68 = ( ^ [A6: set_int] :
% 0.37/0.68 ( collect_set_int
% 0.37/0.68 @ ^ [X8: set_int] :
% 0.37/0.68 ( ( ord_less_eq_set_int @ X8 @ A6 )
% 0.37/0.68 & ( finite_finite_int @ X8 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % Fpow_def
% 0.37/0.68 thf(fact_6696_distinct__finite__set,axiom,
% 0.37/0.68 ! [X: set_VEBT_VEBT] :
% 0.37/0.68 ( finite3004134309566078307T_VEBT
% 0.37/0.68 @ ( collec5608196760682091941T_VEBT
% 0.37/0.68 @ ^ [Ys3: list_VEBT_VEBT] :
% 0.37/0.68 ( ( ( set_VEBT_VEBT2 @ Ys3 )
% 0.37/0.68 = X )
% 0.37/0.68 & ( distinct_VEBT_VEBT @ Ys3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % distinct_finite_set
% 0.37/0.68 thf(fact_6697_distinct__finite__set,axiom,
% 0.37/0.68 ! [X: set_nat] :
% 0.37/0.68 ( finite8100373058378681591st_nat
% 0.37/0.68 @ ( collect_list_nat
% 0.37/0.68 @ ^ [Ys3: list_nat] :
% 0.37/0.68 ( ( ( set_nat2 @ Ys3 )
% 0.37/0.68 = X )
% 0.37/0.68 & ( distinct_nat @ Ys3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % distinct_finite_set
% 0.37/0.68 thf(fact_6698_distinct__finite__set,axiom,
% 0.37/0.68 ! [X: set_real] :
% 0.37/0.68 ( finite306553202115118035t_real
% 0.37/0.68 @ ( collect_list_real
% 0.37/0.68 @ ^ [Ys3: list_real] :
% 0.37/0.68 ( ( ( set_real2 @ Ys3 )
% 0.37/0.68 = X )
% 0.37/0.68 & ( distinct_real @ Ys3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % distinct_finite_set
% 0.37/0.68 thf(fact_6699_distinct__finite__set,axiom,
% 0.37/0.68 ! [X: set_o] :
% 0.37/0.68 ( finite_finite_list_o
% 0.37/0.68 @ ( collect_list_o
% 0.37/0.68 @ ^ [Ys3: list_o] :
% 0.37/0.68 ( ( ( set_o2 @ Ys3 )
% 0.37/0.68 = X )
% 0.37/0.68 & ( distinct_o @ Ys3 ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % distinct_finite_set
% 0.37/0.68 thf(fact_6700_diff__power__eq__sum,axiom,
% 0.37/0.68 ! [X: complex,N: nat,Y: complex] :
% 0.37/0.68 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 0.37/0.68 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.37/0.68 @ ( groups2073611262835488442omplex
% 0.37/0.68 @ ^ [P7: nat] : ( times_times_complex @ ( power_power_complex @ X @ P7 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % diff_power_eq_sum
% 0.37/0.68 thf(fact_6701_diff__power__eq__sum,axiom,
% 0.37/0.68 ! [X: uint32,N: nat,Y: uint32] :
% 0.37/0.68 ( ( minus_minus_uint32 @ ( power_power_uint32 @ X @ ( suc @ N ) ) @ ( power_power_uint32 @ Y @ ( suc @ N ) ) )
% 0.37/0.68 = ( times_times_uint32 @ ( minus_minus_uint32 @ X @ Y )
% 0.37/0.68 @ ( groups833757482993574392uint32
% 0.37/0.68 @ ^ [P7: nat] : ( times_times_uint32 @ ( power_power_uint32 @ X @ P7 ) @ ( power_power_uint32 @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % diff_power_eq_sum
% 0.37/0.68 thf(fact_6702_diff__power__eq__sum,axiom,
% 0.37/0.68 ! [X: int,N: nat,Y: int] :
% 0.37/0.68 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 0.37/0.68 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.37/0.68 @ ( groups3539618377306564664at_int
% 0.37/0.68 @ ^ [P7: nat] : ( times_times_int @ ( power_power_int @ X @ P7 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % diff_power_eq_sum
% 0.37/0.68 thf(fact_6703_diff__power__eq__sum,axiom,
% 0.37/0.68 ! [X: real,N: nat,Y: real] :
% 0.37/0.68 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 0.37/0.68 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.37/0.68 @ ( groups6591440286371151544t_real
% 0.37/0.68 @ ^ [P7: nat] : ( times_times_real @ ( power_power_real @ X @ P7 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % diff_power_eq_sum
% 0.37/0.68 thf(fact_6704_power__diff__sumr2,axiom,
% 0.37/0.68 ! [X: complex,N: nat,Y: complex] :
% 0.37/0.68 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 0.37/0.68 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.37/0.68 @ ( groups2073611262835488442omplex
% 0.37/0.68 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % power_diff_sumr2
% 0.37/0.68 thf(fact_6705_power__diff__sumr2,axiom,
% 0.37/0.68 ! [X: uint32,N: nat,Y: uint32] :
% 0.37/0.68 ( ( minus_minus_uint32 @ ( power_power_uint32 @ X @ N ) @ ( power_power_uint32 @ Y @ N ) )
% 0.37/0.68 = ( times_times_uint32 @ ( minus_minus_uint32 @ X @ Y )
% 0.37/0.68 @ ( groups833757482993574392uint32
% 0.37/0.68 @ ^ [I3: nat] : ( times_times_uint32 @ ( power_power_uint32 @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_uint32 @ X @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % power_diff_sumr2
% 0.37/0.68 thf(fact_6706_power__diff__sumr2,axiom,
% 0.37/0.68 ! [X: int,N: nat,Y: int] :
% 0.37/0.68 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.37/0.68 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.37/0.68 @ ( groups3539618377306564664at_int
% 0.37/0.68 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % power_diff_sumr2
% 0.37/0.68 thf(fact_6707_power__diff__sumr2,axiom,
% 0.37/0.68 ! [X: real,N: nat,Y: real] :
% 0.37/0.68 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 0.37/0.68 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.37/0.68 @ ( groups6591440286371151544t_real
% 0.37/0.68 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_real @ X @ I3 ) )
% 0.37/0.68 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % power_diff_sumr2
% 0.37/0.68 thf(fact_6708_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,B4: real,I: vEBT_VEBT] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups2240296850493347238T_real @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_VEBT_VEBT @ I @ S )
% 0.37/0.68 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6709_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_real,F: real > real,B4: real,I: real] :
% 0.37/0.68 ( ( finite_finite_real @ S )
% 0.37/0.68 => ( ! [I2: real] :
% 0.37/0.68 ( ( member_real @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_real @ I @ S )
% 0.37/0.68 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6710_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_int,F: int > real,B4: real,I: int] :
% 0.37/0.68 ( ( finite_finite_int @ S )
% 0.37/0.68 => ( ! [I2: int] :
% 0.37/0.68 ( ( member_int @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_int @ I @ S )
% 0.37/0.68 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6711_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_complex,F: complex > real,B4: real,I: complex] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ S )
% 0.37/0.68 => ( ! [I2: complex] :
% 0.37/0.68 ( ( member_complex @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_complex @ I @ S )
% 0.37/0.68 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6712_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_Code_integer,F: code_integer > real,B4: real,I: code_integer] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ S )
% 0.37/0.68 => ( ! [I2: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups1270011288395367621r_real @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_Code_integer @ I @ S )
% 0.37/0.68 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6713_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,B4: rat,I: vEBT_VEBT] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_VEBT_VEBT @ I @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6714_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_real,F: real > rat,B4: rat,I: real] :
% 0.37/0.68 ( ( finite_finite_real @ S )
% 0.37/0.68 => ( ! [I2: real] :
% 0.37/0.68 ( ( member_real @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_real @ I @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6715_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_nat,F: nat > rat,B4: rat,I: nat] :
% 0.37/0.68 ( ( finite_finite_nat @ S )
% 0.37/0.68 => ( ! [I2: nat] :
% 0.37/0.68 ( ( member_nat @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_nat @ I @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6716_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_int,F: int > rat,B4: rat,I: int] :
% 0.37/0.68 ( ( finite_finite_int @ S )
% 0.37/0.68 => ( ! [I2: int] :
% 0.37/0.68 ( ( member_int @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_int @ I @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6717_sum__nonneg__leq__bound,axiom,
% 0.37/0.68 ! [S: set_complex,F: complex > rat,B4: rat,I: complex] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ S )
% 0.37/0.68 => ( ! [I2: complex] :
% 0.37/0.68 ( ( member_complex @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.37/0.68 = B4 )
% 0.37/0.68 => ( ( member_complex @ I @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_leq_bound
% 0.37/0.68 thf(fact_6718_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,I: vEBT_VEBT] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups2240296850493347238T_real @ F @ S )
% 0.37/0.68 = zero_zero_real )
% 0.37/0.68 => ( ( member_VEBT_VEBT @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_real ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6719_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_real,F: real > real,I: real] :
% 0.37/0.68 ( ( finite_finite_real @ S )
% 0.37/0.68 => ( ! [I2: real] :
% 0.37/0.68 ( ( member_real @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 0.37/0.68 = zero_zero_real )
% 0.37/0.68 => ( ( member_real @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_real ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6720_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_int,F: int > real,I: int] :
% 0.37/0.68 ( ( finite_finite_int @ S )
% 0.37/0.68 => ( ! [I2: int] :
% 0.37/0.68 ( ( member_int @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 0.37/0.68 = zero_zero_real )
% 0.37/0.68 => ( ( member_int @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_real ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6721_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_complex,F: complex > real,I: complex] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ S )
% 0.37/0.68 => ( ! [I2: complex] :
% 0.37/0.68 ( ( member_complex @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 0.37/0.68 = zero_zero_real )
% 0.37/0.68 => ( ( member_complex @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_real ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6722_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_Code_integer,F: code_integer > real,I: code_integer] :
% 0.37/0.68 ( ( finite6017078050557962740nteger @ S )
% 0.37/0.68 => ( ! [I2: code_integer] :
% 0.37/0.68 ( ( member_Code_integer @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups1270011288395367621r_real @ F @ S )
% 0.37/0.68 = zero_zero_real )
% 0.37/0.68 => ( ( member_Code_integer @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_real ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6723_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 0.37/0.68 ( ( finite5795047828879050333T_VEBT @ S )
% 0.37/0.68 => ( ! [I2: vEBT_VEBT] :
% 0.37/0.68 ( ( member_VEBT_VEBT @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 0.37/0.68 = zero_zero_rat )
% 0.37/0.68 => ( ( member_VEBT_VEBT @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_rat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6724_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_real,F: real > rat,I: real] :
% 0.37/0.68 ( ( finite_finite_real @ S )
% 0.37/0.68 => ( ! [I2: real] :
% 0.37/0.68 ( ( member_real @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 0.37/0.68 = zero_zero_rat )
% 0.37/0.68 => ( ( member_real @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_rat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6725_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_nat,F: nat > rat,I: nat] :
% 0.37/0.68 ( ( finite_finite_nat @ S )
% 0.37/0.68 => ( ! [I2: nat] :
% 0.37/0.68 ( ( member_nat @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 0.37/0.68 = zero_zero_rat )
% 0.37/0.68 => ( ( member_nat @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_rat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6726_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_int,F: int > rat,I: int] :
% 0.37/0.68 ( ( finite_finite_int @ S )
% 0.37/0.68 => ( ! [I2: int] :
% 0.37/0.68 ( ( member_int @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 0.37/0.68 = zero_zero_rat )
% 0.37/0.68 => ( ( member_int @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_rat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6727_sum__nonneg__0,axiom,
% 0.37/0.68 ! [S: set_complex,F: complex > rat,I: complex] :
% 0.37/0.68 ( ( finite3207457112153483333omplex @ S )
% 0.37/0.68 => ( ! [I2: complex] :
% 0.37/0.68 ( ( member_complex @ I2 @ S )
% 0.37/0.68 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 0.37/0.68 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 0.37/0.68 = zero_zero_rat )
% 0.37/0.68 => ( ( member_complex @ I @ S )
% 0.37/0.68 => ( ( F @ I )
% 0.37/0.68 = zero_zero_rat ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % sum_nonneg_0
% 0.37/0.68 thf(fact_6728_add__mset__in__multiset,axiom,
% 0.37/0.68 ! [M7: list_nat > nat,A: list_nat] :
% 0.37/0.68 ( ( finite8100373058378681591st_nat
% 0.37/0.68 @ ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite8100373058378681591st_nat
% 0.37/0.68 @ ( collect_list_nat
% 0.37/0.68 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 0.37/0.68
% 0.37/0.68 % add_mset_in_multiset
% 0.37/0.68 thf(fact_6729_add__mset__in__multiset,axiom,
% 0.37/0.68 ! [M7: set_nat > nat,A: set_nat] :
% 0.37/0.68 ( ( finite1152437895449049373et_nat
% 0.37/0.68 @ ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.68 => ( finite1152437895449049373et_nat
% 0.37/0.68 @ ( collect_set_nat
% 0.37/0.68 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % add_mset_in_multiset
% 0.37/0.69 thf(fact_6730_add__mset__in__multiset,axiom,
% 0.37/0.69 ! [M7: nat > nat,A: nat] :
% 0.37/0.69 ( ( finite_finite_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite_finite_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % add_mset_in_multiset
% 0.37/0.69 thf(fact_6731_add__mset__in__multiset,axiom,
% 0.37/0.69 ! [M7: int > nat,A: int] :
% 0.37/0.69 ( ( finite_finite_int
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite_finite_int
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % add_mset_in_multiset
% 0.37/0.69 thf(fact_6732_add__mset__in__multiset,axiom,
% 0.37/0.69 ! [M7: complex > nat,A: complex] :
% 0.37/0.69 ( ( finite3207457112153483333omplex
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite3207457112153483333omplex
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % add_mset_in_multiset
% 0.37/0.69 thf(fact_6733_add__mset__in__multiset,axiom,
% 0.37/0.69 ! [M7: code_integer > nat,A: code_integer] :
% 0.37/0.69 ( ( finite6017078050557962740nteger
% 0.37/0.69 @ ( collect_Code_integer
% 0.37/0.69 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite6017078050557962740nteger
% 0.37/0.69 @ ( collect_Code_integer
% 0.37/0.69 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % add_mset_in_multiset
% 0.37/0.69 thf(fact_6734_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,R2: set_nat,G: vEBT_VEBT > nat,F: nat > uint32] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( finite_finite_nat @ R2 )
% 0.37/0.69 => ( ( ord_less_eq_set_nat @ ( image_VEBT_VEBT_nat @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups8325533452322294502uint32
% 0.37/0.69 @ ^ [X4: vEBT_VEBT] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups833757482993574392uint32
% 0.37/0.69 @ ^ [Y4: nat] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6735_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_real,R2: set_nat,G: real > nat,F: nat > uint32] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( finite_finite_nat @ R2 )
% 0.37/0.69 => ( ( ord_less_eq_set_nat @ ( image_real_nat @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups5944083974425963860uint32
% 0.37/0.69 @ ^ [X4: real] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups833757482993574392uint32
% 0.37/0.69 @ ^ [Y4: nat] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [X4: real] :
% 0.37/0.69 ( ( member_real @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6736_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_literal,R2: set_nat,G: literal > nat,F: nat > uint32] :
% 0.37/0.69 ( ( finite5847741373460823677iteral @ S3 )
% 0.37/0.69 => ( ( finite_finite_nat @ R2 )
% 0.37/0.69 => ( ( ord_less_eq_set_nat @ ( image_literal_nat @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups4542640294765070598uint32
% 0.37/0.69 @ ^ [X4: literal] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups833757482993574392uint32
% 0.37/0.69 @ ^ [Y4: nat] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [X4: literal] :
% 0.37/0.69 ( ( member_literal @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6737_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,R2: set_complex,G: vEBT_VEBT > complex,F: complex > uint32] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( finite3207457112153483333omplex @ R2 )
% 0.37/0.69 => ( ( ord_le211207098394363844omplex @ ( image_3793382806556112285omplex @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups8325533452322294502uint32
% 0.37/0.69 @ ^ [X4: vEBT_VEBT] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups8736914816313324502uint32
% 0.37/0.69 @ ^ [Y4: complex] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6738_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_real,R2: set_complex,G: real > complex,F: complex > uint32] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( finite3207457112153483333omplex @ R2 )
% 0.37/0.69 => ( ( ord_le211207098394363844omplex @ ( image_real_complex @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups5944083974425963860uint32
% 0.37/0.69 @ ^ [X4: real] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups8736914816313324502uint32
% 0.37/0.69 @ ^ [Y4: complex] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [X4: real] :
% 0.37/0.69 ( ( member_real @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6739_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_literal,R2: set_complex,G: literal > complex,F: complex > uint32] :
% 0.37/0.69 ( ( finite5847741373460823677iteral @ S3 )
% 0.37/0.69 => ( ( finite3207457112153483333omplex @ R2 )
% 0.37/0.69 => ( ( ord_le211207098394363844omplex @ ( image_5274195009022015549omplex @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups4542640294765070598uint32
% 0.37/0.69 @ ^ [X4: literal] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups8736914816313324502uint32
% 0.37/0.69 @ ^ [Y4: complex] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [X4: literal] :
% 0.37/0.69 ( ( member_literal @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6740_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,R2: set_Code_integer,G: vEBT_VEBT > code_integer,F: code_integer > uint32] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( finite6017078050557962740nteger @ R2 )
% 0.37/0.69 => ( ( ord_le7084787975880047091nteger @ ( image_2092689629700589388nteger @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups8325533452322294502uint32
% 0.37/0.69 @ ^ [X4: vEBT_VEBT] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups8847630953604152069uint32
% 0.37/0.69 @ ^ [Y4: code_integer] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [X4: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6741_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_real,R2: set_Code_integer,G: real > code_integer,F: code_integer > uint32] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( finite6017078050557962740nteger @ R2 )
% 0.37/0.69 => ( ( ord_le7084787975880047091nteger @ ( image_4958697645175560720nteger @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups5944083974425963860uint32
% 0.37/0.69 @ ^ [X4: real] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups8847630953604152069uint32
% 0.37/0.69 @ ^ [Y4: code_integer] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [X4: real] :
% 0.37/0.69 ( ( member_real @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6742_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_literal,R2: set_Code_integer,G: literal > code_integer,F: code_integer > uint32] :
% 0.37/0.69 ( ( finite5847741373460823677iteral @ S3 )
% 0.37/0.69 => ( ( finite6017078050557962740nteger @ R2 )
% 0.37/0.69 => ( ( ord_le7084787975880047091nteger @ ( image_4442872163159017964nteger @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups4542640294765070598uint32
% 0.37/0.69 @ ^ [X4: literal] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups8847630953604152069uint32
% 0.37/0.69 @ ^ [Y4: code_integer] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [X4: literal] :
% 0.37/0.69 ( ( member_literal @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6743_sum__fun__comp,axiom,
% 0.37/0.69 ! [S3: set_nat,R2: set_nat,G: nat > nat,F: nat > uint32] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( finite_finite_nat @ R2 )
% 0.37/0.69 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G @ S3 ) @ R2 )
% 0.37/0.69 => ( ( groups833757482993574392uint32
% 0.37/0.69 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups833757482993574392uint32
% 0.37/0.69 @ ^ [Y4: nat] :
% 0.37/0.69 ( times_times_uint32
% 0.37/0.69 @ ( semiri2565882477558803405uint32
% 0.37/0.69 @ ( finite_card_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] :
% 0.37/0.69 ( ( member_nat @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) ) )
% 0.37/0.69 @ ( F @ Y4 ) )
% 0.37/0.69 @ R2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_fun_comp
% 0.37/0.69 thf(fact_6744_diff__preserves__multiset,axiom,
% 0.37/0.69 ! [M7: list_nat > nat,N8: list_nat > nat] :
% 0.37/0.69 ( ( finite8100373058378681591st_nat
% 0.37/0.69 @ ( collect_list_nat
% 0.37/0.69 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite8100373058378681591st_nat
% 0.37/0.69 @ ( collect_list_nat
% 0.37/0.69 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % diff_preserves_multiset
% 0.37/0.69 thf(fact_6745_diff__preserves__multiset,axiom,
% 0.37/0.69 ! [M7: set_nat > nat,N8: set_nat > nat] :
% 0.37/0.69 ( ( finite1152437895449049373et_nat
% 0.37/0.69 @ ( collect_set_nat
% 0.37/0.69 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite1152437895449049373et_nat
% 0.37/0.69 @ ( collect_set_nat
% 0.37/0.69 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % diff_preserves_multiset
% 0.37/0.69 thf(fact_6746_diff__preserves__multiset,axiom,
% 0.37/0.69 ! [M7: nat > nat,N8: nat > nat] :
% 0.37/0.69 ( ( finite_finite_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite_finite_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % diff_preserves_multiset
% 0.37/0.69 thf(fact_6747_diff__preserves__multiset,axiom,
% 0.37/0.69 ! [M7: int > nat,N8: int > nat] :
% 0.37/0.69 ( ( finite_finite_int
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite_finite_int
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % diff_preserves_multiset
% 0.37/0.69 thf(fact_6748_diff__preserves__multiset,axiom,
% 0.37/0.69 ! [M7: complex > nat,N8: complex > nat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite3207457112153483333omplex
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % diff_preserves_multiset
% 0.37/0.69 thf(fact_6749_diff__preserves__multiset,axiom,
% 0.37/0.69 ! [M7: code_integer > nat,N8: code_integer > nat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger
% 0.37/0.69 @ ( collect_Code_integer
% 0.37/0.69 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 0.37/0.69 => ( finite6017078050557962740nteger
% 0.37/0.69 @ ( collect_Code_integer
% 0.37/0.69 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % diff_preserves_multiset
% 0.37/0.69 thf(fact_6750_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_nat,T3: set_complex,G: nat > complex,H2: nat > nat] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.69 => ( ( ord_le211207098394363844omplex @ ( image_nat_complex @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups5693394587270226106ex_nat
% 0.37/0.69 @ ^ [Y4: complex] :
% 0.37/0.69 ( groups3542108847815614940at_nat @ H2
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] :
% 0.37/0.69 ( ( member_nat @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups3542108847815614940at_nat @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6751_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_nat,T3: set_Code_integer,G: nat > code_integer,H2: nat > nat] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.69 => ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups7237345082560585321er_nat
% 0.37/0.69 @ ^ [Y4: code_integer] :
% 0.37/0.69 ( groups3542108847815614940at_nat @ H2
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] :
% 0.37/0.69 ( ( member_nat @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups3542108847815614940at_nat @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6752_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_nat,T3: set_int,G: nat > int,H2: nat > nat] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( finite_finite_int @ T3 )
% 0.37/0.69 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups4541462559716669496nt_nat
% 0.37/0.69 @ ^ [Y4: int] :
% 0.37/0.69 ( groups3542108847815614940at_nat @ H2
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] :
% 0.37/0.69 ( ( member_nat @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups3542108847815614940at_nat @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6753_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_complex,T3: set_nat,G: complex > nat,H2: complex > complex] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( finite_finite_nat @ T3 )
% 0.37/0.69 => ( ( ord_less_eq_set_nat @ ( image_complex_nat @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups2073611262835488442omplex
% 0.37/0.69 @ ^ [Y4: nat] :
% 0.37/0.69 ( groups7754918857620584856omplex @ H2
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] :
% 0.37/0.69 ( ( member_complex @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups7754918857620584856omplex @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6754_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_complex,T3: set_Code_integer,G: complex > code_integer,H2: complex > complex] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.69 => ( ( ord_le7084787975880047091nteger @ ( image_1994230757181692690nteger @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups8024822376189712711omplex
% 0.37/0.69 @ ^ [Y4: code_integer] :
% 0.37/0.69 ( groups7754918857620584856omplex @ H2
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] :
% 0.37/0.69 ( ( member_complex @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups7754918857620584856omplex @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6755_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_complex,T3: set_int,G: complex > int,H2: complex > complex] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( finite_finite_int @ T3 )
% 0.37/0.69 => ( ( ord_less_eq_set_int @ ( image_complex_int @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups3049146728041665814omplex
% 0.37/0.69 @ ^ [Y4: int] :
% 0.37/0.69 ( groups7754918857620584856omplex @ H2
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] :
% 0.37/0.69 ( ( member_complex @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups7754918857620584856omplex @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6756_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_nat,T3: set_complex,G: nat > complex,H2: nat > real] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( finite3207457112153483333omplex @ T3 )
% 0.37/0.69 => ( ( ord_le211207098394363844omplex @ ( image_nat_complex @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups5808333547571424918x_real
% 0.37/0.69 @ ^ [Y4: complex] :
% 0.37/0.69 ( groups6591440286371151544t_real @ H2
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] :
% 0.37/0.69 ( ( member_nat @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups6591440286371151544t_real @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6757_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_nat,T3: set_Code_integer,G: nat > code_integer,H2: nat > real] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( finite6017078050557962740nteger @ T3 )
% 0.37/0.69 => ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups1270011288395367621r_real
% 0.37/0.69 @ ^ [Y4: code_integer] :
% 0.37/0.69 ( groups6591440286371151544t_real @ H2
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] :
% 0.37/0.69 ( ( member_nat @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups6591440286371151544t_real @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6758_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_nat,T3: set_int,G: nat > int,H2: nat > real] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( finite_finite_int @ T3 )
% 0.37/0.69 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups8778361861064173332t_real
% 0.37/0.69 @ ^ [Y4: int] :
% 0.37/0.69 ( groups6591440286371151544t_real @ H2
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [X4: nat] :
% 0.37/0.69 ( ( member_nat @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups6591440286371151544t_real @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6759_sum_Ogroup,axiom,
% 0.37/0.69 ! [S3: set_int,T3: set_nat,G: int > nat,H2: int > int] :
% 0.37/0.69 ( ( finite_finite_int @ S3 )
% 0.37/0.69 => ( ( finite_finite_nat @ T3 )
% 0.37/0.69 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ G @ S3 ) @ T3 )
% 0.37/0.69 => ( ( groups3539618377306564664at_int
% 0.37/0.69 @ ^ [Y4: nat] :
% 0.37/0.69 ( groups4538972089207619220nt_int @ H2
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] :
% 0.37/0.69 ( ( member_int @ X4 @ S3 )
% 0.37/0.69 & ( ( G @ X4 )
% 0.37/0.69 = Y4 ) ) ) )
% 0.37/0.69 @ T3 )
% 0.37/0.69 = ( groups4538972089207619220nt_int @ H2 @ S3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.group
% 0.37/0.69 thf(fact_6760_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_int,G: int > uint32] :
% 0.37/0.69 ( ( finite_finite_int @ A4 )
% 0.37/0.69 => ( ( groups5712668689793887828uint32 @ G
% 0.37/0.69 @ ( minus_minus_set_int @ A4
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_uint32 ) ) ) )
% 0.37/0.69 = ( groups5712668689793887828uint32 @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6761_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_complex,G: complex > uint32] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.69 => ( ( groups8736914816313324502uint32 @ G
% 0.37/0.69 @ ( minus_811609699411566653omplex @ A4
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_uint32 ) ) ) )
% 0.37/0.69 = ( groups8736914816313324502uint32 @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6762_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_Code_integer,G: code_integer > uint32] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.69 => ( ( groups8847630953604152069uint32 @ G
% 0.37/0.69 @ ( minus_2355218937544613996nteger @ A4
% 0.37/0.69 @ ( collect_Code_integer
% 0.37/0.69 @ ^ [X4: code_integer] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_uint32 ) ) ) )
% 0.37/0.69 = ( groups8847630953604152069uint32 @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6763_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_int,G: int > real] :
% 0.37/0.69 ( ( finite_finite_int @ A4 )
% 0.37/0.69 => ( ( groups8778361861064173332t_real @ G
% 0.37/0.69 @ ( minus_minus_set_int @ A4
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_real ) ) ) )
% 0.37/0.69 = ( groups8778361861064173332t_real @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6764_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_complex,G: complex > real] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.69 => ( ( groups5808333547571424918x_real @ G
% 0.37/0.69 @ ( minus_811609699411566653omplex @ A4
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_real ) ) ) )
% 0.37/0.69 = ( groups5808333547571424918x_real @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6765_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_Code_integer,G: code_integer > real] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.69 => ( ( groups1270011288395367621r_real @ G
% 0.37/0.69 @ ( minus_2355218937544613996nteger @ A4
% 0.37/0.69 @ ( collect_Code_integer
% 0.37/0.69 @ ^ [X4: code_integer] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_real ) ) ) )
% 0.37/0.69 = ( groups1270011288395367621r_real @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6766_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_int,G: int > rat] :
% 0.37/0.69 ( ( finite_finite_int @ A4 )
% 0.37/0.69 => ( ( groups3906332499630173760nt_rat @ G
% 0.37/0.69 @ ( minus_minus_set_int @ A4
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_rat ) ) ) )
% 0.37/0.69 = ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6767_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_complex,G: complex > rat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.69 => ( ( groups5058264527183730370ex_rat @ G
% 0.37/0.69 @ ( minus_811609699411566653omplex @ A4
% 0.37/0.69 @ ( collect_complex
% 0.37/0.69 @ ^ [X4: complex] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_rat ) ) ) )
% 0.37/0.69 = ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6768_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_Code_integer,G: code_integer > rat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.69 => ( ( groups6602215022474089585er_rat @ G
% 0.37/0.69 @ ( minus_2355218937544613996nteger @ A4
% 0.37/0.69 @ ( collect_Code_integer
% 0.37/0.69 @ ^ [X4: code_integer] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_rat ) ) ) )
% 0.37/0.69 = ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6769_sum_Osetdiff__irrelevant,axiom,
% 0.37/0.69 ! [A4: set_int,G: int > nat] :
% 0.37/0.69 ( ( finite_finite_int @ A4 )
% 0.37/0.69 => ( ( groups4541462559716669496nt_nat @ G
% 0.37/0.69 @ ( minus_minus_set_int @ A4
% 0.37/0.69 @ ( collect_int
% 0.37/0.69 @ ^ [X4: int] :
% 0.37/0.69 ( ( G @ X4 )
% 0.37/0.69 = zero_zero_nat ) ) ) )
% 0.37/0.69 = ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.setdiff_irrelevant
% 0.37/0.69 thf(fact_6770_sum__Suc,axiom,
% 0.37/0.69 ! [F: complex > nat,A4: set_complex] :
% 0.37/0.69 ( ( groups5693394587270226106ex_nat
% 0.37/0.69 @ ^ [X4: complex] : ( suc @ ( F @ X4 ) )
% 0.37/0.69 @ A4 )
% 0.37/0.69 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( finite_card_complex @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc
% 0.37/0.69 thf(fact_6771_sum__Suc,axiom,
% 0.37/0.69 ! [F: literal > nat,A4: set_literal] :
% 0.37/0.69 ( ( groups8652099787943017962al_nat
% 0.37/0.69 @ ^ [X4: literal] : ( suc @ ( F @ X4 ) )
% 0.37/0.69 @ A4 )
% 0.37/0.69 = ( plus_plus_nat @ ( groups8652099787943017962al_nat @ F @ A4 ) @ ( finite_card_literal @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc
% 0.37/0.69 thf(fact_6772_sum__Suc,axiom,
% 0.37/0.69 ! [F: list_nat > nat,A4: set_list_nat] :
% 0.37/0.69 ( ( groups4396056296759096172at_nat
% 0.37/0.69 @ ^ [X4: list_nat] : ( suc @ ( F @ X4 ) )
% 0.37/0.69 @ A4 )
% 0.37/0.69 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F @ A4 ) @ ( finite_card_list_nat @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc
% 0.37/0.69 thf(fact_6773_sum__Suc,axiom,
% 0.37/0.69 ! [F: set_nat > nat,A4: set_set_nat] :
% 0.37/0.69 ( ( groups8294997508430121362at_nat
% 0.37/0.69 @ ^ [X4: set_nat] : ( suc @ ( F @ X4 ) )
% 0.37/0.69 @ A4 )
% 0.37/0.69 = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( finite_card_set_nat @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc
% 0.37/0.69 thf(fact_6774_sum__Suc,axiom,
% 0.37/0.69 ! [F: nat > nat,A4: set_nat] :
% 0.37/0.69 ( ( groups3542108847815614940at_nat
% 0.37/0.69 @ ^ [X4: nat] : ( suc @ ( F @ X4 ) )
% 0.37/0.69 @ A4 )
% 0.37/0.69 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc
% 0.37/0.69 thf(fact_6775_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,T3: set_VEBT_VEBT,R2: vEBT_VEBT > vEBT_VEBT > $o,K: nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.69 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ X3 @ T3 )
% 0.37/0.69 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups771621172384141258BT_nat
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [J3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite7802652506058667612T_VEBT @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6776_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,T3: set_real,R2: vEBT_VEBT > real > $o,K: nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( finite_finite_real @ T3 )
% 0.37/0.69 => ( ! [X3: real] :
% 0.37/0.69 ( ( member_real @ X3 @ T3 )
% 0.37/0.69 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups771621172384141258BT_nat
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [J3: real] :
% 0.37/0.69 ( ( member_real @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite_card_real @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6777_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_real,T3: set_VEBT_VEBT,R2: real > vEBT_VEBT > $o,K: nat] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.69 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ X3 @ T3 )
% 0.37/0.69 => ( ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [I3: real] :
% 0.37/0.69 ( ( member_real @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups1935376822645274424al_nat
% 0.37/0.69 @ ^ [I3: real] :
% 0.37/0.69 ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [J3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite7802652506058667612T_VEBT @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6778_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_real,T3: set_real,R2: real > real > $o,K: nat] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( finite_finite_real @ T3 )
% 0.37/0.69 => ( ! [X3: real] :
% 0.37/0.69 ( ( member_real @ X3 @ T3 )
% 0.37/0.69 => ( ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [I3: real] :
% 0.37/0.69 ( ( member_real @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups1935376822645274424al_nat
% 0.37/0.69 @ ^ [I3: real] :
% 0.37/0.69 ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [J3: real] :
% 0.37/0.69 ( ( member_real @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite_card_real @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6779_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,T3: set_literal,R2: vEBT_VEBT > literal > $o,K: nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( finite5847741373460823677iteral @ T3 )
% 0.37/0.69 => ( ! [X3: literal] :
% 0.37/0.69 ( ( member_literal @ X3 @ T3 )
% 0.37/0.69 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups771621172384141258BT_nat
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [J3: literal] :
% 0.37/0.69 ( ( member_literal @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite_card_literal @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6780_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_real,T3: set_literal,R2: real > literal > $o,K: nat] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( finite5847741373460823677iteral @ T3 )
% 0.37/0.69 => ( ! [X3: literal] :
% 0.37/0.69 ( ( member_literal @ X3 @ T3 )
% 0.37/0.69 => ( ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [I3: real] :
% 0.37/0.69 ( ( member_real @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups1935376822645274424al_nat
% 0.37/0.69 @ ^ [I3: real] :
% 0.37/0.69 ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [J3: literal] :
% 0.37/0.69 ( ( member_literal @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite_card_literal @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6781_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_literal,T3: set_VEBT_VEBT,R2: literal > vEBT_VEBT > $o,K: nat] :
% 0.37/0.69 ( ( finite5847741373460823677iteral @ S3 )
% 0.37/0.69 => ( ( finite5795047828879050333T_VEBT @ T3 )
% 0.37/0.69 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ X3 @ T3 )
% 0.37/0.69 => ( ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [I3: literal] :
% 0.37/0.69 ( ( member_literal @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups8652099787943017962al_nat
% 0.37/0.69 @ ^ [I3: literal] :
% 0.37/0.69 ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [J3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite7802652506058667612T_VEBT @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6782_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_literal,T3: set_real,R2: literal > real > $o,K: nat] :
% 0.37/0.69 ( ( finite5847741373460823677iteral @ S3 )
% 0.37/0.69 => ( ( finite_finite_real @ T3 )
% 0.37/0.69 => ( ! [X3: real] :
% 0.37/0.69 ( ( member_real @ X3 @ T3 )
% 0.37/0.69 => ( ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [I3: literal] :
% 0.37/0.69 ( ( member_literal @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups8652099787943017962al_nat
% 0.37/0.69 @ ^ [I3: literal] :
% 0.37/0.69 ( finite_card_real
% 0.37/0.69 @ ( collect_real
% 0.37/0.69 @ ^ [J3: real] :
% 0.37/0.69 ( ( member_real @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite_card_real @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6783_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_literal,T3: set_literal,R2: literal > literal > $o,K: nat] :
% 0.37/0.69 ( ( finite5847741373460823677iteral @ S3 )
% 0.37/0.69 => ( ( finite5847741373460823677iteral @ T3 )
% 0.37/0.69 => ( ! [X3: literal] :
% 0.37/0.69 ( ( member_literal @ X3 @ T3 )
% 0.37/0.69 => ( ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [I3: literal] :
% 0.37/0.69 ( ( member_literal @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups8652099787943017962al_nat
% 0.37/0.69 @ ^ [I3: literal] :
% 0.37/0.69 ( finite_card_literal
% 0.37/0.69 @ ( collect_literal
% 0.37/0.69 @ ^ [J3: literal] :
% 0.37/0.69 ( ( member_literal @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite_card_literal @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6784_sum__multicount,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,T3: set_nat,R2: vEBT_VEBT > nat > $o,K: nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( finite_finite_nat @ T3 )
% 0.37/0.69 => ( ! [X3: nat] :
% 0.37/0.69 ( ( member_nat @ X3 @ T3 )
% 0.37/0.69 => ( ( finite7802652506058667612T_VEBT
% 0.37/0.69 @ ( collect_VEBT_VEBT
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 0.37/0.69 & ( R2 @ I3 @ X3 ) ) ) )
% 0.37/0.69 = K ) )
% 0.37/0.69 => ( ( groups771621172384141258BT_nat
% 0.37/0.69 @ ^ [I3: vEBT_VEBT] :
% 0.37/0.69 ( finite_card_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [J3: nat] :
% 0.37/0.69 ( ( member_nat @ J3 @ T3 )
% 0.37/0.69 & ( R2 @ I3 @ J3 ) ) ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( times_times_nat @ K @ ( finite_card_nat @ T3 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_multicount
% 0.37/0.69 thf(fact_6785_card__less,axiom,
% 0.37/0.69 ! [M7: set_nat,I: nat] :
% 0.37/0.69 ( ( member_nat @ zero_zero_nat @ M7 )
% 0.37/0.69 => ( ( finite_card_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [K3: nat] :
% 0.37/0.69 ( ( member_nat @ K3 @ M7 )
% 0.37/0.69 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 0.37/0.69 != zero_zero_nat ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_less
% 0.37/0.69 thf(fact_6786_card__less__Suc,axiom,
% 0.37/0.69 ! [M7: set_nat,I: nat] :
% 0.37/0.69 ( ( member_nat @ zero_zero_nat @ M7 )
% 0.37/0.69 => ( ( suc
% 0.37/0.69 @ ( finite_card_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [K3: nat] :
% 0.37/0.69 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.37/0.69 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 0.37/0.69 = ( finite_card_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [K3: nat] :
% 0.37/0.69 ( ( member_nat @ K3 @ M7 )
% 0.37/0.69 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_less_Suc
% 0.37/0.69 thf(fact_6787_card__less__Suc2,axiom,
% 0.37/0.69 ! [M7: set_nat,I: nat] :
% 0.37/0.69 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 0.37/0.69 => ( ( finite_card_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [K3: nat] :
% 0.37/0.69 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 0.37/0.69 & ( ord_less_nat @ K3 @ I ) ) ) )
% 0.37/0.69 = ( finite_card_nat
% 0.37/0.69 @ ( collect_nat
% 0.37/0.69 @ ^ [K3: nat] :
% 0.37/0.69 ( ( member_nat @ K3 @ M7 )
% 0.37/0.69 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_less_Suc2
% 0.37/0.69 thf(fact_6788_foldr__length__aux,axiom,
% 0.37/0.69 ! [L: list_VEBT_VEBT,A: nat] :
% 0.37/0.69 ( ( foldr_VEBT_VEBT_nat
% 0.37/0.69 @ ^ [X4: vEBT_VEBT] : suc
% 0.37/0.69 @ L
% 0.37/0.69 @ A )
% 0.37/0.69 = ( plus_plus_nat @ A @ ( size_s6755466524823107622T_VEBT @ L ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % foldr_length_aux
% 0.37/0.69 thf(fact_6789_foldr__length__aux,axiom,
% 0.37/0.69 ! [L: list_real,A: nat] :
% 0.37/0.69 ( ( foldr_real_nat
% 0.37/0.69 @ ^ [X4: real] : suc
% 0.37/0.69 @ L
% 0.37/0.69 @ A )
% 0.37/0.69 = ( plus_plus_nat @ A @ ( size_size_list_real @ L ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % foldr_length_aux
% 0.37/0.69 thf(fact_6790_foldr__length__aux,axiom,
% 0.37/0.69 ! [L: list_o,A: nat] :
% 0.37/0.69 ( ( foldr_o_nat
% 0.37/0.69 @ ^ [X4: $o] : suc
% 0.37/0.69 @ L
% 0.37/0.69 @ A )
% 0.37/0.69 = ( plus_plus_nat @ A @ ( size_size_list_o @ L ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % foldr_length_aux
% 0.37/0.69 thf(fact_6791_foldr__length__aux,axiom,
% 0.37/0.69 ! [L: list_nat,A: nat] :
% 0.37/0.69 ( ( foldr_nat_nat
% 0.37/0.69 @ ^ [X4: nat] : suc
% 0.37/0.69 @ L
% 0.37/0.69 @ A )
% 0.37/0.69 = ( plus_plus_nat @ A @ ( size_size_list_nat @ L ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % foldr_length_aux
% 0.37/0.69 thf(fact_6792_bot_Oordering__top__axioms,axiom,
% 0.37/0.69 ( ordering_top_set_nat
% 0.37/0.69 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 0.37/0.69 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 )
% 0.37/0.69 @ bot_bot_set_nat ) ).
% 0.37/0.69
% 0.37/0.69 % bot.ordering_top_axioms
% 0.37/0.69 thf(fact_6793_bot_Oordering__top__axioms,axiom,
% 0.37/0.69 ( ordering_top_assn
% 0.37/0.69 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 0.37/0.69 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 )
% 0.37/0.69 @ bot_bot_assn ) ).
% 0.37/0.69
% 0.37/0.69 % bot.ordering_top_axioms
% 0.37/0.69 thf(fact_6794_bot_Oordering__top__axioms,axiom,
% 0.37/0.69 ( ordering_top_set_o
% 0.37/0.69 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_eq_set_o @ Y4 @ X4 )
% 0.37/0.69 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_set_o @ Y4 @ X4 )
% 0.37/0.69 @ bot_bot_set_o ) ).
% 0.37/0.69
% 0.37/0.69 % bot.ordering_top_axioms
% 0.37/0.69 thf(fact_6795_bot_Oordering__top__axioms,axiom,
% 0.37/0.69 ( ordering_top_set_int
% 0.37/0.69 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 0.37/0.69 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 )
% 0.37/0.69 @ bot_bot_set_int ) ).
% 0.37/0.69
% 0.37/0.69 % bot.ordering_top_axioms
% 0.37/0.69 thf(fact_6796_bot_Oordering__top__axioms,axiom,
% 0.37/0.69 ( ordering_top_nat
% 0.37/0.69 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 0.37/0.69 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 0.37/0.69 @ bot_bot_nat ) ).
% 0.37/0.69
% 0.37/0.69 % bot.ordering_top_axioms
% 0.37/0.69 thf(fact_6797_card__sum__le__nat__sum,axiom,
% 0.37/0.69 ! [S3: set_nat] :
% 0.37/0.69 ( ord_less_eq_nat
% 0.37/0.69 @ ( groups3542108847815614940at_nat
% 0.37/0.69 @ ^ [X4: nat] : X4
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 0.37/0.69 @ ( groups3542108847815614940at_nat
% 0.37/0.69 @ ^ [X4: nat] : X4
% 0.37/0.69 @ S3 ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_sum_le_nat_sum
% 0.37/0.69 thf(fact_6798_set__zip__rightD,axiom,
% 0.37/0.69 ! [X: $o,Y: $o,Xs: list_o,Ys: list_o] :
% 0.37/0.69 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( set_Product_prod_o_o2 @ ( zip_o_o @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_o @ Y @ ( set_o2 @ Ys ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_rightD
% 0.37/0.69 thf(fact_6799_set__zip__rightD,axiom,
% 0.37/0.69 ! [X: uint32,Y: uint32,Xs: list_uint32,Ys: list_uint32] :
% 0.37/0.69 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_uint32 @ Y @ ( set_uint322 @ Ys ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_rightD
% 0.37/0.69 thf(fact_6800_set__zip__rightD,axiom,
% 0.37/0.69 ! [X: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 0.37/0.69 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_rightD
% 0.37/0.69 thf(fact_6801_set__zip__rightD,axiom,
% 0.37/0.69 ! [X: int,Y: int,Xs: list_int,Ys: list_int] :
% 0.37/0.69 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_rightD
% 0.37/0.69 thf(fact_6802_set__zip__rightD,axiom,
% 0.37/0.69 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 0.37/0.69 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( set_Pr364071364088684201et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member6260224972018164377et_nat @ Y @ ( set_Pr3864771053587467565et_nat @ Ys ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_rightD
% 0.37/0.69 thf(fact_6803_set__zip__rightD,axiom,
% 0.37/0.69 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 0.37/0.69 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( set_Pr7458301993993767461et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member1996754912294343701et_nat @ Y @ ( set_Pr364071364088684201et_nat @ Ys ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_rightD
% 0.37/0.69 thf(fact_6804_set__zip__leftD,axiom,
% 0.37/0.69 ! [X: $o,Y: $o,Xs: list_o,Ys: list_o] :
% 0.37/0.69 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( set_Product_prod_o_o2 @ ( zip_o_o @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_o @ X @ ( set_o2 @ Xs ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_leftD
% 0.37/0.69 thf(fact_6805_set__zip__leftD,axiom,
% 0.37/0.69 ! [X: uint32,Y: uint32,Xs: list_uint32,Ys: list_uint32] :
% 0.37/0.69 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_uint32 @ X @ ( set_uint322 @ Xs ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_leftD
% 0.37/0.69 thf(fact_6806_set__zip__leftD,axiom,
% 0.37/0.69 ! [X: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 0.37/0.69 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_leftD
% 0.37/0.69 thf(fact_6807_set__zip__leftD,axiom,
% 0.37/0.69 ! [X: int,Y: int,Xs: list_int,Ys: list_int] :
% 0.37/0.69 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_leftD
% 0.37/0.69 thf(fact_6808_set__zip__leftD,axiom,
% 0.37/0.69 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 0.37/0.69 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( set_Pr364071364088684201et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_leftD
% 0.37/0.69 thf(fact_6809_set__zip__leftD,axiom,
% 0.37/0.69 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 0.37/0.69 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( set_Pr7458301993993767461et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % set_zip_leftD
% 0.37/0.69 thf(fact_6810_in__set__zipE,axiom,
% 0.37/0.69 ! [X: int,Y: vEBT_VEBT,Xs: list_int,Ys: list_VEBT_VEBT] :
% 0.37/0.69 ( ( member2056185340421749780T_VEBT @ ( produc3329399203697025711T_VEBT @ X @ Y ) @ ( set_Pr8714266321650254504T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6811_in__set__zipE,axiom,
% 0.37/0.69 ! [X: int,Y: nat,Xs: list_int,Ys: list_nat] :
% 0.37/0.69 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( set_Pr6647972299459129970nt_nat @ ( zip_int_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6812_in__set__zipE,axiom,
% 0.37/0.69 ! [X: int,Y: real,Xs: list_int,Ys: list_real] :
% 0.37/0.69 ( ( member2744130022092475746t_real @ ( produc801115645435158769t_real @ X @ Y ) @ ( set_Pr112895574167722958t_real @ ( zip_int_real @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6813_in__set__zipE,axiom,
% 0.37/0.69 ! [X: int,Y: $o,Xs: list_int,Ys: list_o] :
% 0.37/0.69 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ X @ Y ) @ ( set_Pr8694291782656941196_int_o @ ( zip_int_o @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ( member_o @ Y @ ( set_o2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6814_in__set__zipE,axiom,
% 0.37/0.69 ! [X: vEBT_VEBT,Y: int,Xs: list_VEBT_VEBT,Ys: list_int] :
% 0.37/0.69 ( ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ X @ Y ) @ ( set_Pr2853735649769556538BT_int @ ( zip_VEBT_VEBT_int @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6815_in__set__zipE,axiom,
% 0.37/0.69 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.37/0.69 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6816_in__set__zipE,axiom,
% 0.37/0.69 ! [X: vEBT_VEBT,Y: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 0.37/0.69 ( ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X @ Y ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6817_in__set__zipE,axiom,
% 0.37/0.69 ! [X: vEBT_VEBT,Y: real,Xs: list_VEBT_VEBT,Ys: list_real] :
% 0.37/0.69 ( ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X @ Y ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6818_in__set__zipE,axiom,
% 0.37/0.69 ! [X: vEBT_VEBT,Y: $o,Xs: list_VEBT_VEBT,Ys: list_o] :
% 0.37/0.69 ( ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X @ Y ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ( member_o @ Y @ ( set_o2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6819_in__set__zipE,axiom,
% 0.37/0.69 ! [X: nat,Y: int,Xs: list_nat,Ys: list_int] :
% 0.37/0.69 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( set_Pr1470767568048878706at_int @ ( zip_nat_int @ Xs @ Ys ) ) )
% 0.37/0.69 => ~ ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.37/0.69 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_zipE
% 0.37/0.69 thf(fact_6820_zip__same,axiom,
% 0.37/0.69 ! [A: set_nat,B: set_nat,Xs: list_set_nat] :
% 0.37/0.69 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ B ) @ ( set_Pr9040384385603167362et_nat @ ( zip_set_nat_set_nat @ Xs @ Xs ) ) )
% 0.37/0.69 = ( ( member_set_nat @ A @ ( set_set_nat2 @ Xs ) )
% 0.37/0.69 & ( A = B ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_same
% 0.37/0.69 thf(fact_6821_zip__same,axiom,
% 0.37/0.69 ! [A: vEBT_VEBT,B: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 0.37/0.69 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ A @ B ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Xs ) ) )
% 0.37/0.69 = ( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 & ( A = B ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_same
% 0.37/0.69 thf(fact_6822_zip__same,axiom,
% 0.37/0.69 ! [A: real,B: real,Xs: list_real] :
% 0.37/0.69 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ A @ B ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs @ Xs ) ) )
% 0.37/0.69 = ( ( member_real @ A @ ( set_real2 @ Xs ) )
% 0.37/0.69 & ( A = B ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_same
% 0.37/0.69 thf(fact_6823_zip__same,axiom,
% 0.37/0.69 ! [A: $o,B: $o,Xs: list_o] :
% 0.37/0.69 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( set_Product_prod_o_o2 @ ( zip_o_o @ Xs @ Xs ) ) )
% 0.37/0.69 = ( ( member_o @ A @ ( set_o2 @ Xs ) )
% 0.37/0.69 & ( A = B ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_same
% 0.37/0.69 thf(fact_6824_zip__same,axiom,
% 0.37/0.69 ! [A: uint32,B: uint32,Xs: list_uint32] :
% 0.37/0.69 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Xs ) ) )
% 0.37/0.69 = ( ( member_uint32 @ A @ ( set_uint322 @ Xs ) )
% 0.37/0.69 & ( A = B ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_same
% 0.37/0.69 thf(fact_6825_zip__same,axiom,
% 0.37/0.69 ! [A: nat,B: nat,Xs: list_nat] :
% 0.37/0.69 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Xs ) ) )
% 0.37/0.69 = ( ( member_nat @ A @ ( set_nat2 @ Xs ) )
% 0.37/0.69 & ( A = B ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_same
% 0.37/0.69 thf(fact_6826_zip__same,axiom,
% 0.37/0.69 ! [A: int,B: int,Xs: list_int] :
% 0.37/0.69 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Xs ) ) )
% 0.37/0.69 = ( ( member_int @ A @ ( set_int2 @ Xs ) )
% 0.37/0.69 & ( A = B ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_same
% 0.37/0.69 thf(fact_6827_of__nat__0__le__iff,axiom,
% 0.37/0.69 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_0_le_iff
% 0.37/0.69 thf(fact_6828_of__nat__0__le__iff,axiom,
% 0.37/0.69 ! [N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_0_le_iff
% 0.37/0.69 thf(fact_6829_of__nat__0__le__iff,axiom,
% 0.37/0.69 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_0_le_iff
% 0.37/0.69 thf(fact_6830_of__nat__0__le__iff,axiom,
% 0.37/0.69 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_0_le_iff
% 0.37/0.69 thf(fact_6831_of__nat__0__le__iff,axiom,
% 0.37/0.69 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_0_le_iff
% 0.37/0.69 thf(fact_6832_of__nat__less__0__iff,axiom,
% 0.37/0.69 ! [M: nat] :
% 0.37/0.69 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_0_iff
% 0.37/0.69 thf(fact_6833_of__nat__less__0__iff,axiom,
% 0.37/0.69 ! [M: nat] :
% 0.37/0.69 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_0_iff
% 0.37/0.69 thf(fact_6834_of__nat__less__0__iff,axiom,
% 0.37/0.69 ! [M: nat] :
% 0.37/0.69 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_0_iff
% 0.37/0.69 thf(fact_6835_of__nat__less__0__iff,axiom,
% 0.37/0.69 ! [M: nat] :
% 0.37/0.69 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_0_iff
% 0.37/0.69 thf(fact_6836_of__nat__less__0__iff,axiom,
% 0.37/0.69 ! [M: nat] :
% 0.37/0.69 ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_0_iff
% 0.37/0.69 thf(fact_6837_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_o,I: nat,X: $o,Ys: list_o,Y: $o] :
% 0.37/0.69 ( ( zip_o_o @ ( list_update_o @ Xs @ I @ X ) @ ( list_update_o @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u1537252308907898773od_o_o @ ( zip_o_o @ Xs @ Ys ) @ I @ ( product_Pair_o_o @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6838_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi,Ys: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 0.37/0.69 ( ( zip_VE793581609497812771_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u30558089781959097_VEBTi @ ( zip_VE793581609497812771_VEBTi @ Xs @ Ys ) @ I @ ( produc436343169921013763_VEBTi @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6839_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.69 ( ( zip_VE7413257051550508102T_VEBT @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u9044509791230035014T_VEBT @ ( zip_VE7413257051550508102T_VEBT @ Xs @ Ys ) @ I @ ( produc7053807326796202854T_VEBT @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6840_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Ys: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 0.37/0.69 ( ( zip_VE6444338338598820466_VEBTi @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u636002643828906794_VEBTi @ ( zip_VE6444338338598820466_VEBTi @ Xs @ Ys ) @ I @ ( produc6084888613844515218_VEBTi @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6841_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.69 ( ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) @ I @ ( produc537772716801021591T_VEBT @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6842_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_uint32,I: nat,X: uint32,Ys: list_uint32,Y: uint32] :
% 0.37/0.69 ( ( zip_uint32_uint32 @ ( list_update_uint32 @ Xs @ I @ X ) @ ( list_update_uint32 @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u2546161786664092711uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) @ I @ ( produc1400373151660368625uint32 @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6843_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_nat,I: nat,X: nat,Ys: list_nat,Y: nat] :
% 0.37/0.69 ( ( zip_nat_nat @ ( list_update_nat @ Xs @ I @ X ) @ ( list_update_nat @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u6180841689913720943at_nat @ ( zip_nat_nat @ Xs @ Ys ) @ I @ ( product_Pair_nat_nat @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6844_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_int,I: nat,X: int,Ys: list_int,Y: int] :
% 0.37/0.69 ( ( zip_int_int @ ( list_update_int @ Xs @ I @ X ) @ ( list_update_int @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u3002344382305578791nt_int @ ( zip_int_int @ Xs @ Ys ) @ I @ ( product_Pair_int_int @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6845_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_P7985473006766602707_nat_o,I: nat,X: produc3658429121746597890et_nat > $o,Ys: list_P9062070895058802706et_nat,Y: produc3658429121746597890et_nat] :
% 0.37/0.69 ( ( zip_Pr7134870689397686104et_nat @ ( list_u6943956310655620667_nat_o @ Xs @ I @ X ) @ ( list_u9060326803697358356et_nat @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u1866171116859985808et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) @ I @ ( produc5001842942810119800et_nat @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6846_zip__update,axiom,
% 0.37/0.69 ! [Xs: list_P7985473006766602707_nat_o,I: nat,X: produc3658429121746597890et_nat > $o,Ys: list_P2321686559999237006et_nat,Y: produc3925858234332021118et_nat] :
% 0.37/0.69 ( ( zip_Pr8136144321567152340et_nat @ ( list_u6943956310655620667_nat_o @ Xs @ I @ X ) @ ( list_u1866171116859985808et_nat @ Ys @ I @ Y ) )
% 0.37/0.69 = ( list_u1913845194572276492et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) @ I @ ( produc2245416461498447860et_nat @ X @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_update
% 0.37/0.69 thf(fact_6847_one__diff__power__eq_H,axiom,
% 0.37/0.69 ! [X: rat,N: nat] :
% 0.37/0.69 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.37/0.69 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 0.37/0.69 @ ( groups2906978787729119204at_rat
% 0.37/0.69 @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.37/0.69 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % one_diff_power_eq'
% 0.37/0.69 thf(fact_6848_one__diff__power__eq_H,axiom,
% 0.37/0.69 ! [X: complex,N: nat] :
% 0.37/0.69 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 0.37/0.69 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 0.37/0.69 @ ( groups2073611262835488442omplex
% 0.37/0.69 @ ^ [I3: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.37/0.69 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % one_diff_power_eq'
% 0.37/0.69 thf(fact_6849_one__diff__power__eq_H,axiom,
% 0.37/0.69 ! [X: uint32,N: nat] :
% 0.37/0.69 ( ( minus_minus_uint32 @ one_one_uint32 @ ( power_power_uint32 @ X @ N ) )
% 0.37/0.69 = ( times_times_uint32 @ ( minus_minus_uint32 @ one_one_uint32 @ X )
% 0.37/0.69 @ ( groups833757482993574392uint32
% 0.37/0.69 @ ^ [I3: nat] : ( power_power_uint32 @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.37/0.69 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % one_diff_power_eq'
% 0.37/0.69 thf(fact_6850_one__diff__power__eq_H,axiom,
% 0.37/0.69 ! [X: int,N: nat] :
% 0.37/0.69 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.37/0.69 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 0.37/0.69 @ ( groups3539618377306564664at_int
% 0.37/0.69 @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.37/0.69 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % one_diff_power_eq'
% 0.37/0.69 thf(fact_6851_one__diff__power__eq_H,axiom,
% 0.37/0.69 ! [X: real,N: nat] :
% 0.37/0.69 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 0.37/0.69 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 0.37/0.69 @ ( groups6591440286371151544t_real
% 0.37/0.69 @ ^ [I3: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.37/0.69 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % one_diff_power_eq'
% 0.37/0.69 thf(fact_6852_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 0.37/0.69 != zero_zero_rat ) ).
% 0.37/0.69
% 0.37/0.69 % semiring_char_0_class.of_nat_neq_0
% 0.37/0.69 thf(fact_6853_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 0.37/0.69 != zero_zero_nat ) ).
% 0.37/0.69
% 0.37/0.69 % semiring_char_0_class.of_nat_neq_0
% 0.37/0.69 thf(fact_6854_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 0.37/0.69 != zero_zero_real ) ).
% 0.37/0.69
% 0.37/0.69 % semiring_char_0_class.of_nat_neq_0
% 0.37/0.69 thf(fact_6855_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.37/0.69 != zero_zero_int ) ).
% 0.37/0.69
% 0.37/0.69 % semiring_char_0_class.of_nat_neq_0
% 0.37/0.69 thf(fact_6856_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( semiri4939895301339042750nteger @ ( suc @ N ) )
% 0.37/0.69 != zero_z3403309356797280102nteger ) ).
% 0.37/0.69
% 0.37/0.69 % semiring_char_0_class.of_nat_neq_0
% 0.37/0.69 thf(fact_6857_of__nat__less__imp__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.37/0.69 => ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_imp_less
% 0.37/0.69 thf(fact_6858_of__nat__less__imp__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.37/0.69 => ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_imp_less
% 0.37/0.69 thf(fact_6859_of__nat__less__imp__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.69 => ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_imp_less
% 0.37/0.69 thf(fact_6860_of__nat__less__imp__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.69 => ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_imp_less
% 0.37/0.69 thf(fact_6861_of__nat__less__imp__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.69 => ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_less_imp_less
% 0.37/0.69 thf(fact_6862_less__imp__of__nat__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_nat @ M @ N )
% 0.37/0.69 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % less_imp_of_nat_less
% 0.37/0.69 thf(fact_6863_less__imp__of__nat__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_nat @ M @ N )
% 0.37/0.69 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % less_imp_of_nat_less
% 0.37/0.69 thf(fact_6864_less__imp__of__nat__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_nat @ M @ N )
% 0.37/0.69 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % less_imp_of_nat_less
% 0.37/0.69 thf(fact_6865_less__imp__of__nat__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_nat @ M @ N )
% 0.37/0.69 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % less_imp_of_nat_less
% 0.37/0.69 thf(fact_6866_less__imp__of__nat__less,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_nat @ M @ N )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % less_imp_of_nat_less
% 0.37/0.69 thf(fact_6867_of__nat__mono,axiom,
% 0.37/0.69 ! [I: nat,J: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.69 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_mono
% 0.37/0.69 thf(fact_6868_of__nat__mono,axiom,
% 0.37/0.69 ! [I: nat,J: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_mono
% 0.37/0.69 thf(fact_6869_of__nat__mono,axiom,
% 0.37/0.69 ! [I: nat,J: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.69 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_mono
% 0.37/0.69 thf(fact_6870_of__nat__mono,axiom,
% 0.37/0.69 ! [I: nat,J: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.69 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_mono
% 0.37/0.69 thf(fact_6871_of__nat__mono,axiom,
% 0.37/0.69 ! [I: nat,J: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.69 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_mono
% 0.37/0.69 thf(fact_6872_Iio__eq__empty__iff,axiom,
% 0.37/0.69 ! [N: $o] :
% 0.37/0.69 ( ( ( set_ord_lessThan_o @ N )
% 0.37/0.69 = bot_bot_set_o )
% 0.37/0.69 = ( N = bot_bot_o ) ) ).
% 0.37/0.69
% 0.37/0.69 % Iio_eq_empty_iff
% 0.37/0.69 thf(fact_6873_Iio__eq__empty__iff,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( ( set_ord_lessThan_nat @ N )
% 0.37/0.69 = bot_bot_set_nat )
% 0.37/0.69 = ( N = bot_bot_nat ) ) ).
% 0.37/0.69
% 0.37/0.69 % Iio_eq_empty_iff
% 0.37/0.69 thf(fact_6874_lessThan__atLeast0,axiom,
% 0.37/0.69 ( set_ord_lessThan_nat
% 0.37/0.69 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_atLeast0
% 0.37/0.69 thf(fact_6875_lessThan__strict__subset__iff,axiom,
% 0.37/0.69 ! [M: rat,N: rat] :
% 0.37/0.69 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 0.37/0.69 = ( ord_less_rat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_strict_subset_iff
% 0.37/0.69 thf(fact_6876_lessThan__strict__subset__iff,axiom,
% 0.37/0.69 ! [M: num,N: num] :
% 0.37/0.69 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 0.37/0.69 = ( ord_less_num @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_strict_subset_iff
% 0.37/0.69 thf(fact_6877_lessThan__strict__subset__iff,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.69 = ( ord_less_nat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_strict_subset_iff
% 0.37/0.69 thf(fact_6878_lessThan__strict__subset__iff,axiom,
% 0.37/0.69 ! [M: int,N: int] :
% 0.37/0.69 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 0.37/0.69 = ( ord_less_int @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_strict_subset_iff
% 0.37/0.69 thf(fact_6879_lessThan__strict__subset__iff,axiom,
% 0.37/0.69 ! [M: real,N: real] :
% 0.37/0.69 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 0.37/0.69 = ( ord_less_real @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_strict_subset_iff
% 0.37/0.69 thf(fact_6880_lessThan__empty__iff,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( ( set_ord_lessThan_nat @ N )
% 0.37/0.69 = bot_bot_set_nat )
% 0.37/0.69 = ( N = zero_zero_nat ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_empty_iff
% 0.37/0.69 thf(fact_6881_lessThan__Suc,axiom,
% 0.37/0.69 ! [K: nat] :
% 0.37/0.69 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.37/0.69 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_Suc
% 0.37/0.69 thf(fact_6882_sum__Suc__diff_H,axiom,
% 0.37/0.69 ! [M: nat,N: nat,F: nat > uint32] :
% 0.37/0.69 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.69 => ( ( groups833757482993574392uint32
% 0.37/0.69 @ ^ [I3: nat] : ( minus_minus_uint32 @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.69 = ( minus_minus_uint32 @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc_diff'
% 0.37/0.69 thf(fact_6883_sum__Suc__diff_H,axiom,
% 0.37/0.69 ! [M: nat,N: nat,F: nat > int] :
% 0.37/0.69 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.69 => ( ( groups3539618377306564664at_int
% 0.37/0.69 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.69 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc_diff'
% 0.37/0.69 thf(fact_6884_sum__Suc__diff_H,axiom,
% 0.37/0.69 ! [M: nat,N: nat,F: nat > real] :
% 0.37/0.69 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.69 => ( ( groups6591440286371151544t_real
% 0.37/0.69 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.37/0.69 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_Suc_diff'
% 0.37/0.69 thf(fact_6885_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_complex,F: complex > real,K: real] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_complex )
% 0.37/0.69 => ( ( lattic4275903605611617917x_real
% 0.37/0.69 @ ( image_complex_real
% 0.37/0.69 @ ^ [X4: complex] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_complex_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6886_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,F: code_integer > real,K: real] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.69 => ( ( lattic4275903605611617917x_real
% 0.37/0.69 @ ( image_7738145705984076560r_real
% 0.37/0.69 @ ^ [X4: code_integer] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_7738145705984076560r_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6887_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_complex,F: complex > rat,K: rat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_complex )
% 0.37/0.69 => ( ( lattic7630753665789217321ax_rat
% 0.37/0.69 @ ( image_complex_rat
% 0.37/0.69 @ ^ [X4: complex] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_rat @ ( lattic7630753665789217321ax_rat @ ( image_complex_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6888_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,F: code_integer > rat,K: rat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.69 => ( ( lattic7630753665789217321ax_rat
% 0.37/0.69 @ ( image_315895873841295420er_rat
% 0.37/0.69 @ ^ [X4: code_integer] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_rat @ ( lattic7630753665789217321ax_rat @ ( image_315895873841295420er_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6889_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_complex,F: complex > int,K: int] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_complex )
% 0.37/0.69 => ( ( lattic8263393255366662781ax_int
% 0.37/0.69 @ ( image_complex_int
% 0.37/0.69 @ ^ [X4: complex] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_int @ ( lattic8263393255366662781ax_int @ ( image_complex_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6890_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,F: code_integer > int,K: int] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.69 => ( ( lattic8263393255366662781ax_int
% 0.37/0.69 @ ( image_948535463418740880er_int
% 0.37/0.69 @ ^ [X4: code_integer] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_int @ ( lattic8263393255366662781ax_int @ ( image_948535463418740880er_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6891_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_nat,F: nat > real,K: real] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_nat )
% 0.37/0.69 => ( ( lattic4275903605611617917x_real
% 0.37/0.69 @ ( image_nat_real
% 0.37/0.69 @ ^ [X4: nat] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_nat_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6892_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_nat,F: nat > rat,K: rat] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_nat )
% 0.37/0.69 => ( ( lattic7630753665789217321ax_rat
% 0.37/0.69 @ ( image_nat_rat
% 0.37/0.69 @ ^ [X4: nat] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_rat @ ( lattic7630753665789217321ax_rat @ ( image_nat_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6893_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_nat,F: nat > int,K: int] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_nat )
% 0.37/0.69 => ( ( lattic8263393255366662781ax_int
% 0.37/0.69 @ ( image_nat_int
% 0.37/0.69 @ ^ [X4: nat] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_int @ ( lattic8263393255366662781ax_int @ ( image_nat_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6894_Max__add__commute,axiom,
% 0.37/0.69 ! [S3: set_int,F: int > real,K: real] :
% 0.37/0.69 ( ( finite_finite_int @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_int )
% 0.37/0.69 => ( ( lattic4275903605611617917x_real
% 0.37/0.69 @ ( image_int_real
% 0.37/0.69 @ ^ [X4: int] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_int_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Max_add_commute
% 0.37/0.69 thf(fact_6895_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_complex,F: complex > real,K: real] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_complex )
% 0.37/0.69 => ( ( lattic3629708407755379051n_real
% 0.37/0.69 @ ( image_complex_real
% 0.37/0.69 @ ^ [X4: complex] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_complex_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6896_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,F: code_integer > real,K: real] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.69 => ( ( lattic3629708407755379051n_real
% 0.37/0.69 @ ( image_7738145705984076560r_real
% 0.37/0.69 @ ^ [X4: code_integer] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_7738145705984076560r_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6897_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_complex,F: complex > rat,K: rat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_complex )
% 0.37/0.69 => ( ( lattic8086005427650270231in_rat
% 0.37/0.69 @ ( image_complex_rat
% 0.37/0.69 @ ^ [X4: complex] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_rat @ ( lattic8086005427650270231in_rat @ ( image_complex_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6898_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,F: code_integer > rat,K: rat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.69 => ( ( lattic8086005427650270231in_rat
% 0.37/0.69 @ ( image_315895873841295420er_rat
% 0.37/0.69 @ ^ [X4: code_integer] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_rat @ ( lattic8086005427650270231in_rat @ ( image_315895873841295420er_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6899_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_complex,F: complex > int,K: int] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_complex )
% 0.37/0.69 => ( ( lattic8718645017227715691in_int
% 0.37/0.69 @ ( image_complex_int
% 0.37/0.69 @ ^ [X4: complex] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_int @ ( lattic8718645017227715691in_int @ ( image_complex_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6900_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,F: code_integer > int,K: int] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bo3990330152332043303nteger )
% 0.37/0.69 => ( ( lattic8718645017227715691in_int
% 0.37/0.69 @ ( image_948535463418740880er_int
% 0.37/0.69 @ ^ [X4: code_integer] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_int @ ( lattic8718645017227715691in_int @ ( image_948535463418740880er_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6901_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_nat,F: nat > real,K: real] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_nat )
% 0.37/0.69 => ( ( lattic3629708407755379051n_real
% 0.37/0.69 @ ( image_nat_real
% 0.37/0.69 @ ^ [X4: nat] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_nat_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6902_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_nat,F: nat > rat,K: rat] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_nat )
% 0.37/0.69 => ( ( lattic8086005427650270231in_rat
% 0.37/0.69 @ ( image_nat_rat
% 0.37/0.69 @ ^ [X4: nat] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_rat @ ( lattic8086005427650270231in_rat @ ( image_nat_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6903_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_nat,F: nat > int,K: int] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_nat )
% 0.37/0.69 => ( ( lattic8718645017227715691in_int
% 0.37/0.69 @ ( image_nat_int
% 0.37/0.69 @ ^ [X4: nat] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_int @ ( lattic8718645017227715691in_int @ ( image_nat_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6904_Min__add__commute,axiom,
% 0.37/0.69 ! [S3: set_int,F: int > real,K: real] :
% 0.37/0.69 ( ( finite_finite_int @ S3 )
% 0.37/0.69 => ( ( S3 != bot_bot_set_int )
% 0.37/0.69 => ( ( lattic3629708407755379051n_real
% 0.37/0.69 @ ( image_int_real
% 0.37/0.69 @ ^ [X4: int] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 0.37/0.69 @ S3 ) )
% 0.37/0.69 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_int_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Min_add_commute
% 0.37/0.69 thf(fact_6905_sum_OatLeastLessThan__rev,axiom,
% 0.37/0.69 ! [G: nat > nat,N: nat,M: nat] :
% 0.37/0.69 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.37/0.69 = ( groups3542108847815614940at_nat
% 0.37/0.69 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.atLeastLessThan_rev
% 0.37/0.69 thf(fact_6906_sum_OatLeastLessThan__rev,axiom,
% 0.37/0.69 ! [G: nat > real,N: nat,M: nat] :
% 0.37/0.69 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.37/0.69 = ( groups6591440286371151544t_real
% 0.37/0.69 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.atLeastLessThan_rev
% 0.37/0.69 thf(fact_6907_of__nat__max,axiom,
% 0.37/0.69 ! [X: nat,Y: nat] :
% 0.37/0.69 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 0.37/0.69 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_max
% 0.37/0.69 thf(fact_6908_of__nat__max,axiom,
% 0.37/0.69 ! [X: nat,Y: nat] :
% 0.37/0.69 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 0.37/0.69 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_max
% 0.37/0.69 thf(fact_6909_of__nat__max,axiom,
% 0.37/0.69 ! [X: nat,Y: nat] :
% 0.37/0.69 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 0.37/0.69 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_max
% 0.37/0.69 thf(fact_6910_of__nat__max,axiom,
% 0.37/0.69 ! [X: nat,Y: nat] :
% 0.37/0.69 ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 0.37/0.69 = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_max
% 0.37/0.69 thf(fact_6911_finite__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_complex,N: nat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.69 => ( finite8712137658972009173omplex
% 0.37/0.69 @ ( collect_list_complex
% 0.37/0.69 @ ^ [Xs2: list_complex] :
% 0.37/0.69 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.37/0.69 = N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_eq
% 0.37/0.69 thf(fact_6912_finite__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_Code_integer,N: nat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.69 => ( finite1283093830868386564nteger
% 0.37/0.69 @ ( collec3483841146883906114nteger
% 0.37/0.69 @ ^ [Xs2: list_Code_integer] :
% 0.37/0.69 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 0.37/0.69 = N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_eq
% 0.37/0.69 thf(fact_6913_finite__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.69 => ( finite3004134309566078307T_VEBT
% 0.37/0.69 @ ( collec5608196760682091941T_VEBT
% 0.37/0.69 @ ^ [Xs2: list_VEBT_VEBT] :
% 0.37/0.69 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.37/0.69 = N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_eq
% 0.37/0.69 thf(fact_6914_finite__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_real,N: nat] :
% 0.37/0.69 ( ( finite_finite_real @ A4 )
% 0.37/0.69 => ( finite306553202115118035t_real
% 0.37/0.69 @ ( collect_list_real
% 0.37/0.69 @ ^ [Xs2: list_real] :
% 0.37/0.69 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_real @ Xs2 )
% 0.37/0.69 = N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_eq
% 0.37/0.69 thf(fact_6915_finite__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_o,N: nat] :
% 0.37/0.69 ( ( finite_finite_o @ A4 )
% 0.37/0.69 => ( finite_finite_list_o
% 0.37/0.69 @ ( collect_list_o
% 0.37/0.69 @ ^ [Xs2: list_o] :
% 0.37/0.69 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_o @ Xs2 )
% 0.37/0.69 = N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_eq
% 0.37/0.69 thf(fact_6916_finite__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_nat,N: nat] :
% 0.37/0.69 ( ( finite_finite_nat @ A4 )
% 0.37/0.69 => ( finite8100373058378681591st_nat
% 0.37/0.69 @ ( collect_list_nat
% 0.37/0.69 @ ^ [Xs2: list_nat] :
% 0.37/0.69 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_nat @ Xs2 )
% 0.37/0.69 = N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_eq
% 0.37/0.69 thf(fact_6917_finite__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_int,N: nat] :
% 0.37/0.69 ( ( finite_finite_int @ A4 )
% 0.37/0.69 => ( finite3922522038869484883st_int
% 0.37/0.69 @ ( collect_list_int
% 0.37/0.69 @ ^ [Xs2: list_int] :
% 0.37/0.69 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_int @ Xs2 )
% 0.37/0.69 = N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_eq
% 0.37/0.69 thf(fact_6918_distinct__finite__subset,axiom,
% 0.37/0.69 ! [X: set_VEBT_VEBT] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ X )
% 0.37/0.69 => ( finite3004134309566078307T_VEBT
% 0.37/0.69 @ ( collec5608196760682091941T_VEBT
% 0.37/0.69 @ ^ [Ys3: list_VEBT_VEBT] :
% 0.37/0.69 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Ys3 ) @ X )
% 0.37/0.69 & ( distinct_VEBT_VEBT @ Ys3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % distinct_finite_subset
% 0.37/0.69 thf(fact_6919_distinct__finite__subset,axiom,
% 0.37/0.69 ! [X: set_real] :
% 0.37/0.69 ( ( finite_finite_real @ X )
% 0.37/0.69 => ( finite306553202115118035t_real
% 0.37/0.69 @ ( collect_list_real
% 0.37/0.69 @ ^ [Ys3: list_real] :
% 0.37/0.69 ( ( ord_less_eq_set_real @ ( set_real2 @ Ys3 ) @ X )
% 0.37/0.69 & ( distinct_real @ Ys3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % distinct_finite_subset
% 0.37/0.69 thf(fact_6920_distinct__finite__subset,axiom,
% 0.37/0.69 ! [X: set_o] :
% 0.37/0.69 ( ( finite_finite_o @ X )
% 0.37/0.69 => ( finite_finite_list_o
% 0.37/0.69 @ ( collect_list_o
% 0.37/0.69 @ ^ [Ys3: list_o] :
% 0.37/0.69 ( ( ord_less_eq_set_o @ ( set_o2 @ Ys3 ) @ X )
% 0.37/0.69 & ( distinct_o @ Ys3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % distinct_finite_subset
% 0.37/0.69 thf(fact_6921_distinct__finite__subset,axiom,
% 0.37/0.69 ! [X: set_nat] :
% 0.37/0.69 ( ( finite_finite_nat @ X )
% 0.37/0.69 => ( finite8100373058378681591st_nat
% 0.37/0.69 @ ( collect_list_nat
% 0.37/0.69 @ ^ [Ys3: list_nat] :
% 0.37/0.69 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Ys3 ) @ X )
% 0.37/0.69 & ( distinct_nat @ Ys3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % distinct_finite_subset
% 0.37/0.69 thf(fact_6922_distinct__finite__subset,axiom,
% 0.37/0.69 ! [X: set_complex] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ X )
% 0.37/0.69 => ( finite8712137658972009173omplex
% 0.37/0.69 @ ( collect_list_complex
% 0.37/0.69 @ ^ [Ys3: list_complex] :
% 0.37/0.69 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Ys3 ) @ X )
% 0.37/0.69 & ( distinct_complex @ Ys3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % distinct_finite_subset
% 0.37/0.69 thf(fact_6923_distinct__finite__subset,axiom,
% 0.37/0.69 ! [X: set_Code_integer] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ X )
% 0.37/0.69 => ( finite1283093830868386564nteger
% 0.37/0.69 @ ( collec3483841146883906114nteger
% 0.37/0.69 @ ^ [Ys3: list_Code_integer] :
% 0.37/0.69 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Ys3 ) @ X )
% 0.37/0.69 & ( distin1543349897113766820nteger @ Ys3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % distinct_finite_subset
% 0.37/0.69 thf(fact_6924_distinct__finite__subset,axiom,
% 0.37/0.69 ! [X: set_int] :
% 0.37/0.69 ( ( finite_finite_int @ X )
% 0.37/0.69 => ( finite3922522038869484883st_int
% 0.37/0.69 @ ( collect_list_int
% 0.37/0.69 @ ^ [Ys3: list_int] :
% 0.37/0.69 ( ( ord_less_eq_set_int @ ( set_int2 @ Ys3 ) @ X )
% 0.37/0.69 & ( distinct_int @ Ys3 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % distinct_finite_subset
% 0.37/0.69 thf(fact_6925_finite__nat__bounded,axiom,
% 0.37/0.69 ! [S3: set_nat] :
% 0.37/0.69 ( ( finite_finite_nat @ S3 )
% 0.37/0.69 => ? [K2: nat] : ( ord_less_eq_set_nat @ S3 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_nat_bounded
% 0.37/0.69 thf(fact_6926_finite__nat__iff__bounded,axiom,
% 0.37/0.69 ( finite_finite_nat
% 0.37/0.69 = ( ^ [S6: set_nat] :
% 0.37/0.69 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_nat_iff_bounded
% 0.37/0.69 thf(fact_6927_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C2: vEBT_VEBT > real] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.69 => ( ( groups2240296850493347238T_real
% 0.37/0.69 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.69 => ( ( groups2240296850493347238T_real
% 0.37/0.69 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups2240296850493347238T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6928_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_real,A: real,B: real > real,C2: real > real] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( ( member_real @ A @ S3 )
% 0.37/0.69 => ( ( groups8097168146408367636l_real
% 0.37/0.69 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_real @ A @ S3 )
% 0.37/0.69 => ( ( groups8097168146408367636l_real
% 0.37/0.69 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups8097168146408367636l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6929_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_complex,A: complex,B: complex > real,C2: complex > real] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( ( member_complex @ A @ S3 )
% 0.37/0.69 => ( ( groups5808333547571424918x_real
% 0.37/0.69 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_complex @ A @ S3 )
% 0.37/0.69 => ( ( groups5808333547571424918x_real
% 0.37/0.69 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups5808333547571424918x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6930_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,A: code_integer,B: code_integer > real,C2: code_integer > real] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( ( member_Code_integer @ A @ S3 )
% 0.37/0.69 => ( ( groups1270011288395367621r_real
% 0.37/0.69 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_real @ ( B @ A ) @ ( groups1270011288395367621r_real @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_Code_integer @ A @ S3 )
% 0.37/0.69 => ( ( groups1270011288395367621r_real
% 0.37/0.69 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups1270011288395367621r_real @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6931_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C2: vEBT_VEBT > rat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.69 => ( ( groups136491112297645522BT_rat
% 0.37/0.69 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.69 => ( ( groups136491112297645522BT_rat
% 0.37/0.69 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups136491112297645522BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6932_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_real,A: real,B: real > rat,C2: real > rat] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( ( member_real @ A @ S3 )
% 0.37/0.69 => ( ( groups1300246762558778688al_rat
% 0.37/0.69 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_real @ A @ S3 )
% 0.37/0.69 => ( ( groups1300246762558778688al_rat
% 0.37/0.69 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups1300246762558778688al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6933_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_complex,A: complex,B: complex > rat,C2: complex > rat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ S3 )
% 0.37/0.69 => ( ( ( member_complex @ A @ S3 )
% 0.37/0.69 => ( ( groups5058264527183730370ex_rat
% 0.37/0.69 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_complex @ A @ S3 )
% 0.37/0.69 => ( ( groups5058264527183730370ex_rat
% 0.37/0.69 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups5058264527183730370ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6934_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_Code_integer,A: code_integer,B: code_integer > rat,C2: code_integer > rat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ S3 )
% 0.37/0.69 => ( ( ( member_Code_integer @ A @ S3 )
% 0.37/0.69 => ( ( groups6602215022474089585er_rat
% 0.37/0.69 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_rat @ ( B @ A ) @ ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_Code_integer @ A @ S3 )
% 0.37/0.69 => ( ( groups6602215022474089585er_rat
% 0.37/0.69 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6935_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C2: vEBT_VEBT > nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ S3 )
% 0.37/0.69 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.69 => ( ( groups771621172384141258BT_nat
% 0.37/0.69 @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 0.37/0.69 => ( ( groups771621172384141258BT_nat
% 0.37/0.69 @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups771621172384141258BT_nat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6936_sum_Odelta__remove,axiom,
% 0.37/0.69 ! [S3: set_real,A: real,B: real > nat,C2: real > nat] :
% 0.37/0.69 ( ( finite_finite_real @ S3 )
% 0.37/0.69 => ( ( ( member_real @ A @ S3 )
% 0.37/0.69 => ( ( groups1935376822645274424al_nat
% 0.37/0.69 @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( plus_plus_nat @ ( B @ A ) @ ( groups1935376822645274424al_nat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.37/0.69 & ( ~ ( member_real @ A @ S3 )
% 0.37/0.69 => ( ( groups1935376822645274424al_nat
% 0.37/0.69 @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.37/0.69 @ S3 )
% 0.37/0.69 = ( groups1935376822645274424al_nat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum.delta_remove
% 0.37/0.69 thf(fact_6937_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_literal,N: nat] :
% 0.37/0.69 ( ( finite5847741373460823677iteral @ A4 )
% 0.37/0.69 => ( ( finite7554361855635516162iteral
% 0.37/0.69 @ ( collect_list_literal
% 0.37/0.69 @ ^ [Xs2: list_literal] :
% 0.37/0.69 ( ( ord_le7307670543136651348iteral @ ( set_literal2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s2501651207091587910iteral @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_literal @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6938_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_list_nat,N: nat] :
% 0.37/0.69 ( ( finite8100373058378681591st_nat @ A4 )
% 0.37/0.69 => ( ( finite7325466520557071688st_nat
% 0.37/0.69 @ ( collec5989764272469232197st_nat
% 0.37/0.69 @ ^ [Xs2: list_list_nat] :
% 0.37/0.69 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s3023201423986296836st_nat @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_list_nat @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6939_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_set_nat,N: nat] :
% 0.37/0.69 ( ( finite1152437895449049373et_nat @ A4 )
% 0.37/0.69 => ( ( finite5631907774883551598et_nat
% 0.37/0.69 @ ( collect_list_set_nat
% 0.37/0.69 @ ^ [Xs2: list_set_nat] :
% 0.37/0.69 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s3254054031482475050et_nat @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_set_nat @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6940_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_complex,N: nat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.69 => ( ( finite5120063068150530198omplex
% 0.37/0.69 @ ( collect_list_complex
% 0.37/0.69 @ ^ [Xs2: list_complex] :
% 0.37/0.69 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_complex @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6941_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_Code_integer,N: nat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.69 => ( ( finite5823187341872139973nteger
% 0.37/0.69 @ ( collec3483841146883906114nteger
% 0.37/0.69 @ ^ [Xs2: list_Code_integer] :
% 0.37/0.69 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite4902975817058060853nteger @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6942_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.69 => ( ( finite5915292604075114978T_VEBT
% 0.37/0.69 @ ( collec5608196760682091941T_VEBT
% 0.37/0.69 @ ^ [Xs2: list_VEBT_VEBT] :
% 0.37/0.69 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6943_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_real,N: nat] :
% 0.37/0.69 ( ( finite_finite_real @ A4 )
% 0.37/0.69 => ( ( finite4141703471298347796t_real
% 0.37/0.69 @ ( collect_list_real
% 0.37/0.69 @ ^ [Xs2: list_real] :
% 0.37/0.69 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_real @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_real @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6944_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_o,N: nat] :
% 0.37/0.69 ( ( finite_finite_o @ A4 )
% 0.37/0.69 => ( ( finite_card_list_o
% 0.37/0.69 @ ( collect_list_o
% 0.37/0.69 @ ^ [Xs2: list_o] :
% 0.37/0.69 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_o @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_o @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6945_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_nat,N: nat] :
% 0.37/0.69 ( ( finite_finite_nat @ A4 )
% 0.37/0.69 => ( ( finite_card_list_nat
% 0.37/0.69 @ ( collect_list_nat
% 0.37/0.69 @ ^ [Xs2: list_nat] :
% 0.37/0.69 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_nat @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_nat @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6946_card__lists__length__eq,axiom,
% 0.37/0.69 ! [A4: set_int,N: nat] :
% 0.37/0.69 ( ( finite_finite_int @ A4 )
% 0.37/0.69 => ( ( finite_card_list_int
% 0.37/0.69 @ ( collect_list_int
% 0.37/0.69 @ ^ [Xs2: list_int] :
% 0.37/0.69 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ( size_size_list_int @ Xs2 )
% 0.37/0.69 = N ) ) ) )
% 0.37/0.69 = ( power_power_nat @ ( finite_card_int @ A4 ) @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % card_lists_length_eq
% 0.37/0.69 thf(fact_6947_finite__lists__length__le,axiom,
% 0.37/0.69 ! [A4: set_complex,N: nat] :
% 0.37/0.69 ( ( finite3207457112153483333omplex @ A4 )
% 0.37/0.69 => ( finite8712137658972009173omplex
% 0.37/0.69 @ ( collect_list_complex
% 0.37/0.69 @ ^ [Xs2: list_complex] :
% 0.37/0.69 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_le
% 0.37/0.69 thf(fact_6948_finite__lists__length__le,axiom,
% 0.37/0.69 ! [A4: set_Code_integer,N: nat] :
% 0.37/0.69 ( ( finite6017078050557962740nteger @ A4 )
% 0.37/0.69 => ( finite1283093830868386564nteger
% 0.37/0.69 @ ( collec3483841146883906114nteger
% 0.37/0.69 @ ^ [Xs2: list_Code_integer] :
% 0.37/0.69 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ord_less_eq_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_le
% 0.37/0.69 thf(fact_6949_finite__lists__length__le,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.37/0.69 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.37/0.69 => ( finite3004134309566078307T_VEBT
% 0.37/0.69 @ ( collec5608196760682091941T_VEBT
% 0.37/0.69 @ ^ [Xs2: list_VEBT_VEBT] :
% 0.37/0.69 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_le
% 0.37/0.69 thf(fact_6950_finite__lists__length__le,axiom,
% 0.37/0.69 ! [A4: set_real,N: nat] :
% 0.37/0.69 ( ( finite_finite_real @ A4 )
% 0.37/0.69 => ( finite306553202115118035t_real
% 0.37/0.69 @ ( collect_list_real
% 0.37/0.69 @ ^ [Xs2: list_real] :
% 0.37/0.69 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ord_less_eq_nat @ ( size_size_list_real @ Xs2 ) @ N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_le
% 0.37/0.69 thf(fact_6951_finite__lists__length__le,axiom,
% 0.37/0.69 ! [A4: set_o,N: nat] :
% 0.37/0.69 ( ( finite_finite_o @ A4 )
% 0.37/0.69 => ( finite_finite_list_o
% 0.37/0.69 @ ( collect_list_o
% 0.37/0.69 @ ^ [Xs2: list_o] :
% 0.37/0.69 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_le
% 0.37/0.69 thf(fact_6952_finite__lists__length__le,axiom,
% 0.37/0.69 ! [A4: set_nat,N: nat] :
% 0.37/0.69 ( ( finite_finite_nat @ A4 )
% 0.37/0.69 => ( finite8100373058378681591st_nat
% 0.37/0.69 @ ( collect_list_nat
% 0.37/0.69 @ ^ [Xs2: list_nat] :
% 0.37/0.69 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_le
% 0.37/0.69 thf(fact_6953_finite__lists__length__le,axiom,
% 0.37/0.69 ! [A4: set_int,N: nat] :
% 0.37/0.69 ( ( finite_finite_int @ A4 )
% 0.37/0.69 => ( finite3922522038869484883st_int
% 0.37/0.69 @ ( collect_list_int
% 0.37/0.69 @ ^ [Xs2: list_int] :
% 0.37/0.69 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 )
% 0.37/0.69 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % finite_lists_length_le
% 0.37/0.69 thf(fact_6954_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_uint32,Ys: list_uint32,Y: uint32] :
% 0.37/0.69 ( ( ( size_s4844771616002835472uint32 @ Xs )
% 0.37/0.69 = ( size_s4844771616002835472uint32 @ Ys ) )
% 0.37/0.69 => ( ( member_uint32 @ Y @ ( set_uint322 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: uint32] :
% 0.37/0.69 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6955_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_int,Y: int] :
% 0.37/0.69 ( ( ( size_size_list_int @ Xs )
% 0.37/0.69 = ( size_size_list_int @ Ys ) )
% 0.37/0.69 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: int] :
% 0.37/0.69 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6956_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_int,Y: int] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_size_list_int @ Ys ) )
% 0.37/0.69 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.69 ~ ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ X3 @ Y ) @ ( set_Pr2853735649769556538BT_int @ ( zip_VEBT_VEBT_int @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6957_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.69 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.69 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X3 @ Y ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6958_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_real,Y: real] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_size_list_real @ Ys ) )
% 0.37/0.69 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.69 ~ ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X3 @ Y ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6959_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_o,Y: $o] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_size_list_o @ Ys ) )
% 0.37/0.69 => ( ( member_o @ Y @ ( set_o2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.69 ~ ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X3 @ Y ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6960_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_nat,Y: nat] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_size_list_nat @ Ys ) )
% 0.37/0.69 => ( ( member_nat @ Y @ ( set_nat2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: vEBT_VEBT] :
% 0.37/0.69 ~ ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X3 @ Y ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6961_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_real,Ys: list_int,Y: int] :
% 0.37/0.69 ( ( ( size_size_list_real @ Xs )
% 0.37/0.69 = ( size_size_list_int @ Ys ) )
% 0.37/0.69 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: real] :
% 0.37/0.69 ~ ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X3 @ Y ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6962_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_real,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.69 ( ( ( size_size_list_real @ Xs )
% 0.37/0.69 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.69 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: real] :
% 0.37/0.69 ~ ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X3 @ Y ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6963_in__set__impl__in__set__zip2,axiom,
% 0.37/0.69 ! [Xs: list_real,Ys: list_real,Y: real] :
% 0.37/0.69 ( ( ( size_size_list_real @ Xs )
% 0.37/0.69 = ( size_size_list_real @ Ys ) )
% 0.37/0.69 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 0.37/0.69 => ~ ! [X3: real] :
% 0.37/0.69 ~ ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X3 @ Y ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip2
% 0.37/0.69 thf(fact_6964_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_uint32,Ys: list_uint32,X: uint32] :
% 0.37/0.69 ( ( ( size_s4844771616002835472uint32 @ Xs )
% 0.37/0.69 = ( size_s4844771616002835472uint32 @ Ys ) )
% 0.37/0.69 => ( ( member_uint32 @ X @ ( set_uint322 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: uint32] :
% 0.37/0.69 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y3 ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6965_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_int,X: int] :
% 0.37/0.69 ( ( ( size_size_list_int @ Xs )
% 0.37/0.69 = ( size_size_list_int @ Ys ) )
% 0.37/0.69 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: int] :
% 0.37/0.69 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y3 ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6966_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_VEBT_VEBT,X: int] :
% 0.37/0.69 ( ( ( size_size_list_int @ Xs )
% 0.37/0.69 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.69 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: vEBT_VEBT] :
% 0.37/0.69 ~ ( member2056185340421749780T_VEBT @ ( produc3329399203697025711T_VEBT @ X @ Y3 ) @ ( set_Pr8714266321650254504T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6967_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_real,X: int] :
% 0.37/0.69 ( ( ( size_size_list_int @ Xs )
% 0.37/0.69 = ( size_size_list_real @ Ys ) )
% 0.37/0.69 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: real] :
% 0.37/0.69 ~ ( member2744130022092475746t_real @ ( produc801115645435158769t_real @ X @ Y3 ) @ ( set_Pr112895574167722958t_real @ ( zip_int_real @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6968_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_o,X: int] :
% 0.37/0.69 ( ( ( size_size_list_int @ Xs )
% 0.37/0.69 = ( size_size_list_o @ Ys ) )
% 0.37/0.69 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: $o] :
% 0.37/0.69 ~ ( member4489920277610959864_int_o @ ( product_Pair_int_o @ X @ Y3 ) @ ( set_Pr8694291782656941196_int_o @ ( zip_int_o @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6969_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_nat,X: int] :
% 0.37/0.69 ( ( ( size_size_list_int @ Xs )
% 0.37/0.69 = ( size_size_list_nat @ Ys ) )
% 0.37/0.69 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: nat] :
% 0.37/0.69 ~ ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X @ Y3 ) @ ( set_Pr6647972299459129970nt_nat @ ( zip_int_nat @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6970_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.37/0.69 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: vEBT_VEBT] :
% 0.37/0.69 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y3 ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6971_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_real,X: vEBT_VEBT] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_size_list_real @ Ys ) )
% 0.37/0.69 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: real] :
% 0.37/0.69 ~ ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X @ Y3 ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6972_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_o,X: vEBT_VEBT] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_size_list_o @ Ys ) )
% 0.37/0.69 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: $o] :
% 0.37/0.69 ~ ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X @ Y3 ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6973_in__set__impl__in__set__zip1,axiom,
% 0.37/0.69 ! [Xs: list_VEBT_VEBT,Ys: list_nat,X: vEBT_VEBT] :
% 0.37/0.69 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.37/0.69 = ( size_size_list_nat @ Ys ) )
% 0.37/0.69 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 0.37/0.69 => ~ ! [Y3: nat] :
% 0.37/0.69 ~ ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X @ Y3 ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % in_set_impl_in_set_zip1
% 0.37/0.69 thf(fact_6974_ex__less__of__nat__mult,axiom,
% 0.37/0.69 ! [X: rat,Y: rat] :
% 0.37/0.69 ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.37/0.69 => ? [N2: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % ex_less_of_nat_mult
% 0.37/0.69 thf(fact_6975_ex__less__of__nat__mult,axiom,
% 0.37/0.69 ! [X: real,Y: real] :
% 0.37/0.69 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.69 => ? [N2: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % ex_less_of_nat_mult
% 0.37/0.69 thf(fact_6976_of__nat__gt__0,axiom,
% 0.37/0.69 ! [K: nat] :
% 0.37/0.69 ( ( ( semiri2565882477558803405uint32 @ K )
% 0.37/0.69 != zero_zero_uint32 )
% 0.37/0.69 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_gt_0
% 0.37/0.69 thf(fact_6977_of__nat__gt__0,axiom,
% 0.37/0.69 ! [K: nat] :
% 0.37/0.69 ( ( ( semiri681578069525770553at_rat @ K )
% 0.37/0.69 != zero_zero_rat )
% 0.37/0.69 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_gt_0
% 0.37/0.69 thf(fact_6978_of__nat__gt__0,axiom,
% 0.37/0.69 ! [K: nat] :
% 0.37/0.69 ( ( ( semiri1316708129612266289at_nat @ K )
% 0.37/0.69 != zero_zero_nat )
% 0.37/0.69 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_gt_0
% 0.37/0.69 thf(fact_6979_of__nat__gt__0,axiom,
% 0.37/0.69 ! [K: nat] :
% 0.37/0.69 ( ( ( semiri5074537144036343181t_real @ K )
% 0.37/0.69 != zero_zero_real )
% 0.37/0.69 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_gt_0
% 0.37/0.69 thf(fact_6980_of__nat__gt__0,axiom,
% 0.37/0.69 ! [K: nat] :
% 0.37/0.69 ( ( ( semiri1314217659103216013at_int @ K )
% 0.37/0.69 != zero_zero_int )
% 0.37/0.69 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_gt_0
% 0.37/0.69 thf(fact_6981_of__nat__gt__0,axiom,
% 0.37/0.69 ! [K: nat] :
% 0.37/0.69 ( ( ( semiri4939895301339042750nteger @ K )
% 0.37/0.69 != zero_z3403309356797280102nteger )
% 0.37/0.69 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_gt_0
% 0.37/0.69 thf(fact_6982_of__nat__diff,axiom,
% 0.37/0.69 ! [N: nat,M: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.69 => ( ( semiri2565882477558803405uint32 @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.69 = ( minus_minus_uint32 @ ( semiri2565882477558803405uint32 @ M ) @ ( semiri2565882477558803405uint32 @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_diff
% 0.37/0.69 thf(fact_6983_of__nat__diff,axiom,
% 0.37/0.69 ! [N: nat,M: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.69 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.69 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_diff
% 0.37/0.69 thf(fact_6984_of__nat__diff,axiom,
% 0.37/0.69 ! [N: nat,M: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.69 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.69 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_diff
% 0.37/0.69 thf(fact_6985_of__nat__diff,axiom,
% 0.37/0.69 ! [N: nat,M: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.69 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.69 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_diff
% 0.37/0.69 thf(fact_6986_of__nat__diff,axiom,
% 0.37/0.69 ! [N: nat,M: nat] :
% 0.37/0.69 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.69 => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.69 = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % of_nat_diff
% 0.37/0.69 thf(fact_6987_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_nat,Xy: product_prod_int_nat,Xys: list_P8198026277950538467nt_nat] :
% 0.37/0.69 ( ( ( zip_int_nat @ Xs @ Ys )
% 0.37/0.69 = ( cons_P7512249878480867347nt_nat @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: int,Xs5: list_int] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_int @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: nat,Ys4: list_nat] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_nat @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_int_nat @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_int_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6988_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_o,Xy: product_prod_int_o,Xys: list_P5087981734274514673_int_o] :
% 0.37/0.69 ( ( ( zip_int_o @ Xs @ Ys )
% 0.37/0.69 = ( cons_P7321330006258091179_int_o @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: int,Xs5: list_int] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_int @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: $o,Ys4: list_o] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_o @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_int_o @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_int_o @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6989_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_nat,Ys: list_int,Xy: product_prod_nat_int,Xys: list_P3521021558325789923at_int] :
% 0.37/0.69 ( ( ( zip_nat_int @ Xs @ Ys )
% 0.37/0.69 = ( cons_P2335045147070616083at_int @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: nat,Xs5: list_nat] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_nat @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: int,Ys4: list_int] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_int @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_nat_int @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_nat_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6990_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_nat,Ys: list_o,Xy: product_prod_nat_o,Xys: list_P7333126701944960589_nat_o] :
% 0.37/0.69 ( ( ( zip_nat_o @ Xs @ Ys )
% 0.37/0.69 = ( cons_P9142372351690779143_nat_o @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: nat,Xs5: list_nat] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_nat @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: $o,Ys4: list_o] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_o @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_nat_o @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_nat_o @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6991_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_o,Ys: list_int,Xy: product_prod_o_int,Xys: list_P3795440434834930179_o_int] :
% 0.37/0.69 ( ( ( zip_o_int @ Xs @ Ys )
% 0.37/0.69 = ( cons_P1455986808126089405_o_int @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: $o,Xs5: list_o] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_o @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: int,Ys4: list_int] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_int @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_o_int @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_o_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6992_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_o,Ys: list_nat,Xy: product_prod_o_nat,Xys: list_P6285523579766656935_o_nat] :
% 0.37/0.69 ( ( ( zip_o_nat @ Xs @ Ys )
% 0.37/0.69 = ( cons_P5633837827635286113_o_nat @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: $o,Xs5: list_o] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_o @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: nat,Ys4: list_nat] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_nat @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_o_nat @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_o_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6993_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_o,Ys: list_o,Xy: product_prod_o_o,Xys: list_P4002435161011370285od_o_o] :
% 0.37/0.69 ( ( ( zip_o_o @ Xs @ Ys )
% 0.37/0.69 = ( cons_P8766293264717362397od_o_o @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: $o,Xs5: list_o] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_o @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: $o,Ys4: list_o] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_o @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_o_o @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_o_o @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6994_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_uint32,Ys: list_uint32,Xy: produc827990862158126777uint32,Xys: list_P3069071885182933823uint32] :
% 0.37/0.69 ( ( ( zip_uint32_uint32 @ Xs @ Ys )
% 0.37/0.69 = ( cons_P3149448846263281007uint32 @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: uint32,Xs5: list_uint32] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_uint32 @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: uint32,Ys4: list_uint32] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_uint32 @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( produc1400373151660368625uint32 @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_uint32_uint32 @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6995_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_nat,Ys: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 0.37/0.69 ( ( ( zip_nat_nat @ Xs @ Ys )
% 0.37/0.69 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: nat,Xs5: list_nat] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_nat @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: nat,Ys4: list_nat] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_nat @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_nat_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6996_zip__eq__ConsE,axiom,
% 0.37/0.69 ! [Xs: list_int,Ys: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 0.37/0.69 ( ( ( zip_int_int @ Xs @ Ys )
% 0.37/0.69 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 0.37/0.69 => ~ ! [X3: int,Xs5: list_int] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_int @ X3 @ Xs5 ) )
% 0.37/0.69 => ! [Y3: int,Ys4: list_int] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_int @ Y3 @ Ys4 ) )
% 0.37/0.69 => ( ( Xy
% 0.37/0.69 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 0.37/0.69 => ( Xys
% 0.37/0.69 != ( zip_int_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zip_eq_ConsE
% 0.37/0.69 thf(fact_6997_lenlex__irreflexive,axiom,
% 0.37/0.69 ! [R: set_Pr1773385645901665561uint32,Xs: list_uint32] :
% 0.37/0.69 ( ! [X3: uint32] :
% 0.37/0.69 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ X3 ) @ R )
% 0.37/0.69 => ~ ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Xs ) @ ( lenlex_uint32 @ R ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lenlex_irreflexive
% 0.37/0.69 thf(fact_6998_lenlex__irreflexive,axiom,
% 0.37/0.69 ! [R: set_Pr1261947904930325089at_nat,Xs: list_nat] :
% 0.37/0.69 ( ! [X3: nat] :
% 0.37/0.69 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R )
% 0.37/0.69 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Xs ) @ ( lenlex_nat @ R ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lenlex_irreflexive
% 0.37/0.69 thf(fact_6999_lenlex__irreflexive,axiom,
% 0.37/0.69 ! [R: set_Pr958786334691620121nt_int,Xs: list_int] :
% 0.37/0.69 ( ! [X3: int] :
% 0.37/0.69 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ R )
% 0.37/0.69 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Xs ) @ ( lenlex_int @ R ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lenlex_irreflexive
% 0.37/0.69 thf(fact_7000_reals__Archimedean3,axiom,
% 0.37/0.69 ! [X: real] :
% 0.37/0.69 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.69 => ! [Y5: real] :
% 0.37/0.69 ? [N2: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % reals_Archimedean3
% 0.37/0.69 thf(fact_7001_image__minus__const__atLeastLessThan__nat,axiom,
% 0.37/0.69 ! [C2: nat,Y: nat,X: nat] :
% 0.37/0.69 ( ( ( ord_less_nat @ C2 @ Y )
% 0.37/0.69 => ( ( image_nat_nat
% 0.37/0.69 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C2 )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.37/0.69 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C2 ) @ ( minus_minus_nat @ Y @ C2 ) ) ) )
% 0.37/0.69 & ( ~ ( ord_less_nat @ C2 @ Y )
% 0.37/0.69 => ( ( ( ord_less_nat @ X @ Y )
% 0.37/0.69 => ( ( image_nat_nat
% 0.37/0.69 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C2 )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.37/0.69 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.37/0.69 & ( ~ ( ord_less_nat @ X @ Y )
% 0.37/0.69 => ( ( image_nat_nat
% 0.37/0.69 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C2 )
% 0.37/0.69 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.37/0.69 = bot_bot_set_nat ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % image_minus_const_atLeastLessThan_nat
% 0.37/0.69 thf(fact_7002_listrel1I1,axiom,
% 0.37/0.69 ! [X: $o,Y: $o,R: set_Product_prod_o_o,Xs: list_o] :
% 0.37/0.69 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 0.37/0.69 => ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Xs ) ) @ ( listrel1_o @ R ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % listrel1I1
% 0.37/0.69 thf(fact_7003_listrel1I1,axiom,
% 0.37/0.69 ! [X: uint32,Y: uint32,R: set_Pr1773385645901665561uint32,Xs: list_uint32] :
% 0.37/0.69 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 0.37/0.69 => ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Xs ) ) @ ( listrel1_uint32 @ R ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % listrel1I1
% 0.37/0.69 thf(fact_7004_listrel1I1,axiom,
% 0.37/0.69 ! [X: nat,Y: nat,R: set_Pr1261947904930325089at_nat,Xs: list_nat] :
% 0.37/0.69 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.37/0.69 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Xs ) ) @ ( listrel1_nat @ R ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % listrel1I1
% 0.37/0.69 thf(fact_7005_listrel1I1,axiom,
% 0.37/0.69 ! [X: int,Y: int,R: set_Pr958786334691620121nt_int,Xs: list_int] :
% 0.37/0.69 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 0.37/0.69 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Xs ) ) @ ( listrel1_int @ R ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % listrel1I1
% 0.37/0.69 thf(fact_7006_Cons__listrel1E1,axiom,
% 0.37/0.69 ! [X: $o,Xs: list_o,Ys: list_o,R: set_Product_prod_o_o] :
% 0.37/0.69 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ Ys ) @ ( listrel1_o @ R ) )
% 0.37/0.69 => ( ! [Y3: $o] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_o @ Y3 @ Xs ) )
% 0.37/0.69 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y3 ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_o] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_o @ X @ Zs2 ) )
% 0.37/0.69 => ~ ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Zs2 ) @ ( listrel1_o @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E1
% 0.37/0.69 thf(fact_7007_Cons__listrel1E1,axiom,
% 0.37/0.69 ! [X: uint32,Xs: list_uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.69 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ Ys ) @ ( listrel1_uint32 @ R ) )
% 0.37/0.69 => ( ! [Y3: uint32] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_uint32 @ Y3 @ Xs ) )
% 0.37/0.69 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y3 ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_uint32] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_uint32 @ X @ Zs2 ) )
% 0.37/0.69 => ~ ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Zs2 ) @ ( listrel1_uint32 @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E1
% 0.37/0.69 thf(fact_7008_Cons__listrel1E1,axiom,
% 0.37/0.69 ! [X: nat,Xs: list_nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.69 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ Ys ) @ ( listrel1_nat @ R ) )
% 0.37/0.69 => ( ! [Y3: nat] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_nat @ Y3 @ Xs ) )
% 0.37/0.69 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_nat] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_nat @ X @ Zs2 ) )
% 0.37/0.69 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Zs2 ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E1
% 0.37/0.69 thf(fact_7009_Cons__listrel1E1,axiom,
% 0.37/0.69 ! [X: int,Xs: list_int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.69 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ Ys ) @ ( listrel1_int @ R ) )
% 0.37/0.69 => ( ! [Y3: int] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_int @ Y3 @ Xs ) )
% 0.37/0.69 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y3 ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_int] :
% 0.37/0.69 ( ( Ys
% 0.37/0.69 = ( cons_int @ X @ Zs2 ) )
% 0.37/0.69 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Zs2 ) @ ( listrel1_int @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E1
% 0.37/0.69 thf(fact_7010_Cons__listrel1E2,axiom,
% 0.37/0.69 ! [Xs: list_o,Y: $o,Ys: list_o,R: set_Product_prod_o_o] :
% 0.37/0.69 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ ( cons_o @ Y @ Ys ) ) @ ( listrel1_o @ R ) )
% 0.37/0.69 => ( ! [X3: $o] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_o @ X3 @ Ys ) )
% 0.37/0.69 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ Y ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_o] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_o @ Y @ Zs2 ) )
% 0.37/0.69 => ~ ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Zs2 @ Ys ) @ ( listrel1_o @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E2
% 0.37/0.69 thf(fact_7011_Cons__listrel1E2,axiom,
% 0.37/0.69 ! [Xs: list_uint32,Y: uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 0.37/0.69 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ ( cons_uint32 @ Y @ Ys ) ) @ ( listrel1_uint32 @ R ) )
% 0.37/0.69 => ( ! [X3: uint32] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_uint32 @ X3 @ Ys ) )
% 0.37/0.69 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_uint32] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_uint32 @ Y @ Zs2 ) )
% 0.37/0.69 => ~ ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Zs2 @ Ys ) @ ( listrel1_uint32 @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E2
% 0.37/0.69 thf(fact_7012_Cons__listrel1E2,axiom,
% 0.37/0.69 ! [Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.69 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 0.37/0.69 => ( ! [X3: nat] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_nat @ X3 @ Ys ) )
% 0.37/0.69 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_nat] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_nat @ Y @ Zs2 ) )
% 0.37/0.69 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Zs2 @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E2
% 0.37/0.69 thf(fact_7013_Cons__listrel1E2,axiom,
% 0.37/0.69 ! [Xs: list_int,Y: int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 0.37/0.69 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ ( cons_int @ Y @ Ys ) ) @ ( listrel1_int @ R ) )
% 0.37/0.69 => ( ! [X3: int] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_int @ X3 @ Ys ) )
% 0.37/0.69 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ R ) )
% 0.37/0.69 => ~ ! [Zs2: list_int] :
% 0.37/0.69 ( ( Xs
% 0.37/0.69 = ( cons_int @ Y @ Zs2 ) )
% 0.37/0.69 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Zs2 @ Ys ) @ ( listrel1_int @ R ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % Cons_listrel1E2
% 0.37/0.69 thf(fact_7014_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,K4: real,F: vEBT_VEBT > real] :
% 0.37/0.69 ( ! [I2: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) @ ( groups2240296850493347238T_real @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7015_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_real,K4: real,F: real > real] :
% 0.37/0.69 ( ! [I2: real] :
% 0.37/0.69 ( ( member_real @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K4 ) @ ( groups8097168146408367636l_real @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7016_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_int,K4: real,F: int > real] :
% 0.37/0.69 ( ! [I2: int] :
% 0.37/0.69 ( ( member_int @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K4 ) @ ( groups8778361861064173332t_real @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7017_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_complex,K4: real,F: complex > real] :
% 0.37/0.69 ( ! [I2: complex] :
% 0.37/0.69 ( ( member_complex @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K4 ) @ ( groups5808333547571424918x_real @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7018_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_literal,K4: real,F: literal > real] :
% 0.37/0.69 ( ! [I2: literal] :
% 0.37/0.69 ( ( member_literal @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_literal @ A4 ) ) @ K4 ) @ ( groups2795228986978005958l_real @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7019_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,K4: code_integer,F: vEBT_VEBT > code_integer] :
% 0.37/0.69 ( ! [I2: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) @ ( groups5748017345553531991nteger @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7020_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_real,K4: code_integer,F: real > code_integer] :
% 0.37/0.69 ( ! [I2: real] :
% 0.37/0.69 ( ( member_real @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_real @ A4 ) ) @ K4 ) @ ( groups7713935264441627589nteger @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7021_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_int,K4: code_integer,F: int > code_integer] :
% 0.37/0.69 ( ! [I2: int] :
% 0.37/0.69 ( ( member_int @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A4 ) ) @ K4 ) @ ( groups7873554091576472773nteger @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7022_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_complex,K4: code_integer,F: complex > code_integer] :
% 0.37/0.69 ( ! [I2: complex] :
% 0.37/0.69 ( ( member_complex @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_complex @ A4 ) ) @ K4 ) @ ( groups6621422865394947399nteger @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7023_sum__bounded__below,axiom,
% 0.37/0.69 ! [A4: set_literal,K4: code_integer,F: literal > code_integer] :
% 0.37/0.69 ( ! [I2: literal] :
% 0.37/0.69 ( ( member_literal @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_literal @ A4 ) ) @ K4 ) @ ( groups8556826181031883383nteger @ F @ A4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_below
% 0.37/0.69 thf(fact_7024_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real,K4: real] :
% 0.37/0.69 ( ! [I2: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7025_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_real,F: real > real,K4: real] :
% 0.37/0.69 ( ! [I2: real] :
% 0.37/0.69 ( ( member_real @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7026_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_int,F: int > real,K4: real] :
% 0.37/0.69 ( ! [I2: int] :
% 0.37/0.69 ( ( member_int @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7027_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_complex,F: complex > real,K4: real] :
% 0.37/0.69 ( ! [I2: complex] :
% 0.37/0.69 ( ( member_complex @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7028_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_literal,F: literal > real,K4: real] :
% 0.37/0.69 ( ! [I2: literal] :
% 0.37/0.69 ( ( member_literal @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_less_eq_real @ ( groups2795228986978005958l_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7029_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( groups5748017345553531991nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7030_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_real,F: real > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: real] :
% 0.37/0.69 ( ( member_real @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( groups7713935264441627589nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7031_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_int,F: int > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: int] :
% 0.37/0.69 ( ( member_int @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7032_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_complex,F: complex > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: complex] :
% 0.37/0.69 ( ( member_complex @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( groups6621422865394947399nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7033_sum__bounded__above,axiom,
% 0.37/0.69 ! [A4: set_literal,F: literal > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: literal] :
% 0.37/0.69 ( ( member_literal @ I2 @ A4 )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ord_le3102999989581377725nteger @ ( groups8556826181031883383nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above
% 0.37/0.69 thf(fact_7034_nat__less__real__le,axiom,
% 0.37/0.69 ( ord_less_nat
% 0.37/0.69 = ( ^ [N6: nat,M5: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N6 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M5 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % nat_less_real_le
% 0.37/0.69 thf(fact_7035_nat__le__real__less,axiom,
% 0.37/0.69 ( ord_less_eq_nat
% 0.37/0.69 = ( ^ [N6: nat,M5: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N6 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M5 ) @ one_one_real ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % nat_le_real_less
% 0.37/0.69 thf(fact_7036_lessThan__Suc__eq__insert__0,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 0.37/0.69 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lessThan_Suc_eq_insert_0
% 0.37/0.69 thf(fact_7037_lenlex__length,axiom,
% 0.37/0.69 ! [Ms: list_VEBT_VEBT,Ns: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 0.37/0.69 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R ) )
% 0.37/0.69 => ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lenlex_length
% 0.37/0.69 thf(fact_7038_lenlex__length,axiom,
% 0.37/0.69 ! [Ms: list_real,Ns: list_real,R: set_Pr6218003697084177305l_real] :
% 0.37/0.69 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Ms @ Ns ) @ ( lenlex_real @ R ) )
% 0.37/0.69 => ( ord_less_eq_nat @ ( size_size_list_real @ Ms ) @ ( size_size_list_real @ Ns ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lenlex_length
% 0.37/0.69 thf(fact_7039_lenlex__length,axiom,
% 0.37/0.69 ! [Ms: list_o,Ns: list_o,R: set_Product_prod_o_o] :
% 0.37/0.69 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R ) )
% 0.37/0.69 => ( ord_less_eq_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lenlex_length
% 0.37/0.69 thf(fact_7040_lenlex__length,axiom,
% 0.37/0.69 ! [Ms: list_nat,Ns: list_nat,R: set_Pr1261947904930325089at_nat] :
% 0.37/0.69 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R ) )
% 0.37/0.69 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % lenlex_length
% 0.37/0.69 thf(fact_7041_real__archimedian__rdiv__eq__0,axiom,
% 0.37/0.69 ! [X: real,C2: real] :
% 0.37/0.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.69 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.37/0.69 => ( ! [M3: nat] :
% 0.37/0.69 ( ( ord_less_nat @ zero_zero_nat @ M3 )
% 0.37/0.69 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ X ) @ C2 ) )
% 0.37/0.69 => ( X = zero_zero_real ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % real_archimedian_rdiv_eq_0
% 0.37/0.69 thf(fact_7042_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > int,K4: int] :
% 0.37/0.69 ( ! [I2: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 0.37/0.69 => ( ord_less_int @ ( groups769130701875090982BT_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7043_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_real,F: real > int,K4: int] :
% 0.37/0.69 ( ! [I2: real] :
% 0.37/0.69 ( ( member_real @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 0.37/0.69 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7044_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_complex,F: complex > int,K4: int] :
% 0.37/0.69 ( ! [I2: complex] :
% 0.37/0.69 ( ( member_complex @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.37/0.69 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7045_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_literal,F: literal > int,K4: int] :
% 0.37/0.69 ( ! [I2: literal] :
% 0.37/0.69 ( ( member_literal @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 0.37/0.69 => ( ord_less_int @ ( groups8649609317433967686al_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7046_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_nat,F: nat > int,K4: int] :
% 0.37/0.69 ( ! [I2: nat] :
% 0.37/0.69 ( ( member_nat @ I2 @ A4 )
% 0.37/0.69 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 0.37/0.69 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7047_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: vEBT_VEBT] :
% 0.37/0.69 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( groups5748017345553531991nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7048_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_real,F: real > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: real] :
% 0.37/0.69 ( ( member_real @ I2 @ A4 )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( groups7713935264441627589nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7049_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_int,F: int > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: int] :
% 0.37/0.69 ( ( member_int @ I2 @ A4 )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( groups7873554091576472773nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7050_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_complex,F: complex > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: complex] :
% 0.37/0.69 ( ( member_complex @ I2 @ A4 )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( groups6621422865394947399nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7051_sum__bounded__above__strict,axiom,
% 0.37/0.69 ! [A4: set_literal,F: literal > code_integer,K4: code_integer] :
% 0.37/0.69 ( ! [I2: literal] :
% 0.37/0.69 ( ( member_literal @ I2 @ A4 )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 0.37/0.69 => ( ord_le6747313008572928689nteger @ ( groups8556826181031883383nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % sum_bounded_above_strict
% 0.37/0.69 thf(fact_7052_linear__plus__1__le__power,axiom,
% 0.37/0.69 ! [X: real,N: nat] :
% 0.37/0.69 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.69 => ( 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 ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % linear_plus_1_le_power
% 0.37/0.69 thf(fact_7053_cnt__cnt__eq,axiom,
% 0.37/0.69 ( vEBT_VEBT_cnt
% 0.37/0.69 = ( ^ [T2: vEBT_VEBT] : ( semiri5074537144036343181t_real @ ( vEBT_VEBT_cnt2 @ T2 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % cnt_cnt_eq
% 0.37/0.69 thf(fact_7054_minNulli__rule,axiom,
% 0.37/0.69 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 0.37/0.69 ( hoare_hoare_triple_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_minNulli @ Ti )
% 0.37/0.69 @ ^ [R5: $o] :
% 0.37/0.69 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.69 @ ( pure_assn
% 0.37/0.69 @ ( R5
% 0.37/0.69 = ( vEBT_VEBT_minNull @ T ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % minNulli_rule
% 0.37/0.69 thf(fact_7055_builupi_Hcorr,axiom,
% 0.37/0.69 ! [N: nat] : ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % builupi'corr
% 0.37/0.69 thf(fact_7056_builupicorr,axiom,
% 0.37/0.69 ! [N: nat] : ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % builupicorr
% 0.37/0.69 thf(fact_7057_vebt__maxtilist,axiom,
% 0.37/0.69 ! [I: nat,Ts2: list_VEBT_VEBT,Tsi: list_VEBT_VEBTi] :
% 0.37/0.69 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ts2 ) )
% 0.37/0.69 => ( hoare_7629718768684598413on_nat @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) @ ( vEBT_vebt_maxti @ ( nth_VEBT_VEBTi @ Tsi @ I ) )
% 0.37/0.69 @ ^ [R5: option_nat] :
% 0.37/0.69 ( times_times_assn
% 0.37/0.69 @ ( pure_assn
% 0.37/0.69 @ ( R5
% 0.37/0.69 = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Ts2 @ I ) ) ) )
% 0.37/0.69 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % vebt_maxtilist
% 0.37/0.69 thf(fact_7058_vebt__mintilist,axiom,
% 0.37/0.69 ! [I: nat,Ts2: list_VEBT_VEBT,Tsi: list_VEBT_VEBTi] :
% 0.37/0.69 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ts2 ) )
% 0.37/0.69 => ( hoare_7629718768684598413on_nat @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) @ ( vEBT_vebt_minti @ ( nth_VEBT_VEBTi @ Tsi @ I ) )
% 0.37/0.69 @ ^ [R5: option_nat] :
% 0.37/0.69 ( times_times_assn
% 0.37/0.69 @ ( pure_assn
% 0.37/0.69 @ ( R5
% 0.37/0.69 = ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ Ts2 @ I ) ) ) )
% 0.37/0.69 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % vebt_mintilist
% 0.37/0.69 thf(fact_7059_negative__zless,axiom,
% 0.37/0.69 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.37/0.69
% 0.37/0.69 % negative_zless
% 0.37/0.69 thf(fact_7060_negative__eq__positive,axiom,
% 0.37/0.69 ! [N: nat,M: nat] :
% 0.37/0.69 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.69 = ( semiri1314217659103216013at_int @ M ) )
% 0.37/0.69 = ( ( N = zero_zero_nat )
% 0.37/0.69 & ( M = zero_zero_nat ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % negative_eq_positive
% 0.37/0.69 thf(fact_7061_vebt__minti__h,axiom,
% 0.37/0.69 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 0.37/0.69 ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 0.37/0.69 @ ^ [R5: option_nat] :
% 0.37/0.69 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.69 @ ( pure_assn
% 0.37/0.69 @ ( R5
% 0.37/0.69 = ( vEBT_vebt_mint @ T ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % vebt_minti_h
% 0.37/0.69 thf(fact_7062_vebt__maxti__h,axiom,
% 0.37/0.69 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 0.37/0.69 ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 0.37/0.69 @ ^ [R5: option_nat] :
% 0.37/0.69 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.69 @ ( pure_assn
% 0.37/0.69 @ ( R5
% 0.37/0.69 = ( vEBT_vebt_maxt @ T ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % vebt_maxti_h
% 0.37/0.69 thf(fact_7063_zless__iff__Suc__zadd,axiom,
% 0.37/0.69 ( ord_less_int
% 0.37/0.69 = ( ^ [W3: int,Z2: int] :
% 0.37/0.69 ? [N6: nat] :
% 0.37/0.69 ( Z2
% 0.37/0.69 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N6 ) ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zless_iff_Suc_zadd
% 0.37/0.69 thf(fact_7064_int__Suc,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.37/0.69 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 0.37/0.69
% 0.37/0.69 % int_Suc
% 0.37/0.69 thf(fact_7065_int__ops_I4_J,axiom,
% 0.37/0.69 ! [A: nat] :
% 0.37/0.69 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.37/0.69 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.37/0.69
% 0.37/0.69 % int_ops(4)
% 0.37/0.69 thf(fact_7066_negative__zless__0,axiom,
% 0.37/0.69 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 0.37/0.69
% 0.37/0.69 % negative_zless_0
% 0.37/0.69 thf(fact_7067_negD,axiom,
% 0.37/0.69 ! [X: int] :
% 0.37/0.69 ( ( ord_less_int @ X @ zero_zero_int )
% 0.37/0.69 => ? [N2: nat] :
% 0.37/0.69 ( X
% 0.37/0.69 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % negD
% 0.37/0.69 thf(fact_7068_not__zle__0__negative,axiom,
% 0.37/0.69 ! [N: nat] :
% 0.37/0.69 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % not_zle_0_negative
% 0.37/0.69 thf(fact_7069_int__cases,axiom,
% 0.37/0.69 ! [Z: int] :
% 0.37/0.69 ( ! [N2: nat] :
% 0.37/0.69 ( Z
% 0.37/0.69 != ( semiri1314217659103216013at_int @ N2 ) )
% 0.37/0.69 => ~ ! [N2: nat] :
% 0.37/0.69 ( Z
% 0.37/0.69 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % int_cases
% 0.37/0.69 thf(fact_7070_int__of__nat__induct,axiom,
% 0.37/0.69 ! [P2: int > $o,Z: int] :
% 0.37/0.69 ( ! [N2: nat] : ( P2 @ ( semiri1314217659103216013at_int @ N2 ) )
% 0.37/0.69 => ( ! [N2: nat] : ( P2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 0.37/0.69 => ( P2 @ Z ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % int_of_nat_induct
% 0.37/0.69 thf(fact_7071_int__ops_I1_J,axiom,
% 0.37/0.69 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.37/0.69 = zero_zero_int ) ).
% 0.37/0.69
% 0.37/0.69 % int_ops(1)
% 0.37/0.69 thf(fact_7072_int__zle__neg,axiom,
% 0.37/0.69 ! [N: nat,M: nat] :
% 0.37/0.69 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.37/0.69 = ( ( N = zero_zero_nat )
% 0.37/0.69 & ( M = zero_zero_nat ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % int_zle_neg
% 0.37/0.69 thf(fact_7073_nat__int__comparison_I2_J,axiom,
% 0.37/0.69 ( ord_less_nat
% 0.37/0.69 = ( ^ [A7: nat,B7: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % nat_int_comparison(2)
% 0.37/0.69 thf(fact_7074_zle__int,axiom,
% 0.37/0.69 ! [M: nat,N: nat] :
% 0.37/0.69 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.69 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.69
% 0.37/0.69 % zle_int
% 0.37/0.69 thf(fact_7075_nat__int__comparison_I3_J,axiom,
% 0.37/0.69 ( ord_less_eq_nat
% 0.37/0.69 = ( ^ [A7: nat,B7: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % nat_int_comparison(3)
% 0.37/0.69 thf(fact_7076_int__ops_I6_J,axiom,
% 0.37/0.69 ! [A: nat,B: nat] :
% 0.37/0.69 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.37/0.69 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.37/0.69 = zero_zero_int ) )
% 0.37/0.69 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 0.37/0.69 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 0.37/0.69 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % int_ops(6)
% 0.37/0.69 thf(fact_7077_nat__less__as__int,axiom,
% 0.37/0.69 ( ord_less_nat
% 0.37/0.69 = ( ^ [A7: nat,B7: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % nat_less_as_int
% 0.37/0.69 thf(fact_7078_nat__leq__as__int,axiom,
% 0.37/0.69 ( ord_less_eq_nat
% 0.37/0.69 = ( ^ [A7: nat,B7: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % nat_leq_as_int
% 0.37/0.69 thf(fact_7079_zmult__zless__mono2__lemma,axiom,
% 0.37/0.69 ! [I: int,J: int,K: nat] :
% 0.37/0.69 ( ( ord_less_int @ I @ J )
% 0.37/0.69 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.69 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zmult_zless_mono2_lemma
% 0.37/0.69 thf(fact_7080_zero__less__imp__eq__int,axiom,
% 0.37/0.69 ! [K: int] :
% 0.37/0.69 ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.69 => ? [N2: nat] :
% 0.37/0.69 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.37/0.69 & ( K
% 0.37/0.69 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.37/0.69
% 0.37/0.69 % zero_less_imp_eq_int
% 0.37/0.69 thf(fact_7081_pos__int__cases,axiom,
% 0.37/0.69 ! [K: int] :
% 0.37/0.69 ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ~ ! [N2: nat] :
% 0.37/0.70 ( ( K
% 0.37/0.70 = ( semiri1314217659103216013at_int @ N2 ) )
% 0.37/0.70 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % pos_int_cases
% 0.37/0.70 thf(fact_7082_int__cases4,axiom,
% 0.37/0.70 ! [M: int] :
% 0.37/0.70 ( ! [N2: nat] :
% 0.37/0.70 ( M
% 0.37/0.70 != ( semiri1314217659103216013at_int @ N2 ) )
% 0.37/0.70 => ~ ! [N2: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.37/0.70 => ( M
% 0.37/0.70 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_cases4
% 0.37/0.70 thf(fact_7083_int__cases3,axiom,
% 0.37/0.70 ! [K: int] :
% 0.37/0.70 ( ( K != zero_zero_int )
% 0.37/0.70 => ( ! [N2: nat] :
% 0.37/0.70 ( ( K
% 0.37/0.70 = ( semiri1314217659103216013at_int @ N2 ) )
% 0.37/0.70 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 0.37/0.70 => ~ ! [N2: nat] :
% 0.37/0.70 ( ( K
% 0.37/0.70 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.37/0.70 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_cases3
% 0.37/0.70 thf(fact_7084_neg__int__cases,axiom,
% 0.37/0.70 ! [K: int] :
% 0.37/0.70 ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.70 => ~ ! [N2: nat] :
% 0.37/0.70 ( ( K
% 0.37/0.70 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 0.37/0.70 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % neg_int_cases
% 0.37/0.70 thf(fact_7085_zdiff__int__split,axiom,
% 0.37/0.70 ! [P2: int > $o,X: nat,Y: nat] :
% 0.37/0.70 ( ( P2 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 0.37/0.70 = ( ( ( ord_less_eq_nat @ Y @ X )
% 0.37/0.70 => ( P2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 0.37/0.70 & ( ( ord_less_nat @ X @ Y )
% 0.37/0.70 => ( P2 @ zero_zero_int ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiff_int_split
% 0.37/0.70 thf(fact_7086_VEBT__internal_Ocnt_H_Osimps_I1_J,axiom,
% 0.37/0.70 ! [A: $o,B: $o] :
% 0.37/0.70 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Leaf @ A @ B ) )
% 0.37/0.70 = one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.cnt'.simps(1)
% 0.37/0.70 thf(fact_7087_bot__nat__0_Oordering__top__axioms,axiom,
% 0.37/0.70 ( ordering_top_nat
% 0.37/0.70 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 0.37/0.70 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 0.37/0.70 @ zero_zero_nat ) ).
% 0.37/0.70
% 0.37/0.70 % bot_nat_0.ordering_top_axioms
% 0.37/0.70 thf(fact_7088_Chebyshev__sum__upper__nat,axiom,
% 0.37/0.70 ! [N: nat,A: nat > nat,B: nat > nat] :
% 0.37/0.70 ( ! [I2: nat,J2: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.37/0.70 => ( ( ord_less_nat @ J2 @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( A @ I2 ) @ ( A @ J2 ) ) ) )
% 0.37/0.70 => ( ! [I2: nat,J2: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.37/0.70 => ( ( ord_less_nat @ J2 @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I2 ) ) ) )
% 0.37/0.70 => ( ord_less_eq_nat
% 0.37/0.70 @ ( times_times_nat @ N
% 0.37/0.70 @ ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 0.37/0.70 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 0.37/0.70 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Chebyshev_sum_upper_nat
% 0.37/0.70 thf(fact_7089_minNrulli__ruleT,axiom,
% 0.37/0.70 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 0.37/0.70 ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_minNulli @ Ti )
% 0.37/0.70 @ ^ [R5: $o] :
% 0.37/0.70 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( R5
% 0.37/0.70 = ( vEBT_VEBT_minNull @ T ) ) ) )
% 0.37/0.70 @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % minNrulli_ruleT
% 0.37/0.70 thf(fact_7090_T__vebt__buildupi,axiom,
% 0.37/0.70 ! [N: nat,H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ ( vEBT_V739175172307565963ildupi @ N ) @ H2 ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % T_vebt_buildupi
% 0.37/0.70 thf(fact_7091_vebt__maxti__hT,axiom,
% 0.37/0.70 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 0.37/0.70 ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 0.37/0.70 @ ^ [R5: option_nat] :
% 0.37/0.70 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( R5
% 0.37/0.70 = ( vEBT_vebt_maxt @ T ) ) ) )
% 0.37/0.70 @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_maxti_hT
% 0.37/0.70 thf(fact_7092_vebt__minti__hT,axiom,
% 0.37/0.70 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 0.37/0.70 ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 0.37/0.70 @ ^ [R5: option_nat] :
% 0.37/0.70 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( R5
% 0.37/0.70 = ( vEBT_vebt_mint @ T ) ) ) )
% 0.37/0.70 @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti_hT
% 0.37/0.70 thf(fact_7093_htt__vebt__buildupi_H,axiom,
% 0.37/0.70 ! [N: nat] : ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % htt_vebt_buildupi'
% 0.37/0.70 thf(fact_7094_htt__vebt__buildupi,axiom,
% 0.37/0.70 ! [N: nat] : ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % htt_vebt_buildupi
% 0.37/0.70 thf(fact_7095_finite__interval__int1,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( finite_finite_int
% 0.37/0.70 @ ( collect_int
% 0.37/0.70 @ ^ [I3: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ A @ I3 )
% 0.37/0.70 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_interval_int1
% 0.37/0.70 thf(fact_7096_finite__interval__int4,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( finite_finite_int
% 0.37/0.70 @ ( collect_int
% 0.37/0.70 @ ^ [I3: int] :
% 0.37/0.70 ( ( ord_less_int @ A @ I3 )
% 0.37/0.70 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_interval_int4
% 0.37/0.70 thf(fact_7097_finite__interval__int3,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( finite_finite_int
% 0.37/0.70 @ ( collect_int
% 0.37/0.70 @ ^ [I3: int] :
% 0.37/0.70 ( ( ord_less_int @ A @ I3 )
% 0.37/0.70 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_interval_int3
% 0.37/0.70 thf(fact_7098_finite__interval__int2,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( finite_finite_int
% 0.37/0.70 @ ( collect_int
% 0.37/0.70 @ ^ [I3: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ A @ I3 )
% 0.37/0.70 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_interval_int2
% 0.37/0.70 thf(fact_7099_negative__zle,axiom,
% 0.37/0.70 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.37/0.70
% 0.37/0.70 % negative_zle
% 0.37/0.70 thf(fact_7100_zle__add1__eq__le,axiom,
% 0.37/0.70 ! [W2: int,Z: int] :
% 0.37/0.70 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.37/0.70 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 0.37/0.70
% 0.37/0.70 % zle_add1_eq_le
% 0.37/0.70 thf(fact_7101_zle__diff1__eq,axiom,
% 0.37/0.70 ! [W2: int,Z: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.37/0.70 = ( ord_less_int @ W2 @ Z ) ) ).
% 0.37/0.70
% 0.37/0.70 % zle_diff1_eq
% 0.37/0.70 thf(fact_7102_nonpos__int__cases,axiom,
% 0.37/0.70 ! [K: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.37/0.70 => ~ ! [N2: nat] :
% 0.37/0.70 ( K
% 0.37/0.70 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nonpos_int_cases
% 0.37/0.70 thf(fact_7103_negative__zle__0,axiom,
% 0.37/0.70 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 0.37/0.70
% 0.37/0.70 % negative_zle_0
% 0.37/0.70 thf(fact_7104_zero__le__imp__eq__int,axiom,
% 0.37/0.70 ! [K: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.70 => ? [N2: nat] :
% 0.37/0.70 ( K
% 0.37/0.70 = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zero_le_imp_eq_int
% 0.37/0.70 thf(fact_7105_nonneg__int__cases,axiom,
% 0.37/0.70 ! [K: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.70 => ~ ! [N2: nat] :
% 0.37/0.70 ( K
% 0.37/0.70 != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nonneg_int_cases
% 0.37/0.70 thf(fact_7106_zle__iff__zadd,axiom,
% 0.37/0.70 ( ord_less_eq_int
% 0.37/0.70 = ( ^ [W3: int,Z2: int] :
% 0.37/0.70 ? [N6: nat] :
% 0.37/0.70 ( Z2
% 0.37/0.70 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N6 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zle_iff_zadd
% 0.37/0.70 thf(fact_7107_not__int__zless__negative,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % not_int_zless_negative
% 0.37/0.70 thf(fact_7108_pos__zmult__eq__1__iff,axiom,
% 0.37/0.70 ! [M: int,N: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ M )
% 0.37/0.70 => ( ( ( times_times_int @ M @ N )
% 0.37/0.70 = one_one_int )
% 0.37/0.70 = ( ( M = one_one_int )
% 0.37/0.70 & ( N = one_one_int ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % pos_zmult_eq_1_iff
% 0.37/0.70 thf(fact_7109_zmult__zless__mono2,axiom,
% 0.37/0.70 ! [I: int,J: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ I @ J )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmult_zless_mono2
% 0.37/0.70 thf(fact_7110_less__int__code_I1_J,axiom,
% 0.37/0.70 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.37/0.70
% 0.37/0.70 % less_int_code(1)
% 0.37/0.70 thf(fact_7111_zless__add1__eq,axiom,
% 0.37/0.70 ! [W2: int,Z: int] :
% 0.37/0.70 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.37/0.70 = ( ( ord_less_int @ W2 @ Z )
% 0.37/0.70 | ( W2 = Z ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zless_add1_eq
% 0.37/0.70 thf(fact_7112_int__gr__induct,axiom,
% 0.37/0.70 ! [K: int,I: int,P2: int > $o] :
% 0.37/0.70 ( ( ord_less_int @ K @ I )
% 0.37/0.70 => ( ( P2 @ ( plus_plus_int @ K @ one_one_int ) )
% 0.37/0.70 => ( ! [I2: int] :
% 0.37/0.70 ( ( ord_less_int @ K @ I2 )
% 0.37/0.70 => ( ( P2 @ I2 )
% 0.37/0.70 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.37/0.70 => ( P2 @ I ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_gr_induct
% 0.37/0.70 thf(fact_7113_int__less__induct,axiom,
% 0.37/0.70 ! [I: int,K: int,P2: int > $o] :
% 0.37/0.70 ( ( ord_less_int @ I @ K )
% 0.37/0.70 => ( ( P2 @ ( minus_minus_int @ K @ one_one_int ) )
% 0.37/0.70 => ( ! [I2: int] :
% 0.37/0.70 ( ( ord_less_int @ I2 @ K )
% 0.37/0.70 => ( ( P2 @ I2 )
% 0.37/0.70 => ( P2 @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 0.37/0.70 => ( P2 @ I ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_less_induct
% 0.37/0.70 thf(fact_7114_odd__less__0__iff,axiom,
% 0.37/0.70 ! [Z: int] :
% 0.37/0.70 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.37/0.70 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.37/0.70
% 0.37/0.70 % odd_less_0_iff
% 0.37/0.70 thf(fact_7115_plusinfinity,axiom,
% 0.37/0.70 ! [D: int,P6: int > $o,P2: int > $o] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D )
% 0.37/0.70 => ( ! [X3: int,K2: int] :
% 0.37/0.70 ( ( P6 @ X3 )
% 0.37/0.70 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 0.37/0.70 => ( ? [Z5: int] :
% 0.37/0.70 ! [X3: int] :
% 0.37/0.70 ( ( ord_less_int @ Z5 @ X3 )
% 0.37/0.70 => ( ( P2 @ X3 )
% 0.37/0.70 = ( P6 @ X3 ) ) )
% 0.37/0.70 => ( ? [X_12: int] : ( P6 @ X_12 )
% 0.37/0.70 => ? [X_1: int] : ( P2 @ X_1 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % plusinfinity
% 0.37/0.70 thf(fact_7116_minusinfinity,axiom,
% 0.37/0.70 ! [D: int,P1: int > $o,P2: int > $o] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D )
% 0.37/0.70 => ( ! [X3: int,K2: int] :
% 0.37/0.70 ( ( P1 @ X3 )
% 0.37/0.70 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 0.37/0.70 => ( ? [Z5: int] :
% 0.37/0.70 ! [X3: int] :
% 0.37/0.70 ( ( ord_less_int @ X3 @ Z5 )
% 0.37/0.70 => ( ( P2 @ X3 )
% 0.37/0.70 = ( P1 @ X3 ) ) )
% 0.37/0.70 => ( ? [X_12: int] : ( P1 @ X_12 )
% 0.37/0.70 => ? [X_1: int] : ( P2 @ X_1 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % minusinfinity
% 0.37/0.70 thf(fact_7117_verit__la__generic,axiom,
% 0.37/0.70 ! [A: int,X: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ A @ X )
% 0.37/0.70 | ( A = X )
% 0.37/0.70 | ( ord_less_eq_int @ X @ A ) ) ).
% 0.37/0.70
% 0.37/0.70 % verit_la_generic
% 0.37/0.70 thf(fact_7118_zless__imp__add1__zle,axiom,
% 0.37/0.70 ! [W2: int,Z: int] :
% 0.37/0.70 ( ( ord_less_int @ W2 @ Z )
% 0.37/0.70 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z ) ) ).
% 0.37/0.70
% 0.37/0.70 % zless_imp_add1_zle
% 0.37/0.70 thf(fact_7119_add1__zle__eq,axiom,
% 0.37/0.70 ! [W2: int,Z: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z )
% 0.37/0.70 = ( ord_less_int @ W2 @ Z ) ) ).
% 0.37/0.70
% 0.37/0.70 % add1_zle_eq
% 0.37/0.70 thf(fact_7120_int__ge__induct,axiom,
% 0.37/0.70 ! [K: int,I: int,P2: int > $o] :
% 0.37/0.70 ( ( ord_less_eq_int @ K @ I )
% 0.37/0.70 => ( ( P2 @ K )
% 0.37/0.70 => ( ! [I2: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ K @ I2 )
% 0.37/0.70 => ( ( P2 @ I2 )
% 0.37/0.70 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.37/0.70 => ( P2 @ I ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_ge_induct
% 0.37/0.70 thf(fact_7121_int__le__induct,axiom,
% 0.37/0.70 ! [I: int,K: int,P2: int > $o] :
% 0.37/0.70 ( ( ord_less_eq_int @ I @ K )
% 0.37/0.70 => ( ( P2 @ K )
% 0.37/0.70 => ( ! [I2: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ I2 @ K )
% 0.37/0.70 => ( ( P2 @ I2 )
% 0.37/0.70 => ( P2 @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 0.37/0.70 => ( P2 @ I ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_le_induct
% 0.37/0.70 thf(fact_7122_int__induct,axiom,
% 0.37/0.70 ! [P2: int > $o,K: int,I: int] :
% 0.37/0.70 ( ( P2 @ K )
% 0.37/0.70 => ( ! [I2: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ K @ I2 )
% 0.37/0.70 => ( ( P2 @ I2 )
% 0.37/0.70 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.37/0.70 => ( ! [I2: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ I2 @ K )
% 0.37/0.70 => ( ( P2 @ I2 )
% 0.37/0.70 => ( P2 @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 0.37/0.70 => ( P2 @ I ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_induct
% 0.37/0.70 thf(fact_7123_unique__quotient__lemma__neg,axiom,
% 0.37/0.70 ! [B: int,Q7: int,R6: int,Q3: int,R: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ B @ R )
% 0.37/0.70 => ( ( ord_less_int @ B @ R6 )
% 0.37/0.70 => ( ord_less_eq_int @ Q3 @ Q7 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % unique_quotient_lemma_neg
% 0.37/0.70 thf(fact_7124_unique__quotient__lemma,axiom,
% 0.37/0.70 ! [B: int,Q7: int,R6: int,Q3: int,R: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 0.37/0.70 => ( ( ord_less_int @ R6 @ B )
% 0.37/0.70 => ( ( ord_less_int @ R @ B )
% 0.37/0.70 => ( ord_less_eq_int @ Q7 @ Q3 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % unique_quotient_lemma
% 0.37/0.70 thf(fact_7125_zdiv__mono2__neg__lemma,axiom,
% 0.37/0.70 ! [B: int,Q3: int,R: int,B2: int,Q7: int,R6: int] :
% 0.37/0.70 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R )
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 0.37/0.70 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ R @ B )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.37/0.70 => ( ( ord_less_eq_int @ B2 @ B )
% 0.37/0.70 => ( ord_less_eq_int @ Q7 @ Q3 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_mono2_neg_lemma
% 0.37/0.70 thf(fact_7126_zdiv__mono2__lemma,axiom,
% 0.37/0.70 ! [B: int,Q3: int,R: int,B2: int,Q7: int,R6: int] :
% 0.37/0.70 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R )
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 0.37/0.70 => ( ( ord_less_int @ R6 @ B2 )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.37/0.70 => ( ( ord_less_eq_int @ B2 @ B )
% 0.37/0.70 => ( ord_less_eq_int @ Q3 @ Q7 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_mono2_lemma
% 0.37/0.70 thf(fact_7127_q__pos__lemma,axiom,
% 0.37/0.70 ! [B2: int,Q7: int,R6: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 0.37/0.70 => ( ( ord_less_int @ R6 @ B2 )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.37/0.70 => ( ord_less_eq_int @ zero_zero_int @ Q7 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % q_pos_lemma
% 0.37/0.70 thf(fact_7128_incr__mult__lemma,axiom,
% 0.37/0.70 ! [D: int,P2: int > $o,K: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D )
% 0.37/0.70 => ( ! [X3: int] :
% 0.37/0.70 ( ( P2 @ X3 )
% 0.37/0.70 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ( P2 @ X5 )
% 0.37/0.70 => ( P2 @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % incr_mult_lemma
% 0.37/0.70 thf(fact_7129_pos__mult__pos__ge,axiom,
% 0.37/0.70 ! [X: int,N: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ X )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.37/0.70 => ( ord_less_eq_int @ ( times_times_int @ N @ one_one_int ) @ ( times_times_int @ N @ X ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % pos_mult_pos_ge
% 0.37/0.70 thf(fact_7130_decr__mult__lemma,axiom,
% 0.37/0.70 ! [D: int,P2: int > $o,K: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D )
% 0.37/0.70 => ( ! [X3: int] :
% 0.37/0.70 ( ( P2 @ X3 )
% 0.37/0.70 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ( P2 @ X5 )
% 0.37/0.70 => ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % decr_mult_lemma
% 0.37/0.70 thf(fact_7131_le__imp__0__less,axiom,
% 0.37/0.70 ! [Z: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.70 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % le_imp_0_less
% 0.37/0.70 thf(fact_7132_less__1__helper,axiom,
% 0.37/0.70 ! [N: int,M: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ N @ M )
% 0.37/0.70 => ( ord_less_int @ ( minus_minus_int @ N @ one_one_int ) @ M ) ) ).
% 0.37/0.70
% 0.37/0.70 % less_1_helper
% 0.37/0.70 thf(fact_7133_imp__le__cong,axiom,
% 0.37/0.70 ! [X: int,X9: int,P2: $o,P6: $o] :
% 0.37/0.70 ( ( X = X9 )
% 0.37/0.70 => ( ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 0.37/0.70 => ( P2 = P6 ) )
% 0.37/0.70 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.70 => P2 )
% 0.37/0.70 = ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 0.37/0.70 => P6 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % imp_le_cong
% 0.37/0.70 thf(fact_7134_conj__le__cong,axiom,
% 0.37/0.70 ! [X: int,X9: int,P2: $o,P6: $o] :
% 0.37/0.70 ( ( X = X9 )
% 0.37/0.70 => ( ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 0.37/0.70 => ( P2 = P6 ) )
% 0.37/0.70 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.70 & P2 )
% 0.37/0.70 = ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 0.37/0.70 & P6 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % conj_le_cong
% 0.37/0.70 thf(fact_7135_less__eq__int__code_I1_J,axiom,
% 0.37/0.70 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.37/0.70
% 0.37/0.70 % less_eq_int_code(1)
% 0.37/0.70 thf(fact_7136_int__one__le__iff__zero__less,axiom,
% 0.37/0.70 ! [Z: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.37/0.70 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_one_le_iff_zero_less
% 0.37/0.70 thf(fact_7137_Gcd__int__greater__eq__0,axiom,
% 0.37/0.70 ! [K4: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K4 ) ) ).
% 0.37/0.70
% 0.37/0.70 % Gcd_int_greater_eq_0
% 0.37/0.70 thf(fact_7138_one__integer_Orsp,axiom,
% 0.37/0.70 one_one_int = one_one_int ).
% 0.37/0.70
% 0.37/0.70 % one_integer.rsp
% 0.37/0.70 thf(fact_7139_Tbuildupi__buildupi_H,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( semiri1314217659103216013at_int @ ( vEBT_V441764108873111860ildupi @ N ) )
% 0.37/0.70 = ( vEBT_V9176841429113362141ildupi @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % Tbuildupi_buildupi'
% 0.37/0.70 thf(fact_7140_VEBT__internal_OT__vebt__buildupi_H_Osimps_I1_J,axiom,
% 0.37/0.70 ( ( vEBT_V9176841429113362141ildupi @ zero_zero_nat )
% 0.37/0.70 = one_one_int ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.T_vebt_buildupi'.simps(1)
% 0.37/0.70 thf(fact_7141_VEBT__internal_OT__vebt__buildupi_H_Osimps_I2_J,axiom,
% 0.37/0.70 ( ( vEBT_V9176841429113362141ildupi @ ( suc @ zero_zero_nat ) )
% 0.37/0.70 = one_one_int ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.T_vebt_buildupi'.simps(2)
% 0.37/0.70 thf(fact_7142_finite__nth__roots,axiom,
% 0.37/0.70 ! [N: nat,C2: complex] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( finite3207457112153483333omplex
% 0.37/0.70 @ ( collect_complex
% 0.37/0.70 @ ^ [Z2: complex] :
% 0.37/0.70 ( ( power_power_complex @ Z2 @ N )
% 0.37/0.70 = C2 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_nth_roots
% 0.37/0.70 thf(fact_7143_foldr__same,axiom,
% 0.37/0.70 ! [Xs: list_real,Y: real] :
% 0.37/0.70 ( ! [X3: real,Y3: real] :
% 0.37/0.70 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.37/0.70 => ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 0.37/0.70 => ( X3 = Y3 ) ) )
% 0.37/0.70 => ( ! [X3: real] :
% 0.37/0.70 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 0.37/0.70 => ( X3 = Y ) )
% 0.37/0.70 => ( ( foldr_real_real @ plus_plus_real @ Xs @ zero_zero_real )
% 0.37/0.70 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_real @ Xs ) ) @ Y ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % foldr_same
% 0.37/0.70 thf(fact_7144_vebt__maxti__rule,axiom,
% 0.37/0.70 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,Y: nat] :
% 0.37/0.70 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 0.37/0.70 @ ^ [R5: option_nat] :
% 0.37/0.70 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( ( R5
% 0.37/0.70 = ( some_nat @ Y ) )
% 0.37/0.70 = ( vEBT_VEBT_max_in_set @ S @ Y ) ) ) )
% 0.37/0.70 @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_maxti_rule
% 0.37/0.70 thf(fact_7145_foldr0,axiom,
% 0.37/0.70 ! [Xs: list_real,C2: real,D: real] :
% 0.37/0.70 ( ( foldr_real_real @ plus_plus_real @ Xs @ ( plus_plus_real @ C2 @ D ) )
% 0.37/0.70 = ( plus_plus_real @ ( foldr_real_real @ plus_plus_real @ Xs @ D ) @ C2 ) ) ).
% 0.37/0.70
% 0.37/0.70 % foldr0
% 0.37/0.70 thf(fact_7146_VEBT__internal_Ocnt_H_Osimps_I2_J,axiom,
% 0.37/0.70 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.70 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 0.37/0.70 = ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList ) @ zero_zero_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.cnt'.simps(2)
% 0.37/0.70 thf(fact_7147_VEBT__internal_Ocnt_H_Oelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.70 ( ( ( vEBT_VEBT_cnt2 @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.70 => ( Y != one_one_nat ) )
% 0.37/0.70 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.cnt'.elims
% 0.37/0.70 thf(fact_7148_card__nth__roots,axiom,
% 0.37/0.70 ! [C2: complex,N: nat] :
% 0.37/0.70 ( ( C2 != zero_zero_complex )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( finite_card_complex
% 0.37/0.70 @ ( collect_complex
% 0.37/0.70 @ ^ [Z2: complex] :
% 0.37/0.70 ( ( power_power_complex @ Z2 @ N )
% 0.37/0.70 = C2 ) ) )
% 0.37/0.70 = N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % card_nth_roots
% 0.37/0.70 thf(fact_7149_card__roots__unity__eq,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( finite_card_complex
% 0.37/0.70 @ ( collect_complex
% 0.37/0.70 @ ^ [Z2: complex] :
% 0.37/0.70 ( ( power_power_complex @ Z2 @ N )
% 0.37/0.70 = one_one_complex ) ) )
% 0.37/0.70 = N ) ) ).
% 0.37/0.70
% 0.37/0.70 % card_roots_unity_eq
% 0.37/0.70 thf(fact_7150_sum__roots__unity,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ one_one_nat @ N )
% 0.37/0.70 => ( ( groups7754918857620584856omplex
% 0.37/0.70 @ ^ [X4: complex] : X4
% 0.37/0.70 @ ( collect_complex
% 0.37/0.70 @ ^ [Z2: complex] :
% 0.37/0.70 ( ( power_power_complex @ Z2 @ N )
% 0.37/0.70 = one_one_complex ) ) )
% 0.37/0.70 = zero_zero_complex ) ) ).
% 0.37/0.70
% 0.37/0.70 % sum_roots_unity
% 0.37/0.70 thf(fact_7151_sum__nth__roots,axiom,
% 0.37/0.70 ! [N: nat,C2: complex] :
% 0.37/0.70 ( ( ord_less_nat @ one_one_nat @ N )
% 0.37/0.70 => ( ( groups7754918857620584856omplex
% 0.37/0.70 @ ^ [X4: complex] : X4
% 0.37/0.70 @ ( collect_complex
% 0.37/0.70 @ ^ [Z2: complex] :
% 0.37/0.70 ( ( power_power_complex @ Z2 @ N )
% 0.37/0.70 = C2 ) ) )
% 0.37/0.70 = zero_zero_complex ) ) ).
% 0.37/0.70
% 0.37/0.70 % sum_nth_roots
% 0.37/0.70 thf(fact_7152_vebt__buildupi__rule__basic,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_Intf_vebt_assn @ N @ bot_bot_set_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_buildupi_rule_basic
% 0.37/0.70 thf(fact_7153_vebt__minti__rule,axiom,
% 0.37/0.70 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,Y: nat] :
% 0.37/0.70 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 0.37/0.70 @ ^ [R5: option_nat] :
% 0.37/0.70 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( ( R5
% 0.37/0.70 = ( some_nat @ Y ) )
% 0.37/0.70 = ( vEBT_VEBT_min_in_set @ S @ Y ) ) ) )
% 0.37/0.70 @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti_rule
% 0.37/0.70 thf(fact_7154_VEBT__internal_Ocnt_H_Opelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.70 ( ( ( vEBT_VEBT_cnt2 @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ X )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.70 => ( ( Y = one_one_nat )
% 0.37/0.70 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.70 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList2 ) @ zero_zero_nat ) ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.cnt'.pelims
% 0.37/0.70 thf(fact_7155_VEBT__internal_Ocnt_Osimps_I2_J,axiom,
% 0.37/0.70 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.70 ( ( vEBT_VEBT_cnt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 0.37/0.70 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList ) @ zero_zero_real ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.cnt.simps(2)
% 0.37/0.70 thf(fact_7156_VEBT__internal_Ocnt_Oelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBT,Y: real] :
% 0.37/0.70 ( ( ( vEBT_VEBT_cnt @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.70 => ( Y != one_one_real ) )
% 0.37/0.70 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.cnt.elims
% 0.37/0.70 thf(fact_7157_VEBT__internal_Ocnt_Opelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBT,Y: real] :
% 0.37/0.70 ( ( ( vEBT_VEBT_cnt @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ X )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.70 => ( ( Y = one_one_real )
% 0.37/0.70 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.70 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.cnt.pelims
% 0.37/0.70 thf(fact_7158_prod__decode__aux_Opelims,axiom,
% 0.37/0.70 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 0.37/0.70 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.37/0.70 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.37/0.70 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 0.37/0.70 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % prod_decode_aux.pelims
% 0.37/0.70 thf(fact_7159_vebt__buildupi__refines,axiom,
% 0.37/0.70 ! [N: nat] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_V739175172307565963ildupi @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_buildupi_refines
% 0.37/0.70 thf(fact_7160_vebt__deletei__refines,axiom,
% 0.37/0.70 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_deletei @ Ti @ X ) @ ( vEBT_V1365221501068881998eletei @ T @ Ti @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_deletei_refines
% 0.37/0.70 thf(fact_7161_vebt__inserti__refines,axiom,
% 0.37/0.70 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_inserti_refines
% 0.37/0.70 thf(fact_7162_VEBTi_Osize_I3_J,axiom,
% 0.37/0.70 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 0.37/0.70 ( ( size_size_VEBT_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 0.37/0.70 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ size_size_VEBT_VEBTi @ X13 ) @ ( size_size_VEBT_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBTi.size(3)
% 0.37/0.70 thf(fact_7163_vebt__succi__refines,axiom,
% 0.37/0.70 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine7594492741263601813on_nat @ ( vEBT_vebt_succi @ Ti @ X ) @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_succi_refines
% 0.37/0.70 thf(fact_7164_vebt__predi__refines,axiom,
% 0.37/0.70 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine7594492741263601813on_nat @ ( vEBT_vebt_predi @ Ti @ X ) @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_predi_refines
% 0.37/0.70 thf(fact_7165_vebt__memberi__refines,axiom,
% 0.37/0.70 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine_Imp_refines_o @ ( vEBT_vebt_memberi @ Ti @ X ) @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_memberi_refines
% 0.37/0.70 thf(fact_7166_VEBTi_Osize__gen_I1_J,axiom,
% 0.37/0.70 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 0.37/0.70 ( ( vEBT_size_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 0.37/0.70 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ vEBT_size_VEBTi @ X13 ) @ ( vEBT_size_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBTi.size_gen(1)
% 0.37/0.70 thf(fact_7167_TBOUND__minNull,axiom,
% 0.37/0.70 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.70 ( ( vEBT_VEBT_minNull @ T )
% 0.37/0.70 => ( time_T5737551269749752165_VEBTi @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) @ one_one_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % TBOUND_minNull
% 0.37/0.70 thf(fact_7168_TBOUND__vebt__buildupi,axiom,
% 0.37/0.70 ! [N: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % TBOUND_vebt_buildupi
% 0.37/0.70 thf(fact_7169_finite__atMost,axiom,
% 0.37/0.70 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_atMost
% 0.37/0.70 thf(fact_7170_card__atMost,axiom,
% 0.37/0.70 ! [U: nat] :
% 0.37/0.70 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.37/0.70 = ( suc @ U ) ) ).
% 0.37/0.70
% 0.37/0.70 % card_atMost
% 0.37/0.70 thf(fact_7171_atMost__0,axiom,
% 0.37/0.70 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.37/0.70 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % atMost_0
% 0.37/0.70 thf(fact_7172_lessThan__Suc__atMost,axiom,
% 0.37/0.70 ! [K: nat] :
% 0.37/0.70 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 0.37/0.70 = ( set_ord_atMost_nat @ K ) ) ).
% 0.37/0.70
% 0.37/0.70 % lessThan_Suc_atMost
% 0.37/0.70 thf(fact_7173_atMost__Suc,axiom,
% 0.37/0.70 ! [K: nat] :
% 0.37/0.70 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 0.37/0.70 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atMost_Suc
% 0.37/0.70 thf(fact_7174_finite__nat__iff__bounded__le,axiom,
% 0.37/0.70 ( finite_finite_nat
% 0.37/0.70 = ( ^ [S6: set_nat] :
% 0.37/0.70 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_nat_iff_bounded_le
% 0.37/0.70 thf(fact_7175_atMost__Suc__eq__insert__0,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 0.37/0.70 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atMost_Suc_eq_insert_0
% 0.37/0.70 thf(fact_7176_polynomial__product__nat,axiom,
% 0.37/0.70 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 0.37/0.70 ( ! [I2: nat] :
% 0.37/0.70 ( ( ord_less_nat @ M @ I2 )
% 0.37/0.70 => ( ( A @ I2 )
% 0.37/0.70 = zero_zero_nat ) )
% 0.37/0.70 => ( ! [J2: nat] :
% 0.37/0.70 ( ( ord_less_nat @ N @ J2 )
% 0.37/0.70 => ( ( B @ J2 )
% 0.37/0.70 = zero_zero_nat ) )
% 0.37/0.70 => ( ( times_times_nat
% 0.37/0.70 @ ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X @ I3 ) )
% 0.37/0.70 @ ( set_ord_atMost_nat @ M ) )
% 0.37/0.70 @ ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 0.37/0.70 @ ( set_ord_atMost_nat @ N ) ) )
% 0.37/0.70 = ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [R5: nat] :
% 0.37/0.70 ( times_times_nat
% 0.37/0.70 @ ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 0.37/0.70 @ ( set_ord_atMost_nat @ R5 ) )
% 0.37/0.70 @ ( power_power_nat @ X @ R5 ) )
% 0.37/0.70 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % polynomial_product_nat
% 0.37/0.70 thf(fact_7177_TBOUND__vebt__minti,axiom,
% 0.37/0.70 ! [T: vEBT_VEBTi] : ( time_T8353473612707095248on_nat @ ( vEBT_vebt_minti @ T ) @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % TBOUND_vebt_minti
% 0.37/0.70 thf(fact_7178_TBOUND__vebt__maxti,axiom,
% 0.37/0.70 ! [T: vEBT_VEBTi] : ( time_T8353473612707095248on_nat @ ( vEBT_vebt_maxti @ T ) @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % TBOUND_vebt_maxti
% 0.37/0.70 thf(fact_7179_TBOUND__minNulli,axiom,
% 0.37/0.70 ! [T: vEBT_VEBTi] : ( time_TBOUND_o @ ( vEBT_VEBT_minNulli @ T ) @ one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % TBOUND_minNulli
% 0.37/0.70 thf(fact_7180_finite__atLeastAtMost,axiom,
% 0.37/0.70 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_atLeastAtMost
% 0.37/0.70 thf(fact_7181_image__Suc__atLeastAtMost,axiom,
% 0.37/0.70 ! [I: nat,J: nat] :
% 0.37/0.70 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.37/0.70 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % image_Suc_atLeastAtMost
% 0.37/0.70 thf(fact_7182_card__atLeastAtMost,axiom,
% 0.37/0.70 ! [L: nat,U: nat] :
% 0.37/0.70 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.37/0.70 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 0.37/0.70
% 0.37/0.70 % card_atLeastAtMost
% 0.37/0.70 thf(fact_7183_all__nat__less,axiom,
% 0.37/0.70 ! [N: nat,P2: nat > $o] :
% 0.37/0.70 ( ( ! [M5: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M5 @ N )
% 0.37/0.70 => ( P2 @ M5 ) ) )
% 0.37/0.70 = ( ! [X4: nat] :
% 0.37/0.70 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.37/0.70 => ( P2 @ X4 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % all_nat_less
% 0.37/0.70 thf(fact_7184_ex__nat__less,axiom,
% 0.37/0.70 ! [N: nat,P2: nat > $o] :
% 0.37/0.70 ( ( ? [M5: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M5 @ N )
% 0.37/0.70 & ( P2 @ M5 ) ) )
% 0.37/0.70 = ( ? [X4: nat] :
% 0.37/0.70 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.37/0.70 & ( P2 @ X4 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % ex_nat_less
% 0.37/0.70 thf(fact_7185_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.37/0.70 ! [L: nat,U: nat] :
% 0.37/0.70 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 0.37/0.70 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.37/0.70
% 0.37/0.70 % atLeastLessThanSuc_atLeastAtMost
% 0.37/0.70 thf(fact_7186_atMost__atLeast0,axiom,
% 0.37/0.70 ( set_ord_atMost_nat
% 0.37/0.70 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % atMost_atLeast0
% 0.37/0.70 thf(fact_7187_complex__mod__minus__le__complex__mod,axiom,
% 0.37/0.70 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % complex_mod_minus_le_complex_mod
% 0.37/0.70 thf(fact_7188_complex__mod__triangle__ineq2,axiom,
% 0.37/0.70 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 0.37/0.70
% 0.37/0.70 % complex_mod_triangle_ineq2
% 0.37/0.70 thf(fact_7189_atLeast0__atMost__Suc,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.37/0.70 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atLeast0_atMost_Suc
% 0.37/0.70 thf(fact_7190_Icc__eq__insert__lb__nat,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 0.37/0.70 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Icc_eq_insert_lb_nat
% 0.37/0.70 thf(fact_7191_atLeastAtMostSuc__conv,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.37/0.70 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 0.37/0.70 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atLeastAtMostSuc_conv
% 0.37/0.70 thf(fact_7192_atLeastAtMost__insertL,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.37/0.70 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atLeastAtMost_insertL
% 0.37/0.70 thf(fact_7193_subset__eq__atLeast0__atMost__finite,axiom,
% 0.37/0.70 ! [N8: set_nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_set_nat @ N8 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.37/0.70 => ( finite_finite_nat @ N8 ) ) ).
% 0.37/0.70
% 0.37/0.70 % subset_eq_atLeast0_atMost_finite
% 0.37/0.70 thf(fact_7194_image__Suc__lessThan,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.70 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % image_Suc_lessThan
% 0.37/0.70 thf(fact_7195_image__Suc__atMost,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 0.37/0.70 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % image_Suc_atMost
% 0.37/0.70 thf(fact_7196_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.37/0.70 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atLeast0_atMost_Suc_eq_insert_0
% 0.37/0.70 thf(fact_7197_atLeast1__atMost__eq__remove0,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.70 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atLeast1_atMost_eq_remove0
% 0.37/0.70 thf(fact_7198_atLeastAtMostPlus1__int__conv,axiom,
% 0.37/0.70 ! [M: int,N: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.37/0.70 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.37/0.70 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % atLeastAtMostPlus1_int_conv
% 0.37/0.70 thf(fact_7199_simp__from__to,axiom,
% 0.37/0.70 ( set_or1266510415728281911st_int
% 0.37/0.70 = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % simp_from_to
% 0.37/0.70 thf(fact_7200_aset_I7_J,axiom,
% 0.37/0.70 ! [D4: int,A4: set_int,T: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ A4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_int @ T @ X5 )
% 0.37/0.70 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % aset(7)
% 0.37/0.70 thf(fact_7201_aset_I5_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,A4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ T @ A4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ A4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_int @ X5 @ T )
% 0.37/0.70 => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % aset(5)
% 0.37/0.70 thf(fact_7202_aset_I4_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,A4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ T @ A4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ A4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( X5 != T )
% 0.37/0.70 => ( ( plus_plus_int @ X5 @ D4 )
% 0.37/0.70 != T ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % aset(4)
% 0.37/0.70 thf(fact_7203_aset_I3_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,A4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ A4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( X5 = T )
% 0.37/0.70 => ( ( plus_plus_int @ X5 @ D4 )
% 0.37/0.70 = T ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % aset(3)
% 0.37/0.70 thf(fact_7204_bset_I7_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,B4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ T @ B4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ B4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_int @ T @ X5 )
% 0.37/0.70 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % bset(7)
% 0.37/0.70 thf(fact_7205_bset_I5_J,axiom,
% 0.37/0.70 ! [D4: int,B4: set_int,T: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ B4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_int @ X5 @ T )
% 0.37/0.70 => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % bset(5)
% 0.37/0.70 thf(fact_7206_bset_I4_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,B4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ T @ B4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ B4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( X5 != T )
% 0.37/0.70 => ( ( minus_minus_int @ X5 @ D4 )
% 0.37/0.70 != T ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % bset(4)
% 0.37/0.70 thf(fact_7207_bset_I3_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,B4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ B4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( X5 = T )
% 0.37/0.70 => ( ( minus_minus_int @ X5 @ D4 )
% 0.37/0.70 = T ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % bset(3)
% 0.37/0.70 thf(fact_7208_periodic__finite__ex,axiom,
% 0.37/0.70 ! [D: int,P2: int > $o] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D )
% 0.37/0.70 => ( ! [X3: int,K2: int] :
% 0.37/0.70 ( ( P2 @ X3 )
% 0.37/0.70 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 0.37/0.70 => ( ( ? [X8: int] : ( P2 @ X8 ) )
% 0.37/0.70 = ( ? [X4: int] :
% 0.37/0.70 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 0.37/0.70 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % periodic_finite_ex
% 0.37/0.70 thf(fact_7209_aset_I8_J,axiom,
% 0.37/0.70 ! [D4: int,A4: set_int,T: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ A4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ T @ X5 )
% 0.37/0.70 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % aset(8)
% 0.37/0.70 thf(fact_7210_aset_I6_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,A4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ A4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ X5 @ T )
% 0.37/0.70 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % aset(6)
% 0.37/0.70 thf(fact_7211_bset_I8_J,axiom,
% 0.37/0.70 ! [D4: int,T: int,B4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ B4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ T @ X5 )
% 0.37/0.70 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % bset(8)
% 0.37/0.70 thf(fact_7212_bset_I6_J,axiom,
% 0.37/0.70 ! [D4: int,B4: set_int,T: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ! [X5: int] :
% 0.37/0.70 ( ! [Xa3: int] :
% 0.37/0.70 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb2: int] :
% 0.37/0.70 ( ( member_int @ Xb2 @ B4 )
% 0.37/0.70 => ( X5
% 0.37/0.70 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ X5 @ T )
% 0.37/0.70 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % bset(6)
% 0.37/0.70 thf(fact_7213_cpmi,axiom,
% 0.37/0.70 ! [D4: int,P2: int > $o,P6: int > $o,B4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ? [Z5: int] :
% 0.37/0.70 ! [X3: int] :
% 0.37/0.70 ( ( ord_less_int @ X3 @ Z5 )
% 0.37/0.70 => ( ( P2 @ X3 )
% 0.37/0.70 = ( P6 @ X3 ) ) )
% 0.37/0.70 => ( ! [X3: int] :
% 0.37/0.70 ( ! [Xa: int] :
% 0.37/0.70 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb3: int] :
% 0.37/0.70 ( ( member_int @ Xb3 @ B4 )
% 0.37/0.70 => ( X3
% 0.37/0.70 != ( plus_plus_int @ Xb3 @ Xa ) ) ) )
% 0.37/0.70 => ( ( P2 @ X3 )
% 0.37/0.70 => ( P2 @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 0.37/0.70 => ( ! [X3: int,K2: int] :
% 0.37/0.70 ( ( P6 @ X3 )
% 0.37/0.70 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.37/0.70 => ( ( ? [X8: int] : ( P2 @ X8 ) )
% 0.37/0.70 = ( ? [X4: int] :
% 0.37/0.70 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 & ( P6 @ X4 ) )
% 0.37/0.70 | ? [X4: int] :
% 0.37/0.70 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 & ? [Y4: int] :
% 0.37/0.70 ( ( member_int @ Y4 @ B4 )
% 0.37/0.70 & ( P2 @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % cpmi
% 0.37/0.70 thf(fact_7214_cppi,axiom,
% 0.37/0.70 ! [D4: int,P2: int > $o,P6: int > $o,A4: set_int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D4 )
% 0.37/0.70 => ( ? [Z5: int] :
% 0.37/0.70 ! [X3: int] :
% 0.37/0.70 ( ( ord_less_int @ Z5 @ X3 )
% 0.37/0.70 => ( ( P2 @ X3 )
% 0.37/0.70 = ( P6 @ X3 ) ) )
% 0.37/0.70 => ( ! [X3: int] :
% 0.37/0.70 ( ! [Xa: int] :
% 0.37/0.70 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 => ! [Xb3: int] :
% 0.37/0.70 ( ( member_int @ Xb3 @ A4 )
% 0.37/0.70 => ( X3
% 0.37/0.70 != ( minus_minus_int @ Xb3 @ Xa ) ) ) )
% 0.37/0.70 => ( ( P2 @ X3 )
% 0.37/0.70 => ( P2 @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 0.37/0.70 => ( ! [X3: int,K2: int] :
% 0.37/0.70 ( ( P6 @ X3 )
% 0.37/0.70 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 0.37/0.70 => ( ( ? [X8: int] : ( P2 @ X8 ) )
% 0.37/0.70 = ( ? [X4: int] :
% 0.37/0.70 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 & ( P6 @ X4 ) )
% 0.37/0.70 | ? [X4: int] :
% 0.37/0.70 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 0.37/0.70 & ? [Y4: int] :
% 0.37/0.70 ( ( member_int @ Y4 @ A4 )
% 0.37/0.70 & ( P2 @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % cppi
% 0.37/0.70 thf(fact_7215_nat__mult__div__cancel__disj,axiom,
% 0.37/0.70 ! [K: nat,M: nat,N: nat] :
% 0.37/0.70 ( ( ( K = zero_zero_nat )
% 0.37/0.70 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.70 = zero_zero_nat ) )
% 0.37/0.70 & ( ( K != zero_zero_nat )
% 0.37/0.70 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.70 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_mult_div_cancel_disj
% 0.37/0.70 thf(fact_7216_zdiv__int,axiom,
% 0.37/0.70 ! [A: nat,B: nat] :
% 0.37/0.70 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 0.37/0.70 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_int
% 0.37/0.70 thf(fact_7217_real__of__nat__div4,axiom,
% 0.37/0.70 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % real_of_nat_div4
% 0.37/0.70 thf(fact_7218_real__of__nat__div2,axiom,
% 0.37/0.70 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % real_of_nat_div2
% 0.37/0.70 thf(fact_7219_real__of__nat__div3,axiom,
% 0.37/0.70 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 0.37/0.70
% 0.37/0.70 % real_of_nat_div3
% 0.37/0.70 thf(fact_7220_pos__imp__zdiv__neg__iff,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.37/0.70 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % pos_imp_zdiv_neg_iff
% 0.37/0.70 thf(fact_7221_neg__imp__zdiv__neg__iff,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.37/0.70 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % neg_imp_zdiv_neg_iff
% 0.37/0.70 thf(fact_7222_div__neg__pos__less0,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_neg_pos_less0
% 0.37/0.70 thf(fact_7223_nat__mult__div__cancel1,axiom,
% 0.37/0.70 ! [K: nat,M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.70 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.70 = ( divide_divide_nat @ M @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_mult_div_cancel1
% 0.37/0.70 thf(fact_7224_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.37/0.70 = ( ( ord_less_eq_int @ B @ A )
% 0.37/0.70 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nonneg1_imp_zdiv_pos_iff
% 0.37/0.70 thf(fact_7225_pos__imp__zdiv__nonneg__iff,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.37/0.70 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % pos_imp_zdiv_nonneg_iff
% 0.37/0.70 thf(fact_7226_neg__imp__zdiv__nonneg__iff,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.37/0.70 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % neg_imp_zdiv_nonneg_iff
% 0.37/0.70 thf(fact_7227_pos__imp__zdiv__pos__iff,axiom,
% 0.37/0.70 ! [K: int,I: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 0.37/0.70 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % pos_imp_zdiv_pos_iff
% 0.37/0.70 thf(fact_7228_div__nonpos__pos__le0,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_nonpos_pos_le0
% 0.37/0.70 thf(fact_7229_div__nonneg__neg__le0,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.70 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_nonneg_neg_le0
% 0.37/0.70 thf(fact_7230_div__positive__int,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ L @ K )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ L )
% 0.37/0.70 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_positive_int
% 0.37/0.70 thf(fact_7231_div__int__pos__iff,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 0.37/0.70 = ( ( K = zero_zero_int )
% 0.37/0.70 | ( L = zero_zero_int )
% 0.37/0.70 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.70 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 0.37/0.70 | ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.70 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_int_pos_iff
% 0.37/0.70 thf(fact_7232_zdiv__mono2__neg,axiom,
% 0.37/0.70 ! [A: int,B2: int,B: int] :
% 0.37/0.70 ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.37/0.70 => ( ( ord_less_eq_int @ B2 @ B )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_mono2_neg
% 0.37/0.70 thf(fact_7233_zdiv__mono1__neg,axiom,
% 0.37/0.70 ! [A: int,A2: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ A @ A2 )
% 0.37/0.70 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_mono1_neg
% 0.37/0.70 thf(fact_7234_zdiv__eq__0__iff,axiom,
% 0.37/0.70 ! [I: int,K: int] :
% 0.37/0.70 ( ( ( divide_divide_int @ I @ K )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 = ( ( K = zero_zero_int )
% 0.37/0.70 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.37/0.70 & ( ord_less_int @ I @ K ) )
% 0.37/0.70 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.37/0.70 & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_eq_0_iff
% 0.37/0.70 thf(fact_7235_zdiv__mono2,axiom,
% 0.37/0.70 ! [A: int,B2: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.37/0.70 => ( ( ord_less_eq_int @ B2 @ B )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_mono2
% 0.37/0.70 thf(fact_7236_zdiv__mono1,axiom,
% 0.37/0.70 ! [A: int,A2: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ A @ A2 )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_mono1
% 0.37/0.70 thf(fact_7237_int__div__less__self,axiom,
% 0.37/0.70 ! [X: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ X )
% 0.37/0.70 => ( ( ord_less_int @ one_one_int @ K )
% 0.37/0.70 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_div_less_self
% 0.37/0.70 thf(fact_7238_div__geq,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ~ ( ord_less_nat @ M @ N )
% 0.37/0.70 => ( ( divide_divide_nat @ M @ N )
% 0.37/0.70 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_geq
% 0.37/0.70 thf(fact_7239_msrevs_I1_J,axiom,
% 0.37/0.70 ! [N: nat,K: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) @ N )
% 0.37/0.70 = ( plus_plus_nat @ ( divide_divide_nat @ M @ N ) @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % msrevs(1)
% 0.37/0.70 thf(fact_7240_verit__less__mono__div__int2,axiom,
% 0.37/0.70 ! [A4: int,B4: int,N: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ A4 @ B4 )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A4 @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % verit_less_mono_div_int2
% 0.37/0.70 thf(fact_7241_div__eq__minus1,axiom,
% 0.37/0.70 ! [B: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.37/0.70 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_eq_minus1
% 0.37/0.70 thf(fact_7242_int__div__pos__eq,axiom,
% 0.37/0.70 ! [A: int,B: int,Q3: int,R: int] :
% 0.37/0.70 ( ( A
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.37/0.70 => ( ( ord_less_int @ R @ B )
% 0.37/0.70 => ( ( divide_divide_int @ A @ B )
% 0.37/0.70 = Q3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_div_pos_eq
% 0.37/0.70 thf(fact_7243_int__div__neg__eq,axiom,
% 0.37/0.70 ! [A: int,B: int,Q3: int,R: int] :
% 0.37/0.70 ( ( A
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ B @ R )
% 0.37/0.70 => ( ( divide_divide_int @ A @ B )
% 0.37/0.70 = Q3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_div_neg_eq
% 0.37/0.70 thf(fact_7244_split__zdiv,axiom,
% 0.37/0.70 ! [P2: int > $o,N: int,K: int] :
% 0.37/0.70 ( ( P2 @ ( divide_divide_int @ N @ K ) )
% 0.37/0.70 = ( ( ( K = zero_zero_int )
% 0.37/0.70 => ( P2 @ zero_zero_int ) )
% 0.37/0.70 & ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ! [I3: int,J3: int] :
% 0.37/0.70 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.37/0.70 & ( ord_less_int @ J3 @ K )
% 0.37/0.70 & ( N
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.37/0.70 => ( P2 @ I3 ) ) )
% 0.37/0.70 & ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.70 => ! [I3: int,J3: int] :
% 0.37/0.70 ( ( ( ord_less_int @ K @ J3 )
% 0.37/0.70 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.37/0.70 & ( N
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.37/0.70 => ( P2 @ I3 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % split_zdiv
% 0.37/0.70 thf(fact_7245_int__power__div__base,axiom,
% 0.37/0.70 ! [M: nat,K: int] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 0.37/0.70 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_power_div_base
% 0.37/0.70 thf(fact_7246_div__pos__geq,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ L )
% 0.37/0.70 => ( ( ord_less_eq_int @ L @ K )
% 0.37/0.70 => ( ( divide_divide_int @ K @ L )
% 0.37/0.70 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_pos_geq
% 0.37/0.70 thf(fact_7247_int__div__minus__is__minus1,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_int @ A @ zero_zero_int )
% 0.37/0.70 => ( ( ( divide_divide_int @ A @ B )
% 0.37/0.70 = ( uminus_uminus_int @ A ) )
% 0.37/0.70 = ( B
% 0.37/0.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_div_minus_is_minus1
% 0.37/0.70 thf(fact_7248_int__div__same__is__1,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.70 => ( ( ( divide_divide_int @ A @ B )
% 0.37/0.70 = A )
% 0.37/0.70 = ( B = one_one_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_div_same_is_1
% 0.37/0.70 thf(fact_7249_div__by__Suc__0,axiom,
% 0.37/0.70 ! [M: nat] :
% 0.37/0.70 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.37/0.70 = M ) ).
% 0.37/0.70
% 0.37/0.70 % div_by_Suc_0
% 0.37/0.70 thf(fact_7250_div__less,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ M @ N )
% 0.37/0.70 => ( ( divide_divide_nat @ M @ N )
% 0.37/0.70 = zero_zero_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_less
% 0.37/0.70 thf(fact_7251_div__eq__dividend__iff,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.70 => ( ( ( divide_divide_nat @ M @ N )
% 0.37/0.70 = M )
% 0.37/0.70 = ( N = one_one_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_eq_dividend_iff
% 0.37/0.70 thf(fact_7252_div__mult__self1__is__m,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 0.37/0.70 = M ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_mult_self1_is_m
% 0.37/0.70 thf(fact_7253_div__mult__self__is__m,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 0.37/0.70 = M ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_mult_self_is_m
% 0.37/0.70 thf(fact_7254_div__neg__neg__trivial,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ L @ K )
% 0.37/0.70 => ( ( divide_divide_int @ K @ L )
% 0.37/0.70 = zero_zero_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_neg_neg_trivial
% 0.37/0.70 thf(fact_7255_div__pos__pos__trivial,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ( ord_less_int @ K @ L )
% 0.37/0.70 => ( ( divide_divide_int @ K @ L )
% 0.37/0.70 = zero_zero_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_pos_pos_trivial
% 0.37/0.70 thf(fact_7256_div__le__mono,axiom,
% 0.37/0.70 ! [M: nat,N: nat,K: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_le_mono
% 0.37/0.70 thf(fact_7257_div__le__dividend,axiom,
% 0.37/0.70 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.37/0.70
% 0.37/0.70 % div_le_dividend
% 0.37/0.70 thf(fact_7258_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ( divide_divide_nat @ M @ N )
% 0.37/0.70 = zero_zero_nat )
% 0.37/0.70 = ( ( ord_less_nat @ M @ N )
% 0.37/0.70 | ( N = zero_zero_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Euclidean_Division.div_eq_0_iff
% 0.37/0.70 thf(fact_7259_Suc__div__le__mono,axiom,
% 0.37/0.70 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_div_le_mono
% 0.37/0.70 thf(fact_7260_less__mult__imp__div__less,axiom,
% 0.37/0.70 ! [M: nat,I: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 0.37/0.70 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 0.37/0.70
% 0.37/0.70 % less_mult_imp_div_less
% 0.37/0.70 thf(fact_7261_times__div__less__eq__dividend,axiom,
% 0.37/0.70 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 0.37/0.70
% 0.37/0.70 % times_div_less_eq_dividend
% 0.37/0.70 thf(fact_7262_div__times__less__eq__dividend,axiom,
% 0.37/0.70 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 0.37/0.70
% 0.37/0.70 % div_times_less_eq_dividend
% 0.37/0.70 thf(fact_7263_div__mult__le,axiom,
% 0.37/0.70 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ A ) ).
% 0.37/0.70
% 0.37/0.70 % div_mult_le
% 0.37/0.70 thf(fact_7264_div__greater__zero__iff,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 0.37/0.70 = ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.70 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_greater_zero_iff
% 0.37/0.70 thf(fact_7265_div__le__mono2,axiom,
% 0.37/0.70 ! [M: nat,N: nat,K: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.70 => ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_le_mono2
% 0.37/0.70 thf(fact_7266_div__less__dividend,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ one_one_nat @ N )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.70 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_less_dividend
% 0.37/0.70 thf(fact_7267_div__less__iff__less__mult,axiom,
% 0.37/0.70 ! [Q3: nat,M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 0.37/0.70 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 0.37/0.70 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_less_iff_less_mult
% 0.37/0.70 thf(fact_7268_td__gal__lt,axiom,
% 0.37/0.70 ! [C2: nat,A: nat,B: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.70 => ( ( ord_less_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.37/0.70 = ( ord_less_nat @ ( divide_divide_nat @ A @ C2 ) @ B ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % td_gal_lt
% 0.37/0.70 thf(fact_7269_zdiv__le__dividend,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ A ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_le_dividend
% 0.37/0.70 thf(fact_7270_zdiv__zmult2__eq,axiom,
% 0.37/0.70 ! [C2: int,A: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.70 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.37/0.70 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_zmult2_eq
% 0.37/0.70 thf(fact_7271_div__if,axiom,
% 0.37/0.70 ( divide_divide_nat
% 0.37/0.70 = ( ^ [M5: nat,N6: nat] :
% 0.37/0.70 ( if_nat
% 0.37/0.70 @ ( ( ord_less_nat @ M5 @ N6 )
% 0.37/0.70 | ( N6 = zero_zero_nat ) )
% 0.37/0.70 @ zero_zero_nat
% 0.37/0.70 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M5 @ N6 ) @ N6 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_if
% 0.37/0.70 thf(fact_7272_div__nat__eqI,axiom,
% 0.37/0.70 ! [N: nat,Q3: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 0.37/0.70 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 0.37/0.70 => ( ( divide_divide_nat @ M @ N )
% 0.37/0.70 = Q3 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_nat_eqI
% 0.37/0.70 thf(fact_7273_split__div,axiom,
% 0.37/0.70 ! [P2: nat > $o,M: nat,N: nat] :
% 0.37/0.70 ( ( P2 @ ( divide_divide_nat @ M @ N ) )
% 0.37/0.70 = ( ( ( N = zero_zero_nat )
% 0.37/0.70 => ( P2 @ zero_zero_nat ) )
% 0.37/0.70 & ( ( N != zero_zero_nat )
% 0.37/0.70 => ! [I3: nat,J3: nat] :
% 0.37/0.70 ( ( ord_less_nat @ J3 @ N )
% 0.37/0.70 => ( ( M
% 0.37/0.70 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 0.37/0.70 => ( P2 @ I3 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % split_div
% 0.37/0.70 thf(fact_7274_dividend__less__div__times,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % dividend_less_div_times
% 0.37/0.70 thf(fact_7275_dividend__less__times__div,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % dividend_less_times_div
% 0.37/0.70 thf(fact_7276_less__eq__div__iff__mult__less__eq,axiom,
% 0.37/0.70 ! [Q3: nat,M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 0.37/0.70 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 0.37/0.70 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % less_eq_div_iff_mult_less_eq
% 0.37/0.70 thf(fact_7277_td__gal,axiom,
% 0.37/0.70 ! [C2: nat,B: nat,A: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.70 => ( ( ord_less_eq_nat @ ( times_times_nat @ B @ C2 ) @ A )
% 0.37/0.70 = ( ord_less_eq_nat @ B @ ( divide_divide_nat @ A @ C2 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % td_gal
% 0.37/0.70 thf(fact_7278_divide__nat__def,axiom,
% 0.37/0.70 ( divide_divide_nat
% 0.37/0.70 = ( ^ [M5: nat,N6: nat] :
% 0.37/0.70 ( if_nat @ ( N6 = zero_zero_nat ) @ zero_zero_nat
% 0.37/0.70 @ ( lattic8265883725875713057ax_nat
% 0.37/0.70 @ ( collect_nat
% 0.37/0.70 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N6 ) @ M5 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % divide_nat_def
% 0.37/0.70 thf(fact_7279_le__div__geq,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.70 => ( ( divide_divide_nat @ M @ N )
% 0.37/0.70 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % le_div_geq
% 0.37/0.70 thf(fact_7280_split__div_H,axiom,
% 0.37/0.70 ! [P2: nat > $o,M: nat,N: nat] :
% 0.37/0.70 ( ( P2 @ ( divide_divide_nat @ M @ N ) )
% 0.37/0.70 = ( ( ( N = zero_zero_nat )
% 0.37/0.70 & ( P2 @ zero_zero_nat ) )
% 0.37/0.70 | ? [Q8: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q8 ) @ M )
% 0.37/0.70 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q8 ) ) )
% 0.37/0.70 & ( P2 @ Q8 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % split_div'
% 0.37/0.70 thf(fact_7281_power__sub,axiom,
% 0.37/0.70 ! [N: nat,M: nat,A: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.37/0.70 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.70 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % power_sub
% 0.37/0.70 thf(fact_7282_div__pos__neg__trivial,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.37/0.70 => ( ( divide_divide_int @ K @ L )
% 0.37/0.70 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_pos_neg_trivial
% 0.37/0.70 thf(fact_7283_nat__mod__eq_H,axiom,
% 0.37/0.70 ! [A: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ A @ N )
% 0.37/0.70 => ( ( modulo_modulo_nat @ A @ N )
% 0.37/0.70 = A ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_mod_eq'
% 0.37/0.70 thf(fact_7284_mod__less,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ M @ N )
% 0.37/0.70 => ( ( modulo_modulo_nat @ M @ N )
% 0.37/0.70 = M ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_less
% 0.37/0.70 thf(fact_7285_binomial__Suc__n,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( binomial @ ( suc @ N ) @ N )
% 0.37/0.70 = ( suc @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_Suc_n
% 0.37/0.70 thf(fact_7286_mod__by__Suc__0,axiom,
% 0.37/0.70 ! [M: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.37/0.70 = zero_zero_nat ) ).
% 0.37/0.70
% 0.37/0.70 % mod_by_Suc_0
% 0.37/0.70 thf(fact_7287_binomial__1,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 0.37/0.70 = N ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_1
% 0.37/0.70 thf(fact_7288_binomial__0__Suc,axiom,
% 0.37/0.70 ! [K: nat] :
% 0.37/0.70 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 0.37/0.70 = zero_zero_nat ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_0_Suc
% 0.37/0.70 thf(fact_7289_binomial__eq__0__iff,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( ( binomial @ N @ K )
% 0.37/0.70 = zero_zero_nat )
% 0.37/0.70 = ( ord_less_nat @ N @ K ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_eq_0_iff
% 0.37/0.70 thf(fact_7290_binomial__Suc__Suc,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 0.37/0.70 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_Suc_Suc
% 0.37/0.70 thf(fact_7291_binomial__n__0,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( binomial @ N @ zero_zero_nat )
% 0.37/0.70 = one_one_nat ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_n_0
% 0.37/0.70 thf(fact_7292_Suc__mod__mult__self1,axiom,
% 0.37/0.70 ! [M: nat,K: nat,N: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_mod_mult_self1
% 0.37/0.70 thf(fact_7293_Suc__mod__mult__self2,axiom,
% 0.37/0.70 ! [M: nat,N: nat,K: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_mod_mult_self2
% 0.37/0.70 thf(fact_7294_Suc__mod__mult__self3,axiom,
% 0.37/0.70 ! [K: nat,N: nat,M: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_mod_mult_self3
% 0.37/0.70 thf(fact_7295_Suc__mod__mult__self4,axiom,
% 0.37/0.70 ! [N: nat,K: nat,M: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_mod_mult_self4
% 0.37/0.70 thf(fact_7296_zero__less__binomial__iff,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 0.37/0.70 = ( ord_less_eq_nat @ K @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % zero_less_binomial_iff
% 0.37/0.70 thf(fact_7297_mod__Suc__eq,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_Suc_eq
% 0.37/0.70 thf(fact_7298_mod__Suc__Suc__eq,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_Suc_Suc_eq
% 0.37/0.70 thf(fact_7299_nat__mod__eq,axiom,
% 0.37/0.70 ! [B: nat,N: nat,A: nat] :
% 0.37/0.70 ( ( ord_less_nat @ B @ N )
% 0.37/0.70 => ( ( ( modulo_modulo_nat @ A @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ B @ N ) )
% 0.37/0.70 => ( ( modulo_modulo_nat @ A @ N )
% 0.37/0.70 = B ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_mod_eq
% 0.37/0.70 thf(fact_7300_mod__less__eq__dividend,axiom,
% 0.37/0.70 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 0.37/0.70
% 0.37/0.70 % mod_less_eq_dividend
% 0.37/0.70 thf(fact_7301_binomial__eq__0,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( ord_less_nat @ N @ K )
% 0.37/0.70 => ( ( binomial @ N @ K )
% 0.37/0.70 = zero_zero_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_eq_0
% 0.37/0.70 thf(fact_7302_Suc__times__binomial,axiom,
% 0.37/0.70 ! [K: nat,N: nat] :
% 0.37/0.70 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 0.37/0.70 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_times_binomial
% 0.37/0.70 thf(fact_7303_Suc__times__binomial__eq,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 0.37/0.70 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_times_binomial_eq
% 0.37/0.70 thf(fact_7304_binomial__symmetric,axiom,
% 0.37/0.70 ! [K: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.70 => ( ( binomial @ N @ K )
% 0.37/0.70 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_symmetric
% 0.37/0.70 thf(fact_7305_binomial__le__pow,axiom,
% 0.37/0.70 ! [R: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ R @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_le_pow
% 0.37/0.70 thf(fact_7306_mod__Suc,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.37/0.70 = N )
% 0.37/0.70 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.37/0.70 = zero_zero_nat ) )
% 0.37/0.70 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 0.37/0.70 != N )
% 0.37/0.70 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 0.37/0.70 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_Suc
% 0.37/0.70 thf(fact_7307_mod__induct,axiom,
% 0.37/0.70 ! [P2: nat > $o,N: nat,P3: nat,M: nat] :
% 0.37/0.70 ( ( P2 @ N )
% 0.37/0.70 => ( ( ord_less_nat @ N @ P3 )
% 0.37/0.70 => ( ( ord_less_nat @ M @ P3 )
% 0.37/0.70 => ( ! [N2: nat] :
% 0.37/0.70 ( ( ord_less_nat @ N2 @ P3 )
% 0.37/0.70 => ( ( P2 @ N2 )
% 0.37/0.70 => ( P2 @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P3 ) ) ) )
% 0.37/0.70 => ( P2 @ M ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_induct
% 0.37/0.70 thf(fact_7308_gcd__nat__induct,axiom,
% 0.37/0.70 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 0.37/0.70 ( ! [M3: nat] : ( P2 @ M3 @ zero_zero_nat )
% 0.37/0.70 => ( ! [M3: nat,N2: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.37/0.70 => ( ( P2 @ N2 @ ( modulo_modulo_nat @ M3 @ N2 ) )
% 0.37/0.70 => ( P2 @ M3 @ N2 ) ) )
% 0.37/0.70 => ( P2 @ M @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % gcd_nat_induct
% 0.37/0.70 thf(fact_7309_nat__mod__lem,axiom,
% 0.37/0.70 ! [N: nat,B: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( ord_less_nat @ B @ N )
% 0.37/0.70 = ( ( modulo_modulo_nat @ B @ N )
% 0.37/0.70 = B ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_mod_lem
% 0.37/0.70 thf(fact_7310_mod__less__divisor,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_less_divisor
% 0.37/0.70 thf(fact_7311_mod__Suc__le__divisor,axiom,
% 0.37/0.70 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 0.37/0.70
% 0.37/0.70 % mod_Suc_le_divisor
% 0.37/0.70 thf(fact_7312_word__rot__lem,axiom,
% 0.37/0.70 ! [L: nat,K: nat,D: nat,N: nat] :
% 0.37/0.70 ( ( ( plus_plus_nat @ L @ K )
% 0.37/0.70 = ( plus_plus_nat @ D @ ( modulo_modulo_nat @ K @ L ) ) )
% 0.37/0.70 => ( ( ord_less_nat @ N @ L )
% 0.37/0.70 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ D @ N ) @ L )
% 0.37/0.70 = N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % word_rot_lem
% 0.37/0.70 thf(fact_7313_nat__minus__mod,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( modulo_modulo_nat @ ( minus_minus_nat @ N @ ( modulo_modulo_nat @ N @ M ) ) @ M )
% 0.37/0.70 = zero_zero_nat ) ).
% 0.37/0.70
% 0.37/0.70 % nat_minus_mod
% 0.37/0.70 thf(fact_7314_mod__geq,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ~ ( ord_less_nat @ M @ N )
% 0.37/0.70 => ( ( modulo_modulo_nat @ M @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_geq
% 0.37/0.70 thf(fact_7315_mod__if,axiom,
% 0.37/0.70 ( modulo_modulo_nat
% 0.37/0.70 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( ord_less_nat @ M5 @ N6 ) @ M5 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M5 @ N6 ) @ N6 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_if
% 0.37/0.70 thf(fact_7316_mod__nat__sub,axiom,
% 0.37/0.70 ! [X: nat,Z: nat,Y: nat] :
% 0.37/0.70 ( ( ord_less_nat @ X @ Z )
% 0.37/0.70 => ( ( modulo_modulo_nat @ ( minus_minus_nat @ X @ Y ) @ Z )
% 0.37/0.70 = ( minus_minus_nat @ X @ Y ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_nat_sub
% 0.37/0.70 thf(fact_7317_mod__eq__0D,axiom,
% 0.37/0.70 ! [M: nat,D: nat] :
% 0.37/0.70 ( ( ( modulo_modulo_nat @ M @ D )
% 0.37/0.70 = zero_zero_nat )
% 0.37/0.70 => ? [Q5: nat] :
% 0.37/0.70 ( M
% 0.37/0.70 = ( times_times_nat @ D @ Q5 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_eq_0D
% 0.37/0.70 thf(fact_7318_le__mod__geq,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.70 => ( ( modulo_modulo_nat @ M @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % le_mod_geq
% 0.37/0.70 thf(fact_7319_nat__mod__eq__iff,axiom,
% 0.37/0.70 ! [X: nat,N: nat,Y: nat] :
% 0.37/0.70 ( ( ( modulo_modulo_nat @ X @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ Y @ N ) )
% 0.37/0.70 = ( ? [Q1: nat,Q22: nat] :
% 0.37/0.70 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 0.37/0.70 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_mod_eq_iff
% 0.37/0.70 thf(fact_7320_zero__less__binomial,axiom,
% 0.37/0.70 ! [K: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.70 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zero_less_binomial
% 0.37/0.70 thf(fact_7321_Suc__times__binomial__add,axiom,
% 0.37/0.70 ! [A: nat,B: nat] :
% 0.37/0.70 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.37/0.70 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_times_binomial_add
% 0.37/0.70 thf(fact_7322_binomial__Suc__Suc__eq__times,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 0.37/0.70 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_Suc_Suc_eq_times
% 0.37/0.70 thf(fact_7323_choose__mult,axiom,
% 0.37/0.70 ! [K: nat,M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ K @ M )
% 0.37/0.70 => ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 0.37/0.70 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % choose_mult
% 0.37/0.70 thf(fact_7324_mod__le__divisor,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_le_divisor
% 0.37/0.70 thf(fact_7325_div__less__mono,axiom,
% 0.37/0.70 ! [A4: nat,B4: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ A4 @ B4 )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( ( modulo_modulo_nat @ A4 @ N )
% 0.37/0.70 = zero_zero_nat )
% 0.37/0.70 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 0.37/0.70 = zero_zero_nat )
% 0.37/0.70 => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % div_less_mono
% 0.37/0.70 thf(fact_7326_mod__nat__add,axiom,
% 0.37/0.70 ! [X: nat,Z: nat,Y: nat] :
% 0.37/0.70 ( ( ord_less_nat @ X @ Z )
% 0.37/0.70 => ( ( ord_less_nat @ Y @ Z )
% 0.37/0.70 => ( ( ( ord_less_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 0.37/0.70 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 0.37/0.70 = ( plus_plus_nat @ X @ Y ) ) )
% 0.37/0.70 & ( ~ ( ord_less_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 0.37/0.70 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 0.37/0.70 = ( minus_minus_nat @ ( plus_plus_nat @ X @ Y ) @ Z ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_nat_add
% 0.37/0.70 thf(fact_7327_nat__mod__eq__lemma,axiom,
% 0.37/0.70 ! [X: nat,N: nat,Y: nat] :
% 0.37/0.70 ( ( ( modulo_modulo_nat @ X @ N )
% 0.37/0.70 = ( modulo_modulo_nat @ Y @ N ) )
% 0.37/0.70 => ( ( ord_less_eq_nat @ Y @ X )
% 0.37/0.70 => ? [Q5: nat] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q5 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_mod_eq_lemma
% 0.37/0.70 thf(fact_7328_mod__eq__nat2E,axiom,
% 0.37/0.70 ! [M: nat,Q3: nat,N: nat] :
% 0.37/0.70 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.37/0.70 = ( modulo_modulo_nat @ N @ Q3 ) )
% 0.37/0.70 => ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ~ ! [S4: nat] :
% 0.37/0.70 ( N
% 0.37/0.70 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S4 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_eq_nat2E
% 0.37/0.70 thf(fact_7329_mod__eq__nat1E,axiom,
% 0.37/0.70 ! [M: nat,Q3: nat,N: nat] :
% 0.37/0.70 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.37/0.70 = ( modulo_modulo_nat @ N @ Q3 ) )
% 0.37/0.70 => ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.70 => ~ ! [S4: nat] :
% 0.37/0.70 ( M
% 0.37/0.70 != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S4 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_eq_nat1E
% 0.37/0.70 thf(fact_7330_sum__choose__upper,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 0.37/0.70 @ ( set_ord_atMost_nat @ N ) )
% 0.37/0.70 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % sum_choose_upper
% 0.37/0.70 thf(fact_7331_binomial__absorption,axiom,
% 0.37/0.70 ! [K: nat,N: nat] :
% 0.37/0.70 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 0.37/0.70 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_absorption
% 0.37/0.70 thf(fact_7332_split__mod,axiom,
% 0.37/0.70 ! [P2: nat > $o,M: nat,N: nat] :
% 0.37/0.70 ( ( P2 @ ( modulo_modulo_nat @ M @ N ) )
% 0.37/0.70 = ( ( ( N = zero_zero_nat )
% 0.37/0.70 => ( P2 @ M ) )
% 0.37/0.70 & ( ( N != zero_zero_nat )
% 0.37/0.70 => ! [I3: nat,J3: nat] :
% 0.37/0.70 ( ( ord_less_nat @ J3 @ N )
% 0.37/0.70 => ( ( M
% 0.37/0.70 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 0.37/0.70 => ( P2 @ J3 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % split_mod
% 0.37/0.70 thf(fact_7333_mod__lemma,axiom,
% 0.37/0.70 ! [C2: nat,R: nat,B: nat,Q3: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.70 => ( ( ord_less_nat @ R @ B )
% 0.37/0.70 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ Q3 @ C2 ) ) @ R ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_lemma
% 0.37/0.70 thf(fact_7334_sum__choose__lower,axiom,
% 0.37/0.70 ! [R: nat,N: nat] :
% 0.37/0.70 ( ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R @ K3 ) @ K3 )
% 0.37/0.70 @ ( set_ord_atMost_nat @ N ) )
% 0.37/0.70 = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % sum_choose_lower
% 0.37/0.70 thf(fact_7335_choose__reduce__nat,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.70 => ( ( binomial @ N @ K )
% 0.37/0.70 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % choose_reduce_nat
% 0.37/0.70 thf(fact_7336_times__binomial__minus1__eq,axiom,
% 0.37/0.70 ! [K: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.70 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 0.37/0.70 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % times_binomial_minus1_eq
% 0.37/0.70 thf(fact_7337_Suc__times__mod__eq,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.37/0.70 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 0.37/0.70 = one_one_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % Suc_times_mod_eq
% 0.37/0.70 thf(fact_7338_sum__choose__diagonal,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ( groups3542108847815614940at_nat
% 0.37/0.70 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 0.37/0.70 @ ( set_ord_atMost_nat @ M ) )
% 0.37/0.70 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % sum_choose_diagonal
% 0.37/0.70 thf(fact_7339_binomial__addition__formula,axiom,
% 0.37/0.70 ! [N: nat,K: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ( binomial @ N @ ( suc @ K ) )
% 0.37/0.70 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_addition_formula
% 0.37/0.70 thf(fact_7340_verit__le__mono__div,axiom,
% 0.37/0.70 ! [A4: nat,B4: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ A4 @ B4 )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ord_less_eq_nat
% 0.37/0.70 @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 0.37/0.70 @ ( if_nat
% 0.37/0.70 @ ( ( modulo_modulo_nat @ B4 @ N )
% 0.37/0.70 = zero_zero_nat )
% 0.37/0.70 @ one_one_nat
% 0.37/0.70 @ zero_zero_nat ) )
% 0.37/0.70 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % verit_le_mono_div
% 0.37/0.70 thf(fact_7341_vebt__assn__raw_Osimps_I2_J,axiom,
% 0.37/0.70 ! [Mmo: option4927543243414619207at_nat,Deg: nat,Tree_list: list_VEBT_VEBT,Summary: vEBT_VEBT,Mmoi: option4927543243414619207at_nat,Degi: nat,Tree_array: array_VEBT_VEBTi,Summaryi: vEBT_VEBTi] :
% 0.37/0.70 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ Mmo @ Deg @ Tree_list @ Summary ) @ ( vEBT_Nodei @ Mmoi @ Degi @ Tree_array @ Summaryi ) )
% 0.37/0.70 = ( times_times_assn
% 0.37/0.70 @ ( times_times_assn
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( ( Mmoi = Mmo )
% 0.37/0.70 & ( Degi = Deg ) ) )
% 0.37/0.70 @ ( vEBT_vebt_assn_raw @ Summary @ Summaryi ) )
% 0.37/0.70 @ ( ex_ass463751140784270563_VEBTi
% 0.37/0.70 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list @ Tree_is2 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_assn_raw.simps(2)
% 0.37/0.70 thf(fact_7342_upto__aux__rec,axiom,
% 0.37/0.70 ( upto_aux
% 0.37/0.70 = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % upto_aux_rec
% 0.37/0.70 thf(fact_7343_mod__neg__neg__trivial,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ L @ K )
% 0.37/0.70 => ( ( modulo_modulo_int @ K @ L )
% 0.37/0.70 = K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_neg_neg_trivial
% 0.37/0.70 thf(fact_7344_mod__pos__pos__trivial,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ( ord_less_int @ K @ L )
% 0.37/0.70 => ( ( modulo_modulo_int @ K @ L )
% 0.37/0.70 = K ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_pos_pos_trivial
% 0.37/0.70 thf(fact_7345_zmod__le__nonneg__dividend,axiom,
% 0.37/0.70 ! [M: int,K: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.37/0.70 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_le_nonneg_dividend
% 0.37/0.70 thf(fact_7346_neg__mod__bound,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ L @ zero_zero_int )
% 0.37/0.70 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % neg_mod_bound
% 0.37/0.70 thf(fact_7347_Euclidean__Division_Opos__mod__bound,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ L )
% 0.37/0.70 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 0.37/0.70
% 0.37/0.70 % Euclidean_Division.pos_mod_bound
% 0.37/0.70 thf(fact_7348_zmod__zminus2__not__zero,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 0.37/0.70 != zero_zero_int )
% 0.37/0.70 => ( ( modulo_modulo_int @ K @ L )
% 0.37/0.70 != zero_zero_int ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_zminus2_not_zero
% 0.37/0.70 thf(fact_7349_zmod__zminus1__not__zero,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.37/0.70 != zero_zero_int )
% 0.37/0.70 => ( ( modulo_modulo_int @ K @ L )
% 0.37/0.70 != zero_zero_int ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_zminus1_not_zero
% 0.37/0.70 thf(fact_7350_zmod__eq__0__iff,axiom,
% 0.37/0.70 ! [M: int,D: int] :
% 0.37/0.70 ( ( ( modulo_modulo_int @ M @ D )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 = ( ? [Q8: int] :
% 0.37/0.70 ( M
% 0.37/0.70 = ( times_times_int @ D @ Q8 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_eq_0_iff
% 0.37/0.70 thf(fact_7351_zmod__eq__0D,axiom,
% 0.37/0.70 ! [M: int,D: int] :
% 0.37/0.70 ( ( ( modulo_modulo_int @ M @ D )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 => ? [Q5: int] :
% 0.37/0.70 ( M
% 0.37/0.70 = ( times_times_int @ D @ Q5 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_eq_0D
% 0.37/0.70 thf(fact_7352_zmod__int,axiom,
% 0.37/0.70 ! [A: nat,B: nat] :
% 0.37/0.70 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 0.37/0.70 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_int
% 0.37/0.70 thf(fact_7353_int__mod__eq,axiom,
% 0.37/0.70 ! [B: int,N: int,A: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ( ord_less_int @ B @ N )
% 0.37/0.70 => ( ( ( modulo_modulo_int @ A @ N )
% 0.37/0.70 = ( modulo_modulo_int @ B @ N ) )
% 0.37/0.70 => ( ( modulo_modulo_int @ A @ N )
% 0.37/0.70 = B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_mod_eq
% 0.37/0.70 thf(fact_7354_int__mod__lem,axiom,
% 0.37/0.70 ! [N: int,B: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ N )
% 0.37/0.70 => ( ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.70 & ( ord_less_int @ B @ N ) )
% 0.37/0.70 = ( ( modulo_modulo_int @ B @ N )
% 0.37/0.70 = B ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_mod_lem
% 0.37/0.70 thf(fact_7355_neg__mod__sign,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ L @ zero_zero_int )
% 0.37/0.70 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.37/0.70
% 0.37/0.70 % neg_mod_sign
% 0.37/0.70 thf(fact_7356_Euclidean__Division_Opos__mod__sign,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ L )
% 0.37/0.70 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Euclidean_Division.pos_mod_sign
% 0.37/0.70 thf(fact_7357_int__mod__ge,axiom,
% 0.37/0.70 ! [A: int,N: int] :
% 0.37/0.70 ( ( ord_less_int @ A @ N )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ N )
% 0.37/0.70 => ( ord_less_eq_int @ A @ ( modulo_modulo_int @ A @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_mod_ge
% 0.37/0.70 thf(fact_7358_neg__mod__conj,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.37/0.70 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % neg_mod_conj
% 0.37/0.70 thf(fact_7359_pos__mod__conj,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.37/0.70 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % pos_mod_conj
% 0.37/0.70 thf(fact_7360_zmod__trivial__iff,axiom,
% 0.37/0.70 ! [I: int,K: int] :
% 0.37/0.70 ( ( ( modulo_modulo_int @ I @ K )
% 0.37/0.70 = I )
% 0.37/0.70 = ( ( K = zero_zero_int )
% 0.37/0.70 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.37/0.70 & ( ord_less_int @ I @ K ) )
% 0.37/0.70 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 0.37/0.70 & ( ord_less_int @ K @ I ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_trivial_iff
% 0.37/0.70 thf(fact_7361_int__mod__le_H,axiom,
% 0.37/0.70 ! [B: int,N: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ B @ N ) )
% 0.37/0.70 => ( ord_less_eq_int @ ( modulo_modulo_int @ B @ N ) @ ( minus_minus_int @ B @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_mod_le'
% 0.37/0.70 thf(fact_7362_zmod__zminus2__eq__if,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.37/0.70 = zero_zero_int ) )
% 0.37/0.70 & ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 != zero_zero_int )
% 0.37/0.70 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.37/0.70 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_zminus2_eq_if
% 0.37/0.70 thf(fact_7363_zmod__zminus1__eq__if,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.37/0.70 = zero_zero_int ) )
% 0.37/0.70 & ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 != zero_zero_int )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.37/0.70 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_zminus1_eq_if
% 0.37/0.70 thf(fact_7364_nonneg__mod__div,axiom,
% 0.37/0.70 ! [A: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.37/0.70 & ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nonneg_mod_div
% 0.37/0.70 thf(fact_7365_zdiv__mono__strict,axiom,
% 0.37/0.70 ! [A4: int,B4: int,N: int] :
% 0.37/0.70 ( ( ord_less_int @ A4 @ B4 )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ N )
% 0.37/0.70 => ( ( ( modulo_modulo_int @ A4 @ N )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 => ( ( ( modulo_modulo_int @ B4 @ N )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 => ( ord_less_int @ ( divide_divide_int @ A4 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_mono_strict
% 0.37/0.70 thf(fact_7366_int__mod__ge_H,axiom,
% 0.37/0.70 ! [B: int,N: int] :
% 0.37/0.70 ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ N )
% 0.37/0.70 => ( ord_less_eq_int @ ( plus_plus_int @ B @ N ) @ ( modulo_modulo_int @ B @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_mod_ge'
% 0.37/0.70 thf(fact_7367_mod__pos__neg__trivial,axiom,
% 0.37/0.70 ! [K: int,L: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.37/0.70 => ( ( modulo_modulo_int @ K @ L )
% 0.37/0.70 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_pos_neg_trivial
% 0.37/0.70 thf(fact_7368_mod__pos__geq,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ L )
% 0.37/0.70 => ( ( ord_less_eq_int @ L @ K )
% 0.37/0.70 => ( ( modulo_modulo_int @ K @ L )
% 0.37/0.70 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_pos_geq
% 0.37/0.70 thf(fact_7369_mod__power__lem,axiom,
% 0.37/0.70 ! [A: int,M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_int @ one_one_int @ A )
% 0.37/0.70 => ( ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ M ) )
% 0.37/0.70 = zero_zero_int ) )
% 0.37/0.70 & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ M ) )
% 0.37/0.70 = ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_power_lem
% 0.37/0.70 thf(fact_7370_split__zmod,axiom,
% 0.37/0.70 ! [P2: int > $o,N: int,K: int] :
% 0.37/0.70 ( ( P2 @ ( modulo_modulo_int @ N @ K ) )
% 0.37/0.70 = ( ( ( K = zero_zero_int )
% 0.37/0.70 => ( P2 @ N ) )
% 0.37/0.70 & ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ! [I3: int,J3: int] :
% 0.37/0.70 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.37/0.70 & ( ord_less_int @ J3 @ K )
% 0.37/0.70 & ( N
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.37/0.70 => ( P2 @ J3 ) ) )
% 0.37/0.70 & ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.70 => ! [I3: int,J3: int] :
% 0.37/0.70 ( ( ( ord_less_int @ K @ J3 )
% 0.37/0.70 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.37/0.70 & ( N
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.37/0.70 => ( P2 @ J3 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % split_zmod
% 0.37/0.70 thf(fact_7371_int__mod__neg__eq,axiom,
% 0.37/0.70 ! [A: int,B: int,Q3: int,R: int] :
% 0.37/0.70 ( ( A
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.37/0.70 => ( ( ord_less_int @ B @ R )
% 0.37/0.70 => ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 = R ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_mod_neg_eq
% 0.37/0.70 thf(fact_7372_int__mod__pos__eq,axiom,
% 0.37/0.70 ! [A: int,B: int,Q3: int,R: int] :
% 0.37/0.70 ( ( A
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.37/0.70 => ( ( ord_less_int @ R @ B )
% 0.37/0.70 => ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 = R ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % int_mod_pos_eq
% 0.37/0.70 thf(fact_7373_minus__mod__int__eq,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.37/0.70 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % minus_mod_int_eq
% 0.37/0.70 thf(fact_7374_zmod__minus1,axiom,
% 0.37/0.70 ! [B: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.37/0.70 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_minus1
% 0.37/0.70 thf(fact_7375_mod__add__if__z,axiom,
% 0.37/0.70 ! [X: int,Z: int,Y: int] :
% 0.37/0.70 ( ( ord_less_int @ X @ Z )
% 0.37/0.70 => ( ( ord_less_int @ Y @ Z )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.70 => ( ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 0.37/0.70 = ( plus_plus_int @ X @ Y ) ) )
% 0.37/0.70 & ( ~ ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 0.37/0.70 = ( minus_minus_int @ ( plus_plus_int @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_add_if_z
% 0.37/0.70 thf(fact_7376_mod__sub__if__z,axiom,
% 0.37/0.70 ! [X: int,Z: int,Y: int] :
% 0.37/0.70 ( ( ord_less_int @ X @ Z )
% 0.37/0.70 => ( ( ord_less_int @ Y @ Z )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.70 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.70 => ( ( ( ord_less_eq_int @ Y @ X )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( minus_minus_int @ X @ Y ) @ Z )
% 0.37/0.70 = ( minus_minus_int @ X @ Y ) ) )
% 0.37/0.70 & ( ~ ( ord_less_eq_int @ Y @ X )
% 0.37/0.70 => ( ( modulo_modulo_int @ ( minus_minus_int @ X @ Y ) @ Z )
% 0.37/0.70 = ( plus_plus_int @ ( minus_minus_int @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % mod_sub_if_z
% 0.37/0.70 thf(fact_7377_zmod__zmult2__eq,axiom,
% 0.37/0.70 ! [C2: int,A: int,B: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.37/0.70 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zmod_zmult2_eq
% 0.37/0.70 thf(fact_7378_zdiv__zminus1__eq__if,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( B != zero_zero_int )
% 0.37/0.70 => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.37/0.70 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.37/0.70 & ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 != zero_zero_int )
% 0.37/0.70 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.37/0.70 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_zminus1_eq_if
% 0.37/0.70 thf(fact_7379_zdiv__zminus2__eq__if,axiom,
% 0.37/0.70 ! [B: int,A: int] :
% 0.37/0.70 ( ( B != zero_zero_int )
% 0.37/0.70 => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.37/0.70 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.37/0.70 & ( ( ( modulo_modulo_int @ A @ B )
% 0.37/0.70 != zero_zero_int )
% 0.37/0.70 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.37/0.70 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zdiv_zminus2_eq_if
% 0.37/0.70 thf(fact_7380_verit__le__mono__div__int,axiom,
% 0.37/0.70 ! [A4: int,B4: int,N: int] :
% 0.37/0.70 ( ( ord_less_int @ A4 @ B4 )
% 0.37/0.70 => ( ( ord_less_int @ zero_zero_int @ N )
% 0.37/0.70 => ( ord_less_eq_int
% 0.37/0.70 @ ( plus_plus_int @ ( divide_divide_int @ A4 @ N )
% 0.37/0.70 @ ( if_int
% 0.37/0.70 @ ( ( modulo_modulo_int @ B4 @ N )
% 0.37/0.70 = zero_zero_int )
% 0.37/0.70 @ one_one_int
% 0.37/0.70 @ zero_zero_int ) )
% 0.37/0.70 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % verit_le_mono_div_int
% 0.37/0.70 thf(fact_7381_split__neg__lemma,axiom,
% 0.37/0.70 ! [K: int,P2: int > int > $o,N: int] :
% 0.37/0.70 ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.70 => ( ( P2 @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.37/0.70 = ( ! [I3: int,J3: int] :
% 0.37/0.70 ( ( ( ord_less_int @ K @ J3 )
% 0.37/0.70 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 0.37/0.70 & ( N
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.37/0.70 => ( P2 @ I3 @ J3 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % split_neg_lemma
% 0.37/0.70 thf(fact_7382_split__pos__lemma,axiom,
% 0.37/0.70 ! [K: int,P2: int > int > $o,N: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.70 => ( ( P2 @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 0.37/0.70 = ( ! [I3: int,J3: int] :
% 0.37/0.70 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 0.37/0.70 & ( ord_less_int @ J3 @ K )
% 0.37/0.70 & ( N
% 0.37/0.70 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 0.37/0.70 => ( P2 @ I3 @ J3 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % split_pos_lemma
% 0.37/0.70 thf(fact_7383_vebt__assn__raw_Oelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBT,Xa2: vEBT_VEBTi,Y: assn] :
% 0.37/0.70 ( ( ( vEBT_vebt_assn_raw @ X @ Xa2 )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.70 => ! [Ai: $o,Bi: $o] :
% 0.37/0.70 ( ( Xa2
% 0.37/0.70 = ( vEBT_Leafi @ Ai @ Bi ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( pure_assn
% 0.37/0.70 @ ( ( Ai = A3 )
% 0.37/0.70 & ( Bi = B3 ) ) ) ) ) )
% 0.37/0.70 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) )
% 0.37/0.70 => ! [Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 0.37/0.70 ( ( Xa2
% 0.37/0.70 = ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( times_times_assn
% 0.37/0.70 @ ( times_times_assn
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( ( Mmoi2 = Mmo2 )
% 0.37/0.70 & ( Degi2 = Deg2 ) ) )
% 0.37/0.70 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi2 ) )
% 0.37/0.70 @ ( ex_ass463751140784270563_VEBTi
% 0.37/0.70 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array2 @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list2 @ Tree_is2 ) ) ) ) ) ) )
% 0.37/0.70 => ( ( ? [V: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) )
% 0.37/0.70 => ( ? [Vd3: $o,Ve3: $o] :
% 0.37/0.70 ( Xa2
% 0.37/0.70 = ( vEBT_Leafi @ Vd3 @ Ve3 ) )
% 0.37/0.70 => ( Y != bot_bot_assn ) ) )
% 0.37/0.70 => ~ ( ? [Vd3: $o,Ve3: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Leaf @ Vd3 @ Ve3 ) )
% 0.37/0.70 => ( ? [V: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 0.37/0.70 ( Xa2
% 0.37/0.70 = ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) )
% 0.37/0.70 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_assn_raw.elims
% 0.37/0.70 thf(fact_7384_exp__ge__one__minus__x__over__n__power__n,axiom,
% 0.37/0.70 ! [X: real,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( 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 ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_ge_one_minus_x_over_n_power_n
% 0.37/0.70 thf(fact_7385_exp__ge__one__plus__x__over__n__power__n,axiom,
% 0.37/0.70 ! [N: nat,X: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_ge_one_plus_x_over_n_power_n
% 0.37/0.70 thf(fact_7386_VEBTi_Oinject_I2_J,axiom,
% 0.37/0.70 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 0.37/0.70 ( ( ( vEBT_Leafi @ X21 @ X22 )
% 0.37/0.70 = ( vEBT_Leafi @ Y21 @ Y22 ) )
% 0.37/0.70 = ( ( X21 = Y21 )
% 0.37/0.70 & ( X22 = Y22 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBTi.inject(2)
% 0.37/0.70 thf(fact_7387_exp__less__mono,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ X @ Y )
% 0.37/0.70 => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_less_mono
% 0.37/0.70 thf(fact_7388_exp__less__cancel__iff,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 0.37/0.70 = ( ord_less_real @ X @ Y ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_less_cancel_iff
% 0.37/0.70 thf(fact_7389_exp__le__cancel__iff,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 0.37/0.70 = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_le_cancel_iff
% 0.37/0.70 thf(fact_7390_one__less__exp__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 0.37/0.70 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % one_less_exp_iff
% 0.37/0.70 thf(fact_7391_exp__less__one__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 0.37/0.70 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_less_one_iff
% 0.37/0.70 thf(fact_7392_one__le__exp__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 0.37/0.70 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % one_le_exp_iff
% 0.37/0.70 thf(fact_7393_exp__le__one__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 0.37/0.70 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_le_one_iff
% 0.37/0.70 thf(fact_7394_exp__less__cancel,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 0.37/0.70 => ( ord_less_real @ X @ Y ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_less_cancel
% 0.37/0.70 thf(fact_7395_VEBTi_Odistinct_I1_J,axiom,
% 0.37/0.70 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,X21: $o,X22: $o] :
% 0.37/0.70 ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 0.37/0.70 != ( vEBT_Leafi @ X21 @ X22 ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBTi.distinct(1)
% 0.37/0.70 thf(fact_7396_VEBTi_Oexhaust,axiom,
% 0.37/0.70 ! [Y: vEBT_VEBTi] :
% 0.37/0.70 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: array_VEBT_VEBTi,X142: vEBT_VEBTi] :
% 0.37/0.70 ( Y
% 0.37/0.70 != ( vEBT_Nodei @ X112 @ X122 @ X132 @ X142 ) )
% 0.37/0.70 => ~ ! [X212: $o,X222: $o] :
% 0.37/0.70 ( Y
% 0.37/0.70 != ( vEBT_Leafi @ X212 @ X222 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBTi.exhaust
% 0.37/0.70 thf(fact_7397_not__exp__less__zero,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 0.37/0.70
% 0.37/0.70 % not_exp_less_zero
% 0.37/0.70 thf(fact_7398_exp__gt__zero,axiom,
% 0.37/0.70 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_gt_zero
% 0.37/0.70 thf(fact_7399_exp__total,axiom,
% 0.37/0.70 ! [Y: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.70 => ? [X3: real] :
% 0.37/0.70 ( ( exp_real @ X3 )
% 0.37/0.70 = Y ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_total
% 0.37/0.70 thf(fact_7400_exp__ge__zero,axiom,
% 0.37/0.70 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_ge_zero
% 0.37/0.70 thf(fact_7401_not__exp__le__zero,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 0.37/0.70
% 0.37/0.70 % not_exp_le_zero
% 0.37/0.70 thf(fact_7402_VEBTi_Osize_I4_J,axiom,
% 0.37/0.70 ! [X21: $o,X22: $o] :
% 0.37/0.70 ( ( size_size_VEBT_VEBTi @ ( vEBT_Leafi @ X21 @ X22 ) )
% 0.37/0.70 = zero_zero_nat ) ).
% 0.37/0.70
% 0.37/0.70 % VEBTi.size(4)
% 0.37/0.70 thf(fact_7403_VEBTi_Osize__gen_I2_J,axiom,
% 0.37/0.70 ! [X21: $o,X22: $o] :
% 0.37/0.70 ( ( vEBT_size_VEBTi @ ( vEBT_Leafi @ X21 @ X22 ) )
% 0.37/0.70 = zero_zero_nat ) ).
% 0.37/0.70
% 0.37/0.70 % VEBTi.size_gen(2)
% 0.37/0.70 thf(fact_7404_exp__gt__one,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.70 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_gt_one
% 0.37/0.70 thf(fact_7405_exp__ge__add__one__self,axiom,
% 0.37/0.70 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_ge_add_one_self
% 0.37/0.70 thf(fact_7406_vebt__assn__raw_Ocases,axiom,
% 0.37/0.70 ! [X: produc3625547720036274456_VEBTi] :
% 0.37/0.70 ( ! [A3: $o,B3: $o,Ai: $o,Bi: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A3 @ B3 ) @ ( vEBT_Leafi @ Ai @ Bi ) ) )
% 0.37/0.70 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) @ ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) ) )
% 0.37/0.70 => ( ! [V: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT,Vd3: $o,Ve3: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd3 @ Ve3 ) ) )
% 0.37/0.70 => ~ ! [Vd3: $o,Ve3: $o,V: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd3 @ Ve3 ) @ ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_assn_raw.cases
% 0.37/0.70 thf(fact_7407_VEBT__internal_OminNulli_Ocases,axiom,
% 0.37/0.70 ! [X: vEBT_VEBTi] :
% 0.37/0.70 ( ( X
% 0.37/0.70 != ( vEBT_Leafi @ $false @ $false ) )
% 0.37/0.70 => ( ! [Uv: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( vEBT_Leafi @ $true @ Uv ) )
% 0.37/0.70 => ( ! [Uu: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( vEBT_Leafi @ Uu @ $true ) )
% 0.37/0.70 => ( ! [Uw: nat,Ux: array_VEBT_VEBTi,Uy: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.37/0.70 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: array_VEBT_VEBTi,Vc2: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT_internal.minNulli.cases
% 0.37/0.70 thf(fact_7408_vebt__assn__raw_Osimps_I1_J,axiom,
% 0.37/0.70 ! [A: $o,B: $o,Ai2: $o,Bi2: $o] :
% 0.37/0.70 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ A @ B ) @ ( vEBT_Leafi @ Ai2 @ Bi2 ) )
% 0.37/0.70 = ( pure_assn
% 0.37/0.70 @ ( ( Ai2 = A )
% 0.37/0.70 & ( Bi2 = B ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_assn_raw.simps(1)
% 0.37/0.70 thf(fact_7409_vebt__assn__raw_Osimps_I3_J,axiom,
% 0.37/0.70 ! [V2: option4927543243414619207at_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,Vd2: $o,Ve2: $o] :
% 0.37/0.70 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ V2 @ Va2 @ Vb @ Vc ) @ ( vEBT_Leafi @ Vd2 @ Ve2 ) )
% 0.37/0.70 = bot_bot_assn ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_assn_raw.simps(3)
% 0.37/0.70 thf(fact_7410_exp__ge__add__one__self__aux,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.70 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % exp_ge_add_one_self_aux
% 0.37/0.70 thf(fact_7411_lemma__exp__total,axiom,
% 0.37/0.70 ! [Y: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ one_one_real @ Y )
% 0.37/0.70 => ? [X3: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.37/0.70 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y @ one_one_real ) )
% 0.37/0.70 & ( ( exp_real @ X3 )
% 0.37/0.70 = Y ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % lemma_exp_total
% 0.37/0.70 thf(fact_7412_vebt__minti_Ocases,axiom,
% 0.37/0.70 ! [X: vEBT_VEBTi] :
% 0.37/0.70 ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( vEBT_Leafi @ A3 @ B3 ) )
% 0.37/0.70 => ( ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.70 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 != ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti.cases
% 0.37/0.70 thf(fact_7413_vebt__assn__def,axiom,
% 0.37/0.70 ( vEBT_Intf_vebt_assn
% 0.37/0.70 = ( ^ [N6: nat,S8: set_nat,Ti2: vEBT_VEBTi] :
% 0.37/0.70 ( ex_assn_VEBT_VEBT
% 0.37/0.70 @ ^ [T2: vEBT_VEBT] :
% 0.37/0.70 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T2 @ Ti2 )
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( ( S8
% 0.37/0.70 = ( vEBT_set_vebt @ T2 ) )
% 0.37/0.70 & ( vEBT_invar_vebt @ T2 @ N6 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_assn_def
% 0.37/0.70 thf(fact_7414_vebt__assn__raw_Opelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBT,Xa2: vEBT_VEBTi,Y: assn] :
% 0.37/0.70 ( ( ( vEBT_vebt_assn_raw @ X @ Xa2 )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ X @ Xa2 ) )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.70 => ! [Ai: $o,Bi: $o] :
% 0.37/0.70 ( ( Xa2
% 0.37/0.70 = ( vEBT_Leafi @ Ai @ Bi ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( pure_assn
% 0.37/0.70 @ ( ( Ai = A3 )
% 0.37/0.70 & ( Bi = B3 ) ) ) )
% 0.37/0.70 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A3 @ B3 ) @ ( vEBT_Leafi @ Ai @ Bi ) ) ) ) ) )
% 0.37/0.70 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) )
% 0.37/0.70 => ! [Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 0.37/0.70 ( ( Xa2
% 0.37/0.70 = ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( times_times_assn
% 0.37/0.70 @ ( times_times_assn
% 0.37/0.70 @ ( pure_assn
% 0.37/0.70 @ ( ( Mmoi2 = Mmo2 )
% 0.37/0.70 & ( Degi2 = Deg2 ) ) )
% 0.37/0.70 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi2 ) )
% 0.37/0.70 @ ( ex_ass463751140784270563_VEBTi
% 0.37/0.70 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array2 @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list2 @ Tree_is2 ) ) ) ) )
% 0.37/0.70 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) @ ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) ) ) ) ) )
% 0.37/0.70 => ( ! [V: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) )
% 0.37/0.70 => ! [Vd3: $o,Ve3: $o] :
% 0.37/0.70 ( ( Xa2
% 0.37/0.70 = ( vEBT_Leafi @ Vd3 @ Ve3 ) )
% 0.37/0.70 => ( ( Y = bot_bot_assn )
% 0.37/0.70 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd3 @ Ve3 ) ) ) ) ) )
% 0.37/0.70 => ~ ! [Vd3: $o,Ve3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leaf @ Vd3 @ Ve3 ) )
% 0.37/0.70 => ! [V: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 0.37/0.70 ( ( Xa2
% 0.37/0.70 = ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) )
% 0.37/0.70 => ( ( Y = bot_bot_assn )
% 0.37/0.70 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd3 @ Ve3 ) @ ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_assn_raw.pelims
% 0.37/0.70 thf(fact_7415_vebt__minti_Oelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 0.37/0.70 ( ( ( vEBT_vebt_minti @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leafi @ A3 @ B3 ) )
% 0.37/0.70 => ~ ( ( A3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 0.37/0.70 & ( ~ A3
% 0.37/0.70 => ( ( B3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 0.37/0.70 & ( ~ B3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) )
% 0.37/0.70 => ( ( ? [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( heap_T3487192422709364219on_nat @ none_nat ) ) )
% 0.37/0.70 => ~ ! [Mi2: nat] :
% 0.37/0.70 ( ? [Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi2 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti.elims
% 0.37/0.70 thf(fact_7416_vebt__maxti_Oelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 0.37/0.70 ( ( ( vEBT_vebt_maxti @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leafi @ A3 @ B3 ) )
% 0.37/0.70 => ~ ( ( B3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 0.37/0.70 & ( ~ B3
% 0.37/0.70 => ( ( A3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 0.37/0.70 & ( ~ A3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) )
% 0.37/0.70 => ( ( ? [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( heap_T3487192422709364219on_nat @ none_nat ) ) )
% 0.37/0.70 => ~ ! [Mi2: nat,Ma2: nat] :
% 0.37/0.70 ( ? [Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 0.37/0.70 ( X
% 0.37/0.70 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.70 => ( Y
% 0.37/0.70 != ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma2 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_maxti.elims
% 0.37/0.70 thf(fact_7417_fact__ge__self,axiom,
% 0.37/0.70 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_ge_self
% 0.37/0.70 thf(fact_7418_fact__mono__nat,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_mono_nat
% 0.37/0.70 thf(fact_7419_fact__less__mono__nat,axiom,
% 0.37/0.70 ! [M: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.70 => ( ( ord_less_nat @ M @ N )
% 0.37/0.70 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_less_mono_nat
% 0.37/0.70 thf(fact_7420_fact__ge__Suc__0__nat,axiom,
% 0.37/0.70 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_ge_Suc_0_nat
% 0.37/0.70 thf(fact_7421_fact__div__fact__le__pow,axiom,
% 0.37/0.70 ! [R: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ R @ N )
% 0.37/0.70 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_div_fact_le_pow
% 0.37/0.70 thf(fact_7422_binomial__fact__lemma,axiom,
% 0.37/0.70 ! [K: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.70 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 0.37/0.70 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_fact_lemma
% 0.37/0.70 thf(fact_7423_prod__Suc__fact,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.37/0.70 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % prod_Suc_fact
% 0.37/0.70 thf(fact_7424_prod__Suc__Suc__fact,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.37/0.70 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.37/0.70
% 0.37/0.70 % prod_Suc_Suc_fact
% 0.37/0.70 thf(fact_7425_vebt__minti_Osimps_I2_J,axiom,
% 0.37/0.70 ! [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 0.37/0.70 ( ( vEBT_vebt_minti @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti.simps(2)
% 0.37/0.70 thf(fact_7426_vebt__maxti_Osimps_I2_J,axiom,
% 0.37/0.70 ! [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 0.37/0.70 ( ( vEBT_vebt_maxti @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_maxti.simps(2)
% 0.37/0.70 thf(fact_7427_binomial__altdef__nat,axiom,
% 0.37/0.70 ! [K: nat,N: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ K @ N )
% 0.37/0.70 => ( ( binomial @ N @ K )
% 0.37/0.70 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % binomial_altdef_nat
% 0.37/0.70 thf(fact_7428_vebt__minti_Osimps_I3_J,axiom,
% 0.37/0.70 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz: vEBT_VEBTi] :
% 0.37/0.70 ( ( vEBT_vebt_minti @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti.simps(3)
% 0.37/0.70 thf(fact_7429_vebt__maxti_Osimps_I3_J,axiom,
% 0.37/0.70 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz: vEBT_VEBTi] :
% 0.37/0.70 ( ( vEBT_vebt_maxti @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_maxti.simps(3)
% 0.37/0.70 thf(fact_7430_fact__eq__fact__times,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.70 => ( ( semiri1408675320244567234ct_nat @ M )
% 0.37/0.70 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 0.37/0.70 @ ( groups708209901874060359at_nat
% 0.37/0.70 @ ^ [X4: nat] : X4
% 0.37/0.70 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_eq_fact_times
% 0.37/0.70 thf(fact_7431_vebt__maxti_Osimps_I1_J,axiom,
% 0.37/0.70 ! [B: $o,A: $o] :
% 0.37/0.70 ( ( B
% 0.37/0.70 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A @ B ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 0.37/0.70 & ( ~ B
% 0.37/0.70 => ( ( A
% 0.37/0.70 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A @ B ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 0.37/0.70 & ( ~ A
% 0.37/0.70 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A @ B ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_maxti.simps(1)
% 0.37/0.70 thf(fact_7432_vebt__minti_Osimps_I1_J,axiom,
% 0.37/0.70 ! [A: $o,B: $o] :
% 0.37/0.70 ( ( A
% 0.37/0.70 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A @ B ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 0.37/0.70 & ( ~ A
% 0.37/0.70 => ( ( B
% 0.37/0.70 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A @ B ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 0.37/0.70 & ( ~ B
% 0.37/0.70 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A @ B ) )
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti.simps(1)
% 0.37/0.70 thf(fact_7433_fact__div__fact,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.70 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.37/0.70 = ( groups708209901874060359at_nat
% 0.37/0.70 @ ^ [X4: nat] : X4
% 0.37/0.70 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_div_fact
% 0.37/0.70 thf(fact_7434_vebt__maxti_Opelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 0.37/0.70 ( ( ( vEBT_vebt_maxti @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ X )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leafi @ A3 @ B3 ) )
% 0.37/0.70 => ( ( ( B3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 0.37/0.70 & ( ~ B3
% 0.37/0.70 => ( ( A3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 0.37/0.70 & ( ~ A3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Leafi @ A3 @ B3 ) ) ) )
% 0.37/0.70 => ( ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.37/0.70 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma2 ) ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_maxti.pelims
% 0.37/0.70 thf(fact_7435_vebt__minti_Opelims,axiom,
% 0.37/0.70 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 0.37/0.70 ( ( ( vEBT_vebt_minti @ X )
% 0.37/0.70 = Y )
% 0.37/0.70 => ( ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ X )
% 0.37/0.70 => ( ! [A3: $o,B3: $o] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Leafi @ A3 @ B3 ) )
% 0.37/0.70 => ( ( ( A3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 0.37/0.70 & ( ~ A3
% 0.37/0.70 => ( ( B3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 0.37/0.70 & ( ~ B3
% 0.37/0.70 => ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Leafi @ A3 @ B3 ) ) ) )
% 0.37/0.70 => ( ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ none_nat ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 0.37/0.70 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 0.37/0.70 ( ( X
% 0.37/0.70 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.37/0.70 => ( ( Y
% 0.37/0.70 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi2 ) ) )
% 0.37/0.70 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % vebt_minti.pelims
% 0.37/0.70 thf(fact_7436_Maclaurin__lemma,axiom,
% 0.37/0.70 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.37/0.70 => ? [B8: real] :
% 0.37/0.70 ( ( F @ H2 )
% 0.37/0.70 = ( plus_plus_real
% 0.37/0.70 @ ( groups6591440286371151544t_real
% 0.37/0.70 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 0.37/0.70 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.70 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Maclaurin_lemma
% 0.37/0.70 thf(fact_7437_fact__diff__Suc,axiom,
% 0.37/0.70 ! [N: nat,M: nat] :
% 0.37/0.70 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.37/0.70 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 0.37/0.70 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % fact_diff_Suc
% 0.37/0.70 thf(fact_7438_sumr__cos__zero__one,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( groups6591440286371151544t_real
% 0.37/0.70 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ zero_zero_real @ M5 ) )
% 0.37/0.70 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.37/0.70 = one_one_real ) ).
% 0.37/0.70
% 0.37/0.70 % sumr_cos_zero_one
% 0.37/0.70 thf(fact_7439_Maclaurin__exp__lt,axiom,
% 0.37/0.70 ! [X: real,N: nat] :
% 0.37/0.70 ( ( X != zero_zero_real )
% 0.37/0.70 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.70 => ? [T6: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.37/0.70 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.70 & ( ( exp_real @ X )
% 0.37/0.70 = ( plus_plus_real
% 0.37/0.70 @ ( groups6591440286371151544t_real
% 0.37/0.70 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 0.37/0.70 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.70 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Maclaurin_exp_lt
% 0.37/0.70 thf(fact_7440_Maclaurin__exp__le,axiom,
% 0.37/0.70 ! [X: real,N: nat] :
% 0.37/0.70 ? [T6: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.70 & ( ( exp_real @ X )
% 0.37/0.70 = ( plus_plus_real
% 0.37/0.70 @ ( groups6591440286371151544t_real
% 0.37/0.70 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 0.37/0.70 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.70 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Maclaurin_exp_le
% 0.37/0.70 thf(fact_7441_Least__eq__0,axiom,
% 0.37/0.70 ! [P2: nat > $o] :
% 0.37/0.70 ( ( P2 @ zero_zero_nat )
% 0.37/0.70 => ( ( ord_Least_nat @ P2 )
% 0.37/0.70 = zero_zero_nat ) ) ).
% 0.37/0.70
% 0.37/0.70 % Least_eq_0
% 0.37/0.70 thf(fact_7442_cos__coeff__0,axiom,
% 0.37/0.70 ( ( cos_coeff @ zero_zero_nat )
% 0.37/0.70 = one_one_real ) ).
% 0.37/0.70
% 0.37/0.70 % cos_coeff_0
% 0.37/0.70 thf(fact_7443_artanh__minus__real,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.70 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 0.37/0.70 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % artanh_minus_real
% 0.37/0.70 thf(fact_7444_Least__Suc2,axiom,
% 0.37/0.70 ! [P2: nat > $o,N: nat,Q2: nat > $o,M: nat] :
% 0.37/0.70 ( ( P2 @ N )
% 0.37/0.70 => ( ( Q2 @ M )
% 0.37/0.70 => ( ~ ( P2 @ zero_zero_nat )
% 0.37/0.70 => ( ! [K2: nat] :
% 0.37/0.70 ( ( P2 @ ( suc @ K2 ) )
% 0.37/0.70 = ( Q2 @ K2 ) )
% 0.37/0.70 => ( ( ord_Least_nat @ P2 )
% 0.37/0.70 = ( suc @ ( ord_Least_nat @ Q2 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Least_Suc2
% 0.37/0.70 thf(fact_7445_Least__Suc,axiom,
% 0.37/0.70 ! [P2: nat > $o,N: nat] :
% 0.37/0.70 ( ( P2 @ N )
% 0.37/0.70 => ( ~ ( P2 @ zero_zero_nat )
% 0.37/0.70 => ( ( ord_Least_nat @ P2 )
% 0.37/0.70 = ( suc
% 0.37/0.70 @ ( ord_Least_nat
% 0.37/0.70 @ ^ [M5: nat] : ( P2 @ ( suc @ M5 ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % Least_Suc
% 0.37/0.70 thf(fact_7446_abs__real__def,axiom,
% 0.37/0.70 ( abs_abs_real
% 0.37/0.70 = ( ^ [A7: real] : ( if_real @ ( ord_less_real @ A7 @ zero_zero_real ) @ ( uminus_uminus_real @ A7 ) @ A7 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % abs_real_def
% 0.37/0.70 thf(fact_7447_sin__bound__lemma,axiom,
% 0.37/0.70 ! [X: real,Y: real,U: real,V2: real] :
% 0.37/0.70 ( ( X = Y )
% 0.37/0.70 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V2 )
% 0.37/0.70 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V2 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % sin_bound_lemma
% 0.37/0.70 thf(fact_7448_lemma__interval,axiom,
% 0.37/0.70 ! [A: real,X: real,B: real] :
% 0.37/0.70 ( ( ord_less_real @ A @ X )
% 0.37/0.70 => ( ( ord_less_real @ X @ B )
% 0.37/0.70 => ? [D2: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.70 & ! [Y5: real] :
% 0.37/0.70 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D2 )
% 0.37/0.70 => ( ( ord_less_eq_real @ A @ Y5 )
% 0.37/0.70 & ( ord_less_eq_real @ Y5 @ B ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % lemma_interval
% 0.37/0.70 thf(fact_7449_lemma__interval__lt,axiom,
% 0.37/0.70 ! [A: real,X: real,B: real] :
% 0.37/0.70 ( ( ord_less_real @ A @ X )
% 0.37/0.70 => ( ( ord_less_real @ X @ B )
% 0.37/0.70 => ? [D2: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.70 & ! [Y5: real] :
% 0.37/0.70 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D2 )
% 0.37/0.70 => ( ( ord_less_real @ A @ Y5 )
% 0.37/0.70 & ( ord_less_real @ Y5 @ B ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % lemma_interval_lt
% 0.37/0.70 thf(fact_7450_set__vebt__succ_H,axiom,
% 0.37/0.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.70 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.70 => ( ( ? [X5: nat] :
% 0.37/0.70 ( ( member_nat @ X5 @ ( vEBT_set_vebt @ T ) )
% 0.37/0.70 & ( ord_less_nat @ X @ X5 ) )
% 0.37/0.70 => ( ( vEBT_vebt_succ @ T @ X )
% 0.37/0.70 = ( some_nat
% 0.37/0.70 @ ( ord_Least_nat
% 0.37/0.70 @ ^ [Y4: nat] :
% 0.37/0.70 ( ( member_nat @ Y4 @ ( vEBT_set_vebt @ T ) )
% 0.37/0.70 & ( ord_less_nat @ X @ Y4 ) ) ) ) ) )
% 0.37/0.70 & ( ~ ? [X3: nat] :
% 0.37/0.70 ( ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) )
% 0.37/0.70 & ( ord_less_nat @ X @ X3 ) )
% 0.37/0.70 => ( ( vEBT_vebt_succ @ T @ X )
% 0.37/0.70 = none_nat ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % set_vebt_succ'
% 0.37/0.70 thf(fact_7451_arctan__add,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.70 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.70 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 0.37/0.70 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % arctan_add
% 0.37/0.70 thf(fact_7452_cos__coeff__Suc,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( cos_coeff @ ( suc @ N ) )
% 0.37/0.70 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % cos_coeff_Suc
% 0.37/0.70 thf(fact_7453_zabs__less__one__iff,axiom,
% 0.37/0.70 ! [Z: int] :
% 0.37/0.70 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 0.37/0.70 = ( Z = zero_zero_int ) ) ).
% 0.37/0.70
% 0.37/0.70 % zabs_less_one_iff
% 0.37/0.70 thf(fact_7454_zero__less__arctan__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 0.37/0.70 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % zero_less_arctan_iff
% 0.37/0.70 thf(fact_7455_arctan__less__zero__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 0.37/0.70 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.37/0.70
% 0.37/0.70 % arctan_less_zero_iff
% 0.37/0.70 thf(fact_7456_zero__le__arctan__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 0.37/0.70 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.37/0.70
% 0.37/0.70 % zero_le_arctan_iff
% 0.37/0.70 thf(fact_7457_arctan__le__zero__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 0.37/0.70 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.37/0.70
% 0.37/0.70 % arctan_le_zero_iff
% 0.37/0.70 thf(fact_7458_sin__coeff__0,axiom,
% 0.37/0.70 ( ( sin_coeff @ zero_zero_nat )
% 0.37/0.70 = zero_zero_real ) ).
% 0.37/0.70
% 0.37/0.70 % sin_coeff_0
% 0.37/0.70 thf(fact_7459_set__vebt__pred_H,axiom,
% 0.37/0.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.70 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.70 => ( ( ? [X5: nat] :
% 0.37/0.70 ( ( member_nat @ X5 @ ( vEBT_set_vebt @ T ) )
% 0.37/0.70 & ( ord_less_nat @ X5 @ X ) )
% 0.37/0.70 => ( ( vEBT_vebt_pred @ T @ X )
% 0.37/0.70 = ( some_nat
% 0.37/0.70 @ ( order_Greatest_nat
% 0.37/0.70 @ ^ [Y4: nat] :
% 0.37/0.70 ( ( member_nat @ Y4 @ ( vEBT_set_vebt @ T ) )
% 0.37/0.70 & ( ord_less_nat @ Y4 @ X ) ) ) ) ) )
% 0.37/0.70 & ( ~ ? [X3: nat] :
% 0.37/0.70 ( ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) )
% 0.37/0.70 & ( ord_less_nat @ X3 @ X ) )
% 0.37/0.70 => ( ( vEBT_vebt_pred @ T @ X )
% 0.37/0.70 = none_nat ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % set_vebt_pred'
% 0.37/0.70 thf(fact_7460_arctan__less__iff,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 0.37/0.70 = ( ord_less_real @ X @ Y ) ) ).
% 0.37/0.70
% 0.37/0.70 % arctan_less_iff
% 0.37/0.70 thf(fact_7461_arctan__monotone,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ X @ Y )
% 0.37/0.70 => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % arctan_monotone
% 0.37/0.70 thf(fact_7462_arctan__monotone_H,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.70 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % arctan_monotone'
% 0.37/0.70 thf(fact_7463_arctan__le__iff,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 0.37/0.70 = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.70
% 0.37/0.70 % arctan_le_iff
% 0.37/0.70 thf(fact_7464_finite__int__iff__bounded__le,axiom,
% 0.37/0.70 ( finite_finite_int
% 0.37/0.70 = ( ^ [S6: set_int] :
% 0.37/0.70 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_int_iff_bounded_le
% 0.37/0.70 thf(fact_7465_finite__int__iff__bounded,axiom,
% 0.37/0.70 ( finite_finite_int
% 0.37/0.70 = ( ^ [S6: set_int] :
% 0.37/0.70 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % finite_int_iff_bounded
% 0.37/0.70 thf(fact_7466_infinite__int__iff__unbounded__le,axiom,
% 0.37/0.70 ! [S3: set_int] :
% 0.37/0.70 ( ( ~ ( finite_finite_int @ S3 ) )
% 0.37/0.70 = ( ! [M5: int] :
% 0.37/0.70 ? [N6: int] :
% 0.37/0.70 ( ( ord_less_eq_int @ M5 @ ( abs_abs_int @ N6 ) )
% 0.37/0.70 & ( member_int @ N6 @ S3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % infinite_int_iff_unbounded_le
% 0.37/0.70 thf(fact_7467_infinite__int__iff__unbounded,axiom,
% 0.37/0.70 ! [S3: set_int] :
% 0.37/0.70 ( ( ~ ( finite_finite_int @ S3 ) )
% 0.37/0.70 = ( ! [M5: int] :
% 0.37/0.70 ? [N6: int] :
% 0.37/0.70 ( ( ord_less_int @ M5 @ ( abs_abs_int @ N6 ) )
% 0.37/0.70 & ( member_int @ N6 @ S3 ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % infinite_int_iff_unbounded
% 0.37/0.70 thf(fact_7468_zabs__def,axiom,
% 0.37/0.70 ( abs_abs_int
% 0.37/0.70 = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % zabs_def
% 0.37/0.70 thf(fact_7469_abs__mod__less,axiom,
% 0.37/0.70 ! [L: int,K: int] :
% 0.37/0.70 ( ( L != zero_zero_int )
% 0.37/0.70 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % abs_mod_less
% 0.37/0.70 thf(fact_7470_nat__intermed__int__val,axiom,
% 0.37/0.70 ! [M: nat,N: nat,F: nat > int,K: int] :
% 0.37/0.70 ( ! [I2: nat] :
% 0.37/0.70 ( ( ( ord_less_eq_nat @ M @ I2 )
% 0.37/0.70 & ( ord_less_nat @ I2 @ N ) )
% 0.37/0.70 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 0.37/0.70 => ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.70 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.37/0.70 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.37/0.70 => ? [I2: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ M @ I2 )
% 0.37/0.70 & ( ord_less_eq_nat @ I2 @ N )
% 0.37/0.70 & ( ( F @ I2 )
% 0.37/0.70 = K ) ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_intermed_int_val
% 0.37/0.70 thf(fact_7471_incr__lemma,axiom,
% 0.37/0.70 ! [D: int,Z: int,X: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D )
% 0.37/0.70 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % incr_lemma
% 0.37/0.70 thf(fact_7472_decr__lemma,axiom,
% 0.37/0.70 ! [D: int,X: int,Z: int] :
% 0.37/0.70 ( ( ord_less_int @ zero_zero_int @ D )
% 0.37/0.70 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 0.37/0.70
% 0.37/0.70 % decr_lemma
% 0.37/0.70 thf(fact_7473_nat__ivt__aux,axiom,
% 0.37/0.70 ! [N: nat,F: nat > int,K: int] :
% 0.37/0.70 ( ! [I2: nat] :
% 0.37/0.70 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.70 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.37/0.70 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.37/0.70 => ? [I2: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ I2 @ N )
% 0.37/0.70 & ( ( F @ I2 )
% 0.37/0.70 = K ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat_ivt_aux
% 0.37/0.70 thf(fact_7474_sin__coeff__Suc,axiom,
% 0.37/0.70 ! [N: nat] :
% 0.37/0.70 ( ( sin_coeff @ ( suc @ N ) )
% 0.37/0.70 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % sin_coeff_Suc
% 0.37/0.70 thf(fact_7475_nat0__intermed__int__val,axiom,
% 0.37/0.70 ! [N: nat,F: nat > int,K: int] :
% 0.37/0.70 ( ! [I2: nat] :
% 0.37/0.70 ( ( ord_less_nat @ I2 @ N )
% 0.37/0.70 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 0.37/0.70 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.37/0.70 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.37/0.70 => ? [I2: nat] :
% 0.37/0.70 ( ( ord_less_eq_nat @ I2 @ N )
% 0.37/0.70 & ( ( F @ I2 )
% 0.37/0.70 = K ) ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % nat0_intermed_int_val
% 0.37/0.70 thf(fact_7476_VEBT_Osize_I3_J,axiom,
% 0.37/0.70 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.37/0.70 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.37/0.70 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT.size(3)
% 0.37/0.70 thf(fact_7477_VEBT_Osize__gen_I1_J,axiom,
% 0.37/0.70 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.37/0.70 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.37/0.70 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % VEBT.size_gen(1)
% 0.37/0.70 thf(fact_7478_ln__inj__iff,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.70 => ( ( ( ln_ln_real @ X )
% 0.37/0.70 = ( ln_ln_real @ Y ) )
% 0.37/0.70 = ( X = Y ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % ln_inj_iff
% 0.37/0.70 thf(fact_7479_ln__less__cancel__iff,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.70 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 0.37/0.70 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % ln_less_cancel_iff
% 0.37/0.70 thf(fact_7480_ln__le__cancel__iff,axiom,
% 0.37/0.70 ! [X: real,Y: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.70 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 0.37/0.70 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % ln_le_cancel_iff
% 0.37/0.70 thf(fact_7481_ln__eq__zero__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.70 => ( ( ( ln_ln_real @ X )
% 0.37/0.70 = zero_zero_real )
% 0.37/0.70 = ( X = one_one_real ) ) ) ).
% 0.37/0.70
% 0.37/0.70 % ln_eq_zero_iff
% 0.37/0.70 thf(fact_7482_ln__gt__zero__iff,axiom,
% 0.37/0.70 ! [X: real] :
% 0.37/0.70 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.37/0.71 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_gt_zero_iff
% 0.37/0.71 thf(fact_7483_ln__less__zero__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_less_zero_iff
% 0.37/0.71 thf(fact_7484_exp__ln,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 0.37/0.71 = X ) ) ).
% 0.37/0.71
% 0.37/0.71 % exp_ln
% 0.37/0.71 thf(fact_7485_exp__ln__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 0.37/0.71 = X )
% 0.37/0.71 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % exp_ln_iff
% 0.37/0.71 thf(fact_7486_ln__ge__zero__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.37/0.71 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_ge_zero_iff
% 0.37/0.71 thf(fact_7487_ln__le__zero__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_le_zero_iff
% 0.37/0.71 thf(fact_7488_ln__less__self,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_less_self
% 0.37/0.71 thf(fact_7489_GreatestI__ex__nat,axiom,
% 0.37/0.71 ! [P2: nat > $o,B: nat] :
% 0.37/0.71 ( ? [X_12: nat] : ( P2 @ X_12 )
% 0.37/0.71 => ( ! [Y3: nat] :
% 0.37/0.71 ( ( P2 @ Y3 )
% 0.37/0.71 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.37/0.71 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % GreatestI_ex_nat
% 0.37/0.71 thf(fact_7490_Greatest__le__nat,axiom,
% 0.37/0.71 ! [P2: nat > $o,K: nat,B: nat] :
% 0.37/0.71 ( ( P2 @ K )
% 0.37/0.71 => ( ! [Y3: nat] :
% 0.37/0.71 ( ( P2 @ Y3 )
% 0.37/0.71 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.37/0.71 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Greatest_le_nat
% 0.37/0.71 thf(fact_7491_GreatestI__nat,axiom,
% 0.37/0.71 ! [P2: nat > $o,K: nat,B: nat] :
% 0.37/0.71 ( ( P2 @ K )
% 0.37/0.71 => ( ! [Y3: nat] :
% 0.37/0.71 ( ( P2 @ Y3 )
% 0.37/0.71 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.37/0.71 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % GreatestI_nat
% 0.37/0.71 thf(fact_7492_ln__bound,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_bound
% 0.37/0.71 thf(fact_7493_ln__gt__zero,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_gt_zero
% 0.37/0.71 thf(fact_7494_ln__less__zero,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.71 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_less_zero
% 0.37/0.71 thf(fact_7495_ln__gt__zero__imp__gt__one,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_gt_zero_imp_gt_one
% 0.37/0.71 thf(fact_7496_ln__ge__zero,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_ge_zero
% 0.37/0.71 thf(fact_7497_ln__ge__zero__imp__ge__one,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_ge_zero_imp_ge_one
% 0.37/0.71 thf(fact_7498_ln__add__one__self__le__self,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_add_one_self_le_self
% 0.37/0.71 thf(fact_7499_ln__mult,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 0.37/0.71 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_mult
% 0.37/0.71 thf(fact_7500_ln__eq__minus__one,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ( ln_ln_real @ X )
% 0.37/0.71 = ( minus_minus_real @ X @ one_one_real ) )
% 0.37/0.71 => ( X = one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_eq_minus_one
% 0.37/0.71 thf(fact_7501_ln__div,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 0.37/0.71 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_div
% 0.37/0.71 thf(fact_7502_ln__ge__iff,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 0.37/0.71 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_ge_iff
% 0.37/0.71 thf(fact_7503_ln__x__over__x__mono,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.71 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_x_over_x_mono
% 0.37/0.71 thf(fact_7504_ln__le__minus__one,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_le_minus_one
% 0.37/0.71 thf(fact_7505_ln__diff__le,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_diff_le
% 0.37/0.71 thf(fact_7506_ln__add__one__self__le__self2,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_add_one_self_le_self2
% 0.37/0.71 thf(fact_7507_ln__realpow,axiom,
% 0.37/0.71 ! [X: real,N: nat] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 0.37/0.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_realpow
% 0.37/0.71 thf(fact_7508_ln__one__minus__pos__upper__bound,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.71 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_one_minus_pos_upper_bound
% 0.37/0.71 thf(fact_7509_upto_Opinduct,axiom,
% 0.37/0.71 ! [A0: int,A12: int,P2: int > int > $o] :
% 0.37/0.71 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 0.37/0.71 => ( ! [I2: int,J2: int] :
% 0.37/0.71 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 0.37/0.71 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 0.37/0.71 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 0.37/0.71 => ( P2 @ I2 @ J2 ) ) )
% 0.37/0.71 => ( P2 @ A0 @ A12 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto.pinduct
% 0.37/0.71 thf(fact_7510_card__length__sum__list__rec,axiom,
% 0.37/0.71 ! [M: nat,N8: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.37/0.71 => ( ( finite_card_list_nat
% 0.37/0.71 @ ( collect_list_nat
% 0.37/0.71 @ ^ [L4: list_nat] :
% 0.37/0.71 ( ( ( size_size_list_nat @ L4 )
% 0.37/0.71 = M )
% 0.37/0.71 & ( ( groups4561878855575611511st_nat @ L4 )
% 0.37/0.71 = N8 ) ) ) )
% 0.37/0.71 = ( plus_plus_nat
% 0.37/0.71 @ ( finite_card_list_nat
% 0.37/0.71 @ ( collect_list_nat
% 0.37/0.71 @ ^ [L4: list_nat] :
% 0.37/0.71 ( ( ( size_size_list_nat @ L4 )
% 0.37/0.71 = ( minus_minus_nat @ M @ one_one_nat ) )
% 0.37/0.71 & ( ( groups4561878855575611511st_nat @ L4 )
% 0.37/0.71 = N8 ) ) ) )
% 0.37/0.71 @ ( finite_card_list_nat
% 0.37/0.71 @ ( collect_list_nat
% 0.37/0.71 @ ^ [L4: list_nat] :
% 0.37/0.71 ( ( ( size_size_list_nat @ L4 )
% 0.37/0.71 = M )
% 0.37/0.71 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L4 ) @ one_one_nat )
% 0.37/0.71 = N8 ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % card_length_sum_list_rec
% 0.37/0.71 thf(fact_7511_eucl__rel__int__iff,axiom,
% 0.37/0.71 ! [K: int,L: int,Q3: int,R: int] :
% 0.37/0.71 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.71 = ( ( K
% 0.37/0.71 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R ) )
% 0.37/0.71 & ( ( ord_less_int @ zero_zero_int @ L )
% 0.37/0.71 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.37/0.71 & ( ord_less_int @ R @ L ) ) )
% 0.37/0.71 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.37/0.71 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.37/0.71 => ( ( ord_less_int @ L @ R )
% 0.37/0.71 & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 0.37/0.71 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.37/0.71 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % eucl_rel_int_iff
% 0.37/0.71 thf(fact_7512_bezw__0,axiom,
% 0.37/0.71 ! [X: nat] :
% 0.37/0.71 ( ( bezw @ X @ zero_zero_nat )
% 0.37/0.71 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.37/0.71
% 0.37/0.71 % bezw_0
% 0.37/0.71 thf(fact_7513_unique__quotient,axiom,
% 0.37/0.71 ! [A: int,B: int,Q3: int,R: int,Q7: int,R6: int] :
% 0.37/0.71 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.71 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q7 @ R6 ) )
% 0.37/0.71 => ( Q3 = Q7 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % unique_quotient
% 0.37/0.71 thf(fact_7514_unique__remainder,axiom,
% 0.37/0.71 ! [A: int,B: int,Q3: int,R: int,Q7: int,R6: int] :
% 0.37/0.71 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.71 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q7 @ R6 ) )
% 0.37/0.71 => ( R = R6 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % unique_remainder
% 0.37/0.71 thf(fact_7515_eucl__rel__int__by0,axiom,
% 0.37/0.71 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.37/0.71
% 0.37/0.71 % eucl_rel_int_by0
% 0.37/0.71 thf(fact_7516_mod__int__unique,axiom,
% 0.37/0.71 ! [K: int,L: int,Q3: int,R: int] :
% 0.37/0.71 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.71 => ( ( modulo_modulo_int @ K @ L )
% 0.37/0.71 = R ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_int_unique
% 0.37/0.71 thf(fact_7517_div__int__unique,axiom,
% 0.37/0.71 ! [K: int,L: int,Q3: int,R: int] :
% 0.37/0.71 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.71 => ( ( divide_divide_int @ K @ L )
% 0.37/0.71 = Q3 ) ) ).
% 0.37/0.71
% 0.37/0.71 % div_int_unique
% 0.37/0.71 thf(fact_7518_eucl__rel__int__dividesI,axiom,
% 0.37/0.71 ! [L: int,K: int,Q3: int] :
% 0.37/0.71 ( ( L != zero_zero_int )
% 0.37/0.71 => ( ( K
% 0.37/0.71 = ( times_times_int @ Q3 @ L ) )
% 0.37/0.71 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % eucl_rel_int_dividesI
% 0.37/0.71 thf(fact_7519_eucl__rel__int,axiom,
% 0.37/0.71 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % eucl_rel_int
% 0.37/0.71 thf(fact_7520_zminus1__lemma,axiom,
% 0.37/0.71 ! [A: int,B: int,Q3: int,R: int] :
% 0.37/0.71 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.71 => ( ( B != zero_zero_int )
% 0.37/0.71 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % zminus1_lemma
% 0.37/0.71 thf(fact_7521_finite__enumerate,axiom,
% 0.37/0.71 ! [S3: set_nat] :
% 0.37/0.71 ( ( finite_finite_nat @ S3 )
% 0.37/0.71 => ? [R4: nat > nat] :
% 0.37/0.71 ( ( strict1292158309912662752at_nat @ R4 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 0.37/0.71 & ! [N9: nat] :
% 0.37/0.71 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S3 ) )
% 0.37/0.71 => ( member_nat @ ( R4 @ N9 ) @ S3 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % finite_enumerate
% 0.37/0.71 thf(fact_7522_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.37/0.71 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.37/0.71 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 0.37/0.71 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 0.37/0.71
% 0.37/0.71 % max_nat.semilattice_neutr_order_axioms
% 0.37/0.71 thf(fact_7523_Suc__funpow,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( compow_nat_nat @ N @ suc )
% 0.37/0.71 = ( plus_plus_nat @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_funpow
% 0.37/0.71 thf(fact_7524_eucl__rel__int_Osimps,axiom,
% 0.37/0.71 ( eucl_rel_int
% 0.37/0.71 = ( ^ [A13: int,A24: int,A32: product_prod_int_int] :
% 0.37/0.71 ( ? [K3: int] :
% 0.37/0.71 ( ( A13 = K3 )
% 0.37/0.71 & ( A24 = zero_zero_int )
% 0.37/0.71 & ( A32
% 0.37/0.71 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 0.37/0.71 | ? [L4: int,K3: int,Q8: int] :
% 0.37/0.71 ( ( A13 = K3 )
% 0.37/0.71 & ( A24 = L4 )
% 0.37/0.71 & ( A32
% 0.37/0.71 = ( product_Pair_int_int @ Q8 @ zero_zero_int ) )
% 0.37/0.71 & ( L4 != zero_zero_int )
% 0.37/0.71 & ( K3
% 0.37/0.71 = ( times_times_int @ Q8 @ L4 ) ) )
% 0.37/0.71 | ? [R5: int,L4: int,K3: int,Q8: int] :
% 0.37/0.71 ( ( A13 = K3 )
% 0.37/0.71 & ( A24 = L4 )
% 0.37/0.71 & ( A32
% 0.37/0.71 = ( product_Pair_int_int @ Q8 @ R5 ) )
% 0.37/0.71 & ( ( sgn_sgn_int @ R5 )
% 0.37/0.71 = ( sgn_sgn_int @ L4 ) )
% 0.37/0.71 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L4 ) )
% 0.37/0.71 & ( K3
% 0.37/0.71 = ( plus_plus_int @ ( times_times_int @ Q8 @ L4 ) @ R5 ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % eucl_rel_int.simps
% 0.37/0.71 thf(fact_7525_eucl__rel__int_Ocases,axiom,
% 0.37/0.71 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 0.37/0.71 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 0.37/0.71 => ( ( ( A23 = zero_zero_int )
% 0.37/0.71 => ( A33
% 0.37/0.71 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 0.37/0.71 => ( ! [Q5: int] :
% 0.37/0.71 ( ( A33
% 0.37/0.71 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.37/0.71 => ( ( A23 != zero_zero_int )
% 0.37/0.71 => ( A12
% 0.37/0.71 != ( times_times_int @ Q5 @ A23 ) ) ) )
% 0.37/0.71 => ~ ! [R4: int,Q5: int] :
% 0.37/0.71 ( ( A33
% 0.37/0.71 = ( product_Pair_int_int @ Q5 @ R4 ) )
% 0.37/0.71 => ( ( ( sgn_sgn_int @ R4 )
% 0.37/0.71 = ( sgn_sgn_int @ A23 ) )
% 0.37/0.71 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ A23 ) )
% 0.37/0.71 => ( A12
% 0.37/0.71 != ( plus_plus_int @ ( times_times_int @ Q5 @ A23 ) @ R4 ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % eucl_rel_int.cases
% 0.37/0.71 thf(fact_7526_div__eq__sgn__abs,axiom,
% 0.37/0.71 ! [K: int,L: int] :
% 0.37/0.71 ( ( ( sgn_sgn_int @ K )
% 0.37/0.71 = ( sgn_sgn_int @ L ) )
% 0.37/0.71 => ( ( divide_divide_int @ K @ L )
% 0.37/0.71 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % div_eq_sgn_abs
% 0.37/0.71 thf(fact_7527_zsgn__def,axiom,
% 0.37/0.71 ( sgn_sgn_int
% 0.37/0.71 = ( ^ [I3: int] : ( if_int @ ( I3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % zsgn_def
% 0.37/0.71 thf(fact_7528_div__sgn__abs__cancel,axiom,
% 0.37/0.71 ! [V2: int,K: int,L: int] :
% 0.37/0.71 ( ( V2 != zero_zero_int )
% 0.37/0.71 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ L ) ) )
% 0.37/0.71 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % div_sgn_abs_cancel
% 0.37/0.71 thf(fact_7529_eucl__rel__int__remainderI,axiom,
% 0.37/0.71 ! [R: int,L: int,K: int,Q3: int] :
% 0.37/0.71 ( ( ( sgn_sgn_int @ R )
% 0.37/0.71 = ( sgn_sgn_int @ L ) )
% 0.37/0.71 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L ) )
% 0.37/0.71 => ( ( K
% 0.37/0.71 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R ) )
% 0.37/0.71 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % eucl_rel_int_remainderI
% 0.37/0.71 thf(fact_7530_sinh__real__less__iff,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 0.37/0.71 = ( ord_less_real @ X @ Y ) ) ).
% 0.37/0.71
% 0.37/0.71 % sinh_real_less_iff
% 0.37/0.71 thf(fact_7531_sinh__real__le__iff,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 0.37/0.71 = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.71
% 0.37/0.71 % sinh_real_le_iff
% 0.37/0.71 thf(fact_7532_sinh__real__pos__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 0.37/0.71 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % sinh_real_pos_iff
% 0.37/0.71 thf(fact_7533_sinh__real__neg__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % sinh_real_neg_iff
% 0.37/0.71 thf(fact_7534_sgn__le__0__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % sgn_le_0_iff
% 0.37/0.71 thf(fact_7535_zero__le__sgn__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 0.37/0.71 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % zero_le_sgn_iff
% 0.37/0.71 thf(fact_7536_sinh__real__nonpos__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % sinh_real_nonpos_iff
% 0.37/0.71 thf(fact_7537_sinh__real__nonneg__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 0.37/0.71 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % sinh_real_nonneg_iff
% 0.37/0.71 thf(fact_7538_sgn__real__def,axiom,
% 0.37/0.71 ( sgn_sgn_real
% 0.37/0.71 = ( ^ [A7: real] : ( if_real @ ( A7 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A7 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sgn_real_def
% 0.37/0.71 thf(fact_7539_sgn__power__injE,axiom,
% 0.37/0.71 ! [A: real,N: nat,X: real,B: real] :
% 0.37/0.71 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.37/0.71 = X )
% 0.37/0.71 => ( ( X
% 0.37/0.71 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 0.37/0.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( A = B ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sgn_power_injE
% 0.37/0.71 thf(fact_7540_divmod__nat__def,axiom,
% 0.37/0.71 ( divmod_nat
% 0.37/0.71 = ( ^ [M5: nat,N6: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M5 @ N6 ) @ ( modulo_modulo_nat @ M5 @ N6 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % divmod_nat_def
% 0.37/0.71 thf(fact_7541_ln__root,axiom,
% 0.37/0.71 ! [N: nat,B: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.71 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 0.37/0.71 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_root
% 0.37/0.71 thf(fact_7542_real__root__Suc__0,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 0.37/0.71 = X ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_Suc_0
% 0.37/0.71 thf(fact_7543_real__root__eq__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ( root @ N @ X )
% 0.37/0.71 = ( root @ N @ Y ) )
% 0.37/0.71 = ( X = Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_eq_iff
% 0.37/0.71 thf(fact_7544_root__0,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( root @ zero_zero_nat @ X )
% 0.37/0.71 = zero_zero_real ) ).
% 0.37/0.71
% 0.37/0.71 % root_0
% 0.37/0.71 thf(fact_7545_real__root__eq__0__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ( root @ N @ X )
% 0.37/0.71 = zero_zero_real )
% 0.37/0.71 = ( X = zero_zero_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_eq_0_iff
% 0.37/0.71 thf(fact_7546_real__root__less__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 0.37/0.71 = ( ord_less_real @ X @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_less_iff
% 0.37/0.71 thf(fact_7547_real__root__le__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 0.37/0.71 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_le_iff
% 0.37/0.71 thf(fact_7548_real__root__eq__1__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ( root @ N @ X )
% 0.37/0.71 = one_one_real )
% 0.37/0.71 = ( X = one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_eq_1_iff
% 0.37/0.71 thf(fact_7549_real__root__one,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( root @ N @ one_one_real )
% 0.37/0.71 = one_one_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_one
% 0.37/0.71 thf(fact_7550_real__root__lt__0__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_lt_0_iff
% 0.37/0.71 thf(fact_7551_real__root__gt__0__iff,axiom,
% 0.37/0.71 ! [N: nat,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 0.37/0.71 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_gt_0_iff
% 0.37/0.71 thf(fact_7552_real__root__le__0__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_le_0_iff
% 0.37/0.71 thf(fact_7553_real__root__ge__0__iff,axiom,
% 0.37/0.71 ! [N: nat,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 0.37/0.71 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_ge_0_iff
% 0.37/0.71 thf(fact_7554_real__root__lt__1__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 0.37/0.71 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_lt_1_iff
% 0.37/0.71 thf(fact_7555_real__root__gt__1__iff,axiom,
% 0.37/0.71 ! [N: nat,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 0.37/0.71 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_gt_1_iff
% 0.37/0.71 thf(fact_7556_real__root__le__1__iff,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 0.37/0.71 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_le_1_iff
% 0.37/0.71 thf(fact_7557_real__root__ge__1__iff,axiom,
% 0.37/0.71 ! [N: nat,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 0.37/0.71 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_ge_1_iff
% 0.37/0.71 thf(fact_7558_real__root__pow__pos2,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.37/0.71 = X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_pow_pos2
% 0.37/0.71 thf(fact_7559_sgn__root,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 0.37/0.71 = ( sgn_sgn_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sgn_root
% 0.37/0.71 thf(fact_7560_real__root__pos__pos__le,axiom,
% 0.37/0.71 ! [X: real,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_pos_pos_le
% 0.37/0.71 thf(fact_7561_real__root__less__mono,axiom,
% 0.37/0.71 ! [N: nat,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ X @ Y )
% 0.37/0.71 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_less_mono
% 0.37/0.71 thf(fact_7562_real__root__le__mono,axiom,
% 0.37/0.71 ! [N: nat,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.71 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_le_mono
% 0.37/0.71 thf(fact_7563_real__root__power,axiom,
% 0.37/0.71 ! [N: nat,X: real,K: nat] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 0.37/0.71 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_power
% 0.37/0.71 thf(fact_7564_real__root__abs,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 0.37/0.71 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_abs
% 0.37/0.71 thf(fact_7565_real__root__gt__zero,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_gt_zero
% 0.37/0.71 thf(fact_7566_real__root__strict__decreasing,axiom,
% 0.37/0.71 ! [N: nat,N8: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_nat @ N @ N8 )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ord_less_real @ ( root @ N8 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_strict_decreasing
% 0.37/0.71 thf(fact_7567_root__abs__power,axiom,
% 0.37/0.71 ! [N: nat,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 0.37/0.71 = ( abs_abs_real @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % root_abs_power
% 0.37/0.71 thf(fact_7568_real__root__pos__pos,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_pos_pos
% 0.37/0.71 thf(fact_7569_real__root__strict__increasing,axiom,
% 0.37/0.71 ! [N: nat,N8: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_nat @ N @ N8 )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.71 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N8 @ X ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_strict_increasing
% 0.37/0.71 thf(fact_7570_real__root__decreasing,axiom,
% 0.37/0.71 ! [N: nat,N8: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.71 => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( root @ N8 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_decreasing
% 0.37/0.71 thf(fact_7571_real__root__pow__pos,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.37/0.71 = X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_pow_pos
% 0.37/0.71 thf(fact_7572_real__root__pos__unique,axiom,
% 0.37/0.71 ! [N: nat,Y: real,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( ( power_power_real @ Y @ N )
% 0.37/0.71 = X )
% 0.37/0.71 => ( ( root @ N @ X )
% 0.37/0.71 = Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_pos_unique
% 0.37/0.71 thf(fact_7573_real__root__power__cancel,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 0.37/0.71 = X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_power_cancel
% 0.37/0.71 thf(fact_7574_sgn__power__root,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 0.37/0.71 = X ) ) ).
% 0.37/0.71
% 0.37/0.71 % sgn_power_root
% 0.37/0.71 thf(fact_7575_root__sgn__power,axiom,
% 0.37/0.71 ! [N: nat,Y: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 0.37/0.71 = Y ) ) ).
% 0.37/0.71
% 0.37/0.71 % root_sgn_power
% 0.37/0.71 thf(fact_7576_real__root__increasing,axiom,
% 0.37/0.71 ! [N: nat,N8: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_eq_nat @ N @ N8 )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.71 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N8 @ X ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_root_increasing
% 0.37/0.71 thf(fact_7577_split__root,axiom,
% 0.37/0.71 ! [P2: real > $o,N: nat,X: real] :
% 0.37/0.71 ( ( P2 @ ( root @ N @ X ) )
% 0.37/0.71 = ( ( ( N = zero_zero_nat )
% 0.37/0.71 => ( P2 @ zero_zero_real ) )
% 0.37/0.71 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ! [Y4: real] :
% 0.37/0.71 ( ( ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 0.37/0.71 = X )
% 0.37/0.71 => ( P2 @ Y4 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % split_root
% 0.37/0.71 thf(fact_7578_root__powr__inverse,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( root @ N @ X )
% 0.37/0.71 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % root_powr_inverse
% 0.37/0.71 thf(fact_7579_log__base__root,axiom,
% 0.37/0.71 ! [N: nat,B: real,X: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.71 => ( ( log @ ( root @ N @ B ) @ X )
% 0.37/0.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_base_root
% 0.37/0.71 thf(fact_7580_log__root,axiom,
% 0.37/0.71 ! [N: nat,A: real,B: real] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( log @ B @ ( root @ N @ A ) )
% 0.37/0.71 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_root
% 0.37/0.71 thf(fact_7581_powr__gt__zero,axiom,
% 0.37/0.71 ! [X: real,A: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 0.37/0.71 = ( X != zero_zero_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_gt_zero
% 0.37/0.71 thf(fact_7582_powr__nonneg__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 0.37/0.71 = ( A = zero_zero_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_nonneg_iff
% 0.37/0.71 thf(fact_7583_powr__less__cancel__iff,axiom,
% 0.37/0.71 ! [X: real,A: real,B: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.37/0.71 = ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_less_cancel_iff
% 0.37/0.71 thf(fact_7584_zero__less__log__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 0.37/0.71 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % zero_less_log_cancel_iff
% 0.37/0.71 thf(fact_7585_log__less__zero__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_less_zero_cancel_iff
% 0.37/0.71 thf(fact_7586_one__less__log__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 0.37/0.71 = ( ord_less_real @ A @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % one_less_log_cancel_iff
% 0.37/0.71 thf(fact_7587_log__less__one__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 0.37/0.71 = ( ord_less_real @ X @ A ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_less_one_cancel_iff
% 0.37/0.71 thf(fact_7588_log__less__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 0.37/0.71 = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_less_cancel_iff
% 0.37/0.71 thf(fact_7589_log__eq__one,axiom,
% 0.37/0.71 ! [A: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( log @ A @ A )
% 0.37/0.71 = one_one_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_eq_one
% 0.37/0.71 thf(fact_7590_powr__eq__one__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ( powr_real @ A @ X )
% 0.37/0.71 = one_one_real )
% 0.37/0.71 = ( X = zero_zero_real ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_eq_one_iff
% 0.37/0.71 thf(fact_7591_powr__one__gt__zero__iff,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ( powr_real @ X @ one_one_real )
% 0.37/0.71 = X )
% 0.37/0.71 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_one_gt_zero_iff
% 0.37/0.71 thf(fact_7592_powr__one,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( powr_real @ X @ one_one_real )
% 0.37/0.71 = X ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_one
% 0.37/0.71 thf(fact_7593_powr__le__cancel__iff,axiom,
% 0.37/0.71 ! [X: real,A: real,B: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.37/0.71 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_le_cancel_iff
% 0.37/0.71 thf(fact_7594_zero__le__log__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 0.37/0.71 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % zero_le_log_cancel_iff
% 0.37/0.71 thf(fact_7595_log__le__zero__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 0.37/0.71 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_le_zero_cancel_iff
% 0.37/0.71 thf(fact_7596_one__le__log__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 0.37/0.71 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % one_le_log_cancel_iff
% 0.37/0.71 thf(fact_7597_log__le__one__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 0.37/0.71 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_le_one_cancel_iff
% 0.37/0.71 thf(fact_7598_log__le__cancel__iff,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ A )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 0.37/0.71 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_le_cancel_iff
% 0.37/0.71 thf(fact_7599_log__powr__cancel,axiom,
% 0.37/0.71 ! [A: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 0.37/0.71 = Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_powr_cancel
% 0.37/0.71 thf(fact_7600_powr__log__cancel,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 0.37/0.71 = X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_log_cancel
% 0.37/0.71 thf(fact_7601_log__pow__cancel,axiom,
% 0.37/0.71 ! [A: real,B: nat] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 0.37/0.71 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_pow_cancel
% 0.37/0.71 thf(fact_7602_less__log__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 0.37/0.71 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_log_iff
% 0.37/0.71 thf(fact_7603_log__less__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 0.37/0.71 = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_less_iff
% 0.37/0.71 thf(fact_7604_less__powr__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 0.37/0.71 = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_powr_iff
% 0.37/0.71 thf(fact_7605_powr__less__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 0.37/0.71 = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_less_iff
% 0.37/0.71 thf(fact_7606_le__log__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 0.37/0.71 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % le_log_iff
% 0.37/0.71 thf(fact_7607_log__le__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 0.37/0.71 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_le_iff
% 0.37/0.71 thf(fact_7608_le__powr__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 0.37/0.71 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % le_powr_iff
% 0.37/0.71 thf(fact_7609_powr__le__iff,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 0.37/0.71 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_le_iff
% 0.37/0.71 thf(fact_7610_powr__less__mono2__neg,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ A @ zero_zero_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ Y )
% 0.37/0.71 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_less_mono2_neg
% 0.37/0.71 thf(fact_7611_powr__non__neg,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 0.37/0.71
% 0.37/0.71 % powr_non_neg
% 0.37/0.71 thf(fact_7612_powr__mono2,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.71 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_mono2
% 0.37/0.71 thf(fact_7613_powr__ge__pzero,axiom,
% 0.37/0.71 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_ge_pzero
% 0.37/0.71 thf(fact_7614_powr__less__cancel,axiom,
% 0.37/0.71 ! [X: real,A: real,B: real] :
% 0.37/0.71 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ord_less_real @ A @ B ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_less_cancel
% 0.37/0.71 thf(fact_7615_powr__less__mono,axiom,
% 0.37/0.71 ! [A: real,B: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ A @ B )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_less_mono
% 0.37/0.71 thf(fact_7616_powr__mono,axiom,
% 0.37/0.71 ! [A: real,B: real,X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.71 => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_mono
% 0.37/0.71 thf(fact_7617_add__log__eq__powr,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.71 => ( ( B != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 0.37/0.71 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % add_log_eq_powr
% 0.37/0.71 thf(fact_7618_log__add__eq__powr,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.71 => ( ( B != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 0.37/0.71 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_add_eq_powr
% 0.37/0.71 thf(fact_7619_minus__log__eq__powr,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.71 => ( ( B != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 0.37/0.71 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % minus_log_eq_powr
% 0.37/0.71 thf(fact_7620_log__minus__eq__powr,axiom,
% 0.37/0.71 ! [B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.71 => ( ( B != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 0.37/0.71 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_minus_eq_powr
% 0.37/0.71 thf(fact_7621_powr__less__mono2,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ Y )
% 0.37/0.71 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_less_mono2
% 0.37/0.71 thf(fact_7622_powr__mono2_H,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.71 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_mono2'
% 0.37/0.71 thf(fact_7623_gr__one__powr,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % gr_one_powr
% 0.37/0.71 thf(fact_7624_powr__inj,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( ( powr_real @ A @ X )
% 0.37/0.71 = ( powr_real @ A @ Y ) )
% 0.37/0.71 = ( X = Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_inj
% 0.37/0.71 thf(fact_7625_ge__one__powr__ge__zero,axiom,
% 0.37/0.71 ! [X: real,A: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ge_one_powr_ge_zero
% 0.37/0.71 thf(fact_7626_powr__mono__both,axiom,
% 0.37/0.71 ! [A: real,B: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( ord_less_eq_real @ A @ B )
% 0.37/0.71 => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.71 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_mono_both
% 0.37/0.71 thf(fact_7627_powr__le1,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.71 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_le1
% 0.37/0.71 thf(fact_7628_powr__divide,axiom,
% 0.37/0.71 ! [X: real,Y: real,A: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 0.37/0.71 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_divide
% 0.37/0.71 thf(fact_7629_powr__mult,axiom,
% 0.37/0.71 ! [X: real,Y: real,A: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 0.37/0.71 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_mult
% 0.37/0.71 thf(fact_7630_log__base__change,axiom,
% 0.37/0.71 ! [A: real,B: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( log @ B @ X )
% 0.37/0.71 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_base_change
% 0.37/0.71 thf(fact_7631_powr__realpow,axiom,
% 0.37/0.71 ! [X: real,N: nat] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.71 = ( power_power_real @ X @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_realpow
% 0.37/0.71 thf(fact_7632_log__of__power__eq,axiom,
% 0.37/0.71 ! [M: nat,B: real,N: nat] :
% 0.37/0.71 ( ( ( semiri5074537144036343181t_real @ M )
% 0.37/0.71 = ( power_power_real @ B @ N ) )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( semiri5074537144036343181t_real @ N )
% 0.37/0.71 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_of_power_eq
% 0.37/0.71 thf(fact_7633_less__log__of__power,axiom,
% 0.37/0.71 ! [B: real,N: nat,M: real] :
% 0.37/0.71 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_log_of_power
% 0.37/0.71 thf(fact_7634_powr__neg__one,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 0.37/0.71 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_neg_one
% 0.37/0.71 thf(fact_7635_powr__mult__base,axiom,
% 0.37/0.71 ! [X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 0.37/0.71 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_mult_base
% 0.37/0.71 thf(fact_7636_log__mult,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 0.37/0.71 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_mult
% 0.37/0.71 thf(fact_7637_le__log__of__power,axiom,
% 0.37/0.71 ! [B: real,N: nat,M: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % le_log_of_power
% 0.37/0.71 thf(fact_7638_log__base__pow,axiom,
% 0.37/0.71 ! [A: real,N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 0.37/0.71 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_base_pow
% 0.37/0.71 thf(fact_7639_log__nat__power,axiom,
% 0.37/0.71 ! [X: real,B: real,N: nat] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 0.37/0.71 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_nat_power
% 0.37/0.71 thf(fact_7640_log__divide,axiom,
% 0.37/0.71 ! [A: real,X: real,Y: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 0.37/0.71 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_divide
% 0.37/0.71 thf(fact_7641_log__of__power__less,axiom,
% 0.37/0.71 ! [M: nat,B: real,N: nat] :
% 0.37/0.71 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.71 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_of_power_less
% 0.37/0.71 thf(fact_7642_ln__powr__bound,axiom,
% 0.37/0.71 ! [X: real,A: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_powr_bound
% 0.37/0.71 thf(fact_7643_ln__powr__bound2,axiom,
% 0.37/0.71 ! [X: real,A: real] :
% 0.37/0.71 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_powr_bound2
% 0.37/0.71 thf(fact_7644_log__eq__div__ln__mult__log,axiom,
% 0.37/0.71 ! [A: real,B: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.37/0.71 => ( ( B != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( log @ A @ X )
% 0.37/0.71 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_eq_div_ln_mult_log
% 0.37/0.71 thf(fact_7645_log__of__power__le,axiom,
% 0.37/0.71 ! [M: nat,B: real,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.71 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_of_power_le
% 0.37/0.71 thf(fact_7646_ceiling__log__eq__powr__iff,axiom,
% 0.37/0.71 ! [X: real,B: real,K: nat] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 0.37/0.71 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 0.37/0.71 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 0.37/0.71 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ceiling_log_eq_powr_iff
% 0.37/0.71 thf(fact_7647_real__of__int__div4,axiom,
% 0.37/0.71 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_int_div4
% 0.37/0.71 thf(fact_7648_int__le__real__less,axiom,
% 0.37/0.71 ( ord_less_eq_int
% 0.37/0.71 = ( ^ [N6: int,M5: int] : ( ord_less_real @ ( ring_1_of_int_real @ N6 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M5 ) @ one_one_real ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % int_le_real_less
% 0.37/0.71 thf(fact_7649_int__less__real__le,axiom,
% 0.37/0.71 ( ord_less_int
% 0.37/0.71 = ( ^ [N6: int,M5: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N6 ) @ one_one_real ) @ ( ring_1_of_int_real @ M5 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % int_less_real_le
% 0.37/0.71 thf(fact_7650_real__of__int__div2,axiom,
% 0.37/0.71 ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_int_div2
% 0.37/0.71 thf(fact_7651_real__of__int__div3,axiom,
% 0.37/0.71 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_int_div3
% 0.37/0.71 thf(fact_7652_powr__int,axiom,
% 0.37/0.71 ! [X: real,I: int] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 0.37/0.71 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 0.37/0.71 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 0.37/0.71 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 0.37/0.71 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_int
% 0.37/0.71 thf(fact_7653_floor__log__eq__powr__iff,axiom,
% 0.37/0.71 ! [X: real,B: real,K: int] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ one_one_real @ B )
% 0.37/0.71 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 0.37/0.71 = K )
% 0.37/0.71 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 0.37/0.71 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_log_eq_powr_iff
% 0.37/0.71 thf(fact_7654_nat__1,axiom,
% 0.37/0.71 ( ( nat2 @ one_one_int )
% 0.37/0.71 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_1
% 0.37/0.71 thf(fact_7655_nat__0__iff,axiom,
% 0.37/0.71 ! [I: int] :
% 0.37/0.71 ( ( ( nat2 @ I )
% 0.37/0.71 = zero_zero_nat )
% 0.37/0.71 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_0_iff
% 0.37/0.71 thf(fact_7656_nat__le__0,axiom,
% 0.37/0.71 ! [Z: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.37/0.71 => ( ( nat2 @ Z )
% 0.37/0.71 = zero_zero_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_le_0
% 0.37/0.71 thf(fact_7657_zless__nat__conj,axiom,
% 0.37/0.71 ! [W2: int,Z: int] :
% 0.37/0.71 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 0.37/0.71 = ( ( ord_less_int @ zero_zero_int @ Z )
% 0.37/0.71 & ( ord_less_int @ W2 @ Z ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % zless_nat_conj
% 0.37/0.71 thf(fact_7658_nat__zminus__int,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % nat_zminus_int
% 0.37/0.71 thf(fact_7659_int__nat__eq,axiom,
% 0.37/0.71 ! [Z: int] :
% 0.37/0.71 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.37/0.71 = Z ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.37/0.71 = zero_zero_int ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % int_nat_eq
% 0.37/0.71 thf(fact_7660_zero__less__nat__eq,axiom,
% 0.37/0.71 ! [Z: int] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 0.37/0.71 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.37/0.71
% 0.37/0.71 % zero_less_nat_eq
% 0.37/0.71 thf(fact_7661_nat__ceiling__le__eq,axiom,
% 0.37/0.71 ! [X: real,A: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 0.37/0.71 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_ceiling_le_eq
% 0.37/0.71 thf(fact_7662_one__less__nat__eq,axiom,
% 0.37/0.71 ! [Z: int] :
% 0.37/0.71 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 0.37/0.71 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.37/0.71
% 0.37/0.71 % one_less_nat_eq
% 0.37/0.71 thf(fact_7663_nat__floor__neg,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.71 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.37/0.71 = zero_zero_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_floor_neg
% 0.37/0.71 thf(fact_7664_floor__eq3,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.37/0.71 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.37/0.71 = N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_eq3
% 0.37/0.71 thf(fact_7665_le__nat__floor,axiom,
% 0.37/0.71 ! [X: nat,A: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 0.37/0.71 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % le_nat_floor
% 0.37/0.71 thf(fact_7666_floor__eq4,axiom,
% 0.37/0.71 ! [N: nat,X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.37/0.71 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.37/0.71 = N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_eq4
% 0.37/0.71 thf(fact_7667_nat__zero__as__int,axiom,
% 0.37/0.71 ( zero_zero_nat
% 0.37/0.71 = ( nat2 @ zero_zero_int ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_zero_as_int
% 0.37/0.71 thf(fact_7668_nat__mono,axiom,
% 0.37/0.71 ! [X: int,Y: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ X @ Y )
% 0.37/0.71 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_mono
% 0.37/0.71 thf(fact_7669_eq__nat__nat__iff,axiom,
% 0.37/0.71 ! [Z: int,Z7: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 0.37/0.71 => ( ( ( nat2 @ Z )
% 0.37/0.71 = ( nat2 @ Z7 ) )
% 0.37/0.71 = ( Z = Z7 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % eq_nat_nat_iff
% 0.37/0.71 thf(fact_7670_all__nat,axiom,
% 0.37/0.71 ( ( ^ [P4: nat > $o] :
% 0.37/0.71 ! [X7: nat] : ( P4 @ X7 ) )
% 0.37/0.71 = ( ^ [P5: nat > $o] :
% 0.37/0.71 ! [X4: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.37/0.71 => ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % all_nat
% 0.37/0.71 thf(fact_7671_ex__nat,axiom,
% 0.37/0.71 ( ( ^ [P4: nat > $o] :
% 0.37/0.71 ? [X7: nat] : ( P4 @ X7 ) )
% 0.37/0.71 = ( ^ [P5: nat > $o] :
% 0.37/0.71 ? [X4: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 0.37/0.71 & ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ex_nat
% 0.37/0.71 thf(fact_7672_real__of__int__floor__add__one__gt,axiom,
% 0.37/0.71 ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_int_floor_add_one_gt
% 0.37/0.71 thf(fact_7673_floor__eq,axiom,
% 0.37/0.71 ! [N: int,X: real] :
% 0.37/0.71 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.37/0.71 => ( ( archim6058952711729229775r_real @ X )
% 0.37/0.71 = N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_eq
% 0.37/0.71 thf(fact_7674_real__of__int__floor__add__one__ge,axiom,
% 0.37/0.71 ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_int_floor_add_one_ge
% 0.37/0.71 thf(fact_7675_real__of__int__floor__gt__diff__one,axiom,
% 0.37/0.71 ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_int_floor_gt_diff_one
% 0.37/0.71 thf(fact_7676_real__of__int__floor__ge__diff__one,axiom,
% 0.37/0.71 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_int_floor_ge_diff_one
% 0.37/0.71 thf(fact_7677_nat__mono__iff,axiom,
% 0.37/0.71 ! [Z: int,W2: int] :
% 0.37/0.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 0.37/0.71 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_mono_iff
% 0.37/0.71 thf(fact_7678_zless__nat__eq__int__zless,axiom,
% 0.37/0.71 ! [M: nat,Z: int] :
% 0.37/0.71 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 0.37/0.71 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 0.37/0.71
% 0.37/0.71 % zless_nat_eq_int_zless
% 0.37/0.71 thf(fact_7679_nat__le__iff,axiom,
% 0.37/0.71 ! [X: int,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 0.37/0.71 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_le_iff
% 0.37/0.71 thf(fact_7680_nat__0__le,axiom,
% 0.37/0.71 ! [Z: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 0.37/0.71 = Z ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_0_le
% 0.37/0.71 thf(fact_7681_int__eq__iff,axiom,
% 0.37/0.71 ! [M: nat,Z: int] :
% 0.37/0.71 ( ( ( semiri1314217659103216013at_int @ M )
% 0.37/0.71 = Z )
% 0.37/0.71 = ( ( M
% 0.37/0.71 = ( nat2 @ Z ) )
% 0.37/0.71 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % int_eq_iff
% 0.37/0.71 thf(fact_7682_real__nat__ceiling__ge,axiom,
% 0.37/0.71 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_nat_ceiling_ge
% 0.37/0.71 thf(fact_7683_floor__eq2,axiom,
% 0.37/0.71 ! [N: int,X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 0.37/0.71 => ( ( archim6058952711729229775r_real @ X )
% 0.37/0.71 = N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_eq2
% 0.37/0.71 thf(fact_7684_floor__divide__real__eq__div,axiom,
% 0.37/0.71 ! [B: int,A: real] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.71 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 0.37/0.71 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_divide_real_eq_div
% 0.37/0.71 thf(fact_7685_nat__less__eq__zless,axiom,
% 0.37/0.71 ! [W2: int,Z: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.37/0.71 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 0.37/0.71 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_less_eq_zless
% 0.37/0.71 thf(fact_7686_nat__eq__iff2,axiom,
% 0.37/0.71 ! [M: nat,W2: int] :
% 0.37/0.71 ( ( M
% 0.37/0.71 = ( nat2 @ W2 ) )
% 0.37/0.71 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.37/0.71 => ( W2
% 0.37/0.71 = ( semiri1314217659103216013at_int @ M ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.37/0.71 => ( M = zero_zero_nat ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_eq_iff2
% 0.37/0.71 thf(fact_7687_nat__eq__iff,axiom,
% 0.37/0.71 ! [W2: int,M: nat] :
% 0.37/0.71 ( ( ( nat2 @ W2 )
% 0.37/0.71 = M )
% 0.37/0.71 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.37/0.71 => ( W2
% 0.37/0.71 = ( semiri1314217659103216013at_int @ M ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.37/0.71 => ( M = zero_zero_nat ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_eq_iff
% 0.37/0.71 thf(fact_7688_split__nat,axiom,
% 0.37/0.71 ! [P2: nat > $o,I: int] :
% 0.37/0.71 ( ( P2 @ ( nat2 @ I ) )
% 0.37/0.71 = ( ! [N6: nat] :
% 0.37/0.71 ( ( I
% 0.37/0.71 = ( semiri1314217659103216013at_int @ N6 ) )
% 0.37/0.71 => ( P2 @ N6 ) )
% 0.37/0.71 & ( ( ord_less_int @ I @ zero_zero_int )
% 0.37/0.71 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % split_nat
% 0.37/0.71 thf(fact_7689_nat__le__eq__zle,axiom,
% 0.37/0.71 ! [W2: int,Z: int] :
% 0.37/0.71 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 0.37/0.71 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 0.37/0.71 = ( ord_less_eq_int @ W2 @ Z ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_le_eq_zle
% 0.37/0.71 thf(fact_7690_nat__add__distrib,axiom,
% 0.37/0.71 ! [Z: int,Z7: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 0.37/0.71 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 0.37/0.71 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_add_distrib
% 0.37/0.71 thf(fact_7691_le__nat__iff,axiom,
% 0.37/0.71 ! [K: int,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.71 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 0.37/0.71 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % le_nat_iff
% 0.37/0.71 thf(fact_7692_Suc__as__int,axiom,
% 0.37/0.71 ( suc
% 0.37/0.71 = ( ^ [A7: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A7 ) @ one_one_int ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_as_int
% 0.37/0.71 thf(fact_7693_nat__mult__distrib,axiom,
% 0.37/0.71 ! [Z: int,Z7: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 0.37/0.71 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_mult_distrib
% 0.37/0.71 thf(fact_7694_nat__diff__distrib_H,axiom,
% 0.37/0.71 ! [X: int,Y: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.71 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.71 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 0.37/0.71 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_diff_distrib'
% 0.37/0.71 thf(fact_7695_nat__diff__distrib,axiom,
% 0.37/0.71 ! [Z7: int,Z: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 0.37/0.71 => ( ( ord_less_eq_int @ Z7 @ Z )
% 0.37/0.71 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 0.37/0.71 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_diff_distrib
% 0.37/0.71 thf(fact_7696_nat__div__distrib,axiom,
% 0.37/0.71 ! [X: int,Y: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.71 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 0.37/0.71 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_div_distrib
% 0.37/0.71 thf(fact_7697_nat__div__distrib_H,axiom,
% 0.37/0.71 ! [Y: int,X: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.71 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 0.37/0.71 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_div_distrib'
% 0.37/0.71 thf(fact_7698_nat__abs__triangle__ineq,axiom,
% 0.37/0.71 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_abs_triangle_ineq
% 0.37/0.71 thf(fact_7699_nat__power__eq,axiom,
% 0.37/0.71 ! [Z: int,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 0.37/0.71 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_power_eq
% 0.37/0.71 thf(fact_7700_nat__mod__distrib,axiom,
% 0.37/0.71 ! [X: int,Y: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.71 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.71 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 0.37/0.71 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_mod_distrib
% 0.37/0.71 thf(fact_7701_div__abs__eq__div__nat,axiom,
% 0.37/0.71 ! [K: int,L: int] :
% 0.37/0.71 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.37/0.71 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % div_abs_eq_div_nat
% 0.37/0.71 thf(fact_7702_mod__abs__eq__div__nat,axiom,
% 0.37/0.71 ! [K: int,L: int] :
% 0.37/0.71 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 0.37/0.71 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_abs_eq_div_nat
% 0.37/0.71 thf(fact_7703_Suc__nat__eq__nat__zadd1,axiom,
% 0.37/0.71 ! [Z: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.71 => ( ( suc @ ( nat2 @ Z ) )
% 0.37/0.71 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_nat_eq_nat_zadd1
% 0.37/0.71 thf(fact_7704_nat__less__iff,axiom,
% 0.37/0.71 ! [W2: int,M: nat] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.37/0.71 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 0.37/0.71 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_less_iff
% 0.37/0.71 thf(fact_7705_nat__mult__distrib__neg,axiom,
% 0.37/0.71 ! [Z: int,Z7: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.37/0.71 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 0.37/0.71 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_mult_distrib_neg
% 0.37/0.71 thf(fact_7706_nat__abs__int__diff,axiom,
% 0.37/0.71 ! [A: nat,B: nat] :
% 0.37/0.71 ( ( ( ord_less_eq_nat @ A @ B )
% 0.37/0.71 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.37/0.71 = ( minus_minus_nat @ B @ A ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.37/0.71 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.37/0.71 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_abs_int_diff
% 0.37/0.71 thf(fact_7707_image__atLeastZeroLessThan__int,axiom,
% 0.37/0.71 ! [U: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.37/0.71 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.37/0.71 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % image_atLeastZeroLessThan_int
% 0.37/0.71 thf(fact_7708_diff__nat__eq__if,axiom,
% 0.37/0.71 ! [Z7: int,Z: int] :
% 0.37/0.71 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 0.37/0.71 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 0.37/0.71 = ( nat2 @ Z ) ) )
% 0.37/0.71 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 0.37/0.71 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 0.37/0.71 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % diff_nat_eq_if
% 0.37/0.71 thf(fact_7709_powr__real__of__int,axiom,
% 0.37/0.71 ! [X: real,N: int] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.37/0.71 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 0.37/0.71 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 0.37/0.71 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 0.37/0.71 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_real_of_int
% 0.37/0.71 thf(fact_7710_floor__real__def,axiom,
% 0.37/0.71 ( archim6058952711729229775r_real
% 0.37/0.71 = ( ^ [X4: real] :
% 0.37/0.71 ( the_int
% 0.37/0.71 @ ^ [Z2: int] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X4 )
% 0.37/0.71 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_real_def
% 0.37/0.71 thf(fact_7711_inverse__powr,axiom,
% 0.37/0.71 ! [Y: real,A: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.71 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 0.37/0.71 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % inverse_powr
% 0.37/0.71 thf(fact_7712_forall__pos__mono__1,axiom,
% 0.37/0.71 ! [P2: real > $o,E2: real] :
% 0.37/0.71 ( ! [D2: real,E: real] :
% 0.37/0.71 ( ( ord_less_real @ D2 @ E )
% 0.37/0.71 => ( ( P2 @ D2 )
% 0.37/0.71 => ( P2 @ E ) ) )
% 0.37/0.71 => ( ! [N2: nat] : ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.37/0.71 => ( P2 @ E2 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % forall_pos_mono_1
% 0.37/0.71 thf(fact_7713_forall__pos__mono,axiom,
% 0.37/0.71 ! [P2: real > $o,E2: real] :
% 0.37/0.71 ( ! [D2: real,E: real] :
% 0.37/0.71 ( ( ord_less_real @ D2 @ E )
% 0.37/0.71 => ( ( P2 @ D2 )
% 0.37/0.71 => ( P2 @ E ) ) )
% 0.37/0.71 => ( ! [N2: nat] :
% 0.37/0.71 ( ( N2 != zero_zero_nat )
% 0.37/0.71 => ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.37/0.71 => ( P2 @ E2 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % forall_pos_mono
% 0.37/0.71 thf(fact_7714_real__arch__inverse,axiom,
% 0.37/0.71 ! [E2: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.37/0.71 = ( ? [N6: nat] :
% 0.37/0.71 ( ( N6 != zero_zero_nat )
% 0.37/0.71 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N6 ) ) )
% 0.37/0.71 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N6 ) ) @ E2 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_arch_inverse
% 0.37/0.71 thf(fact_7715_ln__inverse,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 0.37/0.71 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_inverse
% 0.37/0.71 thf(fact_7716_log__inverse,axiom,
% 0.37/0.71 ! [A: real,X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ A )
% 0.37/0.71 => ( ( A != one_one_real )
% 0.37/0.71 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 0.37/0.71 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_inverse
% 0.37/0.71 thf(fact_7717_Sup__nat__empty,axiom,
% 0.37/0.71 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % Sup_nat_empty
% 0.37/0.71 thf(fact_7718_Inf__nat__def1,axiom,
% 0.37/0.71 ! [K4: set_nat] :
% 0.37/0.71 ( ( K4 != bot_bot_set_nat )
% 0.37/0.71 => ( member_nat @ ( complete_Inf_Inf_nat @ K4 ) @ K4 ) ) ).
% 0.37/0.71
% 0.37/0.71 % Inf_nat_def1
% 0.37/0.71 thf(fact_7719_Sup__nat__def,axiom,
% 0.37/0.71 ( complete_Sup_Sup_nat
% 0.37/0.71 = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Sup_nat_def
% 0.37/0.71 thf(fact_7720_ln__neg__is__const,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.71 => ( ( ln_ln_real @ X )
% 0.37/0.71 = ( the_real
% 0.37/0.71 @ ^ [X4: real] : $false ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ln_neg_is_const
% 0.37/0.71 thf(fact_7721_floor__rat__def,axiom,
% 0.37/0.71 ( archim3151403230148437115or_rat
% 0.37/0.71 = ( ^ [X4: rat] :
% 0.37/0.71 ( the_int
% 0.37/0.71 @ ^ [Z2: int] :
% 0.37/0.71 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 )
% 0.37/0.71 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % floor_rat_def
% 0.37/0.71 thf(fact_7722_less__eq__rat__def,axiom,
% 0.37/0.71 ( ord_less_eq_rat
% 0.37/0.71 = ( ^ [X4: rat,Y4: rat] :
% 0.37/0.71 ( ( ord_less_rat @ X4 @ Y4 )
% 0.37/0.71 | ( X4 = Y4 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_eq_rat_def
% 0.37/0.71 thf(fact_7723_sgn__rat__def,axiom,
% 0.37/0.71 ( sgn_sgn_rat
% 0.37/0.71 = ( ^ [A7: rat] : ( if_rat @ ( A7 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A7 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sgn_rat_def
% 0.37/0.71 thf(fact_7724_abs__rat__def,axiom,
% 0.37/0.71 ( abs_abs_rat
% 0.37/0.71 = ( ^ [A7: rat] : ( if_rat @ ( ord_less_rat @ A7 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A7 ) @ A7 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % abs_rat_def
% 0.37/0.71 thf(fact_7725_obtain__pos__sum,axiom,
% 0.37/0.71 ! [R: rat] :
% 0.37/0.71 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.37/0.71 => ~ ! [S4: rat] :
% 0.37/0.71 ( ( ord_less_rat @ zero_zero_rat @ S4 )
% 0.37/0.71 => ! [T6: rat] :
% 0.37/0.71 ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 0.37/0.71 => ( R
% 0.37/0.71 != ( plus_plus_rat @ S4 @ T6 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % obtain_pos_sum
% 0.37/0.71 thf(fact_7726_Maclaurin__sin__bound,axiom,
% 0.37/0.71 ! [X: real,N: nat] :
% 0.37/0.71 ( ord_less_eq_real
% 0.37/0.71 @ ( abs_abs_real
% 0.37/0.71 @ ( minus_minus_real @ ( sin_real @ X )
% 0.37/0.71 @ ( groups6591440286371151544t_real
% 0.37/0.71 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.71 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 0.37/0.71 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Maclaurin_sin_bound
% 0.37/0.71 thf(fact_7727_normalize__negative,axiom,
% 0.37/0.71 ! [Q3: int,P3: int] :
% 0.37/0.71 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 0.37/0.71 => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q3 ) )
% 0.37/0.71 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P3 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % normalize_negative
% 0.37/0.71 thf(fact_7728_Cauchy__iff2,axiom,
% 0.37/0.71 ( topolo4055970368930404560y_real
% 0.37/0.71 = ( ^ [X8: nat > real] :
% 0.37/0.71 ! [J3: nat] :
% 0.37/0.71 ? [M9: nat] :
% 0.37/0.71 ! [M5: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ M9 @ M5 )
% 0.37/0.71 => ! [N6: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ M9 @ N6 )
% 0.37/0.71 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N6 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Cauchy_iff2
% 0.37/0.71 thf(fact_7729_sin__x__le__x,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % sin_x_le_x
% 0.37/0.71 thf(fact_7730_sin__le__one,axiom,
% 0.37/0.71 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 0.37/0.71
% 0.37/0.71 % sin_le_one
% 0.37/0.71 thf(fact_7731_abs__sin__x__le__abs__x,axiom,
% 0.37/0.71 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % abs_sin_x_le_abs_x
% 0.37/0.71 thf(fact_7732_sin__x__ge__neg__x,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sin_x_ge_neg_x
% 0.37/0.71 thf(fact_7733_sin__ge__minus__one,axiom,
% 0.37/0.71 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 0.37/0.71
% 0.37/0.71 % sin_ge_minus_one
% 0.37/0.71 thf(fact_7734_abs__sin__le__one,axiom,
% 0.37/0.71 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 0.37/0.71
% 0.37/0.71 % abs_sin_le_one
% 0.37/0.71 thf(fact_7735_normalize__denom__pos,axiom,
% 0.37/0.71 ! [R: product_prod_int_int,P3: int,Q3: int] :
% 0.37/0.71 ( ( ( normalize @ R )
% 0.37/0.71 = ( product_Pair_int_int @ P3 @ Q3 ) )
% 0.37/0.71 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 0.37/0.71
% 0.37/0.71 % normalize_denom_pos
% 0.37/0.71 thf(fact_7736_mod__or__dist,axiom,
% 0.37/0.71 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ H2 )
% 0.37/0.71 = ( ( rep_assn @ P2 @ H2 )
% 0.37/0.71 | ( rep_assn @ Q2 @ H2 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_or_dist
% 0.37/0.71 thf(fact_7737_merge__pure__or,axiom,
% 0.37/0.71 ! [A: $o,B: $o] :
% 0.37/0.71 ( ( sup_sup_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 0.37/0.71 = ( pure_assn
% 0.37/0.71 @ ( A
% 0.37/0.71 | B ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % merge_pure_or
% 0.37/0.71 thf(fact_7738_mod__h__bot__iff_I7_J,axiom,
% 0.37/0.71 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 0.37/0.71 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.37/0.71 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.37/0.71 | ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_h_bot_iff(7)
% 0.37/0.71 thf(fact_7739_sup__nat__def,axiom,
% 0.37/0.71 sup_sup_nat = ord_max_nat ).
% 0.37/0.71
% 0.37/0.71 % sup_nat_def
% 0.37/0.71 thf(fact_7740_ent__disjE,axiom,
% 0.37/0.71 ! [A4: assn,C3: assn,B4: assn] :
% 0.37/0.71 ( ( entails @ A4 @ C3 )
% 0.37/0.71 => ( ( entails @ B4 @ C3 )
% 0.37/0.71 => ( entails @ ( sup_sup_assn @ A4 @ B4 ) @ C3 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_disjE
% 0.37/0.71 thf(fact_7741_ent__disjI1,axiom,
% 0.37/0.71 ! [P2: assn,Q2: assn,R2: assn] :
% 0.37/0.71 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R2 )
% 0.37/0.71 => ( entails @ P2 @ R2 ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_disjI1
% 0.37/0.71 thf(fact_7742_ent__disjI2,axiom,
% 0.37/0.71 ! [P2: assn,Q2: assn,R2: assn] :
% 0.37/0.71 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R2 )
% 0.37/0.71 => ( entails @ Q2 @ R2 ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_disjI2
% 0.37/0.71 thf(fact_7743_ent__disjI1_H,axiom,
% 0.37/0.71 ! [A4: assn,B4: assn,C3: assn] :
% 0.37/0.71 ( ( entails @ A4 @ B4 )
% 0.37/0.71 => ( entails @ A4 @ ( sup_sup_assn @ B4 @ C3 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_disjI1'
% 0.37/0.71 thf(fact_7744_ent__disjI2_H,axiom,
% 0.37/0.71 ! [A4: assn,C3: assn,B4: assn] :
% 0.37/0.71 ( ( entails @ A4 @ C3 )
% 0.37/0.71 => ( entails @ A4 @ ( sup_sup_assn @ B4 @ C3 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_disjI2'
% 0.37/0.71 thf(fact_7745_ent__disjI1__direct,axiom,
% 0.37/0.71 ! [A4: assn,B4: assn] : ( entails @ A4 @ ( sup_sup_assn @ A4 @ B4 ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_disjI1_direct
% 0.37/0.71 thf(fact_7746_ent__disjI2__direct,axiom,
% 0.37/0.71 ! [B4: assn,A4: assn] : ( entails @ B4 @ ( sup_sup_assn @ A4 @ B4 ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_disjI2_direct
% 0.37/0.71 thf(fact_7747_star__or__dist1,axiom,
% 0.37/0.71 ! [A4: assn,B4: assn,C3: assn] :
% 0.37/0.71 ( ( times_times_assn @ ( sup_sup_assn @ A4 @ B4 ) @ C3 )
% 0.37/0.71 = ( sup_sup_assn @ ( times_times_assn @ A4 @ C3 ) @ ( times_times_assn @ B4 @ C3 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % star_or_dist1
% 0.37/0.71 thf(fact_7748_star__or__dist2,axiom,
% 0.37/0.71 ! [C3: assn,A4: assn,B4: assn] :
% 0.37/0.71 ( ( times_times_assn @ C3 @ ( sup_sup_assn @ A4 @ B4 ) )
% 0.37/0.71 = ( sup_sup_assn @ ( times_times_assn @ C3 @ A4 ) @ ( times_times_assn @ C3 @ B4 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % star_or_dist2
% 0.37/0.71 thf(fact_7749_infinite__UNIV__nat,axiom,
% 0.37/0.71 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 0.37/0.71
% 0.37/0.71 % infinite_UNIV_nat
% 0.37/0.71 thf(fact_7750_nat__not__finite,axiom,
% 0.37/0.71 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 0.37/0.71
% 0.37/0.71 % nat_not_finite
% 0.37/0.71 thf(fact_7751_mod__star__conv,axiom,
% 0.37/0.71 ! [A4: assn,B4: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ( rep_assn @ ( times_times_assn @ A4 @ B4 ) @ H2 )
% 0.37/0.71 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As2: set_nat] :
% 0.37/0.71 ( ( H2
% 0.37/0.71 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As2 ) ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( rep_assn @ A4 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 0.37/0.71 & ( rep_assn @ B4 @ ( produc7507926704131184380et_nat @ Hr @ As2 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_star_conv
% 0.37/0.71 thf(fact_7752_star__assnI,axiom,
% 0.37/0.71 ! [P2: assn,H2: heap_e7401611519738050253t_unit,As3: set_nat,Q2: assn,As4: set_nat] :
% 0.37/0.71 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 0.37/0.71 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As4 ) )
% 0.37/0.71 => ( ( ( inf_inf_set_nat @ As3 @ As4 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 => ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As3 @ As4 ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % star_assnI
% 0.37/0.71 thf(fact_7753_atLeastLessThan__add__Un,axiom,
% 0.37/0.71 ! [I: nat,J: nat,K: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.71 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 0.37/0.71 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % atLeastLessThan_add_Un
% 0.37/0.71 thf(fact_7754_range__enumerate,axiom,
% 0.37/0.71 ! [S3: set_nat] :
% 0.37/0.71 ( ~ ( finite_finite_nat @ S3 )
% 0.37/0.71 => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S3 ) @ top_top_set_nat )
% 0.37/0.71 = S3 ) ) ).
% 0.37/0.71
% 0.37/0.71 % range_enumerate
% 0.37/0.71 thf(fact_7755_UNIV__nat__eq,axiom,
% 0.37/0.71 ( top_top_set_nat
% 0.37/0.71 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % UNIV_nat_eq
% 0.37/0.71 thf(fact_7756_range__mod,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ( image_nat_nat
% 0.37/0.71 @ ^ [M5: nat] : ( modulo_modulo_nat @ M5 @ N )
% 0.37/0.71 @ top_top_set_nat )
% 0.37/0.71 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % range_mod
% 0.37/0.71 thf(fact_7757_card__nat,axiom,
% 0.37/0.71 ( ( finite_card_nat @ top_top_set_nat )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % card_nat
% 0.37/0.71 thf(fact_7758_card__num0,axiom,
% 0.37/0.71 ( ( finite6454714172617411596l_num0 @ top_to3689904424835650196l_num0 )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % card_num0
% 0.37/0.71 thf(fact_7759_card__UNIV__unit,axiom,
% 0.37/0.71 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.37/0.71 = one_one_nat ) ).
% 0.37/0.71
% 0.37/0.71 % card_UNIV_unit
% 0.37/0.71 thf(fact_7760_merge__true__star,axiom,
% 0.37/0.71 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 0.37/0.71 = top_top_assn ) ).
% 0.37/0.71
% 0.37/0.71 % merge_true_star
% 0.37/0.71 thf(fact_7761_merge__pure__and,axiom,
% 0.37/0.71 ! [A: $o,B: $o] :
% 0.37/0.71 ( ( inf_inf_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 0.37/0.71 = ( pure_assn
% 0.37/0.71 @ ( A
% 0.37/0.71 & B ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % merge_pure_and
% 0.37/0.71 thf(fact_7762_assn__basic__inequalities_I1_J,axiom,
% 0.37/0.71 top_top_assn != one_one_assn ).
% 0.37/0.71
% 0.37/0.71 % assn_basic_inequalities(1)
% 0.37/0.71 thf(fact_7763_assn__basic__inequalities_I5_J,axiom,
% 0.37/0.71 top_top_assn != bot_bot_assn ).
% 0.37/0.71
% 0.37/0.71 % assn_basic_inequalities(5)
% 0.37/0.71 thf(fact_7764_mod__h__bot__iff_I6_J,axiom,
% 0.37/0.71 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 0.37/0.71 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.37/0.71 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 0.37/0.71 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_h_bot_iff(6)
% 0.37/0.71 thf(fact_7765_card__literal,axiom,
% 0.37/0.71 ( ( finite_card_literal @ top_top_set_literal )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % card_literal
% 0.37/0.71 thf(fact_7766_ent__conjE2,axiom,
% 0.37/0.71 ! [B4: assn,C3: assn,A4: assn] :
% 0.37/0.71 ( ( entails @ B4 @ C3 )
% 0.37/0.71 => ( entails @ ( inf_inf_assn @ A4 @ B4 ) @ C3 ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_conjE2
% 0.37/0.71 thf(fact_7767_ent__conjE1,axiom,
% 0.37/0.71 ! [A4: assn,C3: assn,B4: assn] :
% 0.37/0.71 ( ( entails @ A4 @ C3 )
% 0.37/0.71 => ( entails @ ( inf_inf_assn @ A4 @ B4 ) @ C3 ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_conjE1
% 0.37/0.71 thf(fact_7768_ent__conjI,axiom,
% 0.37/0.71 ! [A4: assn,B4: assn,C3: assn] :
% 0.37/0.71 ( ( entails @ A4 @ B4 )
% 0.37/0.71 => ( ( entails @ A4 @ C3 )
% 0.37/0.71 => ( entails @ A4 @ ( inf_inf_assn @ B4 @ C3 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ent_conjI
% 0.37/0.71 thf(fact_7769_mod__and__dist,axiom,
% 0.37/0.71 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ H2 )
% 0.37/0.71 = ( ( rep_assn @ P2 @ H2 )
% 0.37/0.71 & ( rep_assn @ Q2 @ H2 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_and_dist
% 0.37/0.71 thf(fact_7770_ent__true,axiom,
% 0.37/0.71 ! [P2: assn] : ( entails @ P2 @ top_top_assn ) ).
% 0.37/0.71
% 0.37/0.71 % ent_true
% 0.37/0.71 thf(fact_7771_mod__star__trueE,axiom,
% 0.37/0.71 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 )
% 0.37/0.71 => ~ ! [H5: produc3658429121746597890et_nat] :
% 0.37/0.71 ~ ( rep_assn @ P2 @ H5 ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_star_trueE
% 0.37/0.71 thf(fact_7772_mod__star__trueI,axiom,
% 0.37/0.71 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ( rep_assn @ P2 @ H2 )
% 0.37/0.71 => ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_star_trueI
% 0.37/0.71 thf(fact_7773_mod__h__bot__iff_I2_J,axiom,
% 0.37/0.71 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_h_bot_iff(2)
% 0.37/0.71 thf(fact_7774_root__def,axiom,
% 0.37/0.71 ( root
% 0.37/0.71 = ( ^ [N6: nat,X4: real] :
% 0.37/0.71 ( if_real @ ( N6 = zero_zero_nat ) @ zero_zero_real
% 0.37/0.71 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 0.37/0.71 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N6 ) )
% 0.37/0.71 @ X4 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % root_def
% 0.37/0.71 thf(fact_7775_less__eq__assn__def,axiom,
% 0.37/0.71 ( ord_less_eq_assn
% 0.37/0.71 = ( ^ [A7: assn,B7: assn] :
% 0.37/0.71 ( A7
% 0.37/0.71 = ( inf_inf_assn @ A7 @ B7 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_eq_assn_def
% 0.37/0.71 thf(fact_7776_minus__assn__def,axiom,
% 0.37/0.71 ( minus_minus_assn
% 0.37/0.71 = ( ^ [A7: assn,B7: assn] : ( inf_inf_assn @ A7 @ ( uminus_uminus_assn @ B7 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % minus_assn_def
% 0.37/0.71 thf(fact_7777_times__assn__raw_Oelims_I3_J,axiom,
% 0.37/0.71 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ~ ( times_assn_raw @ X @ Xa2 @ Xb )
% 0.37/0.71 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.37/0.71 ( ( Xb
% 0.37/0.71 = ( produc7507926704131184380et_nat @ H @ As ) )
% 0.37/0.71 => ? [As12: set_nat,As22: set_nat] :
% 0.37/0.71 ( ( As
% 0.37/0.71 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 0.37/0.71 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % times_assn_raw.elims(3)
% 0.37/0.71 thf(fact_7778_less__assn__def,axiom,
% 0.37/0.71 ( ord_less_assn
% 0.37/0.71 = ( ^ [A7: assn,B7: assn] :
% 0.37/0.71 ( ( ord_less_eq_assn @ A7 @ B7 )
% 0.37/0.71 & ( A7 != B7 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_assn_def
% 0.37/0.71 thf(fact_7779_binomial__def,axiom,
% 0.37/0.71 ( binomial
% 0.37/0.71 = ( ^ [N6: nat,K3: nat] :
% 0.37/0.71 ( finite_card_set_nat
% 0.37/0.71 @ ( collect_set_nat
% 0.37/0.71 @ ^ [K5: set_nat] :
% 0.37/0.71 ( ( member_set_nat @ K5 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N6 ) ) )
% 0.37/0.71 & ( ( finite_card_nat @ K5 )
% 0.37/0.71 = K3 ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_def
% 0.37/0.71 thf(fact_7780_times__assn__raw_Osimps,axiom,
% 0.37/0.71 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As3: set_nat] :
% 0.37/0.71 ( ( times_assn_raw @ P2 @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 0.37/0.71 = ( ? [As1: set_nat,As2: set_nat] :
% 0.37/0.71 ( ( As3
% 0.37/0.71 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 0.37/0.71 & ( Q2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % times_assn_raw.simps
% 0.37/0.71 thf(fact_7781_times__assn__raw_Oelims_I1_J,axiom,
% 0.37/0.71 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.37/0.71 ( ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 0.37/0.71 = Y )
% 0.37/0.71 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.37/0.71 ( ( Xb
% 0.37/0.71 = ( produc7507926704131184380et_nat @ H @ As ) )
% 0.37/0.71 => ( Y
% 0.37/0.71 = ( ~ ? [As1: set_nat,As2: set_nat] :
% 0.37/0.71 ( ( As
% 0.37/0.71 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 0.37/0.71 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % times_assn_raw.elims(1)
% 0.37/0.71 thf(fact_7782_times__assn__raw_Oelims_I2_J,axiom,
% 0.37/0.71 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 0.37/0.71 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.37/0.71 ( ( Xb
% 0.37/0.71 = ( produc7507926704131184380et_nat @ H @ As ) )
% 0.37/0.71 => ~ ? [As13: set_nat,As23: set_nat] :
% 0.37/0.71 ( ( As
% 0.37/0.71 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 0.37/0.71 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % times_assn_raw.elims(2)
% 0.37/0.71 thf(fact_7783_times__assn__raw_Opelims_I1_J,axiom,
% 0.37/0.71 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.37/0.71 ( ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 0.37/0.71 = Y )
% 0.37/0.71 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ Xb ) ) )
% 0.37/0.71 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.37/0.71 ( ( Xb
% 0.37/0.71 = ( produc7507926704131184380et_nat @ H @ As ) )
% 0.37/0.71 => ( ( Y
% 0.37/0.71 = ( ? [As1: set_nat,As2: set_nat] :
% 0.37/0.71 ( ( As
% 0.37/0.71 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 0.37/0.71 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) )
% 0.37/0.71 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % times_assn_raw.pelims(1)
% 0.37/0.71 thf(fact_7784_times__assn__raw_Opelims_I2_J,axiom,
% 0.37/0.71 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 0.37/0.71 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ Xb ) ) )
% 0.37/0.71 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.37/0.71 ( ( Xb
% 0.37/0.71 = ( produc7507926704131184380et_nat @ H @ As ) )
% 0.37/0.71 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 0.37/0.71 => ~ ? [As13: set_nat,As23: set_nat] :
% 0.37/0.71 ( ( As
% 0.37/0.71 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 0.37/0.71 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % times_assn_raw.pelims(2)
% 0.37/0.71 thf(fact_7785_times__assn__raw_Opelims_I3_J,axiom,
% 0.37/0.71 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.37/0.71 ( ~ ( times_assn_raw @ X @ Xa2 @ Xb )
% 0.37/0.71 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ Xb ) ) )
% 0.37/0.71 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.37/0.71 ( ( Xb
% 0.37/0.71 = ( produc7507926704131184380et_nat @ H @ As ) )
% 0.37/0.71 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 0.37/0.71 => ? [As12: set_nat,As22: set_nat] :
% 0.37/0.71 ( ( As
% 0.37/0.71 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 0.37/0.71 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 0.37/0.71 = bot_bot_set_nat )
% 0.37/0.71 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 0.37/0.71 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % times_assn_raw.pelims(3)
% 0.37/0.71 thf(fact_7786_sorted__list__of__set__lessThan__Suc,axiom,
% 0.37/0.71 ! [K: nat] :
% 0.37/0.71 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 0.37/0.71 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sorted_list_of_set_lessThan_Suc
% 0.37/0.71 thf(fact_7787_sorted__list__of__set__atMost__Suc,axiom,
% 0.37/0.71 ! [K: nat] :
% 0.37/0.71 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 0.37/0.71 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sorted_list_of_set_atMost_Suc
% 0.37/0.71 thf(fact_7788_upto_Opelims,axiom,
% 0.37/0.71 ! [X: int,Xa2: int,Y: list_int] :
% 0.37/0.71 ( ( ( upto @ X @ Xa2 )
% 0.37/0.71 = Y )
% 0.37/0.71 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 0.37/0.71 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 0.37/0.71 => ( Y
% 0.37/0.71 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 0.37/0.71 => ( Y = nil_int ) ) )
% 0.37/0.71 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto.pelims
% 0.37/0.71 thf(fact_7789_upto__empty,axiom,
% 0.37/0.71 ! [J: int,I: int] :
% 0.37/0.71 ( ( ord_less_int @ J @ I )
% 0.37/0.71 => ( ( upto @ I @ J )
% 0.37/0.71 = nil_int ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_empty
% 0.37/0.71 thf(fact_7790_upto__Nil2,axiom,
% 0.37/0.71 ! [I: int,J: int] :
% 0.37/0.71 ( ( nil_int
% 0.37/0.71 = ( upto @ I @ J ) )
% 0.37/0.71 = ( ord_less_int @ J @ I ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_Nil2
% 0.37/0.71 thf(fact_7791_upto__Nil,axiom,
% 0.37/0.71 ! [I: int,J: int] :
% 0.37/0.71 ( ( ( upto @ I @ J )
% 0.37/0.71 = nil_int )
% 0.37/0.71 = ( ord_less_int @ J @ I ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_Nil
% 0.37/0.71 thf(fact_7792_nth__upto,axiom,
% 0.37/0.71 ! [I: int,K: nat,J: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 0.37/0.71 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 0.37/0.71 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nth_upto
% 0.37/0.71 thf(fact_7793_sorted__wrt__upto,axiom,
% 0.37/0.71 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 0.37/0.71
% 0.37/0.71 % sorted_wrt_upto
% 0.37/0.71 thf(fact_7794_sorted__upto,axiom,
% 0.37/0.71 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % sorted_upto
% 0.37/0.71 thf(fact_7795_upto__split2,axiom,
% 0.37/0.71 ! [I: int,J: int,K: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ I @ J )
% 0.37/0.71 => ( ( ord_less_eq_int @ J @ K )
% 0.37/0.71 => ( ( upto @ I @ K )
% 0.37/0.71 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_split2
% 0.37/0.71 thf(fact_7796_upto__split1,axiom,
% 0.37/0.71 ! [I: int,J: int,K: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ I @ J )
% 0.37/0.71 => ( ( ord_less_eq_int @ J @ K )
% 0.37/0.71 => ( ( upto @ I @ K )
% 0.37/0.71 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_split1
% 0.37/0.71 thf(fact_7797_upto_Osimps,axiom,
% 0.37/0.71 ( upto
% 0.37/0.71 = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto.simps
% 0.37/0.71 thf(fact_7798_upto_Oelims,axiom,
% 0.37/0.71 ! [X: int,Xa2: int,Y: list_int] :
% 0.37/0.71 ( ( ( upto @ X @ Xa2 )
% 0.37/0.71 = Y )
% 0.37/0.71 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 0.37/0.71 => ( Y
% 0.37/0.71 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 0.37/0.71 => ( Y = nil_int ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto.elims
% 0.37/0.71 thf(fact_7799_upto__rec1,axiom,
% 0.37/0.71 ! [I: int,J: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ I @ J )
% 0.37/0.71 => ( ( upto @ I @ J )
% 0.37/0.71 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_rec1
% 0.37/0.71 thf(fact_7800_upto__rec2,axiom,
% 0.37/0.71 ! [I: int,J: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ I @ J )
% 0.37/0.71 => ( ( upto @ I @ J )
% 0.37/0.71 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_rec2
% 0.37/0.71 thf(fact_7801_upto__split3,axiom,
% 0.37/0.71 ! [I: int,J: int,K: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ I @ J )
% 0.37/0.71 => ( ( ord_less_eq_int @ J @ K )
% 0.37/0.71 => ( ( upto @ I @ K )
% 0.37/0.71 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_split3
% 0.37/0.71 thf(fact_7802_upto_Opsimps,axiom,
% 0.37/0.71 ! [I: int,J: int] :
% 0.37/0.71 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 0.37/0.71 => ( ( ( ord_less_eq_int @ I @ J )
% 0.37/0.71 => ( ( upto @ I @ J )
% 0.37/0.71 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ I @ J )
% 0.37/0.71 => ( ( upto @ I @ J )
% 0.37/0.71 = nil_int ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto.psimps
% 0.37/0.71 thf(fact_7803_upto__rec__numeral_I2_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 = nil_int ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_rec_numeral(2)
% 0.37/0.71 thf(fact_7804_upto__rec__numeral_I3_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 = nil_int ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_rec_numeral(3)
% 0.37/0.71 thf(fact_7805_upto__rec__numeral_I4_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.71 = nil_int ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_rec_numeral(4)
% 0.37/0.71 thf(fact_7806_nat__neg__numeral,axiom,
% 0.37/0.71 ! [K: num] :
% 0.37/0.71 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % nat_neg_numeral
% 0.37/0.71 thf(fact_7807_upto__rec__numeral_I1_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.71 = nil_int ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % upto_rec_numeral(1)
% 0.37/0.71 thf(fact_7808_numeral__less__real__of__nat__iff,axiom,
% 0.37/0.71 ! [W2: num,N: nat] :
% 0.37/0.71 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.71 = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % numeral_less_real_of_nat_iff
% 0.37/0.71 thf(fact_7809_real__of__nat__less__numeral__iff,axiom,
% 0.37/0.71 ! [N: nat,W2: num] :
% 0.37/0.71 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W2 ) )
% 0.37/0.71 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_of_nat_less_numeral_iff
% 0.37/0.71 thf(fact_7810_numeral__le__real__of__nat__iff,axiom,
% 0.37/0.71 ! [N: num,M: nat] :
% 0.37/0.71 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 0.37/0.71 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 0.37/0.71
% 0.37/0.71 % numeral_le_real_of_nat_iff
% 0.37/0.71 thf(fact_7811_Suc__times__numeral__mod__eq,axiom,
% 0.37/0.71 ! [K: num,N: nat] :
% 0.37/0.71 ( ( ( numeral_numeral_nat @ K )
% 0.37/0.71 != one_one_nat )
% 0.37/0.71 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 0.37/0.71 = one_one_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_times_numeral_mod_eq
% 0.37/0.71 thf(fact_7812_powr__numeral,axiom,
% 0.37/0.71 ! [X: real,N: num] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 0.37/0.71 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_numeral
% 0.37/0.71 thf(fact_7813_nat__less__numeral__power__cancel__iff,axiom,
% 0.37/0.71 ! [A: int,X: num,N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.37/0.71 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_less_numeral_power_cancel_iff
% 0.37/0.71 thf(fact_7814_numeral__power__less__nat__cancel__iff,axiom,
% 0.37/0.71 ! [X: num,N: nat,A: int] :
% 0.37/0.71 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 0.37/0.71 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.37/0.71
% 0.37/0.71 % numeral_power_less_nat_cancel_iff
% 0.37/0.71 thf(fact_7815_numeral__power__le__nat__cancel__iff,axiom,
% 0.37/0.71 ! [X: num,N: nat,A: int] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 0.37/0.71 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.37/0.71
% 0.37/0.71 % numeral_power_le_nat_cancel_iff
% 0.37/0.71 thf(fact_7816_nat__le__numeral__power__cancel__iff,axiom,
% 0.37/0.71 ! [A: int,X: num,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.37/0.71 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_le_numeral_power_cancel_iff
% 0.37/0.71 thf(fact_7817_powr__neg__numeral,axiom,
% 0.37/0.71 ! [X: real,N: num] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.37/0.71 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % powr_neg_numeral
% 0.37/0.71 thf(fact_7818_enat__ord__number_I1_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.37/0.71 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % enat_ord_number(1)
% 0.37/0.71 thf(fact_7819_enat__ord__number_I2_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.37/0.71 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % enat_ord_number(2)
% 0.37/0.71 thf(fact_7820_i0__less,axiom,
% 0.37/0.71 ! [N: extended_enat] :
% 0.37/0.71 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.37/0.71 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 0.37/0.71
% 0.37/0.71 % i0_less
% 0.37/0.71 thf(fact_7821_enat__less__induct,axiom,
% 0.37/0.71 ! [P2: extended_enat > $o,N: extended_enat] :
% 0.37/0.71 ( ! [N2: extended_enat] :
% 0.37/0.71 ( ! [M2: extended_enat] :
% 0.37/0.71 ( ( ord_le72135733267957522d_enat @ M2 @ N2 )
% 0.37/0.71 => ( P2 @ M2 ) )
% 0.37/0.71 => ( P2 @ N2 ) )
% 0.37/0.71 => ( P2 @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % enat_less_induct
% 0.37/0.71 thf(fact_7822_not__iless0,axiom,
% 0.37/0.71 ! [N: extended_enat] :
% 0.37/0.71 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 0.37/0.71
% 0.37/0.71 % not_iless0
% 0.37/0.71 thf(fact_7823_enat__0__less__mult__iff,axiom,
% 0.37/0.71 ! [M: extended_enat,N: extended_enat] :
% 0.37/0.71 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 0.37/0.71 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 0.37/0.71 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % enat_0_less_mult_iff
% 0.37/0.71 thf(fact_7824_add__diff__assoc__enat,axiom,
% 0.37/0.71 ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 0.37/0.71 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 0.37/0.71 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 0.37/0.71 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % add_diff_assoc_enat
% 0.37/0.71 thf(fact_7825_ile0__eq,axiom,
% 0.37/0.71 ! [N: extended_enat] :
% 0.37/0.71 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 0.37/0.71 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 0.37/0.71
% 0.37/0.71 % ile0_eq
% 0.37/0.71 thf(fact_7826_i0__lb,axiom,
% 0.37/0.71 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 0.37/0.71
% 0.37/0.71 % i0_lb
% 0.37/0.71 thf(fact_7827_insert_H__correct,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( vEBT_set_vebt @ ( vEBT_VEBT_insert @ T @ X ) )
% 0.37/0.71 = ( 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 ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % insert'_correct
% 0.37/0.71 thf(fact_7828_setceilmax,axiom,
% 0.37/0.71 ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ S @ M )
% 0.37/0.71 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.71 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 0.37/0.71 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.37/0.71 => ( ( M
% 0.37/0.71 = ( suc @ N ) )
% 0.37/0.71 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.71 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 0.37/0.71 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X3 ) )
% 0.37/0.71 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 0.37/0.71 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 0.37/0.71 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 0.37/0.71 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 0.37/0.71 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % setceilmax
% 0.37/0.71 thf(fact_7829_pow__sum,axiom,
% 0.37/0.71 ! [A: nat,B: nat] :
% 0.37/0.71 ( ( 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 ) )
% 0.37/0.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 0.37/0.71
% 0.37/0.71 % pow_sum
% 0.37/0.71 thf(fact_7830_mulcomm,axiom,
% 0.37/0.71 ! [I: nat,Va2: nat] :
% 0.37/0.71 ( ( times_times_nat @ I @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.71 = ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ I ) ) ).
% 0.37/0.71
% 0.37/0.71 % mulcomm
% 0.37/0.71 thf(fact_7831_two__realpow__ge__two,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ord_less_eq_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.37/0.71 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % two_realpow_ge_two
% 0.37/0.71 thf(fact_7832_member__bound,axiom,
% 0.37/0.71 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 0.37/0.71 ( ( vEBT_vebt_member @ Tree @ X )
% 0.37/0.71 => ( ( vEBT_invar_vebt @ Tree @ N )
% 0.37/0.71 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % member_bound
% 0.37/0.71 thf(fact_7833_valid__pres__insert,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ T @ X ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % valid_pres_insert
% 0.37/0.71 thf(fact_7834_misiz,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ( some_nat @ M )
% 0.37/0.71 = ( vEBT_vebt_mint @ T ) )
% 0.37/0.71 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % misiz
% 0.37/0.71 thf(fact_7835_insert__simp__mima,axiom,
% 0.37/0.71 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.71 ( ( ( X = Mi )
% 0.37/0.71 | ( X = Ma ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.71 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % insert_simp_mima
% 0.37/0.71 thf(fact_7836_two__powr__height__bound__deg,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % two_powr_height_bound_deg
% 0.37/0.71 thf(fact_7837_helpyd,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.37/0.71 = ( some_nat @ Y ) )
% 0.37/0.71 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % helpyd
% 0.37/0.71 thf(fact_7838_helpypredd,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.37/0.71 = ( some_nat @ Y ) )
% 0.37/0.71 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % helpypredd
% 0.37/0.71 thf(fact_7839_valid__insert__both__member__options__add,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % valid_insert_both_member_options_add
% 0.37/0.71 thf(fact_7840_valid__insert__both__member__options__pres,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.37/0.71 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % valid_insert_both_member_options_pres
% 0.37/0.71 thf(fact_7841_post__member__pre__member,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 0.37/0.71 => ( ( vEBT_vebt_member @ T @ Y )
% 0.37/0.71 | ( X = Y ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % post_member_pre_member
% 0.37/0.71 thf(fact_7842_log__ceil__idem,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.71 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 0.37/0.71 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % log_ceil_idem
% 0.37/0.71 thf(fact_7843_count__buildup,axiom,
% 0.37/0.71 ! [N: nat] : ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % count_buildup
% 0.37/0.71 thf(fact_7844_delt__out__of__range,axiom,
% 0.37/0.71 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.71 ( ( ( ord_less_nat @ X @ Mi )
% 0.37/0.71 | ( ord_less_nat @ Ma @ X ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.71 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % delt_out_of_range
% 0.37/0.71 thf(fact_7845_del__single__cont,axiom,
% 0.37/0.71 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.71 ( ( ( X = Mi )
% 0.37/0.71 & ( X = Ma ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.71 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % del_single_cont
% 0.37/0.71 thf(fact_7846_semiring__norm_I78_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.37/0.71 = ( ord_less_num @ M @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % semiring_norm(78)
% 0.37/0.71 thf(fact_7847_semiring__norm_I71_J,axiom,
% 0.37/0.71 ! [M: num,N: num] :
% 0.37/0.71 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.37/0.71 = ( ord_less_eq_num @ M @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % semiring_norm(71)
% 0.37/0.71 thf(fact_7848_set__n__deg__not__0,axiom,
% 0.37/0.71 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 0.37/0.71 ( ! [X3: vEBT_VEBT] :
% 0.37/0.71 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.71 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.37/0.71 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.71 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.71 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % set_n_deg_not_0
% 0.37/0.71 thf(fact_7849_semiring__norm_I75_J,axiom,
% 0.37/0.71 ! [M: num] :
% 0.37/0.71 ~ ( ord_less_num @ M @ one ) ).
% 0.37/0.71
% 0.37/0.71 % semiring_norm(75)
% 0.37/0.71 thf(fact_7850_semiring__norm_I68_J,axiom,
% 0.37/0.71 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 0.37/0.71
% 0.37/0.71 % semiring_norm(68)
% 0.37/0.71 thf(fact_7851_tdeletemimi_H,axiom,
% 0.37/0.71 ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.71 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X ) @ one_one_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % tdeletemimi'
% 0.37/0.71 thf(fact_7852_count__buildup_H,axiom,
% 0.37/0.71 ! [N: nat] : ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( semiri5074537144036343181t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % count_buildup'
% 0.37/0.71 thf(fact_7853_heigt__uplog__rel,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 0.37/0.71 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % heigt_uplog_rel
% 0.37/0.71 thf(fact_7854_mi__ma__2__deg,axiom,
% 0.37/0.71 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.37/0.71 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.37/0.71 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mi_ma_2_deg
% 0.37/0.71 thf(fact_7855_succ__min,axiom,
% 0.37/0.71 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.71 => ( ( ord_less_nat @ X @ Mi )
% 0.37/0.71 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( some_nat @ Mi ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % succ_min
% 0.37/0.71 thf(fact_7856_pred__max,axiom,
% 0.37/0.71 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.71 => ( ( ord_less_nat @ Ma @ X )
% 0.37/0.71 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( some_nat @ Ma ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % pred_max
% 0.37/0.71 thf(fact_7857_cnt__bound_H,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % cnt_bound'
% 0.37/0.71 thf(fact_7858_delete__bound__size__univ_H,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( U
% 0.37/0.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % delete_bound_size_univ'
% 0.37/0.71 thf(fact_7859_bit__concat__def,axiom,
% 0.37/0.71 ( vEBT_VEBT_bit_concat
% 0.37/0.71 = ( ^ [H4: nat,L4: nat,D5: nat] : ( plus_plus_nat @ ( times_times_nat @ H4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D5 ) ) @ L4 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % bit_concat_def
% 0.37/0.71 thf(fact_7860_TBOUND__vebt__memberi,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_TBOUND_o @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % TBOUND_vebt_memberi
% 0.37/0.71 thf(fact_7861_height__double__log__univ__size,axiom,
% 0.37/0.71 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 0.37/0.71 ( ( U
% 0.37/0.71 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 0.37/0.71 => ( ( vEBT_invar_vebt @ T @ Deg )
% 0.37/0.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % height_double_log_univ_size
% 0.37/0.71 thf(fact_7862_inrange,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( 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 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % inrange
% 0.37/0.71 thf(fact_7863_Suc__numeral,axiom,
% 0.37/0.71 ! [N: num] :
% 0.37/0.71 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 0.37/0.71 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_numeral
% 0.37/0.71 thf(fact_7864_insert__correct,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.37/0.71 = ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % insert_correct
% 0.37/0.71 thf(fact_7865_set__vebt__insert,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) )
% 0.37/0.71 = ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % set_vebt_insert
% 0.37/0.71 thf(fact_7866_insert__corr,axiom,
% 0.37/0.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( sup_sup_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.37/0.71 = ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % insert_corr
% 0.37/0.71 thf(fact_7867_zdiv__numeral__Bit0,axiom,
% 0.37/0.71 ! [V2: num,W2: num] :
% 0.37/0.71 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.37/0.71 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % zdiv_numeral_Bit0
% 0.37/0.71 thf(fact_7868_semiring__norm_I76_J,axiom,
% 0.37/0.71 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % semiring_norm(76)
% 0.37/0.71 thf(fact_7869_semiring__norm_I69_J,axiom,
% 0.37/0.71 ! [M: num] :
% 0.37/0.71 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 0.37/0.71
% 0.37/0.71 % semiring_norm(69)
% 0.37/0.71 thf(fact_7870_mintlistlength,axiom,
% 0.37/0.71 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.37/0.71 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.37/0.71 => ( ( Mi != Ma )
% 0.37/0.71 => ( ( ord_less_nat @ Mi @ Ma )
% 0.37/0.71 & ? [M3: nat] :
% 0.37/0.71 ( ( ( some_nat @ M3 )
% 0.37/0.71 = ( vEBT_vebt_mint @ Summary ) )
% 0.37/0.71 & ( ord_less_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mintlistlength
% 0.37/0.71 thf(fact_7871_add__2__eq__Suc_H,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 = ( suc @ ( suc @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % add_2_eq_Suc'
% 0.37/0.71 thf(fact_7872_add__2__eq__Suc,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.71 = ( suc @ ( suc @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % add_2_eq_Suc
% 0.37/0.71 thf(fact_7873_Suc__1,axiom,
% 0.37/0.71 ( ( suc @ one_one_nat )
% 0.37/0.71 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_1
% 0.37/0.71 thf(fact_7874_div2__Suc__Suc,axiom,
% 0.37/0.71 ! [M: nat] :
% 0.37/0.71 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % div2_Suc_Suc
% 0.37/0.71 thf(fact_7875_mod2__Suc__Suc,axiom,
% 0.37/0.71 ! [M: nat] :
% 0.37/0.71 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod2_Suc_Suc
% 0.37/0.71 thf(fact_7876_zmod__numeral__Bit0,axiom,
% 0.37/0.71 ! [V2: num,W2: num] :
% 0.37/0.71 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.37/0.71 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % zmod_numeral_Bit0
% 0.37/0.71 thf(fact_7877_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 != ( suc @ zero_zero_nat ) )
% 0.37/0.71 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 = zero_zero_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % not_mod2_eq_Suc_0_eq_0
% 0.37/0.71 thf(fact_7878_add__self__mod__2,axiom,
% 0.37/0.71 ! [M: nat] :
% 0.37/0.71 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % add_self_mod_2
% 0.37/0.71 thf(fact_7879_half__nonnegative__int__iff,axiom,
% 0.37/0.71 ! [K: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.37/0.71 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.71
% 0.37/0.71 % half_nonnegative_int_iff
% 0.37/0.71 thf(fact_7880_half__negative__int__iff,axiom,
% 0.37/0.71 ! [K: int] :
% 0.37/0.71 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.37/0.71 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.71
% 0.37/0.71 % half_negative_int_iff
% 0.37/0.71 thf(fact_7881_mod2__gr__0,axiom,
% 0.37/0.71 ! [M: nat] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.71 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 = one_one_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod2_gr_0
% 0.37/0.71 thf(fact_7882_self__le__ge2__pow,axiom,
% 0.37/0.71 ! [K: nat,M: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.37/0.71 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % self_le_ge2_pow
% 0.37/0.71 thf(fact_7883_power2__nat__le__eq__le,axiom,
% 0.37/0.71 ! [M: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.71 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % power2_nat_le_eq_le
% 0.37/0.71 thf(fact_7884_power2__nat__le__imp__le,axiom,
% 0.37/0.71 ! [M: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 0.37/0.71 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % power2_nat_le_imp_le
% 0.37/0.71 thf(fact_7885_numeral__2__eq__2,axiom,
% 0.37/0.71 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.37/0.71 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % numeral_2_eq_2
% 0.37/0.71 thf(fact_7886_double__not__eq__Suc__double,axiom,
% 0.37/0.71 ! [M: nat,N: nat] :
% 0.37/0.71 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.37/0.71 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % double_not_eq_Suc_double
% 0.37/0.71 thf(fact_7887_Suc__double__not__eq__double,axiom,
% 0.37/0.71 ! [M: nat,N: nat] :
% 0.37/0.71 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.71 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_double_not_eq_double
% 0.37/0.71 thf(fact_7888_pos2,axiom,
% 0.37/0.71 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 0.37/0.71
% 0.37/0.71 % pos2
% 0.37/0.71 thf(fact_7889_pos__mod__bound2,axiom,
% 0.37/0.71 ! [A: int] : ( ord_less_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % pos_mod_bound2
% 0.37/0.71 thf(fact_7890_n__less__equal__power__2,axiom,
% 0.37/0.71 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % n_less_equal_power_2
% 0.37/0.71 thf(fact_7891_le__num__One__iff,axiom,
% 0.37/0.71 ! [X: num] :
% 0.37/0.71 ( ( ord_less_eq_num @ X @ one )
% 0.37/0.71 = ( X = one ) ) ).
% 0.37/0.71
% 0.37/0.71 % le_num_One_iff
% 0.37/0.71 thf(fact_7892_num_Osize_I4_J,axiom,
% 0.37/0.71 ( ( size_size_num @ one )
% 0.37/0.71 = zero_zero_nat ) ).
% 0.37/0.71
% 0.37/0.71 % num.size(4)
% 0.37/0.71 thf(fact_7893_less__2__cases__iff,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 = ( ( N = zero_zero_nat )
% 0.37/0.71 | ( N
% 0.37/0.71 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_2_cases_iff
% 0.37/0.71 thf(fact_7894_less__2__cases,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 => ( ( N = zero_zero_nat )
% 0.37/0.71 | ( N
% 0.37/0.71 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_2_cases
% 0.37/0.71 thf(fact_7895_nat__induct2,axiom,
% 0.37/0.71 ! [P2: nat > $o,N: nat] :
% 0.37/0.71 ( ( P2 @ zero_zero_nat )
% 0.37/0.71 => ( ( P2 @ one_one_nat )
% 0.37/0.71 => ( ! [N2: nat] :
% 0.37/0.71 ( ( P2 @ N2 )
% 0.37/0.71 => ( P2 @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.71 => ( P2 @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_induct2
% 0.37/0.71 thf(fact_7896_diff__le__diff__pow,axiom,
% 0.37/0.71 ! [K: nat,M: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.37/0.71 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % diff_le_diff_pow
% 0.37/0.71 thf(fact_7897_nat__2,axiom,
% 0.37/0.71 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.37/0.71 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_2
% 0.37/0.71 thf(fact_7898_realpow__square__minus__le,axiom,
% 0.37/0.71 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % realpow_square_minus_le
% 0.37/0.71 thf(fact_7899_binomial__antimono,axiom,
% 0.37/0.71 ! [K: nat,K6: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ K @ K6 )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 0.37/0.71 => ( ( ord_less_eq_nat @ K6 @ N )
% 0.37/0.71 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_antimono
% 0.37/0.71 thf(fact_7900_binomial__maximum,axiom,
% 0.37/0.71 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_maximum
% 0.37/0.71 thf(fact_7901_pos__mod__sign2,axiom,
% 0.37/0.71 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % pos_mod_sign2
% 0.37/0.71 thf(fact_7902_not__exp__less__eq__0__int,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 0.37/0.71
% 0.37/0.71 % not_exp_less_eq_0_int
% 0.37/0.71 thf(fact_7903_binomial__mono,axiom,
% 0.37/0.71 ! [K: nat,K6: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ K @ K6 )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.37/0.71 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_mono
% 0.37/0.71 thf(fact_7904_binomial__maximum_H,axiom,
% 0.37/0.71 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_maximum'
% 0.37/0.71 thf(fact_7905_two__realpow__ge__one,axiom,
% 0.37/0.71 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % two_realpow_ge_one
% 0.37/0.71 thf(fact_7906_binomial__le__pow2,axiom,
% 0.37/0.71 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_le_pow2
% 0.37/0.71 thf(fact_7907_sin__gt__zero__02,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.71 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sin_gt_zero_02
% 0.37/0.71 thf(fact_7908_mod__exp__less__eq__exp,axiom,
% 0.37/0.71 ! [A: int,N: nat] : ( ord_less_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % mod_exp_less_eq_exp
% 0.37/0.71 thf(fact_7909_ln__2__less__1,axiom,
% 0.37/0.71 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 0.37/0.71
% 0.37/0.71 % ln_2_less_1
% 0.37/0.71 thf(fact_7910_Suc__n__div__2__gt__zero,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.71 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_n_div_2_gt_zero
% 0.37/0.71 thf(fact_7911_div__2__gt__zero,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.71 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % div_2_gt_zero
% 0.37/0.71 thf(fact_7912_nat__bit__induct,axiom,
% 0.37/0.71 ! [P2: nat > $o,N: nat] :
% 0.37/0.71 ( ( P2 @ zero_zero_nat )
% 0.37/0.71 => ( ! [N2: nat] :
% 0.37/0.71 ( ( P2 @ N2 )
% 0.37/0.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.37/0.71 => ( P2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.37/0.71 => ( ! [N2: nat] :
% 0.37/0.71 ( ( P2 @ N2 )
% 0.37/0.71 => ( P2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 0.37/0.71 => ( P2 @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_bit_induct
% 0.37/0.71 thf(fact_7913_two__pow__div__gt__le,axiom,
% 0.37/0.71 ! [V2: nat,N: nat,M: nat] :
% 0.37/0.71 ( ( ord_less_nat @ V2 @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) )
% 0.37/0.71 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % two_pow_div_gt_le
% 0.37/0.71 thf(fact_7914_nat__add__offset__less,axiom,
% 0.37/0.71 ! [Y: nat,N: nat,X: nat,M: nat,Sz: nat] :
% 0.37/0.71 ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.71 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.71 => ( ( Sz
% 0.37/0.71 = ( plus_plus_nat @ M @ N ) )
% 0.37/0.71 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ Y ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Sz ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_add_offset_less
% 0.37/0.71 thf(fact_7915_nat__power__less__diff,axiom,
% 0.37/0.71 ! [N: nat,Q3: nat,M: nat] :
% 0.37/0.71 ( ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Q3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.71 => ( ord_less_nat @ Q3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_power_less_diff
% 0.37/0.71 thf(fact_7916_power__minus__is__div,axiom,
% 0.37/0.71 ! [B: nat,A: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ B @ A )
% 0.37/0.71 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 0.37/0.71 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % power_minus_is_div
% 0.37/0.71 thf(fact_7917_nat__le__power__trans,axiom,
% 0.37/0.71 ! [N: nat,M: nat,K: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ K @ M )
% 0.37/0.71 => ( ord_less_eq_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_le_power_trans
% 0.37/0.71 thf(fact_7918_binomial__less__binomial__Suc,axiom,
% 0.37/0.71 ! [K: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.71 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_less_binomial_Suc
% 0.37/0.71 thf(fact_7919_binomial__strict__mono,axiom,
% 0.37/0.71 ! [K: nat,K6: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ K @ K6 )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.37/0.71 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_strict_mono
% 0.37/0.71 thf(fact_7920_binomial__strict__antimono,axiom,
% 0.37/0.71 ! [K: nat,K6: nat,N: nat] :
% 0.37/0.71 ( ( ord_less_nat @ K @ K6 )
% 0.37/0.71 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ K6 @ N )
% 0.37/0.71 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % binomial_strict_antimono
% 0.37/0.71 thf(fact_7921_square__fact__le__2__fact,axiom,
% 0.37/0.71 ! [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 ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % square_fact_le_2_fact
% 0.37/0.71 thf(fact_7922_exp__half__le2,axiom,
% 0.37/0.71 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.37/0.71
% 0.37/0.71 % exp_half_le2
% 0.37/0.71 thf(fact_7923_exp__plus__inverse__exp,axiom,
% 0.37/0.71 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % exp_plus_inverse_exp
% 0.37/0.71 thf(fact_7924_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 0.37/0.71 ! [V2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.71 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(4)
% 0.37/0.71 thf(fact_7925_triangle__def,axiom,
% 0.37/0.71 ( nat_triangle
% 0.37/0.71 = ( ^ [N6: nat] : ( divide_divide_nat @ ( times_times_nat @ N6 @ ( suc @ N6 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % triangle_def
% 0.37/0.71 thf(fact_7926_ex__power__ivl1,axiom,
% 0.37/0.71 ! [B: nat,K: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.37/0.71 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.37/0.71 => ? [N2: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.37/0.71 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ex_power_ivl1
% 0.37/0.71 thf(fact_7927_ex__power__ivl2,axiom,
% 0.37/0.71 ! [B: nat,K: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.37/0.71 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.37/0.71 => ? [N2: nat] :
% 0.37/0.71 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 0.37/0.71 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % ex_power_ivl2
% 0.37/0.71 thf(fact_7928_less__two__pow__divD,axiom,
% 0.37/0.71 ! [X: nat,N: nat,M: nat] :
% 0.37/0.71 ( ( ord_less_nat @ X @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.71 & ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_two_pow_divD
% 0.37/0.71 thf(fact_7929_less__two__pow__divI,axiom,
% 0.37/0.71 ! [X: nat,N: nat,M: nat] :
% 0.37/0.71 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.71 => ( ord_less_nat @ X @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_two_pow_divI
% 0.37/0.71 thf(fact_7930_nat__less__power__trans,axiom,
% 0.37/0.71 ! [N: nat,M: nat,K: nat] :
% 0.37/0.71 ( ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 0.37/0.71 => ( ( ord_less_eq_nat @ K @ M )
% 0.37/0.71 => ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_less_power_trans
% 0.37/0.71 thf(fact_7931_num_Osize_I5_J,axiom,
% 0.37/0.71 ! [X2: num] :
% 0.37/0.71 ( ( size_size_num @ ( bit0 @ X2 ) )
% 0.37/0.71 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % num.size(5)
% 0.37/0.71 thf(fact_7932_L2__set__mult__ineq__lemma,axiom,
% 0.37/0.71 ! [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 ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % L2_set_mult_ineq_lemma
% 0.37/0.71 thf(fact_7933_plus__inverse__ge__2,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % plus_inverse_ge_2
% 0.37/0.71 thf(fact_7934_numeral__1__eq__Suc__0,axiom,
% 0.37/0.71 ( ( numeral_numeral_nat @ one )
% 0.37/0.71 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % numeral_1_eq_Suc_0
% 0.37/0.71 thf(fact_7935_Suc__nat__number__of__add,axiom,
% 0.37/0.71 ! [V2: num,N: nat] :
% 0.37/0.71 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ N ) )
% 0.37/0.71 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ one ) ) @ N ) ) ).
% 0.37/0.71
% 0.37/0.71 % Suc_nat_number_of_add
% 0.37/0.71 thf(fact_7936_VEBT__internal_Oinsert_H_Osimps_I2_J,axiom,
% 0.37/0.71 ! [Deg: nat,X: nat,Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.71 ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 0.37/0.71 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) )
% 0.37/0.71 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 0.37/0.71 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.71 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % VEBT_internal.insert'.simps(2)
% 0.37/0.71 thf(fact_7937_nat__div__eq__Suc__0__iff,axiom,
% 0.37/0.71 ! [N: nat,M: nat] :
% 0.37/0.71 ( ( ( divide_divide_nat @ N @ M )
% 0.37/0.71 = ( suc @ zero_zero_nat ) )
% 0.37/0.71 = ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.71 & ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % nat_div_eq_Suc_0_iff
% 0.37/0.71 thf(fact_7938_power__2__mult__step__le,axiom,
% 0.37/0.71 ! [N3: nat,N: nat,K6: nat,K: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ N3 @ N )
% 0.37/0.71 => ( ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ K6 ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) )
% 0.37/0.71 => ( ord_less_eq_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( plus_plus_nat @ K6 @ one_one_nat ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % power_2_mult_step_le
% 0.37/0.71 thf(fact_7939_less__log2__of__power,axiom,
% 0.37/0.71 ! [N: nat,M: nat] :
% 0.37/0.71 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.37/0.71 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % less_log2_of_power
% 0.37/0.71 thf(fact_7940_pos__zmod__mult__2,axiom,
% 0.37/0.71 ! [A: int,B: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.71 => ( ( 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 ) )
% 0.37/0.71 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % pos_zmod_mult_2
% 0.37/0.71 thf(fact_7941_le__log2__of__power,axiom,
% 0.37/0.71 ! [N: nat,M: nat] :
% 0.37/0.71 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 0.37/0.71 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % le_log2_of_power
% 0.37/0.71 thf(fact_7942_pos__zdiv__mult__2,axiom,
% 0.37/0.71 ! [A: int,B: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.71 => ( ( 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 ) )
% 0.37/0.71 = ( divide_divide_int @ B @ A ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % pos_zdiv_mult_2
% 0.37/0.71 thf(fact_7943_neg__zdiv__mult__2,axiom,
% 0.37/0.71 ! [A: int,B: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.71 => ( ( 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 ) )
% 0.37/0.71 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % neg_zdiv_mult_2
% 0.37/0.71 thf(fact_7944_exp__bound,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.71 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % exp_bound
% 0.37/0.71 thf(fact_7945_sb__dec__lem_H,axiom,
% 0.37/0.71 ! [K: nat,A: int] :
% 0.37/0.71 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) @ A )
% 0.37/0.71 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % sb_dec_lem'
% 0.37/0.71 thf(fact_7946_real__le__x__sinh,axiom,
% 0.37/0.71 ! [X: real] :
% 0.37/0.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.71 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_le_x_sinh
% 0.37/0.71 thf(fact_7947_real__le__abs__sinh,axiom,
% 0.37/0.71 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % real_le_abs_sinh
% 0.37/0.71 thf(fact_7948_mask__eq__sum__exp__nat,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.71 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.71 @ ( collect_nat
% 0.37/0.71 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % mask_eq_sum_exp_nat
% 0.37/0.71 thf(fact_7949_gauss__sum__nat,axiom,
% 0.37/0.71 ! [N: nat] :
% 0.37/0.71 ( ( groups3542108847815614940at_nat
% 0.37/0.71 @ ^ [X4: nat] : X4
% 0.37/0.71 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.37/0.71 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.71
% 0.37/0.71 % gauss_sum_nat
% 0.37/0.71 thf(fact_7950_sum__power2,axiom,
% 0.37/0.71 ! [K: nat] :
% 0.37/0.71 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.37/0.71 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.37/0.71
% 0.37/0.71 % sum_power2
% 0.37/0.71 thf(fact_7951_VEBT__internal_Oinsert_H_Oelims,axiom,
% 0.37/0.71 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.37/0.71 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 0.37/0.71 = Y )
% 0.37/0.71 => ( ! [A3: $o,B3: $o] :
% 0.37/0.71 ( ( X
% 0.37/0.71 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.71 => ( Y
% 0.37/0.71 != ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) )
% 0.37/0.71 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.71 ( ( X
% 0.37/0.71 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.71 => ~ ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.37/0.71 => ( Y
% 0.37/0.71 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 0.37/0.72 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.insert'.elims
% 0.37/0.72 thf(fact_7952_log2__of__power__less,axiom,
% 0.37/0.72 ! [M: nat,N: nat] :
% 0.37/0.72 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.72 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % log2_of_power_less
% 0.37/0.72 thf(fact_7953_sb__inc__lem,axiom,
% 0.37/0.72 ! [A: int,K: nat] :
% 0.37/0.72 ( ( ord_less_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ zero_zero_int )
% 0.37/0.72 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % sb_inc_lem
% 0.37/0.72 thf(fact_7954_sb__inc__lem_H,axiom,
% 0.37/0.72 ! [A: int,K: nat] :
% 0.37/0.72 ( ( ord_less_int @ A @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) )
% 0.37/0.72 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % sb_inc_lem'
% 0.37/0.72 thf(fact_7955_neg__zmod__mult__2,axiom,
% 0.37/0.72 ! [A: int,B: int] :
% 0.37/0.72 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.72 => ( ( 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 ) )
% 0.37/0.72 = ( 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 ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % neg_zmod_mult_2
% 0.37/0.72 thf(fact_7956_sb__dec__lem,axiom,
% 0.37/0.72 ! [K: nat,A: int] :
% 0.37/0.72 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) )
% 0.37/0.72 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % sb_dec_lem
% 0.37/0.72 thf(fact_7957_ln__one__plus__pos__lower__bound,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.72 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % ln_one_plus_pos_lower_bound
% 0.37/0.72 thf(fact_7958_real__exp__bound__lemma,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.72 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % real_exp_bound_lemma
% 0.37/0.72 thf(fact_7959_pos__eucl__rel__int__mult__2,axiom,
% 0.37/0.72 ! [B: int,A: int,Q3: int,R: int] :
% 0.37/0.72 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.72 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.72 => ( 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 @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % pos_eucl_rel_int_mult_2
% 0.37/0.72 thf(fact_7960_arith__series__nat,axiom,
% 0.37/0.72 ! [A: nat,D: nat,N: nat] :
% 0.37/0.72 ( ( groups3542108847815614940at_nat
% 0.37/0.72 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 0.37/0.72 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.37/0.72 = ( 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 ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % arith_series_nat
% 0.37/0.72 thf(fact_7961_sinh__ln__real,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 0.37/0.72 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % sinh_ln_real
% 0.37/0.72 thf(fact_7962_pred__bound__size__univ_H,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % pred_bound_size_univ'
% 0.37/0.72 thf(fact_7963_succ__bound__size__univ_H,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % succ_bound_size_univ'
% 0.37/0.72 thf(fact_7964_Sum__Icc__int,axiom,
% 0.37/0.72 ! [M: int,N: int] :
% 0.37/0.72 ( ( ord_less_eq_int @ M @ N )
% 0.37/0.72 => ( ( groups4538972089207619220nt_int
% 0.37/0.72 @ ^ [X4: int] : X4
% 0.37/0.72 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 0.37/0.72 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Sum_Icc_int
% 0.37/0.72 thf(fact_7965_log2__of__power__le,axiom,
% 0.37/0.72 ! [M: nat,N: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.72 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % log2_of_power_le
% 0.37/0.72 thf(fact_7966_exp__lower__Taylor__quadratic,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % exp_lower_Taylor_quadratic
% 0.37/0.72 thf(fact_7967_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.72 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 0.37/0.72 thf(fact_7968_floor__log2__div2,axiom,
% 0.37/0.72 ! [N: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.72 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.37/0.72 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % floor_log2_div2
% 0.37/0.72 thf(fact_7969_invar__vebt_Ointros_I2_J,axiom,
% 0.37/0.72 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.37/0.72 ( ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( M = N )
% 0.37/0.72 => ( ( Deg
% 0.37/0.72 = ( plus_plus_nat @ N @ M ) )
% 0.37/0.72 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.37/0.72 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % invar_vebt.intros(2)
% 0.37/0.72 thf(fact_7970_neg__eucl__rel__int__mult__2,axiom,
% 0.37/0.72 ! [B: int,A: int,Q3: int,R: int] :
% 0.37/0.72 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.37/0.72 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.72 => ( 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 @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % neg_eucl_rel_int_mult_2
% 0.37/0.72 thf(fact_7971_binomial__code,axiom,
% 0.37/0.72 ( binomial
% 0.37/0.72 = ( ^ [N6: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N6 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N6 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N6 @ ( minus_minus_nat @ N6 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N6 @ K3 ) @ one_one_nat ) @ N6 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % binomial_code
% 0.37/0.72 thf(fact_7972_floor__log__nat__eq__if,axiom,
% 0.37/0.72 ! [B: nat,N: nat,K: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.37/0.72 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.37/0.72 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.37/0.72 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % floor_log_nat_eq_if
% 0.37/0.72 thf(fact_7973_invar__vebt_Ointros_I3_J,axiom,
% 0.37/0.72 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 0.37/0.72 ( ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( M
% 0.37/0.72 = ( suc @ N ) )
% 0.37/0.72 => ( ( Deg
% 0.37/0.72 = ( plus_plus_nat @ N @ M ) )
% 0.37/0.72 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 0.37/0.72 => ( ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % invar_vebt.intros(3)
% 0.37/0.72 thf(fact_7974_arctan__double,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.72 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 0.37/0.72 = ( 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 ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % arctan_double
% 0.37/0.72 thf(fact_7975_central__binomial__lower__bound,axiom,
% 0.37/0.72 ! [N: nat] :
% 0.37/0.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.72 => ( 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 ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % central_binomial_lower_bound
% 0.37/0.72 thf(fact_7976_floor__log__nat__eq__powr__iff,axiom,
% 0.37/0.72 ! [B: nat,K: nat,N: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.72 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.37/0.72 = ( semiri1314217659103216013at_int @ N ) )
% 0.37/0.72 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.37/0.72 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % floor_log_nat_eq_powr_iff
% 0.37/0.72 thf(fact_7977_ln__one__minus__pos__lower__bound,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.72 => ( 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 ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % ln_one_minus_pos_lower_bound
% 0.37/0.72 thf(fact_7978_abs__ln__one__plus__x__minus__x__bound,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.72 => ( 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 ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % abs_ln_one_plus_x_minus_x_bound
% 0.37/0.72 thf(fact_7979_ceiling__log__nat__eq__if,axiom,
% 0.37/0.72 ! [B: nat,N: nat,K: nat] :
% 0.37/0.72 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.37/0.72 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.37/0.72 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.37/0.72 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % ceiling_log_nat_eq_if
% 0.37/0.72 thf(fact_7980_ceiling__log2__div2,axiom,
% 0.37/0.72 ! [N: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.72 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.37/0.72 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( 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 ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % ceiling_log2_div2
% 0.37/0.72 thf(fact_7981_ceiling__log__nat__eq__powr__iff,axiom,
% 0.37/0.72 ! [B: nat,K: nat,N: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.72 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 0.37/0.72 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 0.37/0.72 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 0.37/0.72 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % ceiling_log_nat_eq_powr_iff
% 0.37/0.72 thf(fact_7982_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.72 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.72 => ( 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 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 0.37/0.72 thf(fact_7983_Tb__T__vebt__buildupi,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ ( vEBT_V441764108873111860ildupi @ N ) ) @ ( minus_minus_int @ ( vEBT_VEBT_Tb @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Tb_T_vebt_buildupi
% 0.37/0.72 thf(fact_7984_Tb__T__vebt__buildupi_H,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_eq_int @ ( vEBT_V9176841429113362141ildupi @ N ) @ ( minus_minus_int @ ( vEBT_VEBT_Tb @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Tb_T_vebt_buildupi'
% 0.37/0.72 thf(fact_7985_htt__vebt__memberi__invar__vebt,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X )
% 0.37/0.72 @ ^ [R5: $o] :
% 0.37/0.72 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.72 @ ( pure_assn
% 0.37/0.72 @ ( R5
% 0.37/0.72 = ( vEBT_vebt_member @ T @ X ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_memberi_invar_vebt
% 0.37/0.72 thf(fact_7986_Tb__T__vebt__buildupi_H_H,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_eq_nat @ ( vEBT_V441764108873111860ildupi @ N ) @ ( minus_minus_nat @ ( vEBT_VEBT_Tb2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Tb_T_vebt_buildupi''
% 0.37/0.72 thf(fact_7987_htt__vebt__predi,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_predi @ Ti @ X )
% 0.37/0.72 @ ^ [R5: option_nat] :
% 0.37/0.72 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.72 @ ( pure_assn
% 0.37/0.72 @ ( R5
% 0.37/0.72 = ( vEBT_vebt_pred @ T @ X ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_predi
% 0.37/0.72 thf(fact_7988_Tb__Tb_H,axiom,
% 0.37/0.72 ( vEBT_VEBT_Tb
% 0.37/0.72 = ( ^ [T2: nat] : ( semiri1314217659103216013at_int @ ( vEBT_VEBT_Tb2 @ T2 ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Tb_Tb'
% 0.37/0.72 thf(fact_7989_T__vebt__buildupi__univ,axiom,
% 0.37/0.72 ! [U: nat,N: nat] :
% 0.37/0.72 ( ( U
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_V441764108873111860ildupi @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T_vebt_buildupi_univ
% 0.37/0.72 thf(fact_7990_tdeletemimi,axiom,
% 0.37/0.72 ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % tdeletemimi
% 0.37/0.72 thf(fact_7991_semiring__norm_I73_J,axiom,
% 0.37/0.72 ! [M: num,N: num] :
% 0.37/0.72 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.37/0.72 = ( ord_less_eq_num @ M @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(73)
% 0.37/0.72 thf(fact_7992_semiring__norm_I80_J,axiom,
% 0.37/0.72 ! [M: num,N: num] :
% 0.37/0.72 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.37/0.72 = ( ord_less_num @ M @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(80)
% 0.37/0.72 thf(fact_7993_minNull__delete__time__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % minNull_delete_time_bound
% 0.37/0.72 thf(fact_7994_Tb_H__cnt,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_eq_nat @ ( vEBT_VEBT_Tb2 @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_cnt2 @ ( vEBT_vebt_buildup @ N ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Tb'_cnt
% 0.37/0.72 thf(fact_7995_TBOUND__vebt__predi,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T8353473612707095248on_nat @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % TBOUND_vebt_predi
% 0.37/0.72 thf(fact_7996_TBOUND__vebt__succi,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T8353473612707095248on_nat @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % TBOUND_vebt_succi
% 0.37/0.72 thf(fact_7997_T__vebt__buildupi__cnt_H,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V441764108873111860ildupi @ N ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T_vebt_buildupi_cnt'
% 0.37/0.72 thf(fact_7998_TBOUND__buildupi,axiom,
% 0.37/0.72 ! [N: nat] :
% 0.37/0.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.72 => ( time_T5737551269749752165_VEBTi @ ( vEBT_vebt_buildupi @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % TBOUND_buildupi
% 0.37/0.72 thf(fact_7999_delete__bound__height,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % delete_bound_height
% 0.37/0.72 thf(fact_8000_cnt__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % cnt_bound
% 0.37/0.72 thf(fact_8001_TBOUND__vebt__inserti,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) @ ( if_nat @ ( vEBT_VEBT_minNull @ T ) @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % TBOUND_vebt_inserti
% 0.37/0.72 thf(fact_8002_htt__vebt__buildupi__univ,axiom,
% 0.37/0.72 ! [U: nat,N: nat] :
% 0.37/0.72 ( ( U
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_buildupi_univ
% 0.37/0.72 thf(fact_8003_htt__vebt__buildupi_H__univ,axiom,
% 0.37/0.72 ! [U: nat,N: nat] :
% 0.37/0.72 ( ( U
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_buildupi'_univ
% 0.37/0.72 thf(fact_8004_delete__bound__size__univ,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % delete_bound_size_univ
% 0.37/0.72 thf(fact_8005_time__vebt__delete,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % time_vebt_delete
% 0.37/0.72 thf(fact_8006_time__vebt__pred,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % time_vebt_pred
% 0.37/0.72 thf(fact_8007_time__vebt__succ,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % time_vebt_succ
% 0.37/0.72 thf(fact_8008_htt__vebt__inserti,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_inserti
% 0.37/0.72 thf(fact_8009_semiring__norm_I81_J,axiom,
% 0.37/0.72 ! [M: num,N: num] :
% 0.37/0.72 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.37/0.72 = ( ord_less_num @ M @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(81)
% 0.37/0.72 thf(fact_8010_semiring__norm_I72_J,axiom,
% 0.37/0.72 ! [M: num,N: num] :
% 0.37/0.72 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.37/0.72 = ( ord_less_eq_num @ M @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(72)
% 0.37/0.72 thf(fact_8011_semiring__norm_I77_J,axiom,
% 0.37/0.72 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(77)
% 0.37/0.72 thf(fact_8012_semiring__norm_I70_J,axiom,
% 0.37/0.72 ! [M: num] :
% 0.37/0.72 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(70)
% 0.37/0.72 thf(fact_8013_TBOUND__vebt__deletei,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V1365221501068881998eletei @ T @ Ti @ X ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) ) @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % TBOUND_vebt_deletei
% 0.37/0.72 thf(fact_8014_htt__vebt__memberi,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.72 ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X )
% 0.37/0.72 @ ^ [R5: $o] :
% 0.37/0.72 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.72 @ ( pure_assn
% 0.37/0.72 @ ( R5
% 0.37/0.72 = ( vEBT_vebt_member @ T @ X ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_memberi
% 0.37/0.72 thf(fact_8015_zdiv__numeral__Bit1,axiom,
% 0.37/0.72 ! [V2: num,W2: num] :
% 0.37/0.72 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.37/0.72 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % zdiv_numeral_Bit1
% 0.37/0.72 thf(fact_8016_semiring__norm_I79_J,axiom,
% 0.37/0.72 ! [M: num,N: num] :
% 0.37/0.72 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.37/0.72 = ( ord_less_eq_num @ M @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(79)
% 0.37/0.72 thf(fact_8017_semiring__norm_I74_J,axiom,
% 0.37/0.72 ! [M: num,N: num] :
% 0.37/0.72 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.37/0.72 = ( ord_less_num @ M @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % semiring_norm(74)
% 0.37/0.72 thf(fact_8018_htt__vebt__inserti__invar__vebt,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_inserti_invar_vebt
% 0.37/0.72 thf(fact_8019_htt__vebt__deletei,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_deletei @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ T @ X ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_deletei
% 0.37/0.72 thf(fact_8020_htt__vebt__succi,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_succi @ Ti @ X )
% 0.37/0.72 @ ^ [R5: option_nat] :
% 0.37/0.72 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 0.37/0.72 @ ( pure_assn
% 0.37/0.72 @ ( R5
% 0.37/0.72 = ( vEBT_vebt_succ @ T @ X ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % htt_vebt_succi
% 0.37/0.72 thf(fact_8021_Suc__div__eq__add3__div__numeral,axiom,
% 0.37/0.72 ! [M: nat,V2: num] :
% 0.37/0.72 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 0.37/0.72 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Suc_div_eq_add3_div_numeral
% 0.37/0.72 thf(fact_8022_div__Suc__eq__div__add3,axiom,
% 0.37/0.72 ! [M: nat,N: nat] :
% 0.37/0.72 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.37/0.72 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % div_Suc_eq_div_add3
% 0.37/0.72 thf(fact_8023_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.37/0.72 ! [M: nat,V2: num] :
% 0.37/0.72 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 0.37/0.72 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % Suc_mod_eq_add3_mod_numeral
% 0.37/0.72 thf(fact_8024_mod__Suc__eq__mod__add3,axiom,
% 0.37/0.72 ! [M: nat,N: nat] :
% 0.37/0.72 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.37/0.72 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % mod_Suc_eq_mod_add3
% 0.37/0.72 thf(fact_8025_zmod__numeral__Bit1,axiom,
% 0.37/0.72 ! [V2: num,W2: num] :
% 0.37/0.72 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.37/0.72 = ( 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 ) ) ).
% 0.37/0.72
% 0.37/0.72 % zmod_numeral_Bit1
% 0.37/0.72 thf(fact_8026_VEBT__internal_OTb_H_Osimps_I1_J,axiom,
% 0.37/0.72 ( ( vEBT_VEBT_Tb2 @ zero_zero_nat )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.Tb'.simps(1)
% 0.37/0.72 thf(fact_8027_VEBT__internal_OTb_H_Osimps_I2_J,axiom,
% 0.37/0.72 ( ( vEBT_VEBT_Tb2 @ ( suc @ zero_zero_nat ) )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.Tb'.simps(2)
% 0.37/0.72 thf(fact_8028_eval__nat__numeral_I3_J,axiom,
% 0.37/0.72 ! [N: num] :
% 0.37/0.72 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.37/0.72 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % eval_nat_numeral(3)
% 0.37/0.72 thf(fact_8029_numeral__3__eq__3,axiom,
% 0.37/0.72 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % numeral_3_eq_3
% 0.37/0.72 thf(fact_8030_Suc3__eq__add__3,axiom,
% 0.37/0.72 ! [N: nat] :
% 0.37/0.72 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.37/0.72 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % Suc3_eq_add_3
% 0.37/0.72 thf(fact_8031_maxt__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % maxt_bound
% 0.37/0.72 thf(fact_8032_VEBT__internal_OTb_Osimps_I1_J,axiom,
% 0.37/0.72 ( ( vEBT_VEBT_Tb @ zero_zero_nat )
% 0.37/0.72 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.Tb.simps(1)
% 0.37/0.72 thf(fact_8033_mint__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % mint_bound
% 0.37/0.72 thf(fact_8034_num_Osize_I6_J,axiom,
% 0.37/0.72 ! [X32: num] :
% 0.37/0.72 ( ( size_size_num @ ( bit1 @ X32 ) )
% 0.37/0.72 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % num.size(6)
% 0.37/0.72 thf(fact_8035_Suc__div__eq__add3__div,axiom,
% 0.37/0.72 ! [M: nat,N: nat] :
% 0.37/0.72 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.37/0.72 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % Suc_div_eq_add3_div
% 0.37/0.72 thf(fact_8036_Suc__mod__eq__add3__mod,axiom,
% 0.37/0.72 ! [M: nat,N: nat] :
% 0.37/0.72 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 0.37/0.72 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % Suc_mod_eq_add3_mod
% 0.37/0.72 thf(fact_8037_exp__le,axiom,
% 0.37/0.72 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 0.37/0.72
% 0.37/0.72 % exp_le
% 0.37/0.72 thf(fact_8038_VEBT__internal_OTb_Osimps_I2_J,axiom,
% 0.37/0.72 ( ( vEBT_VEBT_Tb @ ( suc @ zero_zero_nat ) )
% 0.37/0.72 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.Tb.simps(2)
% 0.37/0.72 thf(fact_8039_mod__exhaust__less__4,axiom,
% 0.37/0.72 ! [M: nat] :
% 0.37/0.72 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = zero_zero_nat )
% 0.37/0.72 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = one_one_nat )
% 0.37/0.72 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.72 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % mod_exhaust_less_4
% 0.37/0.72 thf(fact_8040_insersimp,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,Y: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % insersimp
% 0.37/0.72 thf(fact_8041_insertsimp,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( vEBT_VEBT_minNull @ T )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % insertsimp
% 0.37/0.72 thf(fact_8042_small__powers__of__2,axiom,
% 0.37/0.72 ! [X: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ X )
% 0.37/0.72 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ X @ one_one_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % small_powers_of_2
% 0.37/0.72 thf(fact_8043_log__base__10__eq2,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.72 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % log_base_10_eq2
% 0.37/0.72 thf(fact_8044_pred__bound__height,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % pred_bound_height
% 0.37/0.72 thf(fact_8045_insert__bound__height,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % insert_bound_height
% 0.37/0.72 thf(fact_8046_succ__bound__height,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % succ_bound_height
% 0.37/0.72 thf(fact_8047_log__base__10__eq1,axiom,
% 0.37/0.72 ! [X: real] :
% 0.37/0.72 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.72 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.72 = ( 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 ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % log_base_10_eq1
% 0.37/0.72 thf(fact_8048_pred__bound__size__univ,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % pred_bound_size_univ
% 0.37/0.72 thf(fact_8049_succ__bound__size__univ,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % succ_bound_size_univ
% 0.37/0.72 thf(fact_8050_insert__bound__size__univ,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % insert_bound_size_univ
% 0.37/0.72 thf(fact_8051_VEBT__internal_Ovebt__buildupi__rule,axiom,
% 0.37/0.72 ! [N: nat] : ( time_htt_VEBT_VEBTi @ ( pure_assn @ ( ord_less_nat @ zero_zero_nat @ N ) ) @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.vebt_buildupi_rule
% 0.37/0.72 thf(fact_8052_vebt__buildupi__rule,axiom,
% 0.37/0.72 ! [N: nat] : ( time_htt_VEBT_VEBTi @ ( pure_assn @ ( ord_less_nat @ zero_zero_nat @ N ) ) @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_Intf_vebt_assn @ N @ bot_bot_set_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_buildupi_rule
% 0.37/0.72 thf(fact_8053_vebt__memberi__rule,axiom,
% 0.37/0.72 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,X: nat] :
% 0.37/0.72 ( time_htt_o @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X )
% 0.37/0.72 @ ^ [R5: $o] :
% 0.37/0.72 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 0.37/0.72 @ ( pure_assn
% 0.37/0.72 @ ( R5
% 0.37/0.72 = ( member_nat @ X @ S ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_memberi_rule
% 0.37/0.72 thf(fact_8054_vebt__predi__rule,axiom,
% 0.37/0.72 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,X: nat,Y: nat] :
% 0.37/0.72 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_predi @ Ti @ X )
% 0.37/0.72 @ ^ [R5: option_nat] :
% 0.37/0.72 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 0.37/0.72 @ ( pure_assn
% 0.37/0.72 @ ( ( R5
% 0.37/0.72 = ( some_nat @ Y ) )
% 0.37/0.72 = ( vEBT_is_pred_in_set @ S @ X @ Y ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_predi_rule
% 0.37/0.72 thf(fact_8055_vebt__succi__rule,axiom,
% 0.37/0.72 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,X: nat,Y: nat] :
% 0.37/0.72 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_succi @ Ti @ X )
% 0.37/0.72 @ ^ [R5: option_nat] :
% 0.37/0.72 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 0.37/0.72 @ ( pure_assn
% 0.37/0.72 @ ( ( R5
% 0.37/0.72 = ( some_nat @ Y ) )
% 0.37/0.72 = ( vEBT_is_succ_in_set @ S @ X @ Y ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_succi_rule
% 0.37/0.72 thf(fact_8056_vebt__inserti__rule,axiom,
% 0.37/0.72 ! [X: nat,N: nat,S: set_nat,Ti: vEBT_VEBTi] :
% 0.37/0.72 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( time_htt_VEBT_VEBTi @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_Intf_vebt_assn @ N @ ( sup_sup_set_nat @ S @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_inserti_rule
% 0.37/0.72 thf(fact_8057_space__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_VEBT_space @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % space_bound
% 0.37/0.72 thf(fact_8058_vebt__space__linear__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_VEBT_space @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_space_linear_bound
% 0.37/0.72 thf(fact_8059_space__2__pow__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % space_2_pow_bound
% 0.37/0.72 thf(fact_8060_space__space_H,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT] : ( ord_less_nat @ ( vEBT_VEBT_space @ T ) @ ( vEBT_VEBT_space2 @ T ) ) ).
% 0.37/0.72
% 0.37/0.72 % space_space'
% 0.37/0.72 thf(fact_8061_space_H__bound,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.72 => ( ( U
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_VEBT_space2 @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % space'_bound
% 0.37/0.72 thf(fact_8062_space__cnt,axiom,
% 0.37/0.72 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_cnt @ T ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % space_cnt
% 0.37/0.72 thf(fact_8063_VEBT__internal_Ospace_H_Osimps_I1_J,axiom,
% 0.37/0.72 ! [A: $o,B: $o] :
% 0.37/0.72 ( ( vEBT_VEBT_space2 @ ( vEBT_Leaf @ A @ B ) )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space'.simps(1)
% 0.37/0.72 thf(fact_8064_VEBT__internal_Ospace_Osimps_I1_J,axiom,
% 0.37/0.72 ! [A: $o,B: $o] :
% 0.37/0.72 ( ( vEBT_VEBT_space @ ( vEBT_Leaf @ A @ B ) )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space.simps(1)
% 0.37/0.72 thf(fact_8065_VEBT__internal_Ospace_H_Osimps_I2_J,axiom,
% 0.37/0.72 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( vEBT_VEBT_space2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 0.37/0.72 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList ) @ zero_zero_nat ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space'.simps(2)
% 0.37/0.72 thf(fact_8066_VEBT__internal_Ospace_H_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_VEBT_space2 @ X )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space'.elims
% 0.37/0.72 thf(fact_8067_VEBT__internal_Ospace_Osimps_I2_J,axiom,
% 0.37/0.72 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( vEBT_VEBT_space @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 0.37/0.72 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList ) @ zero_zero_nat ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space.simps(2)
% 0.37/0.72 thf(fact_8068_VEBT__internal_Ospace_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_VEBT_space @ X )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 0.37/0.72 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space.elims
% 0.37/0.72 thf(fact_8069_t__build__cnt,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % t_build_cnt
% 0.37/0.72 thf(fact_8070_t__buildup__cnt,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8346862874174094_d_u_p @ N ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % t_buildup_cnt
% 0.37/0.72 thf(fact_8071_vebt__buildup__bound,axiom,
% 0.37/0.72 ! [U: nat,N: nat] :
% 0.37/0.72 ( ( U
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ord_less_eq_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ U ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_buildup_bound
% 0.37/0.72 thf(fact_8072_buildup__build__time,axiom,
% 0.37/0.72 ! [N: nat] : ( ord_less_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) ).
% 0.37/0.72
% 0.37/0.72 % buildup_build_time
% 0.37/0.72 thf(fact_8073_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I1_J,axiom,
% 0.37/0.72 ( ( vEBT_V8346862874174094_d_u_p @ zero_zero_nat )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(1)
% 0.37/0.72 thf(fact_8074_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I1_J,axiom,
% 0.37/0.72 ( ( vEBT_V8646137997579335489_i_l_d @ zero_zero_nat )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(1)
% 0.37/0.72 thf(fact_8075_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I2_J,axiom,
% 0.37/0.72 ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ zero_zero_nat ) )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(2)
% 0.37/0.72 thf(fact_8076_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I2_J,axiom,
% 0.37/0.72 ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ zero_zero_nat ) )
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(2)
% 0.37/0.72 thf(fact_8077_div__half__nat,axiom,
% 0.37/0.72 ! [Y: nat,X: nat] :
% 0.37/0.72 ( ( Y != zero_zero_nat )
% 0.37/0.72 => ( ( product_Pair_nat_nat @ ( divide_divide_nat @ X @ Y ) @ ( modulo_modulo_nat @ X @ Y ) )
% 0.37/0.72 = ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ Y @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) @ Y ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % div_half_nat
% 0.37/0.72 thf(fact_8078_VEBT__internal_Ospace_Opelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_VEBT_space @ X )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ X )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Y
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.72 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.72 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( Y
% 0.37/0.72 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) )
% 0.37/0.72 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space.pelims
% 0.37/0.72 thf(fact_8079_VEBT__internal_Ospace_H_Opelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_VEBT_space2 @ X )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ X )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Y
% 0.37/0.72 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.72 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.72 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( Y
% 0.37/0.72 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) )
% 0.37/0.72 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.space'.pelims
% 0.37/0.72 thf(fact_8080_VEBT__internal_Oinsert_H_Opelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.37/0.72 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Y
% 0.37/0.72 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.37/0.72 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.72 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 0.37/0.72 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.72 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.insert'.pelims
% 0.37/0.72 thf(fact_8081_pred__list__to__short,axiom,
% 0.37/0.72 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ord_less_eq_nat @ X @ Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = none_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % pred_list_to_short
% 0.37/0.72 thf(fact_8082_high__def,axiom,
% 0.37/0.72 ( vEBT_VEBT_high
% 0.37/0.72 = ( ^ [X4: nat,N6: nat] : ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % high_def
% 0.37/0.72 thf(fact_8083_high__bound__aux,axiom,
% 0.37/0.72 ! [Ma: nat,N: nat,M: nat] :
% 0.37/0.72 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.37/0.72 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % high_bound_aux
% 0.37/0.72 thf(fact_8084_high__inv,axiom,
% 0.37/0.72 ! [X: nat,N: nat,Y: nat] :
% 0.37/0.72 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.37/0.72 = Y ) ) ).
% 0.37/0.72
% 0.37/0.72 % high_inv
% 0.37/0.72 thf(fact_8085_succ__list__to__short,axiom,
% 0.37/0.72 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ord_less_eq_nat @ Mi @ X )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = none_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % succ_list_to_short
% 0.37/0.72 thf(fact_8086_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 0.37/0.72 ! [L: code_integer,U: code_integer] :
% 0.37/0.72 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 0.37/0.72 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 0.37/0.72
% 0.37/0.72 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 0.37/0.72 thf(fact_8087_plus__integer__code_I1_J,axiom,
% 0.37/0.72 ! [K: code_integer] :
% 0.37/0.72 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 0.37/0.72 = K ) ).
% 0.37/0.72
% 0.37/0.72 % plus_integer_code(1)
% 0.37/0.72 thf(fact_8088_plus__integer__code_I2_J,axiom,
% 0.37/0.72 ! [L: code_integer] :
% 0.37/0.72 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 0.37/0.72 = L ) ).
% 0.37/0.72
% 0.37/0.72 % plus_integer_code(2)
% 0.37/0.72 thf(fact_8089_image__add__integer__atLeastLessThan,axiom,
% 0.37/0.72 ! [L: code_integer,U: code_integer] :
% 0.37/0.72 ( ( image_4470545334726330049nteger
% 0.37/0.72 @ ^ [X4: code_integer] : ( plus_p5714425477246183910nteger @ X4 @ L )
% 0.37/0.72 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 0.37/0.72 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 0.37/0.72
% 0.37/0.72 % image_add_integer_atLeastLessThan
% 0.37/0.72 thf(fact_8090_uminus__integer__code_I1_J,axiom,
% 0.37/0.72 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.37/0.72 = zero_z3403309356797280102nteger ) ).
% 0.37/0.72
% 0.37/0.72 % uminus_integer_code(1)
% 0.37/0.72 thf(fact_8091_minus__integer__code_I1_J,axiom,
% 0.37/0.72 ! [K: code_integer] :
% 0.37/0.72 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 0.37/0.72 = K ) ).
% 0.37/0.72
% 0.37/0.72 % minus_integer_code(1)
% 0.37/0.72 thf(fact_8092_minus__integer__code_I2_J,axiom,
% 0.37/0.72 ! [L: code_integer] :
% 0.37/0.72 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 0.37/0.72 = ( uminus1351360451143612070nteger @ L ) ) ).
% 0.37/0.72
% 0.37/0.72 % minus_integer_code(2)
% 0.37/0.72 thf(fact_8093_finite__atLeastZeroLessThan__integer,axiom,
% 0.37/0.72 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 0.37/0.72
% 0.37/0.72 % finite_atLeastZeroLessThan_integer
% 0.37/0.72 thf(fact_8094_times__integer__code_I2_J,axiom,
% 0.37/0.72 ! [L: code_integer] :
% 0.37/0.72 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 0.37/0.72 = zero_z3403309356797280102nteger ) ).
% 0.37/0.72
% 0.37/0.72 % times_integer_code(2)
% 0.37/0.72 thf(fact_8095_times__integer__code_I1_J,axiom,
% 0.37/0.72 ! [K: code_integer] :
% 0.37/0.72 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 0.37/0.72 = zero_z3403309356797280102nteger ) ).
% 0.37/0.72
% 0.37/0.72 % times_integer_code(1)
% 0.37/0.72 thf(fact_8096_less__eq__integer__code_I1_J,axiom,
% 0.37/0.72 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 0.37/0.72
% 0.37/0.72 % less_eq_integer_code(1)
% 0.37/0.72 thf(fact_8097_sgn__integer__code,axiom,
% 0.37/0.72 ( sgn_sgn_Code_integer
% 0.37/0.72 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % sgn_integer_code
% 0.37/0.72 thf(fact_8098_abs__integer__code,axiom,
% 0.37/0.72 ( abs_abs_Code_integer
% 0.37/0.72 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % abs_integer_code
% 0.37/0.72 thf(fact_8099_less__integer__code_I1_J,axiom,
% 0.37/0.72 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 0.37/0.72
% 0.37/0.72 % less_integer_code(1)
% 0.37/0.72 thf(fact_8100_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 0.37/0.72 ! [X: nat,N: nat,M: nat] :
% 0.37/0.72 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.72 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.exp_split_high_low(1)
% 0.37/0.72 thf(fact_8101_nested__mint,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va2: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 0.37/0.72 => ( ( N
% 0.37/0.72 = ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 0.37/0.72 => ( ( Ma != Mi )
% 0.37/0.72 => ( 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 @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % nested_mint
% 0.37/0.72 thf(fact_8102_insert__simp__norm,axiom,
% 0.37/0.72 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( ord_less_nat @ Mi @ X )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( X != Ma )
% 0.37/0.72 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % insert_simp_norm
% 0.37/0.72 thf(fact_8103_insert__simp__excp,axiom,
% 0.37/0.72 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( X != Ma )
% 0.37/0.72 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % insert_simp_excp
% 0.37/0.72 thf(fact_8104_bit__split__inv,axiom,
% 0.37/0.72 ! [X: nat,D: nat] :
% 0.37/0.72 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 0.37/0.72 = X ) ).
% 0.37/0.72
% 0.37/0.72 % bit_split_inv
% 0.37/0.72 thf(fact_8105_low__def,axiom,
% 0.37/0.72 ( vEBT_VEBT_low
% 0.37/0.72 = ( ^ [X4: nat,N6: nat] : ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % low_def
% 0.37/0.72 thf(fact_8106_low__inv,axiom,
% 0.37/0.72 ! [X: nat,N: nat,Y: nat] :
% 0.37/0.72 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.72 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.37/0.72 = X ) ) ).
% 0.37/0.72
% 0.37/0.72 % low_inv
% 0.37/0.72 thf(fact_8107_summaxma,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 0.37/0.72 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % summaxma
% 0.37/0.72 thf(fact_8108_both__member__options__ding,axiom,
% 0.37/0.72 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 0.37/0.72 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.37/0.72 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % both_member_options_ding
% 0.37/0.72 thf(fact_8109_finite__atLeastLessThan__integer,axiom,
% 0.37/0.72 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 0.37/0.72
% 0.37/0.72 % finite_atLeastLessThan_integer
% 0.37/0.72 thf(fact_8110_both__member__options__from__complete__tree__to__child,axiom,
% 0.37/0.72 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.37/0.72 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) )
% 0.37/0.72 | ( X = Mi )
% 0.37/0.72 | ( X = Ma ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % both_member_options_from_complete_tree_to_child
% 0.37/0.72 thf(fact_8111_finite__atLeastAtMost__integer,axiom,
% 0.37/0.72 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 0.37/0.72
% 0.37/0.72 % finite_atLeastAtMost_integer
% 0.37/0.72 thf(fact_8112_member__inv,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 & ( ( X = Mi )
% 0.37/0.72 | ( X = Ma )
% 0.37/0.72 | ( ( ord_less_nat @ X @ Ma )
% 0.37/0.72 & ( ord_less_nat @ Mi @ X )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % member_inv
% 0.37/0.72 thf(fact_8113_both__member__options__from__chilf__to__complete__tree,axiom,
% 0.37/0.72 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.37/0.72 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % both_member_options_from_chilf_to_complete_tree
% 0.37/0.72 thf(fact_8114_del__x__not__mi__newnode__not__nil,axiom,
% 0.37/0.72 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ Mi @ X )
% 0.37/0.72 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( Newnode
% 0.37/0.72 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( Newlist
% 0.37/0.72 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_not_mi_newnode_not_nil
% 0.37/0.72 thf(fact_8115_del__x__mi__lets__in__not__minNull,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.37/0.72 ( ( ( X = Mi )
% 0.37/0.72 & ( ord_less_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( Xn
% 0.37/0.72 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( Newnode
% 0.37/0.72 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 => ( ( Newlist
% 0.37/0.72 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.37/0.72 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_mi_lets_in_not_minNull
% 0.37/0.72 thf(fact_8116_del__x__not__mi,axiom,
% 0.37/0.72 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ Mi @ X )
% 0.37/0.72 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( Newnode
% 0.37/0.72 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 => ( ( Newlist
% 0.37/0.72 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( product_Pair_nat_nat @ Mi
% 0.37/0.72 @ ( if_nat @ ( X = Ma )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ Mi
% 0.37/0.72 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ Newlist
% 0.37/0.72 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.37/0.72 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_not_mi
% 0.37/0.72 thf(fact_8117_del__x__not__mi__new__node__nil,axiom,
% 0.37/0.72 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ Mi @ X )
% 0.37/0.72 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( Newnode
% 0.37/0.72 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( Sn
% 0.37/0.72 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 => ( ( Newlist
% 0.37/0.72 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( product_Pair_nat_nat @ Mi
% 0.37/0.72 @ ( if_nat @ ( X = Ma )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_maxt @ Sn )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ Mi
% 0.37/0.72 @ ( 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 ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ Newlist
% 0.37/0.72 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_not_mi_new_node_nil
% 0.37/0.72 thf(fact_8118_del__x__not__mia,axiom,
% 0.37/0.72 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ Mi @ X )
% 0.37/0.72 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( product_Pair_nat_nat @ Mi
% 0.37/0.72 @ ( if_nat @ ( X = Ma )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ Mi
% 0.37/0.72 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_not_mia
% 0.37/0.72 thf(fact_8119_del__x__mia,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( X = Mi )
% 0.37/0.72 & ( ord_less_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ Summary ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_mia
% 0.37/0.72 thf(fact_8120_del__x__mi__lets__in__minNull,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 0.37/0.72 ( ( ( X = Mi )
% 0.37/0.72 & ( ord_less_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( Xn
% 0.37/0.72 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( Newnode
% 0.37/0.72 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 => ( ( Newlist
% 0.37/0.72 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.37/0.72 => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( Sn
% 0.37/0.72 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( product_Pair_nat_nat @ Xn
% 0.37/0.72 @ ( if_nat @ ( Xn = Ma )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_maxt @ Sn )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ Xn
% 0.37/0.72 @ ( 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 ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ Newlist
% 0.37/0.72 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_mi_lets_in_minNull
% 0.37/0.72 thf(fact_8121_del__x__mi__lets__in,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.37/0.72 ( ( ( X = Mi )
% 0.37/0.72 & ( ord_less_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( Xn
% 0.37/0.72 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( Newnode
% 0.37/0.72 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 => ( ( Newlist
% 0.37/0.72 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 0.37/0.72 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( product_Pair_nat_nat @ Xn
% 0.37/0.72 @ ( if_nat @ ( Xn = Ma )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ Xn
% 0.37/0.72 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ Newlist
% 0.37/0.72 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 0.37/0.72 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_mi_lets_in
% 0.37/0.72 thf(fact_8122_del__x__mi,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat] :
% 0.37/0.72 ( ( ( X = Mi )
% 0.37/0.72 & ( ord_less_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = H2 )
% 0.37/0.72 => ( ( Xn
% 0.37/0.72 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.37/0.72 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 = L )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( product_Pair_nat_nat @ Xn
% 0.37/0.72 @ ( if_nat @ ( Xn = Ma )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ Xn
% 0.37/0.72 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 0.37/0.72 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_x_mi
% 0.37/0.72 thf(fact_8123_del__in__range,axiom,
% 0.37/0.72 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_eq_nat @ Mi @ X )
% 0.37/0.72 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.37/0.72 => ( ( Mi != Ma )
% 0.37/0.72 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( X = Mi )
% 0.37/0.72 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma ) )
% 0.37/0.72 & ( ( X != Mi )
% 0.37/0.72 => ( X = Ma ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( X = Mi )
% 0.37/0.72 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma ) )
% 0.37/0.72 & ( ( X != Mi )
% 0.37/0.72 => ( X = Ma ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ Deg
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ Summary ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % del_in_range
% 0.37/0.72 thf(fact_8124_succ__less__length__list,axiom,
% 0.37/0.72 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ord_less_eq_nat @ Mi @ X )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ none_nat
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % succ_less_length_list
% 0.37/0.72 thf(fact_8125_succ__greatereq__min,axiom,
% 0.37/0.72 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ord_less_eq_nat @ Mi @ X )
% 0.37/0.72 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ none_nat
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ none_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % succ_greatereq_min
% 0.37/0.72 thf(fact_8126_pred__lesseq__max,axiom,
% 0.37/0.72 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ord_less_eq_nat @ X @ Ma )
% 0.37/0.72 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ none_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % pred_lesseq_max
% 0.37/0.72 thf(fact_8127_pred__less__length__list,axiom,
% 0.37/0.72 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.37/0.72 => ( ( ord_less_eq_nat @ X @ Ma )
% 0.37/0.72 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.37/0.72 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % pred_less_length_list
% 0.37/0.72 thf(fact_8128_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 0.37/0.72 ! [X: nat,N: nat,M: nat] :
% 0.37/0.72 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.72 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.72 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.exp_split_high_low(2)
% 0.37/0.72 thf(fact_8129_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I7_J,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 | ( ord_less_nat @ Ma @ X ) )
% 0.37/0.72 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = one_one_nat ) )
% 0.37/0.72 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 | ( ord_less_nat @ Ma @ X ) )
% 0.37/0.72 => ( ( ( ( X = Mi )
% 0.37/0.72 & ( X = Ma ) )
% 0.37/0.72 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = one_one_nat ) )
% 0.37/0.72 & ( ~ ( ( X = Mi )
% 0.37/0.72 & ( X = Ma ) )
% 0.37/0.72 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_nat @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.simps(7)
% 0.37/0.72 thf(fact_8130_vebt__succ_Osimps_I6_J,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( some_nat @ Mi ) ) )
% 0.37/0.72 & ( ~ ( ord_less_nat @ X @ Mi )
% 0.37/0.72 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ none_nat
% 0.37/0.72 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ none_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_succ.simps(6)
% 0.37/0.72 thf(fact_8131_vebt__pred_Osimps_I7_J,axiom,
% 0.37/0.72 ! [Ma: nat,X: nat,Mi: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ Ma @ X )
% 0.37/0.72 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( some_nat @ Ma ) ) )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma @ X )
% 0.37/0.72 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.37/0.72 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ none_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_pred.simps(7)
% 0.37/0.72 thf(fact_8132_vebt__delete_Osimps_I7_J,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 | ( ord_less_nat @ Ma @ X ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 0.37/0.72 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 | ( ord_less_nat @ Ma @ X ) )
% 0.37/0.72 => ( ( ( ( X = Mi )
% 0.37/0.72 & ( X = Ma ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 0.37/0.72 & ( ~ ( ( X = Mi )
% 0.37/0.72 & ( X = Ma ) )
% 0.37/0.72 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( X = Mi )
% 0.37/0.72 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma ) )
% 0.37/0.72 & ( ( X != Mi )
% 0.37/0.72 => ( X = Ma ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.37/0.72 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ ( suc @ ( suc @ Va2 ) )
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( X = Mi )
% 0.37/0.72 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma ) )
% 0.37/0.72 & ( ( X != Mi )
% 0.37/0.72 => ( X = Ma ) ) )
% 0.37/0.72 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma ) ) )
% 0.37/0.72 @ ( suc @ ( suc @ Va2 ) )
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ Summary ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_delete.simps(7)
% 0.37/0.72 thf(fact_8133_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 0.37/0.72 ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S ) @ X )
% 0.37/0.72 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.naive_member.simps(3)
% 0.37/0.72 thf(fact_8134_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.simps(7)
% 0.37/0.72 thf(fact_8135_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.simps(6)
% 0.37/0.72 thf(fact_8136_vebt__delete_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.37/0.72 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 0.37/0.72 => ( ! [A3: $o] :
% 0.37/0.72 ( ? [B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Xa2
% 0.37/0.72 = ( suc @ zero_zero_nat ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ? [N2: nat] :
% 0.37/0.72 ( Xa2
% 0.37/0.72 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.37/0.72 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 0.37/0.72 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.72 => ( ( ( ( Xa2 = Mi2 )
% 0.37/0.72 & ( Xa2 = Ma2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 0.37/0.72 & ( ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 & ( Xa2 = Ma2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.72 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.72 = Ma2 ) )
% 0.37/0.72 & ( ( Xa2 != Mi2 )
% 0.37/0.72 => ( Xa2 = Ma2 ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma2 ) ) )
% 0.37/0.72 @ ( suc @ ( suc @ Va ) )
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( vEBT_Node
% 0.37/0.72 @ ( some_P7363390416028606310at_nat
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.72 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.72 = Ma2 ) )
% 0.37/0.72 & ( ( Xa2 != Mi2 )
% 0.37/0.72 => ( Xa2 = Ma2 ) ) )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ Ma2 ) ) )
% 0.37/0.72 @ ( suc @ ( suc @ Va ) )
% 0.37/0.72 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ Summary2 ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_delete.elims
% 0.37/0.72 thf(fact_8137_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_V1232361888498592333_e_t_e @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Xa2
% 0.37/0.72 = ( suc @ zero_zero_nat ) )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ? [N2: nat] :
% 0.37/0.72 ( Xa2
% 0.37/0.72 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.72 => ( Y = one_one_nat ) )
% 0.37/0.72 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.72 => ( ( ( ( Xa2 = Mi2 )
% 0.37/0.72 & ( Xa2 = Ma2 ) )
% 0.37/0.72 => ( Y = one_one_nat ) )
% 0.37/0.72 & ( ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 & ( Xa2 = Ma2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.elims
% 0.37/0.72 thf(fact_8138_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 0.37/0.72 ! [V2: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) @ X )
% 0.37/0.72 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.membermima.simps(5)
% 0.37/0.72 thf(fact_8139_vebt__succ_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.37/0.72 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ! [Uu: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uu @ B3 ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ~ ( ( B3
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( some_nat @ one_one_nat ) ) )
% 0.37/0.72 & ( ~ B3
% 0.37/0.72 => ( Y = none_nat ) ) ) ) )
% 0.37/0.72 => ( ( ? [Uv: $o,Uw: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.37/0.72 => ( ? [N2: nat] :
% 0.37/0.72 ( Xa2
% 0.37/0.72 = ( suc @ N2 ) )
% 0.37/0.72 => ( Y != none_nat ) ) )
% 0.37/0.72 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.37/0.72 => ( Y != none_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.37/0.72 => ( Y != none_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.37/0.72 => ( Y != none_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( some_nat @ Mi2 ) ) )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ none_nat
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_succ.elims
% 0.37/0.72 thf(fact_8140_vebt__pred_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.37/0.72 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [Uu: $o,Uv: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y != none_nat ) ) )
% 0.37/0.72 => ( ! [A3: $o] :
% 0.37/0.72 ( ? [Uw: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.37/0.72 => ( ( Xa2
% 0.37/0.72 = ( suc @ zero_zero_nat ) )
% 0.37/0.72 => ~ ( ( A3
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( some_nat @ zero_zero_nat ) ) )
% 0.37/0.72 & ( ~ A3
% 0.37/0.72 => ( Y = none_nat ) ) ) ) )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ? [Va: nat] :
% 0.37/0.72 ( Xa2
% 0.37/0.72 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.72 => ~ ( ( B3
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( some_nat @ one_one_nat ) ) )
% 0.37/0.72 & ( ~ B3
% 0.37/0.72 => ( ( A3
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( some_nat @ zero_zero_nat ) ) )
% 0.37/0.72 & ( ~ A3
% 0.37/0.72 => ( Y = none_nat ) ) ) ) ) ) )
% 0.37/0.72 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 0.37/0.72 => ( Y != none_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.37/0.72 => ( Y != none_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.37/0.72 => ( Y != none_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( some_nat @ Ma2 ) ) )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( if_option_nat
% 0.37/0.72 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_pred.elims
% 0.37/0.72 thf(fact_8141_vebt__member_Osimps_I5_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( ( X != Mi )
% 0.37/0.72 => ( ( X != Ma )
% 0.37/0.72 => ( ~ ( ord_less_nat @ X @ Mi )
% 0.37/0.72 & ( ~ ( ord_less_nat @ X @ Mi )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Ma @ X )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma @ X )
% 0.37/0.72 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_member.simps(5)
% 0.37/0.72 thf(fact_8142_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,V2: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V2 ) @ TreeList @ Vc ) @ X )
% 0.37/0.72 = ( ( X = Mi )
% 0.37/0.72 | ( X = Ma )
% 0.37/0.72 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.membermima.simps(4)
% 0.37/0.72 thf(fact_8143_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [Uu: $o,Uv: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [A3: $o,Uw: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.37/0.72 => ( ( Xa2
% 0.37/0.72 = ( suc @ zero_zero_nat ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ? [Va: nat] :
% 0.37/0.72 ( Xa2
% 0.37/0.72 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 0.37/0.72 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.elims
% 0.37/0.72 thf(fact_8144_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [Uu: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uu @ B3 ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.37/0.72 => ( ( ? [Uv: $o,Uw: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.37/0.72 => ( ? [N2: nat] :
% 0.37/0.72 ( Xa2
% 0.37/0.72 = ( suc @ N2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.elims
% 0.37/0.72 thf(fact_8145_vebt__member__code_I3_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( ~ ( ( Deg = zero_zero_nat )
% 0.37/0.72 | ( Deg
% 0.37/0.72 = ( suc @ zero_zero_nat ) ) )
% 0.37/0.72 & ( ~ ( ( Deg = zero_zero_nat )
% 0.37/0.72 | ( Deg
% 0.37/0.72 = ( suc @ zero_zero_nat ) ) )
% 0.37/0.72 => ( ( X != Mi )
% 0.37/0.72 => ( ( X != Ma )
% 0.37/0.72 => ( ~ ( ord_less_nat @ X @ Mi )
% 0.37/0.72 & ( ~ ( ord_less_nat @ X @ Mi )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Ma @ X )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma @ X )
% 0.37/0.72 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_member_code(3)
% 0.37/0.72 thf(fact_8146_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I7_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 | ( ord_less_nat @ Ma @ X ) )
% 0.37/0.72 @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( X = Mi )
% 0.37/0.72 & ( X = Ma ) )
% 0.37/0.72 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( X = Mi )
% 0.37/0.72 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma ) )
% 0.37/0.72 & ( ( X != Mi )
% 0.37/0.72 => ( X = Ma ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( X = Mi )
% 0.37/0.72 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.72 = Ma ) )
% 0.37/0.72 & ( ( X != Mi )
% 0.37/0.72 => ( X = Ma ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.simps(7)
% 0.37/0.72 thf(fact_8147_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.72 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => A3 )
% 0.37/0.72 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.72 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.72 => B3 )
% 0.37/0.72 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.37/0.72 => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.37/0.72 => Y )
% 0.37/0.72 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [S4: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.naive_member.elims(1)
% 0.37/0.72 thf(fact_8148_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.72 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => A3 )
% 0.37/0.72 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.72 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.72 => B3 )
% 0.37/0.72 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.37/0.72 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [S4: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 0.37/0.72 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.naive_member.elims(2)
% 0.37/0.72 thf(fact_8149_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.72 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => A3 )
% 0.37/0.72 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.72 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.72 => B3 )
% 0.37/0.72 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.37/0.72 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.37/0.72 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [S4: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 0.37/0.72 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.naive_member.elims(3)
% 0.37/0.72 thf(fact_8150_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.72 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat] :
% 0.37/0.72 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.37/0.72 => ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 ) ) )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Vc2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 0.37/0.72 => ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 )
% 0.37/0.72 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 0.37/0.72 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Vd: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 0.37/0.72 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.membermima.elims(2)
% 0.37/0.72 thf(fact_8151_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( Xa2
% 0.37/0.72 = ( suc @ zero_zero_nat ) )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ? [N2: nat] :
% 0.37/0.72 ( Xa2
% 0.37/0.72 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.72 @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( Xa2 = Mi2 )
% 0.37/0.72 & ( Xa2 = Ma2 ) )
% 0.37/0.72 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.37/0.72 @ ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.72 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.72 = Ma2 ) )
% 0.37/0.72 & ( ( Xa2 != Mi2 )
% 0.37/0.72 => ( Xa2 = Ma2 ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 = none_nat )
% 0.37/0.72 @ one_one_nat
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.72 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.72 = Ma2 ) )
% 0.37/0.72 & ( ( Xa2 != Mi2 )
% 0.37/0.72 => ( Xa2 = Ma2 ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.elims
% 0.37/0.72 thf(fact_8152_invar__vebt_Ointros_I4_J,axiom,
% 0.37/0.72 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.37/0.72 ( ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( M = N )
% 0.37/0.72 => ( ( Deg
% 0.37/0.72 = ( plus_plus_nat @ N @ M ) )
% 0.37/0.72 => ( ! [I2: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X8 ) )
% 0.37/0.72 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 0.37/0.72 => ( ( ( Mi = Ma )
% 0.37/0.72 => ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 0.37/0.72 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.37/0.72 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.37/0.72 => ( ( ( Mi != Ma )
% 0.37/0.72 => ! [I2: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.37/0.72 = I2 )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.37/0.72 & ! [X3: nat] :
% 0.37/0.72 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 0.37/0.72 = I2 )
% 0.37/0.72 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ Mi @ X3 )
% 0.37/0.72 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % invar_vebt.intros(4)
% 0.37/0.72 thf(fact_8153_vebt__member_Oelims_I2_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.72 ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => A3 )
% 0.37/0.72 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.72 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.72 => B3 )
% 0.37/0.72 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ~ ( ( Xa2 != Mi2 )
% 0.37/0.72 => ( ( Xa2 != Ma2 )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_member.elims(2)
% 0.37/0.72 thf(fact_8154_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.72 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.37/0.72 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 != ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.72 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat] :
% 0.37/0.72 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.37/0.72 => ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 ) ) )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Vc2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 0.37/0.72 => ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 )
% 0.37/0.72 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 0.37/0.72 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Vd: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 0.37/0.72 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.membermima.elims(3)
% 0.37/0.72 thf(fact_8155_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.72 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [Uu: $o,Uv: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.72 => Y )
% 0.37/0.72 => ( ( ? [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.37/0.72 => Y )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat] :
% 0.37/0.72 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 ) ) ) ) )
% 0.37/0.72 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Vc2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 )
% 0.37/0.72 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 0.37/0.72 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Vd: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % VEBT_internal.membermima.elims(1)
% 0.37/0.72 thf(fact_8156_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat @ ( X = Mi ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat @ ( X = Ma ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ord_less_nat @ Mi @ X )
% 0.37/0.72 & ( ord_less_nat @ X @ Ma ) )
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 0.37/0.72 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 0.37/0.72 thf(fact_8157_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_nat
% 0.37/0.72 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 & ~ ( ( X = Mi )
% 0.37/0.72 | ( X = Ma ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.72 @ one_one_nat ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.simps(5)
% 0.37/0.72 thf(fact_8158_vebt__insert_Osimps_I5_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_VEBT_VEBT
% 0.37/0.72 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 & ~ ( ( X = Mi )
% 0.37/0.72 | ( X = Ma ) ) )
% 0.37/0.72 @ ( 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 @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_insert.simps(5)
% 0.37/0.72 thf(fact_8159_invar__vebt_Ointros_I5_J,axiom,
% 0.37/0.72 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.37/0.72 ( ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary @ M )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( M
% 0.37/0.72 = ( suc @ N ) )
% 0.37/0.72 => ( ( Deg
% 0.37/0.72 = ( plus_plus_nat @ N @ M ) )
% 0.37/0.72 => ( ! [I2: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X8 ) )
% 0.37/0.72 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 0.37/0.72 => ( ( ( Mi = Ma )
% 0.37/0.72 => ! [X3: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.72 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 0.37/0.72 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.37/0.72 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.37/0.72 => ( ( ( Mi != Ma )
% 0.37/0.72 => ! [I2: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.37/0.72 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.37/0.72 = I2 )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.37/0.72 & ! [X3: nat] :
% 0.37/0.72 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 0.37/0.72 = I2 )
% 0.37/0.72 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ Mi @ X3 )
% 0.37/0.72 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % invar_vebt.intros(5)
% 0.37/0.72 thf(fact_8160_vebt__member_Oelims_I3_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.72 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => A3 )
% 0.37/0.72 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.72 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.72 => B3 )
% 0.37/0.72 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.37/0.72 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.72 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.72 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( Xa2 != Mi2 )
% 0.37/0.72 => ( ( Xa2 != Ma2 )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_member.elims(3)
% 0.37/0.72 thf(fact_8161_vebt__member_Oelims_I1_J,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.72 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => A3 )
% 0.37/0.72 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.72 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.72 => B3 )
% 0.37/0.72 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.37/0.72 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.72 => Y )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.72 => Y )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.72 => Y )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( ~ ( ( Xa2 != Mi2 )
% 0.37/0.72 => ( ( Xa2 != Ma2 )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.72 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.72 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.72 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_member.elims(1)
% 0.37/0.72 thf(fact_8162_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.72 ( ? [Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ one_one_nat
% 0.37/0.72 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 0.37/0.72 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 0.37/0.72 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ zero_zero_nat )
% 0.37/0.72 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 0.37/0.72 thf(fact_8163_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 0.37/0.72 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.72 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 & ~ ( ( X = Mi )
% 0.37/0.72 | ( X = Ma ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.72 @ one_one_nat ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.simps(5)
% 0.37/0.72 thf(fact_8164_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList2 ) )
% 0.37/0.72 & ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.elims
% 0.37/0.72 thf(fact_8165_invar__vebt_Osimps,axiom,
% 0.37/0.72 ( vEBT_invar_vebt
% 0.37/0.72 = ( ^ [A13: vEBT_VEBT,A24: nat] :
% 0.37/0.72 ( ( ? [A7: $o,B7: $o] :
% 0.37/0.72 ( A13
% 0.37/0.72 = ( vEBT_Leaf @ A7 @ B7 ) )
% 0.37/0.72 & ( A24
% 0.37/0.72 = ( suc @ zero_zero_nat ) ) )
% 0.37/0.72 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT] :
% 0.37/0.72 ( ( A13
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary3 ) )
% 0.37/0.72 & ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 0.37/0.72 & ( vEBT_invar_vebt @ Summary3 @ N6 )
% 0.37/0.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 0.37/0.72 & ( A24
% 0.37/0.72 = ( plus_plus_nat @ N6 @ N6 ) )
% 0.37/0.72 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 0.37/0.72 & ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.72 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT] :
% 0.37/0.72 ( ( A13
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary3 ) )
% 0.37/0.72 & ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 0.37/0.72 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N6 ) )
% 0.37/0.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 0.37/0.72 & ( A24
% 0.37/0.72 = ( plus_plus_nat @ N6 @ ( suc @ N6 ) ) )
% 0.37/0.72 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 0.37/0.72 & ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.72 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.37/0.72 ( ( A13
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary3 ) )
% 0.37/0.72 & ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 0.37/0.72 & ( vEBT_invar_vebt @ Summary3 @ N6 )
% 0.37/0.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 0.37/0.72 & ( A24
% 0.37/0.72 = ( plus_plus_nat @ N6 @ N6 ) )
% 0.37/0.72 & ! [I3: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 0.37/0.72 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ X8 ) )
% 0.37/0.72 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.37/0.72 & ( ( Mi3 = Ma3 )
% 0.37/0.72 => ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.72 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 0.37/0.72 & ( ( Mi3 != Ma3 )
% 0.37/0.72 => ! [I3: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 0.37/0.72 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N6 )
% 0.37/0.72 = I3 )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N6 ) ) )
% 0.37/0.72 & ! [X4: nat] :
% 0.37/0.72 ( ( ( ( vEBT_VEBT_high @ X4 @ N6 )
% 0.37/0.72 = I3 )
% 0.37/0.72 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N6 ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.72 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) )
% 0.37/0.72 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.37/0.72 ( ( A13
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary3 ) )
% 0.37/0.72 & ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 0.37/0.72 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N6 ) )
% 0.37/0.72 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 0.37/0.72 & ( A24
% 0.37/0.72 = ( plus_plus_nat @ N6 @ ( suc @ N6 ) ) )
% 0.37/0.72 & ! [I3: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 0.37/0.72 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ X8 ) )
% 0.37/0.72 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 0.37/0.72 & ( ( Mi3 = Ma3 )
% 0.37/0.72 => ! [X4: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.37/0.72 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.72 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.72 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 0.37/0.72 & ( ( Mi3 != Ma3 )
% 0.37/0.72 => ! [I3: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 0.37/0.72 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N6 )
% 0.37/0.72 = I3 )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N6 ) ) )
% 0.37/0.72 & ! [X4: nat] :
% 0.37/0.72 ( ( ( ( vEBT_VEBT_high @ X4 @ N6 )
% 0.37/0.72 = I3 )
% 0.37/0.72 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N6 ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.72 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % invar_vebt.simps
% 0.37/0.72 thf(fact_8166_invar__vebt_Ocases,axiom,
% 0.37/0.72 ! [A12: vEBT_VEBT,A23: nat] :
% 0.37/0.72 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( A12
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( A23
% 0.37/0.72 != ( suc @ zero_zero_nat ) ) )
% 0.37/0.72 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 0.37/0.72 ( ( A12
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( A23 = Deg2 )
% 0.37/0.72 => ( ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( M3 = N2 )
% 0.37/0.72 => ( ( Deg2
% 0.37/0.72 = ( plus_plus_nat @ N2 @ M3 ) )
% 0.37/0.72 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.37/0.72 => ~ ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 0.37/0.72 ( ( A12
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( A23 = Deg2 )
% 0.37/0.72 => ( ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( M3
% 0.37/0.72 = ( suc @ N2 ) )
% 0.37/0.72 => ( ( Deg2
% 0.37/0.72 = ( plus_plus_nat @ N2 @ M3 ) )
% 0.37/0.72 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 0.37/0.72 => ~ ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.37/0.72 ( ( A12
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( A23 = Deg2 )
% 0.37/0.72 => ( ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( M3 = N2 )
% 0.37/0.72 => ( ( Deg2
% 0.37/0.72 = ( plus_plus_nat @ N2 @ M3 ) )
% 0.37/0.72 => ( ! [I4: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 0.37/0.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.37/0.72 => ( ( ( Mi2 = Ma2 )
% 0.37/0.72 => ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 0.37/0.72 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.37/0.72 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.72 => ~ ( ( Mi2 != Ma2 )
% 0.37/0.72 => ! [I4: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 0.37/0.72 = I4 )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 0.37/0.72 & ! [X5: nat] :
% 0.37/0.72 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 0.37/0.72 = I4 )
% 0.37/0.72 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ Mi2 @ X5 )
% 0.37/0.72 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.72 => ~ ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.37/0.72 ( ( A12
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( ( A23 = Deg2 )
% 0.37/0.72 => ( ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 0.37/0.72 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 0.37/0.72 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.72 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( M3
% 0.37/0.72 = ( suc @ N2 ) )
% 0.37/0.72 => ( ( Deg2
% 0.37/0.72 = ( plus_plus_nat @ N2 @ M3 ) )
% 0.37/0.72 => ( ! [I4: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 0.37/0.72 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.37/0.72 => ( ( ( Mi2 = Ma2 )
% 0.37/0.72 => ! [X5: vEBT_VEBT] :
% 0.37/0.72 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.72 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 0.37/0.72 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.37/0.72 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.72 => ~ ( ( Mi2 != Ma2 )
% 0.37/0.72 => ! [I4: nat] :
% 0.37/0.72 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 0.37/0.72 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 0.37/0.72 = I4 )
% 0.37/0.72 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 0.37/0.72 & ! [X5: nat] :
% 0.37/0.72 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 0.37/0.72 = I4 )
% 0.37/0.72 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 0.37/0.72 => ( ( ord_less_nat @ Mi2 @ X5 )
% 0.37/0.72 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % invar_vebt.cases
% 0.37/0.72 thf(fact_8167_vebt__insert_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.37/0.72 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ! [A3: $o,B3: $o] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 0.37/0.72 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.72 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 0.37/0.72 & ( ( Xa2 != one_one_nat )
% 0.37/0.72 => ( Y
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) ) )
% 0.37/0.72 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) ) )
% 0.37/0.72 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) ) )
% 0.37/0.72 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( if_VEBT_VEBT
% 0.37/0.72 @ ( ( 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 @ TreeList2 ) )
% 0.37/0.72 & ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 ) ) )
% 0.37/0.72 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 ) )
% 0.37/0.72 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % vebt_insert.elims
% 0.37/0.72 thf(fact_8168_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 0.37/0.72 ! [Ma: nat,X: nat,Mi: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ Ma @ X )
% 0.37/0.72 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = one_one_nat ) )
% 0.37/0.72 & ( ~ ( ord_less_nat @ Ma @ X )
% 0.37/0.72 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.simps(7)
% 0.37/0.72 thf(fact_8169_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 0.37/0.72 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.37/0.72 ( ( ( ord_less_nat @ X @ Mi )
% 0.37/0.72 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = one_one_nat ) )
% 0.37/0.72 & ( ~ ( ord_less_nat @ X @ Mi )
% 0.37/0.72 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.72 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 != none_nat )
% 0.37/0.72 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.simps(6)
% 0.37/0.72 thf(fact_8170_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.37/0.72 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 0.37/0.72 => ( Y != one_one_nat ) )
% 0.37/0.72 => ( ( ? [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.72 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.72 ( ( X
% 0.37/0.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.72 => ( Y
% 0.37/0.72 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.72 @ ( if_nat
% 0.37/0.72 @ ( ( 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 @ TreeList2 ) )
% 0.37/0.72 & ~ ( ( Xa2 = Mi2 )
% 0.37/0.72 | ( Xa2 = Ma2 ) ) )
% 0.37/0.72 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.72 @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 0.37/0.72
% 0.37/0.72 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.elims
% 0.37/0.72 thf(fact_8171_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 0.37/0.72 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.72 ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 0.37/0.72 = Y )
% 0.37/0.72 => ( ( ? [Uu: $o,Uv: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.72 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.72 => ( Y != one_one_nat ) ) )
% 0.37/0.72 => ( ( ? [A3: $o,Uw: $o] :
% 0.37/0.72 ( X
% 0.37/0.72 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.37/0.73 => ( ( Xa2
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y != one_one_nat ) ) )
% 0.37/0.73 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ? [Va: nat] :
% 0.37/0.73 ( Xa2
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y != one_one_nat ) ) )
% 0.37/0.73 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 0.37/0.73 => ( Y != one_one_nat ) )
% 0.37/0.73 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.37/0.73 => ( Y != one_one_nat ) )
% 0.37/0.73 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.37/0.73 => ( Y != one_one_nat ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( Y = one_one_nat ) )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.73 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.elims
% 0.37/0.73 thf(fact_8172_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ? [Uu: $o,B3: $o] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ B3 ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( Y != one_one_nat ) ) )
% 0.37/0.73 => ( ( ? [Uv: $o,Uw: $o] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.37/0.73 => ( ? [N2: nat] :
% 0.37/0.73 ( Xa2
% 0.37/0.73 = ( suc @ N2 ) )
% 0.37/0.73 => ( Y != one_one_nat ) ) )
% 0.37/0.73 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.37/0.73 => ( Y != one_one_nat ) )
% 0.37/0.73 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.37/0.73 => ( Y != one_one_nat ) )
% 0.37/0.73 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.37/0.73 => ( Y != one_one_nat ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( Y = one_one_nat ) )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.73 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.elims
% 0.37/0.73 thf(fact_8173_in__children__def,axiom,
% 0.37/0.73 ( vEBT_V5917875025757280293ildren
% 0.37/0.73 = ( ^ [N6: nat,TreeList4: list_VEBT_VEBT,X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ ( vEBT_VEBT_high @ X4 @ N6 ) ) @ ( vEBT_VEBT_low @ X4 @ N6 ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % in_children_def
% 0.37/0.73 thf(fact_8174_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Xa2
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ! [N2: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 0.37/0.73 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.73 @ one_one_nat
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( Xa2 = Mi2 )
% 0.37/0.73 & ( Xa2 = Ma2 ) )
% 0.37/0.73 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 0.37/0.73 @ ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.73 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.73 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.73 = Ma2 ) )
% 0.37/0.73 & ( ( Xa2 != Mi2 )
% 0.37/0.73 => ( Xa2 = Ma2 ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ one_one_nat
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ one_one_nat
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ one_one_nat ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.73 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.73 = Ma2 ) )
% 0.37/0.73 & ( ( Xa2 != Mi2 )
% 0.37/0.73 => ( Xa2 = Ma2 ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.73 @ one_one_nat ) ) ) ) )
% 0.37/0.73 @ one_one_nat ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e.pelims
% 0.37/0.73 thf(fact_8175_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ B3 ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [Uv: $o,Uw: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.37/0.73 => ! [N2: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ N2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 0.37/0.73 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat
% 0.37/0.73 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 0.37/0.73 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ one_one_nat
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ one_one_nat ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c.pelims
% 0.37/0.73 thf(fact_8176_vebt__succ_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.37/0.73 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ B3 ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( ( B3
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( some_nat @ one_one_nat ) ) )
% 0.37/0.73 & ( ~ B3
% 0.37/0.73 => ( Y = none_nat ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [Uv: $o,Uw: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.37/0.73 => ! [N2: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ N2 ) )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 0.37/0.73 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( some_nat @ Mi2 ) ) )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( if_option_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( if_option_nat
% 0.37/0.73 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ none_nat
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ none_nat ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_succ.pelims
% 0.37/0.73 thf(fact_8177_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,Uw: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.37/0.73 => ( ( Xa2
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ! [Va: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 0.37/0.73 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat
% 0.37/0.73 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.37/0.73 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.37/0.73 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ one_one_nat ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d.pelims
% 0.37/0.73 thf(fact_8178_vebt__pred_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.37/0.73 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,Uw: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.37/0.73 => ( ( Xa2
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( ( A3
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( some_nat @ zero_zero_nat ) ) )
% 0.37/0.73 & ( ~ A3
% 0.37/0.73 => ( Y = none_nat ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ! [Va: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( ( ( B3
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( some_nat @ one_one_nat ) ) )
% 0.37/0.73 & ( ~ B3
% 0.37/0.73 => ( ( A3
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( some_nat @ zero_zero_nat ) ) )
% 0.37/0.73 & ( ~ A3
% 0.37/0.73 => ( Y = none_nat ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 0.37/0.73 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.37/0.73 => ( ( Y = none_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( some_nat @ Ma2 ) ) )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( if_option_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( if_option_nat
% 0.37/0.73 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ none_nat ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_pred.pelims
% 0.37/0.73 thf(fact_8179_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_V1232361888498592333_e_t_e @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Xa2
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ! [N2: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 0.37/0.73 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.73 => ( Y = one_one_nat ) )
% 0.37/0.73 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.73 => ( ( ( ( Xa2 = Mi2 )
% 0.37/0.73 & ( Xa2 = Ma2 ) )
% 0.37/0.73 => ( Y = one_one_nat ) )
% 0.37/0.73 & ( ~ ( ( Xa2 = Mi2 )
% 0.37/0.73 & ( Xa2 = Ma2 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T\<^sub>d\<^sub>e\<^sub>l\<^sub>e\<^sub>t\<^sub>e'.pelims
% 0.37/0.73 thf(fact_8180_vebt__delete_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.37/0.73 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Leaf @ $false @ B3 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Xa2
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ $false ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ! [N2: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 0.37/0.73 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 0.37/0.73 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.37/0.73 => ( ( ( ( Xa2 = Mi2 )
% 0.37/0.73 & ( Xa2 = Ma2 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 0.37/0.73 & ( ~ ( ( Xa2 = Mi2 )
% 0.37/0.73 & ( Xa2 = Ma2 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( vEBT_Node
% 0.37/0.73 @ ( some_P7363390416028606310at_nat
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.73 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.73 = Ma2 ) )
% 0.37/0.73 & ( ( Xa2 != Mi2 )
% 0.37/0.73 => ( Xa2 = Ma2 ) ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ Ma2 ) ) )
% 0.37/0.73 @ ( suc @ ( suc @ Va ) )
% 0.37/0.73 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( vEBT_Node
% 0.37/0.73 @ ( some_P7363390416028606310at_nat
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( Xa2 = Mi2 )
% 0.37/0.73 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.37/0.73 = Ma2 ) )
% 0.37/0.73 & ( ( Xa2 != Mi2 )
% 0.37/0.73 => ( Xa2 = Ma2 ) ) )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ Ma2 ) ) )
% 0.37/0.73 @ ( suc @ ( suc @ Va ) )
% 0.37/0.73 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ Summary2 ) )
% 0.37/0.73 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_delete.pelims
% 0.37/0.73 thf(fact_8181_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ B3 ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [Uv: $o,Uw: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uv @ Uw ) )
% 0.37/0.73 => ! [N2: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ N2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 0.37/0.73 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( Y = one_one_nat ) )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.73 @ one_one_nat ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>s\<^sub>u\<^sub>c\<^sub>c'.pelims
% 0.37/0.73 thf(fact_8182_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( 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 @ TreeList2 ) )
% 0.37/0.73 & ~ ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.73 @ one_one_nat ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t.pelims
% 0.37/0.73 thf(fact_8183_vebt__insert_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.37/0.73 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 0.37/0.73 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.73 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 0.37/0.73 & ( ( Xa2 != one_one_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( if_VEBT_VEBT
% 0.37/0.73 @ ( ( 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 @ TreeList2 ) )
% 0.37/0.73 & ~ ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 ) ) )
% 0.37/0.73 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 ) )
% 0.37/0.73 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_insert.pelims
% 0.37/0.73 thf(fact_8184_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.73 => ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,Uw: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.37/0.73 => ( ( Xa2
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ! [Va: nat] :
% 0.37/0.73 ( ( Xa2
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 0.37/0.73 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( Y = one_one_nat ) )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.73 @ one_one_nat ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>p\<^sub>r\<^sub>e\<^sub>d'.pelims
% 0.37/0.73 thf(fact_8185_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( if_nat
% 0.37/0.73 @ ( ( 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 @ TreeList2 ) )
% 0.37/0.73 & ~ ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 0.37/0.73 @ one_one_nat ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>i\<^sub>n\<^sub>s\<^sub>e\<^sub>r\<^sub>t'.pelims
% 0.37/0.73 thf(fact_8186_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.73 => ( ( Y = one_one_nat )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat
% 0.37/0.73 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 0.37/0.73 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 0.37/0.73 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 0.37/0.73 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 0.37/0.73 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 0.37/0.73 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ zero_zero_nat )
% 0.37/0.73 @ zero_zero_nat ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 0.37/0.73 thf(fact_8187_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ? [A3: $o,B3: $o] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 0.37/0.73 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 0.37/0.73 ( ? [Summary2: vEBT_VEBT] :
% 0.37/0.73 ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 0.37/0.73 thf(fact_8188_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 0.37/0.73 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X: nat] :
% 0.37/0.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X )
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 0.37/0.73 thf(fact_8189_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 0.37/0.73 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.37/0.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X )
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 0.37/0.73 thf(fact_8190_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 0.37/0.73 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.37/0.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 0.37/0.73 thf(fact_8191_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 0.37/0.73 ! [A: $o,B: $o,X: nat] :
% 0.37/0.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.37/0.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 0.37/0.73 thf(fact_8192_member__bound__height,axiom,
% 0.37/0.73 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.37/0.73 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.73 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % member_bound_height
% 0.37/0.73 thf(fact_8193_member__bound__size__univ,axiom,
% 0.37/0.73 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 0.37/0.73 ( ( vEBT_invar_vebt @ T @ N )
% 0.37/0.73 => ( ( U
% 0.37/0.73 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.73 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % member_bound_size_univ
% 0.37/0.73 thf(fact_8194_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 0.37/0.73 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.73 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 0.37/0.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 0.37/0.73 thf(fact_8195_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 0.37/0.73 thf(fact_8196_vebt__member_Opelims_I1_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.73 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => A3 )
% 0.37/0.73 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.73 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.73 => B3 )
% 0.37/0.73 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.73 => ( ~ Y
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.73 => ( ~ Y
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.73 => ( ~ Y
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( ( Xa2 != Mi2 )
% 0.37/0.73 => ( ( Xa2 != Ma2 )
% 0.37/0.73 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_member.pelims(1)
% 0.37/0.73 thf(fact_8197_vebt__member_Opelims_I3_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.73 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.37/0.73 => ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => A3 )
% 0.37/0.73 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.73 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.73 => B3 )
% 0.37/0.73 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) )
% 0.37/0.73 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.37/0.73 => ( ( Xa2 != Mi2 )
% 0.37/0.73 => ( ( Xa2 != Ma2 )
% 0.37/0.73 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_member.pelims(3)
% 0.37/0.73 thf(fact_8198_vebt__member_Opelims_I2_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.73 ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.37/0.73 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => A3 )
% 0.37/0.73 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.73 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.73 => B3 )
% 0.37/0.73 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.37/0.73 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.37/0.73 => ~ ( ( Xa2 != Mi2 )
% 0.37/0.73 => ( ( Xa2 != Ma2 )
% 0.37/0.73 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.37/0.73 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.37/0.73 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_member.pelims(2)
% 0.37/0.73 thf(fact_8199_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.73 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.37/0.73 => ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => A3 )
% 0.37/0.73 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.73 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.73 => B3 )
% 0.37/0.73 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.37/0.73 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) )
% 0.37/0.73 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ Xa2 ) )
% 0.37/0.73 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.naive_member.pelims(3)
% 0.37/0.73 thf(fact_8200_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.73 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.37/0.73 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => A3 )
% 0.37/0.73 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.73 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.73 => B3 )
% 0.37/0.73 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.37/0.73 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ Xa2 ) )
% 0.37/0.73 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.naive_member.pelims(2)
% 0.37/0.73 thf(fact_8201_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.73 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [A3: $o,B3: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.73 => A3 )
% 0.37/0.73 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.73 => ( ( ( Xa2 = one_one_nat )
% 0.37/0.73 => B3 )
% 0.37/0.73 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 0.37/0.73 => ( ~ Y
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.naive_member.pelims(1)
% 0.37/0.73 thf(fact_8202_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.73 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.73 => ( ~ Y
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.37/0.73 => ( ~ Y
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 )
% 0.37/0.73 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.37/0.73 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.membermima.pelims(1)
% 0.37/0.73 thf(fact_8203_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.73 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) )
% 0.37/0.73 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.37/0.73 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.37/0.73 => ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 0.37/0.73 => ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 )
% 0.37/0.73 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 0.37/0.73 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ Xa2 ) )
% 0.37/0.73 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.membermima.pelims(3)
% 0.37/0.73 thf(fact_8204_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 0.37/0.73 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.73 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 0.37/0.73 => ~ ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 ) ) ) )
% 0.37/0.73 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 0.37/0.73 => ~ ( ( Xa2 = Mi2 )
% 0.37/0.73 | ( Xa2 = Ma2 )
% 0.37/0.73 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 0.37/0.73 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 0.37/0.73 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ Xa2 ) )
% 0.37/0.73 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.37/0.73 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 0.37/0.73 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.membermima.pelims(2)
% 0.37/0.73 thf(fact_8205_Maclaurin__sin__expansion3,axiom,
% 0.37/0.73 ! [N: nat,X: real] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.73 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ? [T6: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.37/0.73 & ( ord_less_real @ T6 @ X )
% 0.37/0.73 & ( ( sin_real @ X )
% 0.37/0.73 = ( plus_plus_real
% 0.37/0.73 @ ( groups6591440286371151544t_real
% 0.37/0.73 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.73 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.73 @ ( 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 ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Maclaurin_sin_expansion3
% 0.37/0.73 thf(fact_8206_Maclaurin__sin__expansion4,axiom,
% 0.37/0.73 ! [X: real,N: nat] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ? [T6: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.37/0.73 & ( ord_less_eq_real @ T6 @ X )
% 0.37/0.73 & ( ( sin_real @ X )
% 0.37/0.73 = ( plus_plus_real
% 0.37/0.73 @ ( groups6591440286371151544t_real
% 0.37/0.73 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.73 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.73 @ ( 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 ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Maclaurin_sin_expansion4
% 0.37/0.73 thf(fact_8207_Maclaurin__sin__expansion2,axiom,
% 0.37/0.73 ! [X: real,N: nat] :
% 0.37/0.73 ? [T6: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.73 & ( ( sin_real @ X )
% 0.37/0.73 = ( plus_plus_real
% 0.37/0.73 @ ( groups6591440286371151544t_real
% 0.37/0.73 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.73 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.73 @ ( 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 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Maclaurin_sin_expansion2
% 0.37/0.73 thf(fact_8208_sin__cos__npi,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( 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 ) ) ) )
% 0.37/0.73 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_cos_npi
% 0.37/0.73 thf(fact_8209_pi__gt__zero,axiom,
% 0.37/0.73 ord_less_real @ zero_zero_real @ pi ).
% 0.37/0.73
% 0.37/0.73 % pi_gt_zero
% 0.37/0.73 thf(fact_8210_pi__not__less__zero,axiom,
% 0.37/0.73 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 0.37/0.73
% 0.37/0.73 % pi_not_less_zero
% 0.37/0.73 thf(fact_8211_pi__ge__zero,axiom,
% 0.37/0.73 ord_less_eq_real @ zero_zero_real @ pi ).
% 0.37/0.73
% 0.37/0.73 % pi_ge_zero
% 0.37/0.73 thf(fact_8212_sin__gt__zero,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ pi )
% 0.37/0.73 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_gt_zero
% 0.37/0.73 thf(fact_8213_sin__ge__zero,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ pi )
% 0.37/0.73 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_ge_zero
% 0.37/0.73 thf(fact_8214_pi__less__4,axiom,
% 0.37/0.73 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % pi_less_4
% 0.37/0.73 thf(fact_8215_pi__ge__two,axiom,
% 0.37/0.73 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 0.37/0.73
% 0.37/0.73 % pi_ge_two
% 0.37/0.73 thf(fact_8216_sin__eq__0__pi,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ pi )
% 0.37/0.73 => ( ( ( sin_real @ X )
% 0.37/0.73 = zero_zero_real )
% 0.37/0.73 => ( X = zero_zero_real ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_eq_0_pi
% 0.37/0.73 thf(fact_8217_sin__zero__pi__iff,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 0.37/0.73 => ( ( ( sin_real @ X )
% 0.37/0.73 = zero_zero_real )
% 0.37/0.73 = ( X = zero_zero_real ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_zero_pi_iff
% 0.37/0.73 thf(fact_8218_pi__half__less__two,axiom,
% 0.37/0.73 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.37/0.73
% 0.37/0.73 % pi_half_less_two
% 0.37/0.73 thf(fact_8219_pi__half__le__two,axiom,
% 0.37/0.73 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.37/0.73
% 0.37/0.73 % pi_half_le_two
% 0.37/0.73 thf(fact_8220_pi__half__gt__zero,axiom,
% 0.37/0.73 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % pi_half_gt_zero
% 0.37/0.73 thf(fact_8221_pi__half__ge__zero,axiom,
% 0.37/0.73 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % pi_half_ge_zero
% 0.37/0.73 thf(fact_8222_m2pi__less__pi,axiom,
% 0.37/0.73 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 0.37/0.73
% 0.37/0.73 % m2pi_less_pi
% 0.37/0.73 thf(fact_8223_arctan__ubound,axiom,
% 0.37/0.73 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % arctan_ubound
% 0.37/0.73 thf(fact_8224_sin__pi__divide__n__ge__0,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( N != zero_zero_nat )
% 0.37/0.73 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_pi_divide_n_ge_0
% 0.37/0.73 thf(fact_8225_minus__pi__half__less__zero,axiom,
% 0.37/0.73 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 0.37/0.73
% 0.37/0.73 % minus_pi_half_less_zero
% 0.37/0.73 thf(fact_8226_sin__gt__zero2,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_gt_zero2
% 0.37/0.73 thf(fact_8227_sin__lt__zero,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ pi @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.37/0.73 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_lt_zero
% 0.37/0.73 thf(fact_8228_sin__inj__pi,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ( sin_real @ X )
% 0.37/0.73 = ( sin_real @ Y ) )
% 0.37/0.73 => ( X = Y ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_inj_pi
% 0.37/0.73 thf(fact_8229_sin__mono__le__eq,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 0.37/0.73 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_mono_le_eq
% 0.37/0.73 thf(fact_8230_sin__monotone__2pi__le,axiom,
% 0.37/0.73 ! [Y: real,X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_monotone_2pi_le
% 0.37/0.73 thf(fact_8231_arctan__bounded,axiom,
% 0.37/0.73 ! [Y: real] :
% 0.37/0.73 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.37/0.73 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % arctan_bounded
% 0.37/0.73 thf(fact_8232_arctan__lbound,axiom,
% 0.37/0.73 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 0.37/0.73
% 0.37/0.73 % arctan_lbound
% 0.37/0.73 thf(fact_8233_sin__le__zero,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ pi @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.37/0.73 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_le_zero
% 0.37/0.73 thf(fact_8234_sin__less__zero,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.73 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_less_zero
% 0.37/0.73 thf(fact_8235_sin__mono__less__eq,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 0.37/0.73 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_mono_less_eq
% 0.37/0.73 thf(fact_8236_sin__monotone__2pi,axiom,
% 0.37/0.73 ! [Y: real,X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.73 => ( ( ord_less_real @ Y @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_monotone_2pi
% 0.37/0.73 thf(fact_8237_sin__total,axiom,
% 0.37/0.73 ! [Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.73 => ? [X3: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.37/0.73 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 & ( ( sin_real @ X3 )
% 0.37/0.73 = Y )
% 0.37/0.73 & ! [Y5: real] :
% 0.37/0.73 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 0.37/0.73 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 & ( ( sin_real @ Y5 )
% 0.37/0.73 = Y ) )
% 0.37/0.73 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_total
% 0.37/0.73 thf(fact_8238_sin__pi__divide__n__gt__0,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_pi_divide_n_gt_0
% 0.37/0.73 thf(fact_8239_Maclaurin__cos__expansion2,axiom,
% 0.37/0.73 ! [X: real,N: nat] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.73 => ? [T6: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.37/0.73 & ( ord_less_real @ T6 @ X )
% 0.37/0.73 & ( ( cos_real @ X )
% 0.37/0.73 = ( plus_plus_real
% 0.37/0.73 @ ( groups6591440286371151544t_real
% 0.37/0.73 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.73 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.73 @ ( 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 ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Maclaurin_cos_expansion2
% 0.37/0.73 thf(fact_8240_Maclaurin__minus__cos__expansion,axiom,
% 0.37/0.73 ! [N: nat,X: real] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.73 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.73 => ? [T6: real] :
% 0.37/0.73 ( ( ord_less_real @ X @ T6 )
% 0.37/0.73 & ( ord_less_real @ T6 @ zero_zero_real )
% 0.37/0.73 & ( ( cos_real @ X )
% 0.37/0.73 = ( plus_plus_real
% 0.37/0.73 @ ( groups6591440286371151544t_real
% 0.37/0.73 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.73 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.73 @ ( 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 ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Maclaurin_minus_cos_expansion
% 0.37/0.73 thf(fact_8241_monoseq__arctan__series,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.73 => ( topolo6980174941875973593q_real
% 0.37/0.73 @ ^ [N6: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % monoseq_arctan_series
% 0.37/0.73 thf(fact_8242_cos__pi__eq__zero,axiom,
% 0.37/0.73 ! [M: nat] :
% 0.37/0.73 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 = zero_zero_real ) ).
% 0.37/0.73
% 0.37/0.73 % cos_pi_eq_zero
% 0.37/0.73 thf(fact_8243_cos__le__one,axiom,
% 0.37/0.73 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 0.37/0.73
% 0.37/0.73 % cos_le_one
% 0.37/0.73 thf(fact_8244_cos__monotone__0__pi__le,axiom,
% 0.37/0.73 ! [Y: real,X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ pi )
% 0.37/0.73 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_monotone_0_pi_le
% 0.37/0.73 thf(fact_8245_cos__mono__le__eq,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ pi )
% 0.37/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ pi )
% 0.37/0.73 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 0.37/0.73 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_mono_le_eq
% 0.37/0.73 thf(fact_8246_cos__inj__pi,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ pi )
% 0.37/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ pi )
% 0.37/0.73 => ( ( ( cos_real @ X )
% 0.37/0.73 = ( cos_real @ Y ) )
% 0.37/0.73 => ( X = Y ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_inj_pi
% 0.37/0.73 thf(fact_8247_cos__ge__minus__one,axiom,
% 0.37/0.73 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_ge_minus_one
% 0.37/0.73 thf(fact_8248_abs__cos__le__one,axiom,
% 0.37/0.73 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 0.37/0.73
% 0.37/0.73 % abs_cos_le_one
% 0.37/0.73 thf(fact_8249_cos__mono__less__eq,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ pi )
% 0.37/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ pi )
% 0.37/0.73 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 0.37/0.73 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_mono_less_eq
% 0.37/0.73 thf(fact_8250_cos__monotone__0__pi,axiom,
% 0.37/0.73 ! [Y: real,X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.73 => ( ( ord_less_real @ Y @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ pi )
% 0.37/0.73 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_monotone_0_pi
% 0.37/0.73 thf(fact_8251_cos__monotone__minus__pi__0_H,axiom,
% 0.37/0.73 ! [Y: real,X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.73 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_monotone_minus_pi_0'
% 0.37/0.73 thf(fact_8252_cos__two__less__zero,axiom,
% 0.37/0.73 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.37/0.73
% 0.37/0.73 % cos_two_less_zero
% 0.37/0.73 thf(fact_8253_cos__is__zero,axiom,
% 0.37/0.73 ? [X3: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.37/0.73 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.73 & ( ( cos_real @ X3 )
% 0.37/0.73 = zero_zero_real )
% 0.37/0.73 & ! [Y5: real] :
% 0.37/0.73 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 0.37/0.73 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.73 & ( ( cos_real @ Y5 )
% 0.37/0.73 = zero_zero_real ) )
% 0.37/0.73 => ( Y5 = X3 ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_is_zero
% 0.37/0.73 thf(fact_8254_cos__two__le__zero,axiom,
% 0.37/0.73 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 0.37/0.73
% 0.37/0.73 % cos_two_le_zero
% 0.37/0.73 thf(fact_8255_cos__monotone__minus__pi__0,axiom,
% 0.37/0.73 ! [Y: real,X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 0.37/0.73 => ( ( ord_less_real @ Y @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.73 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_monotone_minus_pi_0
% 0.37/0.73 thf(fact_8256_cos__total,axiom,
% 0.37/0.73 ! [Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.73 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.73 => ? [X3: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.37/0.73 & ( ord_less_eq_real @ X3 @ pi )
% 0.37/0.73 & ( ( cos_real @ X3 )
% 0.37/0.73 = Y )
% 0.37/0.73 & ! [Y5: real] :
% 0.37/0.73 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 0.37/0.73 & ( ord_less_eq_real @ Y5 @ pi )
% 0.37/0.73 & ( ( cos_real @ Y5 )
% 0.37/0.73 = Y ) )
% 0.37/0.73 => ( Y5 = X3 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_total
% 0.37/0.73 thf(fact_8257_sincos__principal__value,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ? [Y3: real] :
% 0.37/0.73 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 0.37/0.73 & ( ord_less_eq_real @ Y3 @ pi )
% 0.37/0.73 & ( ( sin_real @ Y3 )
% 0.37/0.73 = ( sin_real @ X ) )
% 0.37/0.73 & ( ( cos_real @ Y3 )
% 0.37/0.73 = ( cos_real @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sincos_principal_value
% 0.37/0.73 thf(fact_8258_monoseq__realpow,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.73 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % monoseq_realpow
% 0.37/0.73 thf(fact_8259_sin__cos__le1,axiom,
% 0.37/0.73 ! [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 ) ).
% 0.37/0.73
% 0.37/0.73 % sin_cos_le1
% 0.37/0.73 thf(fact_8260_cos__double__less__one,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.73 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_double_less_one
% 0.37/0.73 thf(fact_8261_cos__gt__zero,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_gt_zero
% 0.37/0.73 thf(fact_8262_cos__gt__zero__pi,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_gt_zero_pi
% 0.37/0.73 thf(fact_8263_cos__ge__zero,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_ge_zero
% 0.37/0.73 thf(fact_8264_pi__half,axiom,
% 0.37/0.73 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.73 = ( the_real
% 0.37/0.73 @ ^ [X4: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.37/0.73 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.73 & ( ( cos_real @ X4 )
% 0.37/0.73 = zero_zero_real ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % pi_half
% 0.37/0.73 thf(fact_8265_pi__def,axiom,
% 0.37/0.73 ( pi
% 0.37/0.73 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.37/0.73 @ ( the_real
% 0.37/0.73 @ ^ [X4: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.37/0.73 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.73 & ( ( cos_real @ X4 )
% 0.37/0.73 = zero_zero_real ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % pi_def
% 0.37/0.73 thf(fact_8266_sincos__total__pi,axiom,
% 0.37/0.73 ! [Y: real,X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.73 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.73 = one_one_real )
% 0.37/0.73 => ? [T6: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.73 & ( ord_less_eq_real @ T6 @ pi )
% 0.37/0.73 & ( X
% 0.37/0.73 = ( cos_real @ T6 ) )
% 0.37/0.73 & ( Y
% 0.37/0.73 = ( sin_real @ T6 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sincos_total_pi
% 0.37/0.73 thf(fact_8267_sin__expansion__lemma,axiom,
% 0.37/0.73 ! [X: real,M: nat] :
% 0.37/0.73 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_expansion_lemma
% 0.37/0.73 thf(fact_8268_cos__expansion__lemma,axiom,
% 0.37/0.73 ! [X: real,M: nat] :
% 0.37/0.73 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_expansion_lemma
% 0.37/0.73 thf(fact_8269_sincos__total__pi__half,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.73 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.73 = one_one_real )
% 0.37/0.73 => ? [T6: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.73 & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.73 & ( X
% 0.37/0.73 = ( cos_real @ T6 ) )
% 0.37/0.73 & ( Y
% 0.37/0.73 = ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sincos_total_pi_half
% 0.37/0.73 thf(fact_8270_sincos__total__2pi__le,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.73 = one_one_real )
% 0.37/0.73 => ? [T6: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.73 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.37/0.73 & ( X
% 0.37/0.73 = ( cos_real @ T6 ) )
% 0.37/0.73 & ( Y
% 0.37/0.73 = ( sin_real @ T6 ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sincos_total_2pi_le
% 0.37/0.73 thf(fact_8271_sincos__total__2pi,axiom,
% 0.37/0.73 ! [X: real,Y: real] :
% 0.37/0.73 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.73 = one_one_real )
% 0.37/0.73 => ~ ! [T6: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.73 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.37/0.73 => ( ( X
% 0.37/0.73 = ( cos_real @ T6 ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sincos_total_2pi
% 0.37/0.73 thf(fact_8272_Maclaurin__cos__expansion,axiom,
% 0.37/0.73 ! [X: real,N: nat] :
% 0.37/0.73 ? [T6: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.73 & ( ( cos_real @ X )
% 0.37/0.73 = ( plus_plus_real
% 0.37/0.73 @ ( groups6591440286371151544t_real
% 0.37/0.73 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.73 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.73 @ ( 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 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Maclaurin_cos_expansion
% 0.37/0.73 thf(fact_8273_lowi__hT,axiom,
% 0.37/0.73 ! [X: nat,N: nat] :
% 0.37/0.73 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X @ N )
% 0.37/0.73 @ ^ [R5: nat] :
% 0.37/0.73 ( pure_assn
% 0.37/0.73 @ ( R5
% 0.37/0.73 = ( vEBT_VEBT_low @ X @ N ) ) )
% 0.37/0.73 @ one_one_nat ) ).
% 0.37/0.73
% 0.37/0.73 % lowi_hT
% 0.37/0.73 thf(fact_8274_highi__hT,axiom,
% 0.37/0.73 ! [X: nat,N: nat] :
% 0.37/0.73 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X @ N )
% 0.37/0.73 @ ^ [R5: nat] :
% 0.37/0.73 ( pure_assn
% 0.37/0.73 @ ( R5
% 0.37/0.73 = ( vEBT_VEBT_high @ X @ N ) ) )
% 0.37/0.73 @ one_one_nat ) ).
% 0.37/0.73
% 0.37/0.73 % highi_hT
% 0.37/0.73 thf(fact_8275_TBOUND__highi,axiom,
% 0.37/0.73 ! [X: nat,N: nat] : ( time_TBOUND_nat @ ( vEBT_VEBT_highi @ X @ N ) @ one_one_nat ) ).
% 0.37/0.73
% 0.37/0.73 % TBOUND_highi
% 0.37/0.73 thf(fact_8276_TBOUND__lowi,axiom,
% 0.37/0.73 ! [X: nat,N: nat] : ( time_TBOUND_nat @ ( vEBT_VEBT_lowi @ X @ N ) @ one_one_nat ) ).
% 0.37/0.73
% 0.37/0.73 % TBOUND_lowi
% 0.37/0.73 thf(fact_8277_highi__h,axiom,
% 0.37/0.73 ! [X: nat,N: nat] :
% 0.37/0.73 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X @ N )
% 0.37/0.73 @ ^ [R5: nat] :
% 0.37/0.73 ( pure_assn
% 0.37/0.73 @ ( R5
% 0.37/0.73 = ( vEBT_VEBT_high @ X @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % highi_h
% 0.37/0.73 thf(fact_8278_lowi__h,axiom,
% 0.37/0.73 ! [X: nat,N: nat] :
% 0.37/0.73 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X @ N )
% 0.37/0.73 @ ^ [R5: nat] :
% 0.37/0.73 ( pure_assn
% 0.37/0.73 @ ( R5
% 0.37/0.73 = ( vEBT_VEBT_low @ X @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % lowi_h
% 0.37/0.73 thf(fact_8279_set__bit__nonnegative__int__iff,axiom,
% 0.37/0.73 ! [N: nat,K: int] :
% 0.37/0.73 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 0.37/0.73 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.73
% 0.37/0.73 % set_bit_nonnegative_int_iff
% 0.37/0.73 thf(fact_8280_set__bit__negative__int__iff,axiom,
% 0.37/0.73 ! [N: nat,K: int] :
% 0.37/0.73 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 0.37/0.73 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.73
% 0.37/0.73 % set_bit_negative_int_iff
% 0.37/0.73 thf(fact_8281_set__bit__greater__eq,axiom,
% 0.37/0.73 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 0.37/0.73
% 0.37/0.73 % set_bit_greater_eq
% 0.37/0.73 thf(fact_8282_set__encode__insert,axiom,
% 0.37/0.73 ! [A4: set_nat,N: nat] :
% 0.37/0.73 ( ( finite_finite_nat @ A4 )
% 0.37/0.73 => ( ~ ( member_nat @ N @ A4 )
% 0.37/0.73 => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 0.37/0.73 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % set_encode_insert
% 0.37/0.73 thf(fact_8283_sin__coeff__def,axiom,
% 0.37/0.73 ( sin_coeff
% 0.37/0.73 = ( ^ [N6: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N6 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N6 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_coeff_def
% 0.37/0.73 thf(fact_8284_ln__series,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.37/0.73 => ( ( ln_ln_real @ X )
% 0.37/0.73 = ( suminf_real
% 0.37/0.73 @ ^ [N6: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N6 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N6 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N6 ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % ln_series
% 0.37/0.73 thf(fact_8285_nat__dvd__1__iff__1,axiom,
% 0.37/0.73 ! [M: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.37/0.73 = ( M = one_one_nat ) ) ).
% 0.37/0.73
% 0.37/0.73 % nat_dvd_1_iff_1
% 0.37/0.73 thf(fact_8286_dvd__1__left,axiom,
% 0.37/0.73 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_1_left
% 0.37/0.73 thf(fact_8287_dvd__1__iff__1,axiom,
% 0.37/0.73 ! [M: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.37/0.73 = ( M
% 0.37/0.73 = ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_1_iff_1
% 0.37/0.73 thf(fact_8288_nat__mult__dvd__cancel__disj,axiom,
% 0.37/0.73 ! [K: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.73 = ( ( K = zero_zero_nat )
% 0.37/0.73 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % nat_mult_dvd_cancel_disj
% 0.37/0.73 thf(fact_8289_set__encode__empty,axiom,
% 0.37/0.73 ( ( nat_set_encode @ bot_bot_set_nat )
% 0.37/0.73 = zero_zero_nat ) ).
% 0.37/0.73
% 0.37/0.73 % set_encode_empty
% 0.37/0.73 thf(fact_8290_Max__divisors__self__nat,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( N != zero_zero_nat )
% 0.37/0.73 => ( ( lattic8265883725875713057ax_nat
% 0.37/0.73 @ ( collect_nat
% 0.37/0.73 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ N ) ) )
% 0.37/0.73 = N ) ) ).
% 0.37/0.73
% 0.37/0.73 % Max_divisors_self_nat
% 0.37/0.73 thf(fact_8291_even__Suc,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 0.37/0.73 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % even_Suc
% 0.37/0.73 thf(fact_8292_even__Suc__Suc__iff,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.73
% 0.37/0.73 % even_Suc_Suc_iff
% 0.37/0.73 thf(fact_8293_odd__Suc__div__two,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.73 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % odd_Suc_div_two
% 0.37/0.73 thf(fact_8294_even__Suc__div__two,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.73 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % even_Suc_div_two
% 0.37/0.73 thf(fact_8295_odd__Suc__minus__one,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.37/0.73 = N ) ) ).
% 0.37/0.73
% 0.37/0.73 % odd_Suc_minus_one
% 0.37/0.73 thf(fact_8296_even__diff__nat,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.73 = ( ( ord_less_nat @ M @ N )
% 0.37/0.73 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % even_diff_nat
% 0.37/0.73 thf(fact_8297_dvd__diff__nat,axiom,
% 0.37/0.73 ! [K: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ K @ M )
% 0.37/0.73 => ( ( dvd_dvd_nat @ K @ N )
% 0.37/0.73 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_diff_nat
% 0.37/0.73 thf(fact_8298_gcd__nat_Oextremum__uniqueI,axiom,
% 0.37/0.73 ! [A: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.37/0.73 => ( A = zero_zero_nat ) ) ).
% 0.37/0.73
% 0.37/0.73 % gcd_nat.extremum_uniqueI
% 0.37/0.73 thf(fact_8299_gcd__nat_Onot__eq__extremum,axiom,
% 0.37/0.73 ! [A: nat] :
% 0.37/0.73 ( ( A != zero_zero_nat )
% 0.37/0.73 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 0.37/0.73 & ( A != zero_zero_nat ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % gcd_nat.not_eq_extremum
% 0.37/0.73 thf(fact_8300_gcd__nat_Oextremum__unique,axiom,
% 0.37/0.73 ! [A: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.37/0.73 = ( A = zero_zero_nat ) ) ).
% 0.37/0.73
% 0.37/0.73 % gcd_nat.extremum_unique
% 0.37/0.73 thf(fact_8301_gcd__nat_Oextremum__strict,axiom,
% 0.37/0.73 ! [A: nat] :
% 0.37/0.73 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.37/0.73 & ( zero_zero_nat != A ) ) ).
% 0.37/0.73
% 0.37/0.73 % gcd_nat.extremum_strict
% 0.37/0.73 thf(fact_8302_gcd__nat_Oextremum,axiom,
% 0.37/0.73 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.37/0.73
% 0.37/0.73 % gcd_nat.extremum
% 0.37/0.73 thf(fact_8303_dvd__antisym,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ M @ N )
% 0.37/0.73 => ( ( dvd_dvd_nat @ N @ M )
% 0.37/0.73 => ( M = N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_antisym
% 0.37/0.73 thf(fact_8304_dvd__pos__nat,axiom,
% 0.37/0.73 ! [N: nat,M: nat] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.73 => ( ( dvd_dvd_nat @ M @ N )
% 0.37/0.73 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_pos_nat
% 0.37/0.73 thf(fact_8305_nat__dvd__not__less,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.73 => ( ( ord_less_nat @ M @ N )
% 0.37/0.73 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % nat_dvd_not_less
% 0.37/0.73 thf(fact_8306_dvd__minus__self,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 0.37/0.73 = ( ( ord_less_nat @ N @ M )
% 0.37/0.73 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_minus_self
% 0.37/0.73 thf(fact_8307_dvd__diffD,axiom,
% 0.37/0.73 ! [K: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.73 => ( ( dvd_dvd_nat @ K @ N )
% 0.37/0.73 => ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.73 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_diffD
% 0.37/0.73 thf(fact_8308_dvd__diffD1,axiom,
% 0.37/0.73 ! [K: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.37/0.73 => ( ( dvd_dvd_nat @ K @ M )
% 0.37/0.73 => ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.73 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_diffD1
% 0.37/0.73 thf(fact_8309_less__eq__dvd__minus,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.73 => ( ( dvd_dvd_nat @ M @ N )
% 0.37/0.73 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % less_eq_dvd_minus
% 0.37/0.73 thf(fact_8310_set__encode__eq,axiom,
% 0.37/0.73 ! [A4: set_nat,B4: set_nat] :
% 0.37/0.73 ( ( finite_finite_nat @ A4 )
% 0.37/0.73 => ( ( finite_finite_nat @ B4 )
% 0.37/0.73 => ( ( ( nat_set_encode @ A4 )
% 0.37/0.73 = ( nat_set_encode @ B4 ) )
% 0.37/0.73 = ( A4 = B4 ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % set_encode_eq
% 0.37/0.73 thf(fact_8311_even__set__encode__iff,axiom,
% 0.37/0.73 ! [A4: set_nat] :
% 0.37/0.73 ( ( finite_finite_nat @ A4 )
% 0.37/0.73 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 0.37/0.73 = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % even_set_encode_iff
% 0.37/0.73 thf(fact_8312_dvd__imp__le,axiom,
% 0.37/0.73 ! [K: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ K @ N )
% 0.37/0.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.73 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_imp_le
% 0.37/0.73 thf(fact_8313_dvd__mult__cancel,axiom,
% 0.37/0.73 ! [K: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.73 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.73 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_mult_cancel
% 0.37/0.73 thf(fact_8314_nat__mult__dvd__cancel1,axiom,
% 0.37/0.73 ! [K: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.37/0.73 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.37/0.73 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % nat_mult_dvd_cancel1
% 0.37/0.73 thf(fact_8315_bezout__add__strong__nat,axiom,
% 0.37/0.73 ! [A: nat,B: nat] :
% 0.37/0.73 ( ( A != zero_zero_nat )
% 0.37/0.73 => ? [D2: nat,X3: nat,Y3: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ D2 @ A )
% 0.37/0.73 & ( dvd_dvd_nat @ D2 @ B )
% 0.37/0.73 & ( ( times_times_nat @ A @ X3 )
% 0.37/0.73 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D2 ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % bezout_add_strong_nat
% 0.37/0.73 thf(fact_8316_mod__greater__zero__iff__not__dvd,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 0.37/0.73 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % mod_greater_zero_iff_not_dvd
% 0.37/0.73 thf(fact_8317_mod__eq__dvd__iff__nat,axiom,
% 0.37/0.73 ! [N: nat,M: nat,Q3: nat] :
% 0.37/0.73 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.73 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 0.37/0.73 = ( modulo_modulo_nat @ N @ Q3 ) )
% 0.37/0.73 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % mod_eq_dvd_iff_nat
% 0.37/0.73 thf(fact_8318_dvd__fact,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.37/0.73 => ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.73 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_fact
% 0.37/0.73 thf(fact_8319_finite__divisors__nat,axiom,
% 0.37/0.73 ! [M: nat] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.73 => ( finite_finite_nat
% 0.37/0.73 @ ( collect_nat
% 0.37/0.73 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % finite_divisors_nat
% 0.37/0.73 thf(fact_8320_gcd__nat_Oordering__top__axioms,axiom,
% 0.37/0.73 ( ordering_top_nat @ dvd_dvd_nat
% 0.37/0.73 @ ^ [M5: nat,N6: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ M5 @ N6 )
% 0.37/0.73 & ( M5 != N6 ) )
% 0.37/0.73 @ zero_zero_nat ) ).
% 0.37/0.73
% 0.37/0.73 % gcd_nat.ordering_top_axioms
% 0.37/0.73 thf(fact_8321_set__encode__inf,axiom,
% 0.37/0.73 ! [A4: set_nat] :
% 0.37/0.73 ( ~ ( finite_finite_nat @ A4 )
% 0.37/0.73 => ( ( nat_set_encode @ A4 )
% 0.37/0.73 = zero_zero_nat ) ) ).
% 0.37/0.73
% 0.37/0.73 % set_encode_inf
% 0.37/0.73 thf(fact_8322_dvd__mult__cancel1,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.73 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.37/0.73 = ( N = one_one_nat ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_mult_cancel1
% 0.37/0.73 thf(fact_8323_dvd__mult__cancel2,axiom,
% 0.37/0.73 ! [M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.37/0.73 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.37/0.73 = ( N = one_one_nat ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_mult_cancel2
% 0.37/0.73 thf(fact_8324_power__dvd__imp__le,axiom,
% 0.37/0.73 ! [I: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.37/0.73 => ( ( ord_less_nat @ one_one_nat @ I )
% 0.37/0.73 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % power_dvd_imp_le
% 0.37/0.73 thf(fact_8325_dvd__minus__add,axiom,
% 0.37/0.73 ! [Q3: nat,N: nat,R: nat,M: nat] :
% 0.37/0.73 ( ( ord_less_eq_nat @ Q3 @ N )
% 0.37/0.73 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R @ M ) )
% 0.37/0.73 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 0.37/0.73 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q3 ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_minus_add
% 0.37/0.73 thf(fact_8326_diff__mod__le,axiom,
% 0.37/0.73 ! [A: nat,D: nat,B: nat] :
% 0.37/0.73 ( ( ord_less_nat @ A @ D )
% 0.37/0.73 => ( ( dvd_dvd_nat @ B @ D )
% 0.37/0.73 => ( ord_less_eq_nat @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) @ ( minus_minus_nat @ D @ B ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % diff_mod_le
% 0.37/0.73 thf(fact_8327_mod__nat__eqI,axiom,
% 0.37/0.73 ! [R: nat,N: nat,M: nat] :
% 0.37/0.73 ( ( ord_less_nat @ R @ N )
% 0.37/0.73 => ( ( ord_less_eq_nat @ R @ M )
% 0.37/0.73 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 0.37/0.73 => ( ( modulo_modulo_nat @ M @ N )
% 0.37/0.73 = R ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % mod_nat_eqI
% 0.37/0.73 thf(fact_8328_odd__pos,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.37/0.73
% 0.37/0.73 % odd_pos
% 0.37/0.73 thf(fact_8329_dvd__power__iff__le,axiom,
% 0.37/0.73 ! [K: nat,M: nat,N: nat] :
% 0.37/0.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.37/0.73 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 0.37/0.73 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_power_iff_le
% 0.37/0.73 thf(fact_8330_central__binomial__odd,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % central_binomial_odd
% 0.37/0.73 thf(fact_8331_Gcd__eq__Max,axiom,
% 0.37/0.73 ! [M7: set_nat] :
% 0.37/0.73 ( ( finite_finite_nat @ M7 )
% 0.37/0.73 => ( ( M7 != bot_bot_set_nat )
% 0.37/0.73 => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 0.37/0.73 => ( ( gcd_Gcd_nat @ M7 )
% 0.37/0.73 = ( lattic8265883725875713057ax_nat
% 0.37/0.73 @ ( comple7806235888213564991et_nat
% 0.37/0.73 @ ( image_nat_set_nat
% 0.37/0.73 @ ^ [M5: nat] :
% 0.37/0.73 ( collect_nat
% 0.37/0.73 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M5 ) )
% 0.37/0.73 @ M7 ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Gcd_eq_Max
% 0.37/0.73 thf(fact_8332_even__mod__4__div__2,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % even_mod_4_div_2
% 0.37/0.73 thf(fact_8333_odd__mod__4__div__2,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.73 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % odd_mod_4_div_2
% 0.37/0.73 thf(fact_8334_Bernoulli__inequality__even,axiom,
% 0.37/0.73 ! [N: nat,X: real] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( 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 ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Bernoulli_inequality_even
% 0.37/0.73 thf(fact_8335_VEBT__internal_OT__vebt__buildupi_Osimps_I3_J,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T_vebt_buildupi.simps(3)
% 0.37/0.73 thf(fact_8336_vebt__buildup_Osimps_I3_J,axiom,
% 0.37/0.73 ! [Va2: nat] :
% 0.37/0.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_buildup.simps(3)
% 0.37/0.73 thf(fact_8337_VEBT__internal_OT__vebt__buildupi_Oelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_V441764108873111860ildupi @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( suc @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( suc @ zero_zero_nat ) ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T_vebt_buildupi.elims
% 0.37/0.73 thf(fact_8338_VEBT__internal_OTb_H_Osimps_I3_J,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.Tb'.simps(3)
% 0.37/0.73 thf(fact_8339_VEBT__internal_OTb_H_Oelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_VEBT_Tb2 @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.Tb'.elims
% 0.37/0.73 thf(fact_8340_cos__zero__lemma,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ( cos_real @ X )
% 0.37/0.73 = zero_zero_real )
% 0.37/0.73 => ? [N2: nat] :
% 0.37/0.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 & ( X
% 0.37/0.73 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % cos_zero_lemma
% 0.37/0.73 thf(fact_8341_sin__zero__lemma,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.73 => ( ( ( sin_real @ X )
% 0.37/0.73 = zero_zero_real )
% 0.37/0.73 => ? [N2: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 & ( X
% 0.37/0.73 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sin_zero_lemma
% 0.37/0.73 thf(fact_8342_VEBT__internal_OTb_Osimps_I3_J,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_VEBT_Tb @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_VEBT_Tb @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.Tb.simps(3)
% 0.37/0.73 thf(fact_8343_VEBT__internal_OT__vebt__buildupi_H_Osimps_I3_J,axiom,
% 0.37/0.73 ! [N: nat] :
% 0.37/0.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ N ) ) )
% 0.37/0.73 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T_vebt_buildupi'.simps(3)
% 0.37/0.73 thf(fact_8344_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I3_J,axiom,
% 0.37/0.73 ! [Va2: nat] :
% 0.37/0.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.simps(3)
% 0.37/0.73 thf(fact_8345_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I3_J,axiom,
% 0.37/0.73 ! [Va2: nat] :
% 0.37/0.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.simps(3)
% 0.37/0.73 thf(fact_8346_vebt__buildup_Oelims,axiom,
% 0.37/0.73 ! [X: nat,Y: vEBT_VEBT] :
% 0.37/0.73 ( ( ( vEBT_vebt_buildup @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.37/0.73 => ~ ! [Va: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( 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 ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_buildup.elims
% 0.37/0.73 thf(fact_8347_VEBT__internal_OTb_Oelims,axiom,
% 0.37/0.73 ! [X: nat,Y: int] :
% 0.37/0.73 ( ( ( vEBT_VEBT_Tb @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_int @ ( bit1 @ one ) ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_int @ ( bit1 @ one ) ) ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.Tb.elims
% 0.37/0.73 thf(fact_8348_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Oelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 0.37/0.73 => ~ ! [Va: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.elims
% 0.37/0.73 thf(fact_8349_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Oelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 => ~ ! [Va: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.elims
% 0.37/0.73 thf(fact_8350_VEBT__internal_OT__vebt__buildupi_H_Oelims,axiom,
% 0.37/0.73 ! [X: nat,Y: int] :
% 0.37/0.73 ( ( ( vEBT_V9176841429113362141ildupi @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( Y != one_one_int ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( Y != one_one_int ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T_vebt_buildupi'.elims
% 0.37/0.73 thf(fact_8351_arctan__series,axiom,
% 0.37/0.73 ! [X: real] :
% 0.37/0.73 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.73 => ( ( arctan @ X )
% 0.37/0.73 = ( suminf_real
% 0.37/0.73 @ ^ [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 ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % arctan_series
% 0.37/0.73 thf(fact_8352_VEBT__internal_OT__vebt__buildupi_H_Opelims,axiom,
% 0.37/0.73 ! [X: nat,Y: int] :
% 0.37/0.73 ( ( ( vEBT_V9176841429113362141ildupi @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_nat @ vEBT_V3352910403632780892pi_rel @ X )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( ( Y = one_one_int )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y = one_one_int )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T_vebt_buildupi'.pelims
% 0.37/0.73 thf(fact_8353_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Opelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_nat @ vEBT_V5144397997797733112_d_rel @ X )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.73 => ~ ! [Va: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d.pelims
% 0.37/0.73 thf(fact_8354_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Opelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_nat @ vEBT_V1247956027447740395_p_rel @ X )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.73 => ~ ! [Va: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T\<^sub>b\<^sub>u\<^sub>i\<^sub>l\<^sub>d\<^sub>u\<^sub>p.pelims
% 0.37/0.73 thf(fact_8355_zdvd__antisym__nonneg,axiom,
% 0.37/0.73 ! [M: int,N: int] :
% 0.37/0.73 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.37/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.37/0.73 => ( ( dvd_dvd_int @ M @ N )
% 0.37/0.73 => ( ( dvd_dvd_int @ N @ M )
% 0.37/0.73 => ( M = N ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % zdvd_antisym_nonneg
% 0.37/0.73 thf(fact_8356_zdvd__not__zless,axiom,
% 0.37/0.73 ! [M: int,N: int] :
% 0.37/0.73 ( ( ord_less_int @ zero_zero_int @ M )
% 0.37/0.73 => ( ( ord_less_int @ M @ N )
% 0.37/0.73 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % zdvd_not_zless
% 0.37/0.73 thf(fact_8357_abs__div,axiom,
% 0.37/0.73 ! [Y: int,X: int] :
% 0.37/0.73 ( ( dvd_dvd_int @ Y @ X )
% 0.37/0.73 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 0.37/0.73 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % abs_div
% 0.37/0.73 thf(fact_8358_zdvd__imp__le,axiom,
% 0.37/0.73 ! [Z: int,N: int] :
% 0.37/0.73 ( ( dvd_dvd_int @ Z @ N )
% 0.37/0.73 => ( ( ord_less_int @ zero_zero_int @ N )
% 0.37/0.73 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % zdvd_imp_le
% 0.37/0.73 thf(fact_8359_dvd__imp__le__int,axiom,
% 0.37/0.73 ! [I: int,D: int] :
% 0.37/0.73 ( ( I != zero_zero_int )
% 0.37/0.73 => ( ( dvd_dvd_int @ D @ I )
% 0.37/0.73 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % dvd_imp_le_int
% 0.37/0.73 thf(fact_8360_mod__int__pos__iff,axiom,
% 0.37/0.73 ! [K: int,L: int] :
% 0.37/0.73 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 0.37/0.73 = ( ( dvd_dvd_int @ L @ K )
% 0.37/0.73 | ( ( L = zero_zero_int )
% 0.37/0.73 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 0.37/0.73 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % mod_int_pos_iff
% 0.37/0.73 thf(fact_8361_int__div__sub__1,axiom,
% 0.37/0.73 ! [M: int,N: int] :
% 0.37/0.73 ( ( ord_less_eq_int @ one_one_int @ M )
% 0.37/0.73 => ( ( ( dvd_dvd_int @ M @ N )
% 0.37/0.73 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 0.37/0.73 = ( minus_minus_int @ ( divide_divide_int @ N @ M ) @ one_one_int ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_int @ M @ N )
% 0.37/0.73 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 0.37/0.73 = ( divide_divide_int @ N @ M ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % int_div_sub_1
% 0.37/0.73 thf(fact_8362_div__dvd__sgn__abs,axiom,
% 0.37/0.73 ! [L: int,K: int] :
% 0.37/0.73 ( ( dvd_dvd_int @ L @ K )
% 0.37/0.73 => ( ( divide_divide_int @ K @ L )
% 0.37/0.73 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % div_dvd_sgn_abs
% 0.37/0.73 thf(fact_8363_nat__dvd__iff,axiom,
% 0.37/0.73 ! [Z: int,M: nat] :
% 0.37/0.73 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 0.37/0.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.73 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.37/0.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.37/0.73 => ( M = zero_zero_nat ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % nat_dvd_iff
% 0.37/0.73 thf(fact_8364_even__nat__iff,axiom,
% 0.37/0.73 ! [K: int] :
% 0.37/0.73 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.73 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 0.37/0.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % even_nat_iff
% 0.37/0.73 thf(fact_8365_eme1p,axiom,
% 0.37/0.73 ! [N: int,D: int] :
% 0.37/0.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D )
% 0.37/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ D )
% 0.37/0.73 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ N ) @ D )
% 0.37/0.73 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ N @ D ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % eme1p
% 0.37/0.73 thf(fact_8366_emep1,axiom,
% 0.37/0.73 ! [N: int,D: int] :
% 0.37/0.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.37/0.73 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D )
% 0.37/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ D )
% 0.37/0.73 => ( ( modulo_modulo_int @ ( plus_plus_int @ N @ one_one_int ) @ D )
% 0.37/0.73 = ( plus_plus_int @ ( modulo_modulo_int @ N @ D ) @ one_one_int ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % emep1
% 0.37/0.73 thf(fact_8367_vebt__buildup_Opelims,axiom,
% 0.37/0.73 ! [X: nat,Y: vEBT_VEBT] :
% 0.37/0.73 ( ( ( vEBT_vebt_buildup @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Leaf @ $false @ $false ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( vEBT_Leaf @ $false @ $false ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.73 => ~ ! [Va: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( 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 ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( 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 ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_buildup.pelims
% 0.37/0.73 thf(fact_8368_VEBT__internal_OTb_Opelims,axiom,
% 0.37/0.73 ! [X: nat,Y: int] :
% 0.37/0.73 ( ( ( vEBT_VEBT_Tb @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_nat @ vEBT_VEBT_Tb_rel2 @ X )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_int @ ( bit1 @ one ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_int @ ( bit1 @ one ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.Tb.pelims
% 0.37/0.73 thf(fact_8369_VEBT__internal_OTb_H_Opelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_VEBT_Tb2 @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_nat @ vEBT_VEBT_Tb_rel @ X )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.Tb'.pelims
% 0.37/0.73 thf(fact_8370_VEBT__internal_OT__vebt__buildupi_Opelims,axiom,
% 0.37/0.73 ! [X: nat,Y: nat] :
% 0.37/0.73 ( ( ( vEBT_V441764108873111860ildupi @ X )
% 0.37/0.73 = Y )
% 0.37/0.73 => ( ( accp_nat @ vEBT_V2957053500504383685pi_rel @ X )
% 0.37/0.73 => ( ( ( X = zero_zero_nat )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ zero_zero_nat ) ) )
% 0.37/0.73 => ( ( ( X
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ( ( Y
% 0.37/0.73 = ( suc @ zero_zero_nat ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.73 => ~ ! [N2: nat] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( suc @ ( suc @ N2 ) ) )
% 0.37/0.73 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 0.37/0.73 => ( Y
% 0.37/0.73 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % VEBT_internal.T_vebt_buildupi.pelims
% 0.37/0.73 thf(fact_8371_vebt__delete__code_I2_J,axiom,
% 0.37/0.73 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.73 ( ( vEBT_vebt_delete @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.73 = ( case_o2442805151034396888at_nat @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary )
% 0.37/0.73 @ ^ [Mima: product_prod_nat_nat] :
% 0.37/0.73 ( if_VEBT_VEBT @ ( ord_less_eq_nat @ Deg @ one_one_nat ) @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary )
% 0.37/0.73 @ ( produc3169358591047799142T_VEBT
% 0.37/0.73 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.73 ( if_VEBT_VEBT
% 0.37/0.73 @ ( ( ord_less_nat @ X @ Mi3 )
% 0.37/0.73 | ( ord_less_nat @ Ma3 @ X ) )
% 0.37/0.73 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg @ TreeList @ Summary )
% 0.37/0.73 @ ( if_VEBT_VEBT
% 0.37/0.73 @ ( ( X = Mi3 )
% 0.37/0.73 & ( X = Ma3 ) )
% 0.37/0.73 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary )
% 0.37/0.73 @ ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.73 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( vEBT_Node
% 0.37/0.73 @ ( some_P7363390416028606310at_nat
% 0.37/0.73 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( X = Mi3 )
% 0.37/0.73 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.73 = Ma3 ) )
% 0.37/0.73 & ( ( X != Mi3 )
% 0.37/0.73 => ( X = Ma3 ) ) )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 0.37/0.73 @ ( 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 = Mi3 ) @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( 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 = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ Ma3 ) ) )
% 0.37/0.73 @ Deg
% 0.37/0.73 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ ( vEBT_Node
% 0.37/0.73 @ ( some_P7363390416028606310at_nat
% 0.37/0.73 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 0.37/0.73 @ ( if_nat
% 0.37/0.73 @ ( ( ( X = Mi3 )
% 0.37/0.73 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.37/0.73 = Ma3 ) )
% 0.37/0.73 & ( ( X != Mi3 )
% 0.37/0.73 => ( X = Ma3 ) ) )
% 0.37/0.73 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ Ma3 ) ) )
% 0.37/0.73 @ Deg
% 0.37/0.73 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 @ Summary ) )
% 0.37/0.73 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg @ TreeList @ Summary ) ) ) )
% 0.37/0.73 @ Mima ) )
% 0.37/0.73 @ Info ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_delete_code(2)
% 0.37/0.73 thf(fact_8372_divmod__int__def,axiom,
% 0.37/0.73 ( unique5052692396658037445od_int
% 0.37/0.73 = ( ^ [M5: num,N6: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divmod_int_def
% 0.37/0.73 thf(fact_8373_divmod_H__nat__def,axiom,
% 0.37/0.73 ( unique5055182867167087721od_nat
% 0.37/0.73 = ( ^ [M5: num,N6: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N6 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N6 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divmod'_nat_def
% 0.37/0.73 thf(fact_8374_vebt__insert__code_I2_J,axiom,
% 0.37/0.73 ! [Deg: nat,Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.73 ( ( ( ord_less_eq_nat @ Deg @ one_one_nat )
% 0.37/0.73 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.73 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) )
% 0.37/0.73 & ( ~ ( ord_less_eq_nat @ Deg @ one_one_nat )
% 0.37/0.73 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.73 = ( case_o2442805151034396888at_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ Deg @ TreeList @ Summary )
% 0.37/0.73 @ ( produc3169358591047799142T_VEBT
% 0.37/0.73 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.73 ( if_VEBT_VEBT
% 0.37/0.73 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.73 & ~ ( ( X = Mi3 )
% 0.37/0.73 | ( X = Ma3 ) ) )
% 0.37/0.73 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ X @ Mi3 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ Ma3 ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 0.37/0.73 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg @ TreeList @ Summary ) ) )
% 0.37/0.73 @ Info ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_insert_code(2)
% 0.37/0.73 thf(fact_8375_minus__one__div__numeral,axiom,
% 0.37/0.73 ! [N: num] :
% 0.37/0.73 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.73 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % minus_one_div_numeral
% 0.37/0.73 thf(fact_8376_one__div__minus__numeral,axiom,
% 0.37/0.73 ! [N: num] :
% 0.37/0.73 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.73 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % one_div_minus_numeral
% 0.37/0.73 thf(fact_8377_numeral__div__minus__numeral,axiom,
% 0.37/0.73 ! [M: num,N: num] :
% 0.37/0.73 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.73 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % numeral_div_minus_numeral
% 0.37/0.73 thf(fact_8378_minus__numeral__div__numeral,axiom,
% 0.37/0.73 ! [M: num,N: num] :
% 0.37/0.73 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.73 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % minus_numeral_div_numeral
% 0.37/0.73 thf(fact_8379_divmod__nat__if,axiom,
% 0.37/0.73 ( divmod_nat
% 0.37/0.73 = ( ^ [M5: nat,N6: nat] :
% 0.37/0.73 ( if_Pro6206227464963214023at_nat
% 0.37/0.73 @ ( ( N6 = zero_zero_nat )
% 0.37/0.73 | ( ord_less_nat @ M5 @ N6 ) )
% 0.37/0.73 @ ( product_Pair_nat_nat @ zero_zero_nat @ M5 )
% 0.37/0.73 @ ( produc2626176000494625587at_nat
% 0.37/0.73 @ ^ [Q8: nat] : ( product_Pair_nat_nat @ ( suc @ Q8 ) )
% 0.37/0.73 @ ( divmod_nat @ ( minus_minus_nat @ M5 @ N6 ) @ N6 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divmod_nat_if
% 0.37/0.73 thf(fact_8380_divmod__step__integer__def,axiom,
% 0.37/0.73 ( unique4921790084139445826nteger
% 0.37/0.73 = ( ^ [L4: num] :
% 0.37/0.73 ( produc6916734918728496179nteger
% 0.37/0.73 @ ^ [Q8: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L4 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L4 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divmod_step_integer_def
% 0.37/0.73 thf(fact_8381_divmod__step__nat__def,axiom,
% 0.37/0.73 ( unique5026877609467782581ep_nat
% 0.37/0.73 = ( ^ [L4: num] :
% 0.37/0.73 ( produc2626176000494625587at_nat
% 0.37/0.73 @ ^ [Q8: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L4 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L4 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divmod_step_nat_def
% 0.37/0.73 thf(fact_8382_divmod__step__int__def,axiom,
% 0.37/0.73 ( unique5024387138958732305ep_int
% 0.37/0.73 = ( ^ [L4: num] :
% 0.37/0.73 ( produc4245557441103728435nt_int
% 0.37/0.73 @ ^ [Q8: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L4 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L4 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divmod_step_int_def
% 0.37/0.73 thf(fact_8383_vebt__succ__code_I2_J,axiom,
% 0.37/0.73 ! [Deg: nat,Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.37/0.73 ( ( ( ord_less_eq_nat @ Deg @ one_one_nat )
% 0.37/0.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.73 = none_nat ) )
% 0.37/0.73 & ( ~ ( ord_less_eq_nat @ Deg @ one_one_nat )
% 0.37/0.73 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 0.37/0.73 = ( case_o1383228350324149268at_nat @ none_nat
% 0.37/0.73 @ ( produc2484365769952853102on_nat
% 0.37/0.73 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.73 ( if_option_nat @ ( ord_less_nat @ X @ Mi3 ) @ ( some_nat @ Mi3 )
% 0.37/0.73 @ ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.37/0.73 @ ( if_option_nat
% 0.37/0.73 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.73 != none_nat )
% 0.37/0.73 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.37/0.73 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 0.37/0.73 @ ( if_option_nat
% 0.37/0.73 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 = none_nat )
% 0.37/0.73 @ none_nat
% 0.37/0.73 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.37/0.73 @ none_nat ) ) )
% 0.37/0.73 @ Info ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % vebt_succ_code(2)
% 0.37/0.73 thf(fact_8384_integer__of__int__code,axiom,
% 0.37/0.73 ( code_integer_of_int
% 0.37/0.73 = ( ^ [K3: int] :
% 0.37/0.73 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.37/0.73 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.37/0.73 @ ( if_Code_integer
% 0.37/0.73 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.37/0.73 = zero_zero_int )
% 0.37/0.73 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.37/0.73 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % integer_of_int_code
% 0.37/0.73 thf(fact_8385_integer__of__int__eq__of__int,axiom,
% 0.37/0.73 code_integer_of_int = ring_18347121197199848620nteger ).
% 0.37/0.73
% 0.37/0.73 % integer_of_int_eq_of_int
% 0.37/0.73 thf(fact_8386_divmod__integer_H__def,axiom,
% 0.37/0.73 ( unique3479559517661332726nteger
% 0.37/0.73 = ( ^ [M5: num,N6: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N6 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N6 ) ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divmod_integer'_def
% 0.37/0.73 thf(fact_8387_one__integer__def,axiom,
% 0.37/0.73 ( one_one_Code_integer
% 0.37/0.73 = ( code_integer_of_int @ one_one_int ) ) ).
% 0.37/0.73
% 0.37/0.73 % one_integer_def
% 0.37/0.73 thf(fact_8388_less__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: int,X: int] :
% 0.37/0.73 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( ord_less_int @ Xa2 @ X ) ) ).
% 0.37/0.73
% 0.37/0.73 % less_integer.abs_eq
% 0.37/0.73 thf(fact_8389_divide__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: int,X: int] :
% 0.37/0.73 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % divide_integer.abs_eq
% 0.37/0.73 thf(fact_8390_modulo__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: int,X: int] :
% 0.37/0.73 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa2 @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % modulo_integer.abs_eq
% 0.37/0.73 thf(fact_8391_integer__of__int__inject,axiom,
% 0.37/0.73 ! [X: int,Y: int] :
% 0.37/0.73 ( ( member_int @ X @ top_top_set_int )
% 0.37/0.73 => ( ( member_int @ Y @ top_top_set_int )
% 0.37/0.73 => ( ( ( code_integer_of_int @ X )
% 0.37/0.73 = ( code_integer_of_int @ Y ) )
% 0.37/0.73 = ( X = Y ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % integer_of_int_inject
% 0.37/0.73 thf(fact_8392_integer__of__int__induct,axiom,
% 0.37/0.73 ! [P2: code_integer > $o,X: code_integer] :
% 0.37/0.73 ( ! [Y3: int] :
% 0.37/0.73 ( ( member_int @ Y3 @ top_top_set_int )
% 0.37/0.73 => ( P2 @ ( code_integer_of_int @ Y3 ) ) )
% 0.37/0.73 => ( P2 @ X ) ) ).
% 0.37/0.73
% 0.37/0.73 % integer_of_int_induct
% 0.37/0.73 thf(fact_8393_integer__of__int__cases,axiom,
% 0.37/0.73 ! [X: code_integer] :
% 0.37/0.73 ~ ! [Y3: int] :
% 0.37/0.73 ( ( X
% 0.37/0.73 = ( code_integer_of_int @ Y3 ) )
% 0.37/0.73 => ~ ( member_int @ Y3 @ top_top_set_int ) ) ).
% 0.37/0.73
% 0.37/0.73 % integer_of_int_cases
% 0.37/0.73 thf(fact_8394_zero__integer__def,axiom,
% 0.37/0.73 ( zero_z3403309356797280102nteger
% 0.37/0.73 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 0.37/0.73
% 0.37/0.73 % zero_integer_def
% 0.37/0.73 thf(fact_8395_Code__Numeral_Oset__bit__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: nat,X: int] :
% 0.37/0.73 ( ( bit_se2793503036327961859nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa2 @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % Code_Numeral.set_bit_integer.abs_eq
% 0.37/0.73 thf(fact_8396_uminus__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [X: int] :
% 0.37/0.73 ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( uminus_uminus_int @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % uminus_integer.abs_eq
% 0.37/0.73 thf(fact_8397_less__eq__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: int,X: int] :
% 0.37/0.73 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 0.37/0.73
% 0.37/0.73 % less_eq_integer.abs_eq
% 0.37/0.73 thf(fact_8398_plus__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: int,X: int] :
% 0.37/0.73 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % plus_integer.abs_eq
% 0.37/0.73 thf(fact_8399_minus__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: int,X: int] :
% 0.37/0.73 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % minus_integer.abs_eq
% 0.37/0.73 thf(fact_8400_times__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [Xa2: int,X: int] :
% 0.37/0.73 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % times_integer.abs_eq
% 0.37/0.73 thf(fact_8401_abs__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [X: int] :
% 0.37/0.73 ( ( abs_abs_Code_integer @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( abs_abs_int @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % abs_integer.abs_eq
% 0.37/0.73 thf(fact_8402_sgn__integer_Oabs__eq,axiom,
% 0.37/0.73 ! [X: int] :
% 0.37/0.73 ( ( sgn_sgn_Code_integer @ ( code_integer_of_int @ X ) )
% 0.37/0.73 = ( code_integer_of_int @ ( sgn_sgn_int @ X ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % sgn_integer.abs_eq
% 0.37/0.73 thf(fact_8403_signed__take__bit__Suc__bit0,axiom,
% 0.37/0.73 ! [N: nat,K: num] :
% 0.37/0.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.37/0.73 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % signed_take_bit_Suc_bit0
% 0.37/0.73 thf(fact_8404_signed__take__bit__Suc__minus__bit0,axiom,
% 0.37/0.73 ! [N: nat,K: num] :
% 0.37/0.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.37/0.73 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % signed_take_bit_Suc_minus_bit0
% 0.37/0.73 thf(fact_8405_signed__take__bit__Suc__bit1,axiom,
% 0.37/0.73 ! [N: nat,K: num] :
% 0.37/0.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.37/0.73 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.37/0.73
% 0.37/0.73 % signed_take_bit_Suc_bit1
% 0.37/0.73 thf(fact_8406_signed__take__bit__Suc__minus__bit1,axiom,
% 0.37/0.73 ! [N: nat,K: num] :
% 0.37/0.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.37/0.73 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.37/0.73
% 0.37/0.73 % signed_take_bit_Suc_minus_bit1
% 0.37/0.73 thf(fact_8407_signed__take__bit__int__less__exp,axiom,
% 0.37/0.73 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.73
% 0.37/0.73 % signed_take_bit_int_less_exp
% 0.37/0.73 thf(fact_8408_signed__take__bit__int__greater__eq__self__iff,axiom,
% 0.37/0.73 ! [K: int,N: nat] :
% 0.37/0.73 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.37/0.73 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.73
% 0.37/0.73 % signed_take_bit_int_greater_eq_self_iff
% 0.37/0.73 thf(fact_8409_signed__take__bit__int__less__self__iff,axiom,
% 0.37/0.73 ! [N: nat,K: int] :
% 0.37/0.73 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.37/0.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.37/0.73
% 0.37/0.73 % signed_take_bit_int_less_self_iff
% 0.37/0.73 thf(fact_8410_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 0.37/0.73 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_int_greater_eq_minus_exp
% 0.37/0.74 thf(fact_8411_signed__take__bit__int__less__eq__self__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.37/0.74 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_int_less_eq_self_iff
% 0.37/0.74 thf(fact_8412_signed__take__bit__int__greater__self__iff,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.37/0.74 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_int_greater_self_iff
% 0.37/0.74 thf(fact_8413_signed__take__bit__int__less__eq,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.37/0.74 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_int_less_eq
% 0.37/0.74 thf(fact_8414_signed__take__bit__int__eq__self__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.37/0.74 = K )
% 0.37/0.74 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.37/0.74 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_int_eq_self_iff
% 0.37/0.74 thf(fact_8415_signed__take__bit__int__eq__self,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.37/0.74 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.37/0.74 = K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_int_eq_self
% 0.37/0.74 thf(fact_8416_signed__take__bit__int__greater__eq,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.37/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_int_greater_eq
% 0.37/0.74 thf(fact_8417_lowi__def,axiom,
% 0.37/0.74 ( vEBT_VEBT_lowi
% 0.37/0.74 = ( ^ [X4: nat,N6: nat] : ( heap_Time_return_nat @ ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % lowi_def
% 0.37/0.74 thf(fact_8418_summable__arctan__series,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( summable_real
% 0.37/0.74 @ ^ [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 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_arctan_series
% 0.37/0.74 thf(fact_8419_highi__def,axiom,
% 0.37/0.74 ( vEBT_VEBT_highi
% 0.37/0.74 = ( ^ [X4: nat,N6: nat] : ( heap_Time_return_nat @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % highi_def
% 0.37/0.74 thf(fact_8420_highsimp,axiom,
% 0.37/0.74 ! [X: nat,N: nat] :
% 0.37/0.74 ( ( heap_Time_return_nat @ ( vEBT_VEBT_high @ X @ N ) )
% 0.37/0.74 = ( vEBT_VEBT_highi @ X @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % highsimp
% 0.37/0.74 thf(fact_8421_lowsimp,axiom,
% 0.37/0.74 ! [X: nat,N: nat] :
% 0.37/0.74 ( ( heap_Time_return_nat @ ( vEBT_VEBT_low @ X @ N ) )
% 0.37/0.74 = ( vEBT_VEBT_lowi @ X @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % lowsimp
% 0.37/0.74 thf(fact_8422_summable__rabs__comparison__test,axiom,
% 0.37/0.74 ! [F: nat > real,G: nat > real] :
% 0.37/0.74 ( ? [N10: nat] :
% 0.37/0.74 ! [N2: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ N10 @ N2 )
% 0.37/0.74 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 0.37/0.74 => ( ( summable_real @ G )
% 0.37/0.74 => ( summable_real
% 0.37/0.74 @ ^ [N6: nat] : ( abs_abs_real @ ( F @ N6 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_rabs_comparison_test
% 0.37/0.74 thf(fact_8423_summable__rabs,axiom,
% 0.37/0.74 ! [F: nat > real] :
% 0.37/0.74 ( ( summable_real
% 0.37/0.74 @ ^ [N6: nat] : ( abs_abs_real @ ( F @ N6 ) ) )
% 0.37/0.74 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [N6: nat] : ( abs_abs_real @ ( F @ N6 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_rabs
% 0.37/0.74 thf(fact_8424_summable__power__series,axiom,
% 0.37/0.74 ! [F: nat > real,Z: real] :
% 0.37/0.74 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 0.37/0.74 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 0.37/0.74 => ( ( ord_less_real @ Z @ one_one_real )
% 0.37/0.74 => ( summable_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_power_series
% 0.37/0.74 thf(fact_8425_suminf__eq__SUP__real,axiom,
% 0.37/0.74 ! [X6: nat > real] :
% 0.37/0.74 ( ( summable_real @ X6 )
% 0.37/0.74 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X6 @ I2 ) )
% 0.37/0.74 => ( ( suminf_real @ X6 )
% 0.37/0.74 = ( comple1385675409528146559p_real
% 0.37/0.74 @ ( image_nat_real
% 0.37/0.74 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X6 @ ( set_ord_lessThan_nat @ I3 ) )
% 0.37/0.74 @ top_top_set_nat ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % suminf_eq_SUP_real
% 0.37/0.74 thf(fact_8426_sum__pos__lt__pair,axiom,
% 0.37/0.74 ! [F: nat > real,K: nat] :
% 0.37/0.74 ( ( summable_real @ F )
% 0.37/0.74 => ( ! [D2: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D2 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D2 ) @ one_one_nat ) ) ) ) )
% 0.37/0.74 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sum_pos_lt_pair
% 0.37/0.74 thf(fact_8427_tanh__ln__real,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 0.37/0.74 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_ln_real
% 0.37/0.74 thf(fact_8428_unset__bit__nonnegative__int__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 0.37/0.74 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % unset_bit_nonnegative_int_iff
% 0.37/0.74 thf(fact_8429_flip__bit__nonnegative__int__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 0.37/0.74 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % flip_bit_nonnegative_int_iff
% 0.37/0.74 thf(fact_8430_unset__bit__negative__int__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 0.37/0.74 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.74
% 0.37/0.74 % unset_bit_negative_int_iff
% 0.37/0.74 thf(fact_8431_flip__bit__negative__int__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 0.37/0.74 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.74
% 0.37/0.74 % flip_bit_negative_int_iff
% 0.37/0.74 thf(fact_8432_tanh__real__less__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 0.37/0.74 = ( ord_less_real @ X @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_less_iff
% 0.37/0.74 thf(fact_8433_tanh__real__le__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_le_iff
% 0.37/0.74 thf(fact_8434_tanh__real__neg__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 0.37/0.74 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_neg_iff
% 0.37/0.74 thf(fact_8435_tanh__real__pos__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 0.37/0.74 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_pos_iff
% 0.37/0.74 thf(fact_8436_tanh__real__nonneg__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 0.37/0.74 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_nonneg_iff
% 0.37/0.74 thf(fact_8437_tanh__real__nonpos__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 0.37/0.74 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_nonpos_iff
% 0.37/0.74 thf(fact_8438_flip__bit__integer_Oabs__eq,axiom,
% 0.37/0.74 ! [Xa2: nat,X: int] :
% 0.37/0.74 ( ( bit_se1345352211410354436nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 0.37/0.74 = ( code_integer_of_int @ ( bit_se2159334234014336723it_int @ Xa2 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % flip_bit_integer.abs_eq
% 0.37/0.74 thf(fact_8439_unset__bit__integer_Oabs__eq,axiom,
% 0.37/0.74 ! [Xa2: nat,X: int] :
% 0.37/0.74 ( ( bit_se8260200283734997820nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 0.37/0.74 = ( code_integer_of_int @ ( bit_se4203085406695923979it_int @ Xa2 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % unset_bit_integer.abs_eq
% 0.37/0.74 thf(fact_8440_unset__bit__less__eq,axiom,
% 0.37/0.74 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 0.37/0.74
% 0.37/0.74 % unset_bit_less_eq
% 0.37/0.74 thf(fact_8441_tanh__real__lt__1,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_lt_1
% 0.37/0.74 thf(fact_8442_tanh__real__gt__neg1,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % tanh_real_gt_neg1
% 0.37/0.74 thf(fact_8443_complex__unimodular__polar,axiom,
% 0.37/0.74 ! [Z: complex] :
% 0.37/0.74 ( ( ( real_V1022390504157884413omplex @ Z )
% 0.37/0.74 = one_one_real )
% 0.37/0.74 => ~ ! [T6: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.74 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.37/0.74 => ( Z
% 0.37/0.74 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % complex_unimodular_polar
% 0.37/0.74 thf(fact_8444_lemma__tan__total,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.37/0.74 => ? [X3: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.37/0.74 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ord_less_real @ Y @ ( tan_real @ X3 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % lemma_tan_total
% 0.37/0.74 thf(fact_8445_tan__gt__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_gt_zero
% 0.37/0.74 thf(fact_8446_lemma__tan__total1,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ? [X3: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.37/0.74 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( tan_real @ X3 )
% 0.37/0.74 = Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % lemma_tan_total1
% 0.37/0.74 thf(fact_8447_tan__mono__lt__eq,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.74 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 0.37/0.74 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_mono_lt_eq
% 0.37/0.74 thf(fact_8448_tan__monotone_H,axiom,
% 0.37/0.74 ! [Y: real,X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.74 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_real @ Y @ X )
% 0.37/0.74 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_monotone'
% 0.37/0.74 thf(fact_8449_tan__monotone,axiom,
% 0.37/0.74 ! [Y: real,X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.74 => ( ( ord_less_real @ Y @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_monotone
% 0.37/0.74 thf(fact_8450_tan__total,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ? [X3: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 0.37/0.74 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( tan_real @ X3 )
% 0.37/0.74 = Y )
% 0.37/0.74 & ! [Y5: real] :
% 0.37/0.74 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 0.37/0.74 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( tan_real @ Y5 )
% 0.37/0.74 = Y ) )
% 0.37/0.74 => ( Y5 = X3 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_total
% 0.37/0.74 thf(fact_8451_tan__total__pos,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ? [X3: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.37/0.74 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( tan_real @ X3 )
% 0.37/0.74 = Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_total_pos
% 0.37/0.74 thf(fact_8452_tan__pos__pi2__le,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_pos_pi2_le
% 0.37/0.74 thf(fact_8453_tan__less__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.74 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_less_zero
% 0.37/0.74 thf(fact_8454_tan__mono__le__eq,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 0.37/0.74 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_mono_le_eq
% 0.37/0.74 thf(fact_8455_tan__mono__le,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.74 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_mono_le
% 0.37/0.74 thf(fact_8456_tan__bound__pi2,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.74 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_bound_pi2
% 0.37/0.74 thf(fact_8457_arctan,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 0.37/0.74 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( tan_real @ ( arctan @ Y ) )
% 0.37/0.74 = Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % arctan
% 0.37/0.74 thf(fact_8458_arctan__tan,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( arctan @ ( tan_real @ X ) )
% 0.37/0.74 = X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arctan_tan
% 0.37/0.74 thf(fact_8459_arctan__unique,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ( tan_real @ X )
% 0.37/0.74 = Y )
% 0.37/0.74 => ( ( arctan @ Y )
% 0.37/0.74 = X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arctan_unique
% 0.37/0.74 thf(fact_8460_tan__total__pi4,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ? [Z3: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 0.37/0.74 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 0.37/0.74 & ( ( tan_real @ Z3 )
% 0.37/0.74 = X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % tan_total_pi4
% 0.37/0.74 thf(fact_8461_arctan__def,axiom,
% 0.37/0.74 ( arctan
% 0.37/0.74 = ( ^ [Y4: real] :
% 0.37/0.74 ( the_real
% 0.37/0.74 @ ^ [X4: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.37/0.74 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( tan_real @ X4 )
% 0.37/0.74 = Y4 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arctan_def
% 0.37/0.74 thf(fact_8462_arcsin__def,axiom,
% 0.37/0.74 ( arcsin
% 0.37/0.74 = ( ^ [Y4: real] :
% 0.37/0.74 ( the_real
% 0.37/0.74 @ ^ [X4: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 0.37/0.74 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( sin_real @ X4 )
% 0.37/0.74 = Y4 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_def
% 0.37/0.74 thf(fact_8463_sin__tan,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( sin_real @ X )
% 0.37/0.74 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sin_tan
% 0.37/0.74 thf(fact_8464_real__sqrt__less__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 0.37/0.74 = ( ord_less_real @ X @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_less_iff
% 0.37/0.74 thf(fact_8465_real__sqrt__le__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ X @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_le_iff
% 0.37/0.74 thf(fact_8466_real__sqrt__gt__0__iff,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 0.37/0.74 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_gt_0_iff
% 0.37/0.74 thf(fact_8467_real__sqrt__lt__0__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 0.37/0.74 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_lt_0_iff
% 0.37/0.74 thf(fact_8468_real__sqrt__ge__0__iff,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_ge_0_iff
% 0.37/0.74 thf(fact_8469_real__sqrt__le__0__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 0.37/0.74 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_le_0_iff
% 0.37/0.74 thf(fact_8470_real__sqrt__lt__1__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 0.37/0.74 = ( ord_less_real @ X @ one_one_real ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_lt_1_iff
% 0.37/0.74 thf(fact_8471_real__sqrt__gt__1__iff,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 0.37/0.74 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_gt_1_iff
% 0.37/0.74 thf(fact_8472_real__sqrt__ge__1__iff,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_ge_1_iff
% 0.37/0.74 thf(fact_8473_real__sqrt__le__1__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 0.37/0.74 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_le_1_iff
% 0.37/0.74 thf(fact_8474_sin__arcsin,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( sin_real @ ( arcsin @ Y ) )
% 0.37/0.74 = Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sin_arcsin
% 0.37/0.74 thf(fact_8475_real__sqrt__pow2__iff,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.74 = X )
% 0.37/0.74 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_pow2_iff
% 0.37/0.74 thf(fact_8476_real__sqrt__pow2,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.74 = X ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_pow2
% 0.37/0.74 thf(fact_8477_real__sqrt__le__mono,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.74 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_le_mono
% 0.37/0.74 thf(fact_8478_real__sqrt__less__mono,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ X @ Y )
% 0.37/0.74 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_less_mono
% 0.37/0.74 thf(fact_8479_real__sqrt__ge__one,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.74 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_ge_one
% 0.37/0.74 thf(fact_8480_real__sqrt__eq__zero__cancel,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ( sqrt @ X )
% 0.37/0.74 = zero_zero_real )
% 0.37/0.74 => ( X = zero_zero_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_eq_zero_cancel
% 0.37/0.74 thf(fact_8481_real__sqrt__ge__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_ge_zero
% 0.37/0.74 thf(fact_8482_real__sqrt__gt__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_gt_zero
% 0.37/0.74 thf(fact_8483_real__div__sqrt,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 0.37/0.74 = ( sqrt @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_div_sqrt
% 0.37/0.74 thf(fact_8484_sqrt__add__le__add__sqrt,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt_add_le_add_sqrt
% 0.37/0.74 thf(fact_8485_le__real__sqrt__sumsq,axiom,
% 0.37/0.74 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % le_real_sqrt_sumsq
% 0.37/0.74 thf(fact_8486_arcsin__le__arcsin,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_le_arcsin
% 0.37/0.74 thf(fact_8487_arcsin__minus,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.74 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 0.37/0.74 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_minus
% 0.37/0.74 thf(fact_8488_arcsin__le__mono,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_le_mono
% 0.37/0.74 thf(fact_8489_arcsin__eq__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.74 => ( ( ( arcsin @ X )
% 0.37/0.74 = ( arcsin @ Y ) )
% 0.37/0.74 = ( X = Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_eq_iff
% 0.37/0.74 thf(fact_8490_sqrt2__less__2,axiom,
% 0.37/0.74 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt2_less_2
% 0.37/0.74 thf(fact_8491_sqrt__divide__self__eq,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 0.37/0.74 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt_divide_self_eq
% 0.37/0.74 thf(fact_8492_cos__arcsin,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.74 => ( ( cos_real @ ( arcsin @ X ) )
% 0.37/0.74 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cos_arcsin
% 0.37/0.74 thf(fact_8493_real__less__rsqrt,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 0.37/0.74 => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_less_rsqrt
% 0.37/0.74 thf(fact_8494_real__le__rsqrt,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 0.37/0.74 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_le_rsqrt
% 0.37/0.74 thf(fact_8495_sqrt__le__D,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 0.37/0.74 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt_le_D
% 0.37/0.74 thf(fact_8496_arcsin__less__arcsin,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_less_arcsin
% 0.37/0.74 thf(fact_8497_arcsin__less__mono,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 0.37/0.74 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_less_mono
% 0.37/0.74 thf(fact_8498_real__le__lsqrt,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_le_lsqrt
% 0.37/0.74 thf(fact_8499_real__sqrt__unique,axiom,
% 0.37/0.74 ! [Y: real,X: real] :
% 0.37/0.74 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.74 = X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ( sqrt @ X )
% 0.37/0.74 = Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_unique
% 0.37/0.74 thf(fact_8500_lemma__real__divide__sqrt__less,axiom,
% 0.37/0.74 ! [U: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ U )
% 0.37/0.74 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 0.37/0.74
% 0.37/0.74 % lemma_real_divide_sqrt_less
% 0.37/0.74 thf(fact_8501_real__sqrt__sum__squares__ge1,axiom,
% 0.37/0.74 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_sum_squares_ge1
% 0.37/0.74 thf(fact_8502_real__sqrt__sum__squares__ge2,axiom,
% 0.37/0.74 ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_sum_squares_ge2
% 0.37/0.74 thf(fact_8503_real__sqrt__sum__squares__triangle__ineq,axiom,
% 0.37/0.74 ! [A: real,C2: real,B: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_sum_squares_triangle_ineq
% 0.37/0.74 thf(fact_8504_sqrt__ge__absD,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 0.37/0.74 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt_ge_absD
% 0.37/0.74 thf(fact_8505_cos__arcsin__nonzero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.74 => ( ( cos_real @ ( arcsin @ X ) )
% 0.37/0.74 != zero_zero_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cos_arcsin_nonzero
% 0.37/0.74 thf(fact_8506_real__less__lsqrt,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_less_lsqrt
% 0.37/0.74 thf(fact_8507_sqrt__sum__squares__le__sum,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt_sum_squares_le_sum
% 0.37/0.74 thf(fact_8508_real__inv__sqrt__pow2,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.37/0.74 = ( inverse_inverse_real @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_inv_sqrt_pow2
% 0.37/0.74 thf(fact_8509_real__sqrt__ge__abs1,axiom,
% 0.37/0.74 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_ge_abs1
% 0.37/0.74 thf(fact_8510_real__sqrt__ge__abs2,axiom,
% 0.37/0.74 ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_ge_abs2
% 0.37/0.74 thf(fact_8511_sqrt__sum__squares__le__sum__abs,axiom,
% 0.37/0.74 ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt_sum_squares_le_sum_abs
% 0.37/0.74 thf(fact_8512_ln__sqrt,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 0.37/0.74 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % ln_sqrt
% 0.37/0.74 thf(fact_8513_real__sqrt__power__even,axiom,
% 0.37/0.74 ! [N: nat,X: real] :
% 0.37/0.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 0.37/0.74 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_power_even
% 0.37/0.74 thf(fact_8514_arsinh__real__aux,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arsinh_real_aux
% 0.37/0.74 thf(fact_8515_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 0.37/0.74 ! [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 ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_sum_squares_mult_ge_zero
% 0.37/0.74 thf(fact_8516_arith__geo__mean__sqrt,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arith_geo_mean_sqrt
% 0.37/0.74 thf(fact_8517_powr__half__sqrt,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 = ( sqrt @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % powr_half_sqrt
% 0.37/0.74 thf(fact_8518_cos__x__y__le__one,axiom,
% 0.37/0.74 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 0.37/0.74
% 0.37/0.74 % cos_x_y_le_one
% 0.37/0.74 thf(fact_8519_real__sqrt__sum__squares__less,axiom,
% 0.37/0.74 ! [X: real,U: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.37/0.74 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.37/0.74 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % real_sqrt_sum_squares_less
% 0.37/0.74 thf(fact_8520_arcosh__real__def,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ one_one_real @ X )
% 0.37/0.74 => ( ( arcosh_real @ X )
% 0.37/0.74 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcosh_real_def
% 0.37/0.74 thf(fact_8521_arcsin__lt__bounded,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.37/0.74 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_lt_bounded
% 0.37/0.74 thf(fact_8522_arcsin__bounded,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.37/0.74 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_bounded
% 0.37/0.74 thf(fact_8523_arcsin__ubound,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_ubound
% 0.37/0.74 thf(fact_8524_arcsin__lbound,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_lbound
% 0.37/0.74 thf(fact_8525_sqrt__sum__squares__half__less,axiom,
% 0.37/0.74 ! [X: real,U: real,Y: real] :
% 0.37/0.74 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sqrt_sum_squares_half_less
% 0.37/0.74 thf(fact_8526_arcsin__sin,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( arcsin @ ( sin_real @ X ) )
% 0.37/0.74 = X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_sin
% 0.37/0.74 thf(fact_8527_sin__cos__sqrt,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 0.37/0.74 => ( ( sin_real @ X )
% 0.37/0.74 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sin_cos_sqrt
% 0.37/0.74 thf(fact_8528_arcsin,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.37/0.74 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 & ( ( sin_real @ ( arcsin @ Y ) )
% 0.37/0.74 = Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin
% 0.37/0.74 thf(fact_8529_arcsin__pi,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 0.37/0.74 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 0.37/0.74 & ( ( sin_real @ ( arcsin @ Y ) )
% 0.37/0.74 = Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_pi
% 0.37/0.74 thf(fact_8530_arcsin__le__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 0.37/0.74 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcsin_le_iff
% 0.37/0.74 thf(fact_8531_le__arcsin__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 0.37/0.74 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % le_arcsin_iff
% 0.37/0.74 thf(fact_8532_cos__tan,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ( cos_real @ X )
% 0.37/0.74 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cos_tan
% 0.37/0.74 thf(fact_8533_sin__arccos__abs,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.74 => ( ( sin_real @ ( arccos @ Y ) )
% 0.37/0.74 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sin_arccos_abs
% 0.37/0.74 thf(fact_8534_sin__arccos,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.74 => ( ( sin_real @ ( arccos @ X ) )
% 0.37/0.74 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sin_arccos
% 0.37/0.74 thf(fact_8535_cos__arccos,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( cos_real @ ( arccos @ Y ) )
% 0.37/0.74 = Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cos_arccos
% 0.37/0.74 thf(fact_8536_arccos__le__arccos,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_le_arccos
% 0.37/0.74 thf(fact_8537_arccos__eq__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 0.37/0.74 => ( ( ( arccos @ X )
% 0.37/0.74 = ( arccos @ Y ) )
% 0.37/0.74 = ( X = Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_eq_iff
% 0.37/0.74 thf(fact_8538_arccos__le__mono,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_le_mono
% 0.37/0.74 thf(fact_8539_arccos__lbound,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_lbound
% 0.37/0.74 thf(fact_8540_arccos__less__arccos,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_less_arccos
% 0.37/0.74 thf(fact_8541_arccos__less__mono,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.74 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 0.37/0.74 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_less_mono
% 0.37/0.74 thf(fact_8542_arccos__ubound,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_ubound
% 0.37/0.74 thf(fact_8543_arccos__cos,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ pi )
% 0.37/0.74 => ( ( arccos @ ( cos_real @ X ) )
% 0.37/0.74 = X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_cos
% 0.37/0.74 thf(fact_8544_cos__arccos__abs,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.37/0.74 => ( ( cos_real @ ( arccos @ Y ) )
% 0.37/0.74 = Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % cos_arccos_abs
% 0.37/0.74 thf(fact_8545_arccos__cos__eq__abs,axiom,
% 0.37/0.74 ! [Theta: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 0.37/0.74 => ( ( arccos @ ( cos_real @ Theta ) )
% 0.37/0.74 = ( abs_abs_real @ Theta ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_cos_eq_abs
% 0.37/0.74 thf(fact_8546_arccos__lt__bounded,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.37/0.74 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_lt_bounded
% 0.37/0.74 thf(fact_8547_arccos__bounded,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.37/0.74 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_bounded
% 0.37/0.74 thf(fact_8548_sin__arccos__nonzero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.74 => ( ( sin_real @ ( arccos @ X ) )
% 0.37/0.74 != zero_zero_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sin_arccos_nonzero
% 0.37/0.74 thf(fact_8549_arccos__cos2,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 0.37/0.74 => ( ( arccos @ ( cos_real @ X ) )
% 0.37/0.74 = ( uminus_uminus_real @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_cos2
% 0.37/0.74 thf(fact_8550_arccos__minus,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.74 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 0.37/0.74 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_minus
% 0.37/0.74 thf(fact_8551_arccos__def,axiom,
% 0.37/0.74 ( arccos
% 0.37/0.74 = ( ^ [Y4: real] :
% 0.37/0.74 ( the_real
% 0.37/0.74 @ ^ [X4: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.37/0.74 & ( ord_less_eq_real @ X4 @ pi )
% 0.37/0.74 & ( ( cos_real @ X4 )
% 0.37/0.74 = Y4 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_def
% 0.37/0.74 thf(fact_8552_arccos,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 0.37/0.74 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 0.37/0.74 & ( ( cos_real @ ( arccos @ Y ) )
% 0.37/0.74 = Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos
% 0.37/0.74 thf(fact_8553_arccos__minus__abs,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 0.37/0.74 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_minus_abs
% 0.37/0.74 thf(fact_8554_arccos__le__pi2,axiom,
% 0.37/0.74 ! [Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.37/0.74 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arccos_le_pi2
% 0.37/0.74 thf(fact_8555_cot__less__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.74 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cot_less_zero
% 0.37/0.74 thf(fact_8556_power__half__series,axiom,
% 0.37/0.74 ( sums_real
% 0.37/0.74 @ ^ [N6: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N6 ) )
% 0.37/0.74 @ one_one_real ) ).
% 0.37/0.74
% 0.37/0.74 % power_half_series
% 0.37/0.74 thf(fact_8557_cot__gt__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.37/0.74 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cot_gt_zero
% 0.37/0.74 thf(fact_8558_cosh__real__ge__1,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_ge_1
% 0.37/0.74 thf(fact_8559_cosh__real__nonneg,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_nonneg
% 0.37/0.74 thf(fact_8560_cosh__real__nonneg__le__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_nonneg_le_iff
% 0.37/0.74 thf(fact_8561_cosh__real__nonpos__le__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.37/0.74 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_nonpos_le_iff
% 0.37/0.74 thf(fact_8562_cosh__real__pos,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_pos
% 0.37/0.74 thf(fact_8563_sinh__less__cosh__real,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % sinh_less_cosh_real
% 0.37/0.74 thf(fact_8564_sinh__le__cosh__real,axiom,
% 0.37/0.74 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % sinh_le_cosh_real
% 0.37/0.74 thf(fact_8565_cosh__real__strict__mono,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ Y )
% 0.37/0.74 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_strict_mono
% 0.37/0.74 thf(fact_8566_cosh__real__nonneg__less__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.37/0.74 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.37/0.74 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_nonneg_less_iff
% 0.37/0.74 thf(fact_8567_cosh__real__nonpos__less__iff,axiom,
% 0.37/0.74 ! [X: real,Y: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.37/0.74 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.37/0.74 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 0.37/0.74 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_real_nonpos_less_iff
% 0.37/0.74 thf(fact_8568_arcosh__cosh__real,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 0.37/0.74 = X ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcosh_cosh_real
% 0.37/0.74 thf(fact_8569_cosh__ln__real,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 0.37/0.74 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % cosh_ln_real
% 0.37/0.74 thf(fact_8570_divmod__BitM__2__eq,axiom,
% 0.37/0.74 ! [M: num] :
% 0.37/0.74 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 0.37/0.74 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 0.37/0.74
% 0.37/0.74 % divmod_BitM_2_eq
% 0.37/0.74 thf(fact_8571_eval__nat__numeral_I2_J,axiom,
% 0.37/0.74 ! [N: num] :
% 0.37/0.74 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.37/0.74 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % eval_nat_numeral(2)
% 0.37/0.74 thf(fact_8572_int__ge__less__than2__def,axiom,
% 0.37/0.74 ( int_ge_less_than2
% 0.37/0.74 = ( ^ [D5: int] :
% 0.37/0.74 ( collec213857154873943460nt_int
% 0.37/0.74 @ ( produc4947309494688390418_int_o
% 0.37/0.74 @ ^ [Z8: int,Z2: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ D5 @ Z2 )
% 0.37/0.74 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_ge_less_than2_def
% 0.37/0.74 thf(fact_8573_int__ge__less__than__def,axiom,
% 0.37/0.74 ( int_ge_less_than
% 0.37/0.74 = ( ^ [D5: int] :
% 0.37/0.74 ( collec213857154873943460nt_int
% 0.37/0.74 @ ( produc4947309494688390418_int_o
% 0.37/0.74 @ ^ [Z8: int,Z2: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ D5 @ Z8 )
% 0.37/0.74 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_ge_less_than_def
% 0.37/0.74 thf(fact_8574_set__decode__0,axiom,
% 0.37/0.74 ! [X: nat] :
% 0.37/0.74 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 0.37/0.74 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % set_decode_0
% 0.37/0.74 thf(fact_8575_Suc__0__mod__eq,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.74 = ( zero_n2687167440665602831ol_nat
% 0.37/0.74 @ ( N
% 0.37/0.74 != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Suc_0_mod_eq
% 0.37/0.74 thf(fact_8576_set__decode__zero,axiom,
% 0.37/0.74 ( ( nat_set_decode @ zero_zero_nat )
% 0.37/0.74 = bot_bot_set_nat ) ).
% 0.37/0.74
% 0.37/0.74 % set_decode_zero
% 0.37/0.74 thf(fact_8577_set__encode__inverse,axiom,
% 0.37/0.74 ! [A4: set_nat] :
% 0.37/0.74 ( ( finite_finite_nat @ A4 )
% 0.37/0.74 => ( ( nat_set_decode @ ( nat_set_encode @ A4 ) )
% 0.37/0.74 = A4 ) ) ).
% 0.37/0.74
% 0.37/0.74 % set_encode_inverse
% 0.37/0.74 thf(fact_8578_Divides_Oadjust__div__eq,axiom,
% 0.37/0.74 ! [Q3: int,R: int] :
% 0.37/0.74 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R ) )
% 0.37/0.74 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Divides.adjust_div_eq
% 0.37/0.74 thf(fact_8579_set__decode__Suc,axiom,
% 0.37/0.74 ! [N: nat,X: nat] :
% 0.37/0.74 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 0.37/0.74 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % set_decode_Suc
% 0.37/0.74 thf(fact_8580_finite__set__decode,axiom,
% 0.37/0.74 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % finite_set_decode
% 0.37/0.74 thf(fact_8581_Divides_Oadjust__div__def,axiom,
% 0.37/0.74 ( adjust_div
% 0.37/0.74 = ( produc8211389475949308722nt_int
% 0.37/0.74 @ ^ [Q8: int,R5: int] : ( plus_plus_int @ Q8 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Divides.adjust_div_def
% 0.37/0.74 thf(fact_8582_subset__decode__imp__le,axiom,
% 0.37/0.74 ! [M: nat,N: nat] :
% 0.37/0.74 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 0.37/0.74 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % subset_decode_imp_le
% 0.37/0.74 thf(fact_8583_horner__sum__of__bool__2__less,axiom,
% 0.37/0.74 ! [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 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % horner_sum_of_bool_2_less
% 0.37/0.74 thf(fact_8584_div__noneq__sgn__abs,axiom,
% 0.37/0.74 ! [L: int,K: int] :
% 0.37/0.74 ( ( L != zero_zero_int )
% 0.37/0.74 => ( ( ( sgn_sgn_int @ K )
% 0.37/0.74 != ( sgn_sgn_int @ L ) )
% 0.37/0.74 => ( ( divide_divide_int @ K @ L )
% 0.37/0.74 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 0.37/0.74 @ ( zero_n2684676970156552555ol_int
% 0.37/0.74 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % div_noneq_sgn_abs
% 0.37/0.74 thf(fact_8585_divide__int__unfold,axiom,
% 0.37/0.74 ! [L: int,K: int,N: nat,M: nat] :
% 0.37/0.74 ( ( ( ( ( sgn_sgn_int @ L )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( ( sgn_sgn_int @ K )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( N = zero_zero_nat ) )
% 0.37/0.74 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.37/0.74 = zero_zero_int ) )
% 0.37/0.74 & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( ( sgn_sgn_int @ K )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( N = zero_zero_nat ) )
% 0.37/0.74 => ( ( ( ( sgn_sgn_int @ K )
% 0.37/0.74 = ( sgn_sgn_int @ L ) )
% 0.37/0.74 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.37/0.74 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 0.37/0.74 & ( ( ( sgn_sgn_int @ K )
% 0.37/0.74 != ( sgn_sgn_int @ L ) )
% 0.37/0.74 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.37/0.74 = ( uminus_uminus_int
% 0.37/0.74 @ ( semiri1314217659103216013at_int
% 0.37/0.74 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 0.37/0.74 @ ( zero_n2687167440665602831ol_nat
% 0.37/0.74 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % divide_int_unfold
% 0.37/0.74 thf(fact_8586_modulo__int__unfold,axiom,
% 0.37/0.74 ! [L: int,K: int,N: nat,M: nat] :
% 0.37/0.74 ( ( ( ( ( sgn_sgn_int @ L )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( ( sgn_sgn_int @ K )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( N = zero_zero_nat ) )
% 0.37/0.74 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.37/0.74 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 0.37/0.74 & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( ( sgn_sgn_int @ K )
% 0.37/0.74 = zero_zero_int )
% 0.37/0.74 | ( N = zero_zero_nat ) )
% 0.37/0.74 => ( ( ( ( sgn_sgn_int @ K )
% 0.37/0.74 = ( sgn_sgn_int @ L ) )
% 0.37/0.74 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.37/0.74 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 0.37/0.74 & ( ( ( sgn_sgn_int @ K )
% 0.37/0.74 != ( sgn_sgn_int @ L ) )
% 0.37/0.74 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.37/0.74 = ( times_times_int @ ( sgn_sgn_int @ L )
% 0.37/0.74 @ ( minus_minus_int
% 0.37/0.74 @ ( semiri1314217659103216013at_int
% 0.37/0.74 @ ( times_times_nat @ N
% 0.37/0.74 @ ( zero_n2687167440665602831ol_nat
% 0.37/0.74 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 0.37/0.74 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % modulo_int_unfold
% 0.37/0.74 thf(fact_8587_False__map2__or,axiom,
% 0.37/0.74 ! [Xs: list_o,Ys: list_o] :
% 0.37/0.74 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ $false @ bot_bot_set_o ) )
% 0.37/0.74 => ( ( ( size_size_list_o @ Ys )
% 0.37/0.74 = ( size_size_list_o @ Xs ) )
% 0.37/0.74 => ( ( map_Pr7541730621154948341_o_o_o @ ( produc6197397395684419436_o_o_o @ (|) ) @ ( zip_o_o @ Xs @ Ys ) )
% 0.37/0.74 = Ys ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % False_map2_or
% 0.37/0.74 thf(fact_8588_False__map2__and,axiom,
% 0.37/0.74 ! [Xs: list_o,Ys: list_o] :
% 0.37/0.74 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ $false @ bot_bot_set_o ) )
% 0.37/0.74 => ( ( ( size_size_list_o @ Ys )
% 0.37/0.74 = ( size_size_list_o @ Xs ) )
% 0.37/0.74 => ( ( map_Pr7541730621154948341_o_o_o @ ( produc6197397395684419436_o_o_o @ (&) ) @ ( zip_o_o @ Xs @ Ys ) )
% 0.37/0.74 = Xs ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % False_map2_and
% 0.37/0.74 thf(fact_8589_take__bit__of__Suc__0,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_of_Suc_0
% 0.37/0.74 thf(fact_8590_UNIV__bool,axiom,
% 0.37/0.74 ( top_top_set_o
% 0.37/0.74 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % UNIV_bool
% 0.37/0.74 thf(fact_8591_take__bit__tightened__less__eq__int,axiom,
% 0.37/0.74 ! [M: nat,N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.74 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_tightened_less_eq_int
% 0.37/0.74 thf(fact_8592_take__bit__nat__less__eq__self,axiom,
% 0.37/0.74 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_nat_less_eq_self
% 0.37/0.74 thf(fact_8593_take__bit__tightened__less__eq__nat,axiom,
% 0.37/0.74 ! [M: nat,N: nat,Q3: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.74 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_tightened_less_eq_nat
% 0.37/0.74 thf(fact_8594_nat__take__bit__eq,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.74 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.37/0.74 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % nat_take_bit_eq
% 0.37/0.74 thf(fact_8595_take__bit__nat__eq,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.74 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 0.37/0.74 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_nat_eq
% 0.37/0.74 thf(fact_8596_not__take__bit__negative,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 0.37/0.74
% 0.37/0.74 % not_take_bit_negative
% 0.37/0.74 thf(fact_8597_take__bit__int__greater__self__iff,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.37/0.74 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_greater_self_iff
% 0.37/0.74 thf(fact_8598_take__bit__nonnegative,axiom,
% 0.37/0.74 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_nonnegative
% 0.37/0.74 thf(fact_8599_take__bit__int__less__eq__self__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.37/0.74 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_less_eq_self_iff
% 0.37/0.74 thf(fact_8600_take__bit__integer_Oabs__eq,axiom,
% 0.37/0.74 ! [Xa2: nat,X: int] :
% 0.37/0.74 ( ( bit_se1745604003318907178nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 0.37/0.74 = ( code_integer_of_int @ ( bit_se2923211474154528505it_int @ Xa2 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_integer.abs_eq
% 0.37/0.74 thf(fact_8601_take__bit__nat__eq__self,axiom,
% 0.37/0.74 ! [M: nat,N: nat] :
% 0.37/0.74 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.37/0.74 = M ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_nat_eq_self
% 0.37/0.74 thf(fact_8602_take__bit__nat__less__exp,axiom,
% 0.37/0.74 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_nat_less_exp
% 0.37/0.74 thf(fact_8603_take__bit__nat__eq__self__iff,axiom,
% 0.37/0.74 ! [N: nat,M: nat] :
% 0.37/0.74 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 0.37/0.74 = M )
% 0.37/0.74 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_nat_eq_self_iff
% 0.37/0.74 thf(fact_8604_take__bit__int__less__exp,axiom,
% 0.37/0.74 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_less_exp
% 0.37/0.74 thf(fact_8605_take__bit__nat__less__self__iff,axiom,
% 0.37/0.74 ! [N: nat,M: nat] :
% 0.37/0.74 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 0.37/0.74 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_nat_less_self_iff
% 0.37/0.74 thf(fact_8606_take__bit__Suc__minus__bit0,axiom,
% 0.37/0.74 ! [N: nat,K: num] :
% 0.37/0.74 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.37/0.74 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_Suc_minus_bit0
% 0.37/0.74 thf(fact_8607_take__bit__int__less__self__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 0.37/0.74 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_less_self_iff
% 0.37/0.74 thf(fact_8608_take__bit__int__greater__eq__self__iff,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 0.37/0.74 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_greater_eq_self_iff
% 0.37/0.74 thf(fact_8609_take__bit__int__eq__self__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.37/0.74 = K )
% 0.37/0.74 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.74 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_eq_self_iff
% 0.37/0.74 thf(fact_8610_take__bit__int__eq__self,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.74 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.37/0.74 = K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_eq_self
% 0.37/0.74 thf(fact_8611_take__bit__int__less__eq,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 0.37/0.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_less_eq
% 0.37/0.74 thf(fact_8612_take__bit__int__greater__eq,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_int_greater_eq
% 0.37/0.74 thf(fact_8613_signed__take__bit__eq__take__bit__shift,axiom,
% 0.37/0.74 ( bit_ri631733984087533419it_int
% 0.37/0.74 = ( ^ [N6: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N6 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N6 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N6 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_eq_take_bit_shift
% 0.37/0.74 thf(fact_8614_take__bit__minus__small__eq,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( ord_less_int @ zero_zero_int @ K )
% 0.37/0.74 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 0.37/0.74 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_minus_small_eq
% 0.37/0.74 thf(fact_8615_take__bit__Suc__minus__bit1,axiom,
% 0.37/0.74 ! [N: nat,K: num] :
% 0.37/0.74 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.37/0.74 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_Suc_minus_bit1
% 0.37/0.74 thf(fact_8616_take__upt,axiom,
% 0.37/0.74 ! [I: nat,M: nat,N: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 0.37/0.74 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 0.37/0.74 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_upt
% 0.37/0.74 thf(fact_8617_upt__0__eq__Nil__conv,axiom,
% 0.37/0.74 ! [J: nat] :
% 0.37/0.74 ( ( ( upt @ zero_zero_nat @ J )
% 0.37/0.74 = nil_nat )
% 0.37/0.74 = ( J = zero_zero_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_0_eq_Nil_conv
% 0.37/0.74 thf(fact_8618_upt__conv__Nil,axiom,
% 0.37/0.74 ! [J: nat,I: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ J @ I )
% 0.37/0.74 => ( ( upt @ I @ J )
% 0.37/0.74 = nil_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_conv_Nil
% 0.37/0.74 thf(fact_8619_upt__merge,axiom,
% 0.37/0.74 ! [I: nat,J: nat,K: nat] :
% 0.37/0.74 ( ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.74 & ( ord_less_eq_nat @ J @ K ) )
% 0.37/0.74 => ( ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ K ) )
% 0.37/0.74 = ( upt @ I @ K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_merge
% 0.37/0.74 thf(fact_8620_last__upt,axiom,
% 0.37/0.74 ! [I: nat,J: nat] :
% 0.37/0.74 ( ( ord_less_nat @ I @ J )
% 0.37/0.74 => ( ( last_nat @ ( upt @ I @ J ) )
% 0.37/0.74 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % last_upt
% 0.37/0.74 thf(fact_8621_upt__eq__Nil__conv,axiom,
% 0.37/0.74 ! [I: nat,J: nat] :
% 0.37/0.74 ( ( ( upt @ I @ J )
% 0.37/0.74 = nil_nat )
% 0.37/0.74 = ( ( J = zero_zero_nat )
% 0.37/0.74 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_eq_Nil_conv
% 0.37/0.74 thf(fact_8622_nth__upt,axiom,
% 0.37/0.74 ! [I: nat,K: nat,J: nat] :
% 0.37/0.74 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 0.37/0.74 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 0.37/0.74 = ( plus_plus_nat @ I @ K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % nth_upt
% 0.37/0.74 thf(fact_8623_sum__list__upt,axiom,
% 0.37/0.74 ! [M: nat,N: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.74 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 0.37/0.74 = ( groups3542108847815614940at_nat
% 0.37/0.74 @ ^ [X4: nat] : X4
% 0.37/0.74 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sum_list_upt
% 0.37/0.74 thf(fact_8624_upt__rec__numeral,axiom,
% 0.37/0.74 ! [M: num,N: num] :
% 0.37/0.74 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.37/0.74 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.37/0.74 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 0.37/0.74 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.37/0.74 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.37/0.74 = nil_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_rec_numeral
% 0.37/0.74 thf(fact_8625_upt__eq__append__conv,axiom,
% 0.37/0.74 ! [I: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.74 => ( ( ( upt @ I @ J )
% 0.37/0.74 = ( append_nat @ Xs @ Ys ) )
% 0.37/0.74 = ( ? [K3: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ I @ K3 )
% 0.37/0.74 & ( ord_less_eq_nat @ K3 @ J )
% 0.37/0.74 & ( ( upt @ I @ K3 )
% 0.37/0.74 = Xs )
% 0.37/0.74 & ( ( upt @ K3 @ J )
% 0.37/0.74 = Ys ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_eq_append_conv
% 0.37/0.74 thf(fact_8626_sorted__upt,axiom,
% 0.37/0.74 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % sorted_upt
% 0.37/0.74 thf(fact_8627_map__add__upt_H,axiom,
% 0.37/0.74 ! [Ofs: nat,A: nat,B: nat] :
% 0.37/0.74 ( ( map_nat_nat
% 0.37/0.74 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ Ofs )
% 0.37/0.74 @ ( upt @ A @ B ) )
% 0.37/0.74 = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % map_add_upt'
% 0.37/0.74 thf(fact_8628_map__Suc__upt,axiom,
% 0.37/0.74 ! [M: nat,N: nat] :
% 0.37/0.74 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 0.37/0.74 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % map_Suc_upt
% 0.37/0.74 thf(fact_8629_map__add__upt,axiom,
% 0.37/0.74 ! [N: nat,M: nat] :
% 0.37/0.74 ( ( map_nat_nat
% 0.37/0.74 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 0.37/0.74 @ ( upt @ zero_zero_nat @ M ) )
% 0.37/0.74 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % map_add_upt
% 0.37/0.74 thf(fact_8630_sorted__wrt__upt,axiom,
% 0.37/0.74 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % sorted_wrt_upt
% 0.37/0.74 thf(fact_8631_upt__0,axiom,
% 0.37/0.74 ! [I: nat] :
% 0.37/0.74 ( ( upt @ I @ zero_zero_nat )
% 0.37/0.74 = nil_nat ) ).
% 0.37/0.74
% 0.37/0.74 % upt_0
% 0.37/0.74 thf(fact_8632_butlast__upt,axiom,
% 0.37/0.74 ! [M: nat,N: nat] :
% 0.37/0.74 ( ( butlast_nat @ ( upt @ M @ N ) )
% 0.37/0.74 = ( upt @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % butlast_upt
% 0.37/0.74 thf(fact_8633_upt__conv__Cons__Cons,axiom,
% 0.37/0.74 ! [M: nat,N: nat,Ns: list_nat,Q3: nat] :
% 0.37/0.74 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 0.37/0.74 = ( upt @ M @ Q3 ) )
% 0.37/0.74 = ( ( cons_nat @ N @ Ns )
% 0.37/0.74 = ( upt @ ( suc @ M ) @ Q3 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_conv_Cons_Cons
% 0.37/0.74 thf(fact_8634_upt__conv__Cons,axiom,
% 0.37/0.74 ! [I: nat,J: nat] :
% 0.37/0.74 ( ( ord_less_nat @ I @ J )
% 0.37/0.74 => ( ( upt @ I @ J )
% 0.37/0.74 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_conv_Cons
% 0.37/0.74 thf(fact_8635_upt__filter__extend,axiom,
% 0.37/0.74 ! [U: nat,U3: nat,P2: nat > $o] :
% 0.37/0.74 ( ( ord_less_eq_nat @ U @ U3 )
% 0.37/0.74 => ( ! [I2: nat] :
% 0.37/0.74 ( ( ( ord_less_eq_nat @ U @ I2 )
% 0.37/0.74 & ( ord_less_nat @ I2 @ U3 ) )
% 0.37/0.74 => ~ ( P2 @ I2 ) )
% 0.37/0.74 => ( ( filter_nat2 @ P2 @ ( upt @ zero_zero_nat @ U ) )
% 0.37/0.74 = ( filter_nat2 @ P2 @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_filter_extend
% 0.37/0.74 thf(fact_8636_map__decr__upt,axiom,
% 0.37/0.74 ! [M: nat,N: nat] :
% 0.37/0.74 ( ( map_nat_nat
% 0.37/0.74 @ ^ [N6: nat] : ( minus_minus_nat @ N6 @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.37/0.74 = ( upt @ M @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % map_decr_upt
% 0.37/0.74 thf(fact_8637_upt__append,axiom,
% 0.37/0.74 ! [I: nat,J: nat] :
% 0.37/0.74 ( ( ord_less_nat @ I @ J )
% 0.37/0.74 => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 0.37/0.74 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_append
% 0.37/0.74 thf(fact_8638_atLeastAtMost__upt,axiom,
% 0.37/0.74 ( set_or1269000886237332187st_nat
% 0.37/0.74 = ( ^ [N6: nat,M5: nat] : ( set_nat2 @ ( upt @ N6 @ ( suc @ M5 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % atLeastAtMost_upt
% 0.37/0.74 thf(fact_8639_upt__add__eq__append,axiom,
% 0.37/0.74 ! [I: nat,J: nat,K: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.74 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 0.37/0.74 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_add_eq_append
% 0.37/0.74 thf(fact_8640_atLeast__upt,axiom,
% 0.37/0.74 ( set_ord_lessThan_nat
% 0.37/0.74 = ( ^ [N6: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N6 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % atLeast_upt
% 0.37/0.74 thf(fact_8641_upt__eq__Cons__conv,axiom,
% 0.37/0.74 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 0.37/0.74 ( ( ( upt @ I @ J )
% 0.37/0.74 = ( cons_nat @ X @ Xs ) )
% 0.37/0.74 = ( ( ord_less_nat @ I @ J )
% 0.37/0.74 & ( I = X )
% 0.37/0.74 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 0.37/0.74 = Xs ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_eq_Cons_conv
% 0.37/0.74 thf(fact_8642_atMost__upto,axiom,
% 0.37/0.74 ( set_ord_atMost_nat
% 0.37/0.74 = ( ^ [N6: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N6 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % atMost_upto
% 0.37/0.74 thf(fact_8643_upt__rec,axiom,
% 0.37/0.74 ( upt
% 0.37/0.74 = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_rec
% 0.37/0.74 thf(fact_8644_upt__eq__lel__conv,axiom,
% 0.37/0.74 ! [L: nat,H2: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 0.37/0.74 ( ( ( upt @ L @ H2 )
% 0.37/0.74 = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 0.37/0.74 = ( ( Is1
% 0.37/0.74 = ( upt @ L @ I ) )
% 0.37/0.74 & ( Is2
% 0.37/0.74 = ( upt @ ( suc @ I ) @ H2 ) )
% 0.37/0.74 & ( ord_less_eq_nat @ L @ I )
% 0.37/0.74 & ( ord_less_nat @ I @ H2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_eq_lel_conv
% 0.37/0.74 thf(fact_8645_upt__Suc__append,axiom,
% 0.37/0.74 ! [I: nat,J: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.74 => ( ( upt @ I @ ( suc @ J ) )
% 0.37/0.74 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_Suc_append
% 0.37/0.74 thf(fact_8646_upt__Suc,axiom,
% 0.37/0.74 ! [I: nat,J: nat] :
% 0.37/0.74 ( ( ( ord_less_eq_nat @ I @ J )
% 0.37/0.74 => ( ( upt @ I @ ( suc @ J ) )
% 0.37/0.74 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 0.37/0.74 & ( ~ ( ord_less_eq_nat @ I @ J )
% 0.37/0.74 => ( ( upt @ I @ ( suc @ J ) )
% 0.37/0.74 = nil_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % upt_Suc
% 0.37/0.74 thf(fact_8647_signed__take__bit__eq__take__bit__minus,axiom,
% 0.37/0.74 ( bit_ri631733984087533419it_int
% 0.37/0.74 = ( ^ [N6: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N6 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N6 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_eq_take_bit_minus
% 0.37/0.74 thf(fact_8648_signed__take__bit__nonnegative__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.37/0.74 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_nonnegative_iff
% 0.37/0.74 thf(fact_8649_signed__take__bit__negative__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 0.37/0.74 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % signed_take_bit_negative_iff
% 0.37/0.74 thf(fact_8650_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 0.37/0.74 ! [W2: num,N: nat] :
% 0.37/0.74 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( suc @ N ) )
% 0.37/0.74 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_minus_numeral_Bit0_Suc_iff
% 0.37/0.74 thf(fact_8651_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 0.37/0.74 ! [W2: num,N: nat] :
% 0.37/0.74 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( suc @ N ) )
% 0.37/0.74 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_minus_numeral_Bit1_Suc_iff
% 0.37/0.74 thf(fact_8652_bin__nth__minus__Bit0,axiom,
% 0.37/0.74 ! [N: nat,W2: num] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) @ N )
% 0.37/0.74 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % bin_nth_minus_Bit0
% 0.37/0.74 thf(fact_8653_bin__nth__minus__Bit1,axiom,
% 0.37/0.74 ! [N: nat,W2: num] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) @ N )
% 0.37/0.74 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % bin_nth_minus_Bit1
% 0.37/0.74 thf(fact_8654_map__bit__range__eq__if__take__bit__eq,axiom,
% 0.37/0.74 ! [N: nat,K: int,L: int] :
% 0.37/0.74 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.37/0.74 = ( bit_se2923211474154528505it_int @ N @ L ) )
% 0.37/0.74 => ( ( map_nat_o @ ( bit_se1146084159140164899it_int @ K ) @ ( upt @ zero_zero_nat @ N ) )
% 0.37/0.74 = ( map_nat_o @ ( bit_se1146084159140164899it_int @ L ) @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % map_bit_range_eq_if_take_bit_eq
% 0.37/0.74 thf(fact_8655_bit__imp__take__bit__positive,axiom,
% 0.37/0.74 ! [N: nat,M: nat,K: int] :
% 0.37/0.74 ( ( ord_less_nat @ N @ M )
% 0.37/0.74 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 0.37/0.74 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_imp_take_bit_positive
% 0.37/0.74 thf(fact_8656_int__bit__bound,axiom,
% 0.37/0.74 ! [K: int] :
% 0.37/0.74 ~ ! [N2: nat] :
% 0.37/0.74 ( ! [M2: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ N2 @ M2 )
% 0.37/0.74 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 0.37/0.74 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 0.37/0.74 => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.37/0.74 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 0.37/0.74 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_bit_bound
% 0.37/0.74 thf(fact_8657_take__bit__Suc__from__most,axiom,
% 0.37/0.74 ! [N: nat,K: int] :
% 0.37/0.74 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 0.37/0.74 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_Suc_from_most
% 0.37/0.74 thf(fact_8658_num_Osize__gen_I3_J,axiom,
% 0.37/0.74 ! [X32: num] :
% 0.37/0.74 ( ( size_num @ ( bit1 @ X32 ) )
% 0.37/0.74 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % num.size_gen(3)
% 0.37/0.74 thf(fact_8659_bit__Suc__0__iff,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.74 = ( N = zero_zero_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_Suc_0_iff
% 0.37/0.74 thf(fact_8660_not__bit__Suc__0__Suc,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % not_bit_Suc_0_Suc
% 0.37/0.74 thf(fact_8661_bit__integer_Oabs__eq,axiom,
% 0.37/0.74 ! [X: int] :
% 0.37/0.74 ( ( bit_se9216721137139052372nteger @ ( code_integer_of_int @ X ) )
% 0.37/0.74 = ( bit_se1146084159140164899it_int @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_integer.abs_eq
% 0.37/0.74 thf(fact_8662_not__bit__Suc__0__numeral,axiom,
% 0.37/0.74 ! [N: num] :
% 0.37/0.74 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % not_bit_Suc_0_numeral
% 0.37/0.74 thf(fact_8663_bit__nat__iff,axiom,
% 0.37/0.74 ! [K: int,N: nat] :
% 0.37/0.74 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 0.37/0.74 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.74 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_nat_iff
% 0.37/0.74 thf(fact_8664_num_Osize__gen_I1_J,axiom,
% 0.37/0.74 ( ( size_num @ one )
% 0.37/0.74 = zero_zero_nat ) ).
% 0.37/0.74
% 0.37/0.74 % num.size_gen(1)
% 0.37/0.74 thf(fact_8665_num_Osize__gen_I2_J,axiom,
% 0.37/0.74 ! [X2: num] :
% 0.37/0.74 ( ( size_num @ ( bit0 @ X2 ) )
% 0.37/0.74 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % num.size_gen(2)
% 0.37/0.74 thf(fact_8666_Code__Numeral_Opositive__def,axiom,
% 0.37/0.74 code_positive = numera6620942414471956472nteger ).
% 0.37/0.74
% 0.37/0.74 % Code_Numeral.positive_def
% 0.37/0.74 thf(fact_8667_concat__bit__Suc,axiom,
% 0.37/0.74 ! [N: nat,K: int,L: int] :
% 0.37/0.74 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 0.37/0.74 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % concat_bit_Suc
% 0.37/0.74 thf(fact_8668_concat__bit__0,axiom,
% 0.37/0.74 ! [K: int,L: int] :
% 0.37/0.74 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 0.37/0.74 = L ) ).
% 0.37/0.74
% 0.37/0.74 % concat_bit_0
% 0.37/0.74 thf(fact_8669_concat__bit__nonnegative__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int,L: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 0.37/0.74 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 0.37/0.74
% 0.37/0.74 % concat_bit_nonnegative_iff
% 0.37/0.74 thf(fact_8670_concat__bit__negative__iff,axiom,
% 0.37/0.74 ! [N: nat,K: int,L: int] :
% 0.37/0.74 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 0.37/0.74 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 0.37/0.74
% 0.37/0.74 % concat_bit_negative_iff
% 0.37/0.74 thf(fact_8671_bit__concat__bit__iff,axiom,
% 0.37/0.74 ! [M: nat,K: int,L: int,N: nat] :
% 0.37/0.74 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 0.37/0.74 = ( ( ( ord_less_nat @ N @ M )
% 0.37/0.74 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 0.37/0.74 | ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.74 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_concat_bit_iff
% 0.37/0.74 thf(fact_8672_xor__Suc__0__eq,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.37/0.74 @ ( zero_n2687167440665602831ol_nat
% 0.37/0.74 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_Suc_0_eq
% 0.37/0.74 thf(fact_8673_xor__nat__numerals_I1_J,axiom,
% 0.37/0.74 ! [Y: num] :
% 0.37/0.74 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_nat_numerals(1)
% 0.37/0.74 thf(fact_8674_xor__nat__numerals_I2_J,axiom,
% 0.37/0.74 ! [Y: num] :
% 0.37/0.74 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_nat_numerals(2)
% 0.37/0.74 thf(fact_8675_xor__nat__numerals_I3_J,axiom,
% 0.37/0.74 ! [X: num] :
% 0.37/0.74 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_nat_numerals(3)
% 0.37/0.74 thf(fact_8676_xor__nat__numerals_I4_J,axiom,
% 0.37/0.74 ! [X: num] :
% 0.37/0.74 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_nat_numerals(4)
% 0.37/0.74 thf(fact_8677_xor__nat__unfold,axiom,
% 0.37/0.74 ( bit_se6528837805403552850or_nat
% 0.37/0.74 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N6 @ ( if_nat @ ( N6 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_nat_unfold
% 0.37/0.74 thf(fact_8678_Suc__0__xor__eq,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.74 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.37/0.74 @ ( zero_n2687167440665602831ol_nat
% 0.37/0.74 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Suc_0_xor_eq
% 0.37/0.74 thf(fact_8679_or__nat__unfold,axiom,
% 0.37/0.74 ( bit_se1412395901928357646or_nat
% 0.37/0.74 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N6 @ ( if_nat @ ( N6 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_nat_unfold
% 0.37/0.74 thf(fact_8680_xor__nonnegative__int__iff,axiom,
% 0.37/0.74 ! [K: int,L: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 0.37/0.74 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.74 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_nonnegative_int_iff
% 0.37/0.74 thf(fact_8681_xor__negative__int__iff,axiom,
% 0.37/0.74 ! [K: int,L: int] :
% 0.37/0.74 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 0.37/0.74 = ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.74 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_negative_int_iff
% 0.37/0.74 thf(fact_8682_or__nat__numerals_I2_J,axiom,
% 0.37/0.74 ! [Y: num] :
% 0.37/0.74 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_nat_numerals(2)
% 0.37/0.74 thf(fact_8683_or__nat__numerals_I4_J,axiom,
% 0.37/0.74 ! [X: num] :
% 0.37/0.74 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_nat_numerals(4)
% 0.37/0.74 thf(fact_8684_or__nat__numerals_I3_J,axiom,
% 0.37/0.74 ! [X: num] :
% 0.37/0.74 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_nat_numerals(3)
% 0.37/0.74 thf(fact_8685_or__nat__numerals_I1_J,axiom,
% 0.37/0.74 ! [Y: num] :
% 0.37/0.74 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.37/0.74 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_nat_numerals(1)
% 0.37/0.74 thf(fact_8686_xor__integer_Oabs__eq,axiom,
% 0.37/0.74 ! [Xa2: int,X: int] :
% 0.37/0.74 ( ( bit_se3222712562003087583nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.74 = ( code_integer_of_int @ ( bit_se6526347334894502574or_int @ Xa2 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_integer.abs_eq
% 0.37/0.74 thf(fact_8687_XOR__lower,axiom,
% 0.37/0.74 ! [X: int,Y: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.74 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % XOR_lower
% 0.37/0.74 thf(fact_8688_XOR__upper,axiom,
% 0.37/0.74 ! [X: int,N: nat,Y: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.74 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % XOR_upper
% 0.37/0.74 thf(fact_8689_or__Suc__0__eq,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.37/0.74 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_Suc_0_eq
% 0.37/0.74 thf(fact_8690_Suc__0__or__eq,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.74 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Suc_0_or_eq
% 0.37/0.74 thf(fact_8691_or__nonnegative__int__iff,axiom,
% 0.37/0.74 ! [K: int,L: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 0.37/0.74 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.74 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_nonnegative_int_iff
% 0.37/0.74 thf(fact_8692_or__negative__int__iff,axiom,
% 0.37/0.74 ! [K: int,L: int] :
% 0.37/0.74 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 0.37/0.74 = ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.74 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_negative_int_iff
% 0.37/0.74 thf(fact_8693_OR__lower,axiom,
% 0.37/0.74 ! [X: int,Y: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.74 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % OR_lower
% 0.37/0.74 thf(fact_8694_or__greater__eq,axiom,
% 0.37/0.74 ! [L: int,K: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.37/0.74 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_greater_eq
% 0.37/0.74 thf(fact_8695_or__integer_Oabs__eq,axiom,
% 0.37/0.74 ! [Xa2: int,X: int] :
% 0.37/0.74 ( ( bit_se1080825931792720795nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.74 = ( code_integer_of_int @ ( bit_se1409905431419307370or_int @ Xa2 @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_integer.abs_eq
% 0.37/0.74 thf(fact_8696_OR__upper,axiom,
% 0.37/0.74 ! [X: int,N: nat,Y: int] :
% 0.37/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.74 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.37/0.74 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % OR_upper
% 0.37/0.74 thf(fact_8697_DERIV__even__real__root,axiom,
% 0.37/0.74 ! [N: nat,X: real] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.74 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.74 => ( 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 ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_even_real_root
% 0.37/0.74 thf(fact_8698_has__real__derivative__pos__inc__right,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real,S3: set_real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ L )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( member_real @ ( plus_plus_real @ X @ H6 ) @ S3 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H6 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % has_real_derivative_pos_inc_right
% 0.37/0.74 thf(fact_8699_has__real__derivative__neg__dec__right,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real,S3: set_real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 0.37/0.74 => ( ( ord_less_real @ L @ zero_zero_real )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( member_real @ ( plus_plus_real @ X @ H6 ) @ S3 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % has_real_derivative_neg_dec_right
% 0.37/0.74 thf(fact_8700_MVT2,axiom,
% 0.37/0.74 ! [A: real,B: real,F: real > real,F6: real > real] :
% 0.37/0.74 ( ( ord_less_real @ A @ B )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ A @ X3 )
% 0.37/0.74 => ( ( ord_less_eq_real @ X3 @ B )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.37/0.74 => ? [Z3: real] :
% 0.37/0.74 ( ( ord_less_real @ A @ Z3 )
% 0.37/0.74 & ( ord_less_real @ Z3 @ B )
% 0.37/0.74 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 0.37/0.74 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F6 @ Z3 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % MVT2
% 0.37/0.74 thf(fact_8701_DERIV__neg__dec__right,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ L @ zero_zero_real )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_neg_dec_right
% 0.37/0.74 thf(fact_8702_DERIV__pos__inc__right,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ L )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H6 ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_pos_inc_right
% 0.37/0.74 thf(fact_8703_DERIV__ln,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_ln
% 0.37/0.74 thf(fact_8704_DERIV__pos__imp__increasing,axiom,
% 0.37/0.74 ! [A: real,B: real,F: real > real] :
% 0.37/0.74 ( ( ord_less_real @ A @ B )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ A @ X3 )
% 0.37/0.74 => ( ( ord_less_eq_real @ X3 @ B )
% 0.37/0.74 => ? [Y5: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.74 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 0.37/0.74 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_pos_imp_increasing
% 0.37/0.74 thf(fact_8705_DERIV__neg__imp__decreasing,axiom,
% 0.37/0.74 ! [A: real,B: real,F: real > real] :
% 0.37/0.74 ( ( ord_less_real @ A @ B )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ A @ X3 )
% 0.37/0.74 => ( ( ord_less_eq_real @ X3 @ B )
% 0.37/0.74 => ? [Y5: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.74 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 0.37/0.74 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_neg_imp_decreasing
% 0.37/0.74 thf(fact_8706_deriv__nonneg__imp__mono,axiom,
% 0.37/0.74 ! [A: real,B: real,G: real > real,G3: real > real] :
% 0.37/0.74 ( ! [X3: real] :
% 0.37/0.74 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ G @ ( G3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.37/0.74 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X3 ) ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ A @ B )
% 0.37/0.74 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % deriv_nonneg_imp_mono
% 0.37/0.74 thf(fact_8707_DERIV__nonpos__imp__nonincreasing,axiom,
% 0.37/0.74 ! [A: real,B: real,F: real > real] :
% 0.37/0.74 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ A @ X3 )
% 0.37/0.74 => ( ( ord_less_eq_real @ X3 @ B )
% 0.37/0.74 => ? [Y5: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.74 & ( ord_less_eq_real @ Y5 @ zero_zero_real ) ) ) )
% 0.37/0.74 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_nonpos_imp_nonincreasing
% 0.37/0.74 thf(fact_8708_DERIV__nonneg__imp__nondecreasing,axiom,
% 0.37/0.74 ! [A: real,B: real,F: real > real] :
% 0.37/0.74 ( ( ord_less_eq_real @ A @ B )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ A @ X3 )
% 0.37/0.74 => ( ( ord_less_eq_real @ X3 @ B )
% 0.37/0.74 => ? [Y5: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.74 & ( ord_less_eq_real @ zero_zero_real @ Y5 ) ) ) )
% 0.37/0.74 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_nonneg_imp_nondecreasing
% 0.37/0.74 thf(fact_8709_DERIV__neg__dec__left,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ L @ zero_zero_real )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H6 ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_neg_dec_left
% 0.37/0.74 thf(fact_8710_DERIV__pos__inc__left,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ L )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_pos_inc_left
% 0.37/0.74 thf(fact_8711_has__real__derivative__pos__inc__left,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real,S3: set_real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ L )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( member_real @ ( minus_minus_real @ X @ H6 ) @ S3 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % has_real_derivative_pos_inc_left
% 0.37/0.74 thf(fact_8712_has__real__derivative__neg__dec__left,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real,S3: set_real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 0.37/0.74 => ( ( ord_less_real @ L @ zero_zero_real )
% 0.37/0.74 => ? [D2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.37/0.74 & ! [H6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H6 )
% 0.37/0.74 => ( ( member_real @ ( minus_minus_real @ X @ H6 ) @ S3 )
% 0.37/0.74 => ( ( ord_less_real @ H6 @ D2 )
% 0.37/0.74 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H6 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % has_real_derivative_neg_dec_left
% 0.37/0.74 thf(fact_8713_DERIV__local__const,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real,D: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ D )
% 0.37/0.74 => ( ! [Y3: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 0.37/0.74 => ( ( F @ X )
% 0.37/0.74 = ( F @ Y3 ) ) )
% 0.37/0.74 => ( L = zero_zero_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_local_const
% 0.37/0.74 thf(fact_8714_DERIV__local__max,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real,D: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ D )
% 0.37/0.74 => ( ! [Y3: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 0.37/0.74 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 0.37/0.74 => ( L = zero_zero_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_local_max
% 0.37/0.74 thf(fact_8715_DERIV__local__min,axiom,
% 0.37/0.74 ! [F: real > real,L: real,X: real,D: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ D )
% 0.37/0.74 => ( ! [Y3: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 0.37/0.74 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 0.37/0.74 => ( L = zero_zero_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_local_min
% 0.37/0.74 thf(fact_8716_DERIV__ln__divide,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_ln_divide
% 0.37/0.74 thf(fact_8717_DERIV__pow,axiom,
% 0.37/0.74 ! [N: nat,X: real,S: set_real] :
% 0.37/0.74 ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [X4: real] : ( power_power_real @ X4 @ N )
% 0.37/0.74 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_pow
% 0.37/0.74 thf(fact_8718_has__real__derivative__powr,axiom,
% 0.37/0.74 ! [Z: real,R: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.37/0.74 => ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [Z2: real] : ( powr_real @ Z2 @ R )
% 0.37/0.74 @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % has_real_derivative_powr
% 0.37/0.74 thf(fact_8719_DERIV__fun__powr,axiom,
% 0.37/0.74 ! [G: real > real,M: real,X: real,R: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [X4: real] : ( powr_real @ ( G @ X4 ) @ R )
% 0.37/0.74 @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_fun_powr
% 0.37/0.74 thf(fact_8720_DERIV__log,axiom,
% 0.37/0.74 ! [X: real,B: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_log
% 0.37/0.74 thf(fact_8721_DERIV__powr,axiom,
% 0.37/0.74 ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 0.37/0.74 => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [X4: real] : ( powr_real @ ( G @ X4 ) @ ( F @ X4 ) )
% 0.37/0.74 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_powr
% 0.37/0.74 thf(fact_8722_DERIV__real__sqrt,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_real_sqrt
% 0.37/0.74 thf(fact_8723_DERIV__real__sqrt__generic,axiom,
% 0.37/0.74 ! [X: real,D4: real] :
% 0.37/0.74 ( ( X != zero_zero_real )
% 0.37/0.74 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( D4
% 0.37/0.74 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.37/0.74 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.74 => ( D4
% 0.37/0.74 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_real_sqrt_generic
% 0.37/0.74 thf(fact_8724_arcosh__real__has__field__derivative,axiom,
% 0.37/0.74 ! [X: real,A4: set_real] :
% 0.37/0.74 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A4 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % arcosh_real_has_field_derivative
% 0.37/0.74 thf(fact_8725_artanh__real__has__field__derivative,axiom,
% 0.37/0.74 ! [X: real,A4: set_real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A4 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % artanh_real_has_field_derivative
% 0.37/0.74 thf(fact_8726_DERIV__real__root,axiom,
% 0.37/0.74 ! [N: nat,X: real] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( 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 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_real_root
% 0.37/0.74 thf(fact_8727_DERIV__arccos,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_arccos
% 0.37/0.74 thf(fact_8728_DERIV__arcsin,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_arcsin
% 0.37/0.74 thf(fact_8729_Maclaurin__all__le,axiom,
% 0.37/0.74 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 0.37/0.74 ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.74 & ( ( F @ X )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin_all_le
% 0.37/0.74 thf(fact_8730_Maclaurin__all__le__objl,axiom,
% 0.37/0.74 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 0.37/0.74 ( ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 & ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.74 & ( ( F @ X )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin_all_le_objl
% 0.37/0.74 thf(fact_8731_DERIV__odd__real__root,axiom,
% 0.37/0.74 ! [N: nat,X: real] :
% 0.37/0.74 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.74 => ( ( X != zero_zero_real )
% 0.37/0.74 => ( 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 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_odd_real_root
% 0.37/0.74 thf(fact_8732_Maclaurin,axiom,
% 0.37/0.74 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.37/0.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.37/0.74 & ( ord_less_real @ T6 @ H2 )
% 0.37/0.74 & ( ( F @ H2 )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin
% 0.37/0.74 thf(fact_8733_Maclaurin2,axiom,
% 0.37/0.74 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ H2 )
% 0.37/0.74 => ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ H2 )
% 0.37/0.74 & ( ( F @ H2 )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin2
% 0.37/0.74 thf(fact_8734_Maclaurin__minus,axiom,
% 0.37/0.74 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 0.37/0.74 ( ( ord_less_real @ H2 @ zero_zero_real )
% 0.37/0.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ H2 @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_real @ H2 @ T6 )
% 0.37/0.74 & ( ord_less_real @ T6 @ zero_zero_real )
% 0.37/0.74 & ( ( F @ H2 )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin_minus
% 0.37/0.74 thf(fact_8735_Maclaurin__all__lt,axiom,
% 0.37/0.74 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 0.37/0.74 ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( X != zero_zero_real )
% 0.37/0.74 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.37/0.74 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.74 & ( ( F @ X )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin_all_lt
% 0.37/0.74 thf(fact_8736_Maclaurin__bi__le,axiom,
% 0.37/0.74 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 0.37/0.74 ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.37/0.74 & ( ( F @ X )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin_bi_le
% 0.37/0.74 thf(fact_8737_Taylor,axiom,
% 0.37/0.74 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C2: real,X: real] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ A @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ B ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ A @ C2 )
% 0.37/0.74 => ( ( ord_less_eq_real @ C2 @ B )
% 0.37/0.74 => ( ( ord_less_eq_real @ A @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ B )
% 0.37/0.74 => ( ( X != C2 )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ( ord_less_real @ X @ C2 )
% 0.37/0.74 => ( ( ord_less_real @ X @ T6 )
% 0.37/0.74 & ( ord_less_real @ T6 @ C2 ) ) )
% 0.37/0.74 & ( ~ ( ord_less_real @ X @ C2 )
% 0.37/0.74 => ( ( ord_less_real @ C2 @ T6 )
% 0.37/0.74 & ( ord_less_real @ T6 @ X ) ) )
% 0.37/0.74 & ( ( F @ X )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C2 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Taylor
% 0.37/0.74 thf(fact_8738_Taylor__up,axiom,
% 0.37/0.74 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C2: real] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ A @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ B ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ( ( ord_less_eq_real @ A @ C2 )
% 0.37/0.74 => ( ( ord_less_real @ C2 @ B )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_real @ C2 @ T6 )
% 0.37/0.74 & ( ord_less_real @ T6 @ B )
% 0.37/0.74 & ( ( F @ B )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C2 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Taylor_up
% 0.37/0.74 thf(fact_8739_Taylor__down,axiom,
% 0.37/0.74 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C2: real] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( ( Diff @ zero_zero_nat )
% 0.37/0.74 = F )
% 0.37/0.74 => ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ A @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ B ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ( ( ord_less_real @ A @ C2 )
% 0.37/0.74 => ( ( ord_less_eq_real @ C2 @ B )
% 0.37/0.74 => ? [T6: real] :
% 0.37/0.74 ( ( ord_less_real @ A @ T6 )
% 0.37/0.74 & ( ord_less_real @ T6 @ C2 )
% 0.37/0.74 & ( ( F @ A )
% 0.37/0.74 = ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C2 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ M5 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ N ) )
% 0.37/0.74 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Taylor_down
% 0.37/0.74 thf(fact_8740_Maclaurin__lemma2,axiom,
% 0.37/0.74 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B4: real] :
% 0.37/0.74 ( ! [M3: nat,T6: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M3 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.37/0.74 & ( ord_less_eq_real @ T6 @ H2 ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.37/0.74 => ( ( N
% 0.37/0.74 = ( suc @ K ) )
% 0.37/0.74 => ! [M2: nat,T7: real] :
% 0.37/0.74 ( ( ( ord_less_nat @ M2 @ N )
% 0.37/0.74 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 0.37/0.74 & ( ord_less_eq_real @ T7 @ H2 ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [U2: real] :
% 0.37/0.74 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 0.37/0.74 @ ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [P7: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P7 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P7 ) ) @ ( power_power_real @ U2 @ P7 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 0.37/0.74 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 0.37/0.74 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 0.37/0.74 @ ( plus_plus_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [P7: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P7 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P7 ) ) @ ( power_power_real @ T7 @ P7 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 0.37/0.74 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Maclaurin_lemma2
% 0.37/0.74 thf(fact_8741_DERIV__arctan__series,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [X10: real] :
% 0.37/0.74 ( suminf_real
% 0.37/0.74 @ ^ [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 @ X10 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [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 ) ) ) ) ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_arctan_series
% 0.37/0.74 thf(fact_8742_DERIV__real__root__generic,axiom,
% 0.37/0.74 ! [N: nat,X: real,D4: real] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( X != zero_zero_real )
% 0.37/0.74 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.37/0.74 => ( D4
% 0.37/0.74 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 0.37/0.74 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.74 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.37/0.74 => ( D4
% 0.37/0.74 = ( 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 ) ) ) ) ) ) ) ) )
% 0.37/0.74 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.74 => ( D4
% 0.37/0.74 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_real_root_generic
% 0.37/0.74 thf(fact_8743_DERIV__power__series_H,axiom,
% 0.37/0.74 ! [R2: real,F: nat > real,X0: real] :
% 0.37/0.74 ( ! [X3: real] :
% 0.37/0.74 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 0.37/0.74 => ( summable_real
% 0.37/0.74 @ ^ [N6: nat] : ( times_times_real @ ( times_times_real @ ( F @ N6 ) @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) @ ( power_power_real @ X3 @ N6 ) ) ) )
% 0.37/0.74 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.37/0.74 => ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [X4: real] :
% 0.37/0.74 ( suminf_real
% 0.37/0.74 @ ^ [N6: nat] : ( times_times_real @ ( F @ N6 ) @ ( power_power_real @ X4 @ ( suc @ N6 ) ) ) )
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [N6: nat] : ( times_times_real @ ( times_times_real @ ( F @ N6 ) @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) @ ( power_power_real @ X0 @ N6 ) ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_power_series'
% 0.37/0.74 thf(fact_8744_DERIV__isconst3,axiom,
% 0.37/0.74 ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 0.37/0.74 ( ( ord_less_real @ A @ B )
% 0.37/0.74 => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.37/0.74 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.37/0.74 => ( ( F @ X )
% 0.37/0.74 = ( F @ Y ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_isconst3
% 0.37/0.74 thf(fact_8745_DERIV__series_H,axiom,
% 0.37/0.74 ! [F: real > nat > real,F6: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 0.37/0.74 ( ! [N2: nat] :
% 0.37/0.74 ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [X4: real] : ( F @ X4 @ N2 )
% 0.37/0.74 @ ( F6 @ X0 @ N2 )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 0.37/0.74 => ( ! [X3: real] :
% 0.37/0.74 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.37/0.74 => ( summable_real @ ( F @ X3 ) ) )
% 0.37/0.74 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.37/0.74 => ( ( summable_real @ ( F6 @ X0 ) )
% 0.37/0.74 => ( ( summable_real @ L5 )
% 0.37/0.74 => ( ! [N2: nat,X3: real,Y3: real] :
% 0.37/0.74 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.37/0.74 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.37/0.74 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N2 ) @ ( F @ Y3 @ N2 ) ) ) @ ( times_times_real @ ( L5 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 0.37/0.74 => ( has_fi5821293074295781190e_real
% 0.37/0.74 @ ^ [X4: real] : ( suminf_real @ ( F @ X4 ) )
% 0.37/0.74 @ ( suminf_real @ ( F6 @ X0 ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_series'
% 0.37/0.74 thf(fact_8746_int__of__integer__code,axiom,
% 0.37/0.74 ( code_int_of_integer
% 0.37/0.74 = ( ^ [K3: code_integer] :
% 0.37/0.74 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 0.37/0.74 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.37/0.74 @ ( produc1553301316500091796er_int
% 0.37/0.74 @ ^ [L4: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L4 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L4 ) ) @ one_one_int ) )
% 0.37/0.74 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_code
% 0.37/0.74 thf(fact_8747_int__of__integer__max,axiom,
% 0.37/0.74 ! [K: code_integer,L: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L ) )
% 0.37/0.74 = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_max
% 0.37/0.74 thf(fact_8748_finite__greaterThanLessThan,axiom,
% 0.37/0.74 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.37/0.74
% 0.37/0.74 % finite_greaterThanLessThan
% 0.37/0.74 thf(fact_8749_finite__greaterThanLessThan__integer,axiom,
% 0.37/0.74 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 0.37/0.74
% 0.37/0.74 % finite_greaterThanLessThan_integer
% 0.37/0.74 thf(fact_8750_int__of__integer__of__nat,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.74 = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_of_nat
% 0.37/0.74 thf(fact_8751_integer__of__int__int__of__integer,axiom,
% 0.37/0.74 ! [K: code_integer] :
% 0.37/0.74 ( ( code_integer_of_int @ ( code_int_of_integer @ K ) )
% 0.37/0.74 = K ) ).
% 0.37/0.74
% 0.37/0.74 % integer_of_int_int_of_integer
% 0.37/0.74 thf(fact_8752_int__of__integer__integer__of__int,axiom,
% 0.37/0.74 ! [K: int] :
% 0.37/0.74 ( ( code_int_of_integer @ ( code_integer_of_int @ K ) )
% 0.37/0.74 = K ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_integer_of_int
% 0.37/0.74 thf(fact_8753_int__of__integer__inverse,axiom,
% 0.37/0.74 ! [X: code_integer] :
% 0.37/0.74 ( ( code_integer_of_int @ ( code_int_of_integer @ X ) )
% 0.37/0.74 = X ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_inverse
% 0.37/0.74 thf(fact_8754_of__int__integer__of,axiom,
% 0.37/0.74 ! [K: code_integer] :
% 0.37/0.74 ( ( ring_18347121197199848620nteger @ ( code_int_of_integer @ K ) )
% 0.37/0.74 = K ) ).
% 0.37/0.74
% 0.37/0.74 % of_int_integer_of
% 0.37/0.74 thf(fact_8755_int__of__integer__of__int,axiom,
% 0.37/0.74 ! [K: int] :
% 0.37/0.74 ( ( code_int_of_integer @ ( ring_18347121197199848620nteger @ K ) )
% 0.37/0.74 = K ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_of_int
% 0.37/0.74 thf(fact_8756_zero__integer_Orep__eq,axiom,
% 0.37/0.74 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 0.37/0.74 = zero_zero_int ) ).
% 0.37/0.74
% 0.37/0.74 % zero_integer.rep_eq
% 0.37/0.74 thf(fact_8757_card__greaterThanLessThan,axiom,
% 0.37/0.74 ! [L: nat,U: nat] :
% 0.37/0.74 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.37/0.74 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % card_greaterThanLessThan
% 0.37/0.74 thf(fact_8758_int__of__integer__numeral,axiom,
% 0.37/0.74 ! [K: num] :
% 0.37/0.74 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 0.37/0.74 = ( numeral_numeral_int @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_numeral
% 0.37/0.74 thf(fact_8759_one__integer_Orep__eq,axiom,
% 0.37/0.74 ( ( code_int_of_integer @ one_one_Code_integer )
% 0.37/0.74 = one_one_int ) ).
% 0.37/0.74
% 0.37/0.74 % one_integer.rep_eq
% 0.37/0.74 thf(fact_8760_uminus__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X ) )
% 0.37/0.74 = ( uminus_uminus_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % uminus_integer.rep_eq
% 0.37/0.74 thf(fact_8761_plus__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % plus_integer.rep_eq
% 0.37/0.74 thf(fact_8762_minus__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % minus_integer.rep_eq
% 0.37/0.74 thf(fact_8763_times__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % times_integer.rep_eq
% 0.37/0.74 thf(fact_8764_abs__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( abs_abs_Code_integer @ X ) )
% 0.37/0.74 = ( abs_abs_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % abs_integer.rep_eq
% 0.37/0.74 thf(fact_8765_divide__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % divide_integer.rep_eq
% 0.37/0.74 thf(fact_8766_modulo__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( modulo_modulo_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % modulo_integer.rep_eq
% 0.37/0.74 thf(fact_8767_sgn__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( sgn_sgn_Code_integer @ X ) )
% 0.37/0.74 = ( sgn_sgn_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sgn_integer.rep_eq
% 0.37/0.74 thf(fact_8768_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.37/0.74 ! [L: nat,U: nat] :
% 0.37/0.74 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 0.37/0.74 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.37/0.74
% 0.37/0.74 % atLeastSucLessThan_greaterThanLessThan
% 0.37/0.74 thf(fact_8769_or__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( bit_se1080825931792720795nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( bit_se1409905431419307370or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % or_integer.rep_eq
% 0.37/0.74 thf(fact_8770_bit__integer_Orep__eq,axiom,
% 0.37/0.74 ( bit_se9216721137139052372nteger
% 0.37/0.74 = ( ^ [X4: code_integer] : ( bit_se1146084159140164899it_int @ ( code_int_of_integer @ X4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % bit_integer.rep_eq
% 0.37/0.74 thf(fact_8771_int__of__integer__induct,axiom,
% 0.37/0.74 ! [Y: int,P2: int > $o] :
% 0.37/0.74 ( ( member_int @ Y @ top_top_set_int )
% 0.37/0.74 => ( ! [X3: code_integer] : ( P2 @ ( code_int_of_integer @ X3 ) )
% 0.37/0.74 => ( P2 @ Y ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_induct
% 0.37/0.74 thf(fact_8772_int__of__integer__cases,axiom,
% 0.37/0.74 ! [Y: int] :
% 0.37/0.74 ( ( member_int @ Y @ top_top_set_int )
% 0.37/0.74 => ~ ! [X3: code_integer] :
% 0.37/0.74 ( Y
% 0.37/0.74 != ( code_int_of_integer @ X3 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_cases
% 0.37/0.74 thf(fact_8773_int__of__integer,axiom,
% 0.37/0.74 ! [X: code_integer] : ( member_int @ ( code_int_of_integer @ X ) @ top_top_set_int ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer
% 0.37/0.74 thf(fact_8774_type__definition__integer,axiom,
% 0.37/0.74 type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 0.37/0.74
% 0.37/0.74 % type_definition_integer
% 0.37/0.74 thf(fact_8775_integer__of__int__inverse,axiom,
% 0.37/0.74 ! [Y: int] :
% 0.37/0.74 ( ( member_int @ Y @ top_top_set_int )
% 0.37/0.74 => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 0.37/0.74 = Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % integer_of_int_inverse
% 0.37/0.74 thf(fact_8776_int__of__integer__less__iff,axiom,
% 0.37/0.74 ! [X: code_integer,Y: code_integer] :
% 0.37/0.74 ( ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Y ) )
% 0.37/0.74 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_less_iff
% 0.37/0.74 thf(fact_8777_less__integer_Orep__eq,axiom,
% 0.37/0.74 ( ord_le6747313008572928689nteger
% 0.37/0.74 = ( ^ [X4: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % less_integer.rep_eq
% 0.37/0.74 thf(fact_8778_integer__less__iff,axiom,
% 0.37/0.74 ( ord_le6747313008572928689nteger
% 0.37/0.74 = ( ^ [K3: code_integer,L4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % integer_less_iff
% 0.37/0.74 thf(fact_8779_int__of__integer__inject,axiom,
% 0.37/0.74 ! [X: code_integer,Y: code_integer] :
% 0.37/0.74 ( ( ( code_int_of_integer @ X )
% 0.37/0.74 = ( code_int_of_integer @ Y ) )
% 0.37/0.74 = ( X = Y ) ) ).
% 0.37/0.74
% 0.37/0.74 % int_of_integer_inject
% 0.37/0.74 thf(fact_8780_integer__eqI,axiom,
% 0.37/0.74 ! [K: code_integer,L: code_integer] :
% 0.37/0.74 ( ( ( code_int_of_integer @ K )
% 0.37/0.74 = ( code_int_of_integer @ L ) )
% 0.37/0.74 => ( K = L ) ) ).
% 0.37/0.74
% 0.37/0.74 % integer_eqI
% 0.37/0.74 thf(fact_8781_integer__eq__iff,axiom,
% 0.37/0.74 ( ( ^ [Y6: code_integer,Z4: code_integer] : ( Y6 = Z4 ) )
% 0.37/0.74 = ( ^ [K3: code_integer,L4: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ K3 )
% 0.37/0.74 = ( code_int_of_integer @ L4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % integer_eq_iff
% 0.37/0.74 thf(fact_8782_less__eq__integer_Orep__eq,axiom,
% 0.37/0.74 ( ord_le3102999989581377725nteger
% 0.37/0.74 = ( ^ [X4: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % less_eq_integer.rep_eq
% 0.37/0.74 thf(fact_8783_integer__less__eq__iff,axiom,
% 0.37/0.74 ( ord_le3102999989581377725nteger
% 0.37/0.74 = ( ^ [K3: code_integer,L4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % integer_less_eq_iff
% 0.37/0.74 thf(fact_8784_xor__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( bit_se3222712562003087583nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( bit_se6526347334894502574or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % xor_integer.rep_eq
% 0.37/0.74 thf(fact_8785_take__bit__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: nat,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( bit_se1745604003318907178nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( bit_se2923211474154528505it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % take_bit_integer.rep_eq
% 0.37/0.74 thf(fact_8786_unset__bit__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: nat,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( bit_se8260200283734997820nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( bit_se4203085406695923979it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % unset_bit_integer.rep_eq
% 0.37/0.74 thf(fact_8787_LIM__fun__less__zero,axiom,
% 0.37/0.74 ! [F: real > real,L: real,C2: real] :
% 0.37/0.74 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ L @ zero_zero_real )
% 0.37/0.74 => ? [R4: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.37/0.74 & ! [X5: real] :
% 0.37/0.74 ( ( ( X5 != C2 )
% 0.37/0.74 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X5 ) ) @ R4 ) )
% 0.37/0.74 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIM_fun_less_zero
% 0.37/0.74 thf(fact_8788_LIM__fun__not__zero,axiom,
% 0.37/0.74 ! [F: real > real,L: real,C2: real] :
% 0.37/0.74 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.37/0.74 => ( ( L != zero_zero_real )
% 0.37/0.74 => ? [R4: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.37/0.74 & ! [X5: real] :
% 0.37/0.74 ( ( ( X5 != C2 )
% 0.37/0.74 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X5 ) ) @ R4 ) )
% 0.37/0.74 => ( ( F @ X5 )
% 0.37/0.74 != zero_zero_real ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIM_fun_not_zero
% 0.37/0.74 thf(fact_8789_LIM__fun__gt__zero,axiom,
% 0.37/0.74 ! [F: real > real,L: real,C2: real] :
% 0.37/0.74 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ L )
% 0.37/0.74 => ? [R4: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.37/0.74 & ! [X5: real] :
% 0.37/0.74 ( ( ( X5 != C2 )
% 0.37/0.74 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X5 ) ) @ R4 ) )
% 0.37/0.74 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIM_fun_gt_zero
% 0.37/0.74 thf(fact_8790_Code__Numeral_Oset__bit__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: nat,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( bit_se2793503036327961859nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( bit_se7879613467334960850it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % Code_Numeral.set_bit_integer.rep_eq
% 0.37/0.74 thf(fact_8791_flip__bit__integer_Orep__eq,axiom,
% 0.37/0.74 ! [X: nat,Xa2: code_integer] :
% 0.37/0.74 ( ( code_int_of_integer @ ( bit_se1345352211410354436nteger @ X @ Xa2 ) )
% 0.37/0.74 = ( bit_se2159334234014336723it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % flip_bit_integer.rep_eq
% 0.37/0.74 thf(fact_8792_greaterThanLessThan__upt,axiom,
% 0.37/0.74 ( set_or5834768355832116004an_nat
% 0.37/0.74 = ( ^ [N6: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N6 ) @ M5 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % greaterThanLessThan_upt
% 0.37/0.74 thf(fact_8793_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 0.37/0.74 ! [L: code_integer,U: code_integer] :
% 0.37/0.74 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.37/0.74 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 0.37/0.74
% 0.37/0.74 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 0.37/0.74 thf(fact_8794_sorted__list__of__set__greaterThanLessThan,axiom,
% 0.37/0.74 ! [I: nat,J: nat] :
% 0.37/0.74 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 0.37/0.74 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 0.37/0.74 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sorted_list_of_set_greaterThanLessThan
% 0.37/0.74 thf(fact_8795_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.37/0.74 ! [N: nat,J: nat,I: nat] :
% 0.37/0.74 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 0.37/0.74 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 0.37/0.74 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % nth_sorted_list_of_set_greaterThanLessThan
% 0.37/0.74 thf(fact_8796_divmod__integer__def,axiom,
% 0.37/0.74 ( code_divmod_integer
% 0.37/0.74 = ( ^ [K3: code_integer,L4: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L4 ) @ ( modulo364778990260209775nteger @ K3 @ L4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % divmod_integer_def
% 0.37/0.74 thf(fact_8797_summable__Leibniz_I2_J,axiom,
% 0.37/0.74 ! [A: nat > real] :
% 0.37/0.74 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ( ( topolo6980174941875973593q_real @ A )
% 0.37/0.74 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 0.37/0.74 => ! [N9: nat] :
% 0.37/0.74 ( member_real
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.37/0.74 @ ( set_or1222579329274155063t_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_Leibniz(2)
% 0.37/0.74 thf(fact_8798_summable__Leibniz_I3_J,axiom,
% 0.37/0.74 ! [A: nat > real] :
% 0.37/0.74 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ( ( topolo6980174941875973593q_real @ A )
% 0.37/0.74 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 0.37/0.74 => ! [N9: nat] :
% 0.37/0.74 ( member_real
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.37/0.74 @ ( set_or1222579329274155063t_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_Leibniz(3)
% 0.37/0.74 thf(fact_8799_filterlim__Suc,axiom,
% 0.37/0.74 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 0.37/0.74
% 0.37/0.74 % filterlim_Suc
% 0.37/0.74 thf(fact_8800_mult__nat__left__at__top,axiom,
% 0.37/0.74 ! [C2: nat] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.74 => ( filterlim_nat_nat @ ( times_times_nat @ C2 ) @ at_top_nat @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % mult_nat_left_at_top
% 0.37/0.74 thf(fact_8801_mult__nat__right__at__top,axiom,
% 0.37/0.74 ! [C2: nat] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.37/0.74 => ( filterlim_nat_nat
% 0.37/0.74 @ ^ [X4: nat] : ( times_times_nat @ X4 @ C2 )
% 0.37/0.74 @ at_top_nat
% 0.37/0.74 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % mult_nat_right_at_top
% 0.37/0.74 thf(fact_8802_monoseq__convergent,axiom,
% 0.37/0.74 ! [X6: nat > real,B4: real] :
% 0.37/0.74 ( ( topolo6980174941875973593q_real @ X6 )
% 0.37/0.74 => ( ! [I2: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X6 @ I2 ) ) @ B4 )
% 0.37/0.74 => ~ ! [L6: real] :
% 0.37/0.74 ~ ( filterlim_nat_real @ X6 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % monoseq_convergent
% 0.37/0.74 thf(fact_8803_nested__sequence__unique,axiom,
% 0.37/0.74 ! [F: nat > real,G: nat > real] :
% 0.37/0.74 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N2 ) ) @ ( G @ N2 ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 0.37/0.74 => ( ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( minus_minus_real @ ( F @ N6 ) @ ( G @ N6 ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.37/0.74 @ at_top_nat )
% 0.37/0.74 => ? [L2: real] :
% 0.37/0.74 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L2 )
% 0.37/0.74 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat )
% 0.37/0.74 & ! [N9: nat] : ( ord_less_eq_real @ L2 @ ( G @ N9 ) )
% 0.37/0.74 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % nested_sequence_unique
% 0.37/0.74 thf(fact_8804_LIMSEQ__inverse__zero,axiom,
% 0.37/0.74 ! [X6: nat > real] :
% 0.37/0.74 ( ! [R4: real] :
% 0.37/0.74 ? [N10: nat] :
% 0.37/0.74 ! [N2: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ N10 @ N2 )
% 0.37/0.74 => ( ord_less_real @ R4 @ ( X6 @ N2 ) ) )
% 0.37/0.74 => ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( inverse_inverse_real @ ( X6 @ N6 ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.37/0.74 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_inverse_zero
% 0.37/0.74 thf(fact_8805_LIMSEQ__inverse__real__of__nat,axiom,
% 0.37/0.74 ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.37/0.74 @ at_top_nat ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_inverse_real_of_nat
% 0.37/0.74 thf(fact_8806_LIMSEQ__root__const,axiom,
% 0.37/0.74 ! [C2: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.37/0.74 => ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( root @ N6 @ C2 )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.37/0.74 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_root_const
% 0.37/0.74 thf(fact_8807_LIMSEQ__inverse__real__of__nat__add,axiom,
% 0.37/0.74 ! [R: real] :
% 0.37/0.74 ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ R )
% 0.37/0.74 @ at_top_nat ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_inverse_real_of_nat_add
% 0.37/0.74 thf(fact_8808_increasing__LIMSEQ,axiom,
% 0.37/0.74 ! [F: nat > real,L: real] :
% 0.37/0.74 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 0.37/0.74 => ( ! [E: real] :
% 0.37/0.74 ( ( ord_less_real @ zero_zero_real @ E )
% 0.37/0.74 => ? [N9: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N9 ) @ E ) ) )
% 0.37/0.74 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % increasing_LIMSEQ
% 0.37/0.74 thf(fact_8809_LIMSEQ__realpow__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_real @ X @ one_one_real )
% 0.37/0.74 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_realpow_zero
% 0.37/0.74 thf(fact_8810_LIMSEQ__divide__realpow__zero,axiom,
% 0.37/0.74 ! [X: real,A: real] :
% 0.37/0.74 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.74 => ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N6 ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.37/0.74 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_divide_realpow_zero
% 0.37/0.74 thf(fact_8811_LIMSEQ__abs__realpow__zero,axiom,
% 0.37/0.74 ! [C2: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ C2 ) @ one_one_real )
% 0.37/0.74 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C2 ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_abs_realpow_zero
% 0.37/0.74 thf(fact_8812_LIMSEQ__abs__realpow__zero2,axiom,
% 0.37/0.74 ! [C2: real] :
% 0.37/0.74 ( ( ord_less_real @ ( abs_abs_real @ C2 ) @ one_one_real )
% 0.37/0.74 => ( filterlim_nat_real @ ( power_power_real @ C2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_abs_realpow_zero2
% 0.37/0.74 thf(fact_8813_LIMSEQ__inverse__realpow__zero,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_real @ one_one_real @ X )
% 0.37/0.74 => ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N6 ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.37/0.74 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_inverse_realpow_zero
% 0.37/0.74 thf(fact_8814_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 0.37/0.74 ! [R: real] :
% 0.37/0.74 ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ R )
% 0.37/0.74 @ at_top_nat ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_inverse_real_of_nat_add_minus
% 0.37/0.74 thf(fact_8815_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 0.37/0.74 ! [R: real] :
% 0.37/0.74 ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ R )
% 0.37/0.74 @ at_top_nat ) ).
% 0.37/0.74
% 0.37/0.74 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 0.37/0.74 thf(fact_8816_summable,axiom,
% 0.37/0.74 ! [A: nat > real] :
% 0.37/0.74 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.37/0.74 => ( summable_real
% 0.37/0.74 @ ^ [N6: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N6 ) @ ( A @ N6 ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable
% 0.37/0.74 thf(fact_8817_zeroseq__arctan__series,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.37/0.74 => ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.37/0.74 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % zeroseq_arctan_series
% 0.37/0.74 thf(fact_8818_summable__Leibniz_H_I2_J,axiom,
% 0.37/0.74 ! [A: nat > real,N: nat] :
% 0.37/0.74 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.37/0.74 => ( ord_less_eq_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_Leibniz'(2)
% 0.37/0.74 thf(fact_8819_summable__Leibniz_H_I3_J,axiom,
% 0.37/0.74 ! [A: nat > real] :
% 0.37/0.74 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.37/0.74 => ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] :
% 0.37/0.74 ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.37/0.74 @ at_top_nat ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_Leibniz'(3)
% 0.37/0.74 thf(fact_8820_sums__alternating__upper__lower,axiom,
% 0.37/0.74 ! [A: nat > real] :
% 0.37/0.74 ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.37/0.74 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ? [L2: real] :
% 0.37/0.74 ( ! [N9: nat] :
% 0.37/0.74 ( ord_less_eq_real
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 0.37/0.74 @ L2 )
% 0.37/0.74 & ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] :
% 0.37/0.74 ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ L2 )
% 0.37/0.74 @ at_top_nat )
% 0.37/0.74 & ! [N9: nat] :
% 0.37/0.74 ( ord_less_eq_real @ L2
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 0.37/0.74 & ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] :
% 0.37/0.74 ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real @ L2 )
% 0.37/0.74 @ at_top_nat ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % sums_alternating_upper_lower
% 0.37/0.74 thf(fact_8821_summable__Leibniz_H_I4_J,axiom,
% 0.37/0.74 ! [A: nat > real,N: nat] :
% 0.37/0.74 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.37/0.74 => ( ord_less_eq_real
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 0.37/0.74 @ ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_Leibniz'(4)
% 0.37/0.74 thf(fact_8822_summable__Leibniz_H_I5_J,axiom,
% 0.37/0.74 ! [A: nat > real] :
% 0.37/0.74 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 0.37/0.74 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 0.37/0.74 => ( filterlim_nat_real
% 0.37/0.74 @ ^ [N6: nat] :
% 0.37/0.74 ( groups6591440286371151544t_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 0.37/0.74 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 0.37/0.74 @ ( topolo2815343760600316023s_real
% 0.37/0.74 @ ( suminf_real
% 0.37/0.74 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 0.37/0.74 @ at_top_nat ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % summable_Leibniz'(5)
% 0.37/0.74 thf(fact_8823_num__of__integer__code,axiom,
% 0.37/0.74 ( code_num_of_integer
% 0.37/0.74 = ( ^ [K3: code_integer] :
% 0.37/0.74 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 0.37/0.74 @ ( produc7336495610019696514er_num
% 0.37/0.74 @ ^ [L4: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L4 ) @ ( code_num_of_integer @ L4 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L4 ) @ ( code_num_of_integer @ L4 ) ) @ one ) )
% 0.37/0.74 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % num_of_integer_code
% 0.37/0.74 thf(fact_8824_nat__of__integer__code,axiom,
% 0.37/0.74 ( code_nat_of_integer
% 0.37/0.74 = ( ^ [K3: code_integer] :
% 0.37/0.74 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.37/0.74 @ ( produc1555791787009142072er_nat
% 0.37/0.74 @ ^ [L4: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L4 ) @ ( code_nat_of_integer @ L4 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L4 ) @ ( code_nat_of_integer @ L4 ) ) @ one_one_nat ) )
% 0.37/0.74 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % nat_of_integer_code
% 0.37/0.74 thf(fact_8825_nat__of__integer__of__nat,axiom,
% 0.37/0.74 ! [N: nat] :
% 0.37/0.74 ( ( code_nat_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.37/0.74 = N ) ).
% 0.37/0.74
% 0.37/0.74 % nat_of_integer_of_nat
% 0.37/0.74 thf(fact_8826_nat__of__integer__non__positive,axiom,
% 0.37/0.74 ! [K: code_integer] :
% 0.37/0.74 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 0.37/0.74 => ( ( code_nat_of_integer @ K )
% 0.37/0.74 = zero_zero_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % nat_of_integer_non_positive
% 0.37/0.74 thf(fact_8827_of__nat__of__integer,axiom,
% 0.37/0.74 ! [K: code_integer] :
% 0.37/0.74 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 0.37/0.74 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 0.37/0.74
% 0.37/0.74 % of_nat_of_integer
% 0.37/0.74 thf(fact_8828_nat__of__integer_Orep__eq,axiom,
% 0.37/0.74 ( code_nat_of_integer
% 0.37/0.74 = ( ^ [X4: code_integer] : ( nat2 @ ( code_int_of_integer @ X4 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % nat_of_integer.rep_eq
% 0.37/0.74 thf(fact_8829_nat__of__integer_Oabs__eq,axiom,
% 0.37/0.74 ! [X: int] :
% 0.37/0.74 ( ( code_nat_of_integer @ ( code_integer_of_int @ X ) )
% 0.37/0.74 = ( nat2 @ X ) ) ).
% 0.37/0.74
% 0.37/0.74 % nat_of_integer.abs_eq
% 0.37/0.74 thf(fact_8830_nat__of__integer__code__post_I1_J,axiom,
% 0.37/0.74 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 0.37/0.74 = zero_zero_nat ) ).
% 0.37/0.74
% 0.37/0.74 % nat_of_integer_code_post(1)
% 0.37/0.74 thf(fact_8831_nat__of__integer__less__iff,axiom,
% 0.37/0.74 ! [X: code_integer,Y: code_integer] :
% 0.37/0.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.37/0.74 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.37/0.74 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 0.37/0.74 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % nat_of_integer_less_iff
% 0.37/0.74 thf(fact_8832_image__atLeastZeroLessThan__integer,axiom,
% 0.37/0.74 ! [U: code_integer] :
% 0.37/0.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.37/0.74 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 0.37/0.74 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % image_atLeastZeroLessThan_integer
% 0.37/0.74 thf(fact_8833_filterlim__pow__at__bot__odd,axiom,
% 0.37/0.74 ! [N: nat,F: real > real,F2: filter_real] :
% 0.37/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.74 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 0.37/0.74 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.74 => ( filterlim_real_real
% 0.37/0.74 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N )
% 0.37/0.74 @ at_bot_real
% 0.37/0.74 @ F2 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % filterlim_pow_at_bot_odd
% 0.37/0.74 thf(fact_8834_eventually__sequentially__Suc,axiom,
% 0.37/0.74 ! [P2: nat > $o] :
% 0.37/0.74 ( ( eventually_nat
% 0.37/0.74 @ ^ [I3: nat] : ( P2 @ ( suc @ I3 ) )
% 0.37/0.74 @ at_top_nat )
% 0.37/0.74 = ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % eventually_sequentially_Suc
% 0.37/0.74 thf(fact_8835_at__bot__le__at__infinity,axiom,
% 0.37/0.74 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 0.37/0.74
% 0.37/0.74 % at_bot_le_at_infinity
% 0.37/0.74 thf(fact_8836_eventually__sequentiallyI,axiom,
% 0.37/0.74 ! [C2: nat,P2: nat > $o] :
% 0.37/0.74 ( ! [X3: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ C2 @ X3 )
% 0.37/0.74 => ( P2 @ X3 ) )
% 0.37/0.74 => ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % eventually_sequentiallyI
% 0.37/0.74 thf(fact_8837_eventually__sequentially,axiom,
% 0.37/0.74 ! [P2: nat > $o] :
% 0.37/0.74 ( ( eventually_nat @ P2 @ at_top_nat )
% 0.37/0.74 = ( ? [N7: nat] :
% 0.37/0.74 ! [N6: nat] :
% 0.37/0.74 ( ( ord_less_eq_nat @ N7 @ N6 )
% 0.37/0.74 => ( P2 @ N6 ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % eventually_sequentially
% 0.37/0.74 thf(fact_8838_le__sequentially,axiom,
% 0.37/0.74 ! [F2: filter_nat] :
% 0.37/0.74 ( ( ord_le2510731241096832064er_nat @ F2 @ at_top_nat )
% 0.37/0.74 = ( ! [N7: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N7 ) @ F2 ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % le_sequentially
% 0.37/0.74 thf(fact_8839_eventually__at__left__real,axiom,
% 0.37/0.74 ! [B: real,A: real] :
% 0.37/0.74 ( ( ord_less_real @ B @ A )
% 0.37/0.74 => ( eventually_real
% 0.37/0.74 @ ^ [X4: real] : ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 0.37/0.74 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % eventually_at_left_real
% 0.37/0.74 thf(fact_8840_DERIV__pos__imp__increasing__at__bot,axiom,
% 0.37/0.74 ! [B: real,F: real > real,Flim: real] :
% 0.37/0.74 ( ! [X3: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ X3 @ B )
% 0.37/0.74 => ? [Y5: real] :
% 0.37/0.74 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.74 & ( ord_less_real @ zero_zero_real @ Y5 ) ) )
% 0.37/0.74 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 0.37/0.74 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.37/0.74
% 0.37/0.74 % DERIV_pos_imp_increasing_at_bot
% 0.37/0.74 thf(fact_8841_at__top__le__at__infinity,axiom,
% 0.37/0.74 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 0.37/0.74
% 0.37/0.74 % at_top_le_at_infinity
% 0.37/0.74 thf(fact_8842_Bseq__eq__bounded,axiom,
% 0.37/0.74 ! [F: nat > real,A: real,B: real] :
% 0.37/0.74 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 0.37/0.74 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 0.37/0.74
% 0.37/0.74 % Bseq_eq_bounded
% 0.37/0.74 thf(fact_8843_Bseq__realpow,axiom,
% 0.37/0.74 ! [X: real] :
% 0.37/0.74 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.37/0.74 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.37/0.74 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Bseq_realpow
% 0.37/0.75 thf(fact_8844_DERIV__neg__imp__decreasing__at__top,axiom,
% 0.37/0.75 ! [B: real,F: real > real,Flim: real] :
% 0.37/0.75 ( ! [X3: real] :
% 0.37/0.75 ( ( ord_less_eq_real @ B @ X3 )
% 0.37/0.75 => ? [Y5: real] :
% 0.37/0.75 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.37/0.75 & ( ord_less_real @ Y5 @ zero_zero_real ) ) )
% 0.37/0.75 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 0.37/0.75 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % DERIV_neg_imp_decreasing_at_top
% 0.37/0.75 thf(fact_8845_filterlim__pow__at__bot__even,axiom,
% 0.37/0.75 ! [N: nat,F: real > real,F2: filter_real] :
% 0.37/0.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.75 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 0.37/0.75 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.37/0.75 => ( filterlim_real_real
% 0.37/0.75 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N )
% 0.37/0.75 @ at_top_real
% 0.37/0.75 @ F2 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % filterlim_pow_at_bot_even
% 0.37/0.75 thf(fact_8846_finite__greaterThanAtMost,axiom,
% 0.37/0.75 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.37/0.75
% 0.37/0.75 % finite_greaterThanAtMost
% 0.37/0.75 thf(fact_8847_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.37/0.75 ! [L: nat,U: nat] :
% 0.37/0.75 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 0.37/0.75 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.37/0.75
% 0.37/0.75 % atLeastSucAtMost_greaterThanAtMost
% 0.37/0.75 thf(fact_8848_greaterThanAtMost__upt,axiom,
% 0.37/0.75 ( set_or6659071591806873216st_nat
% 0.37/0.75 = ( ^ [N6: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N6 ) @ ( suc @ M5 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % greaterThanAtMost_upt
% 0.37/0.75 thf(fact_8849_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.37/0.75 ! [I: nat,J: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 0.37/0.75 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 0.37/0.75 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % sorted_list_of_set_greaterThanAtMost
% 0.37/0.75 thf(fact_8850_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.37/0.75 ! [N: nat,J: nat,I: nat] :
% 0.37/0.75 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 0.37/0.75 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 0.37/0.75 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % nth_sorted_list_of_set_greaterThanAtMost
% 0.37/0.75 thf(fact_8851_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.75 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.37/0.75 = Y )
% 0.37/0.75 => ( ( ? [Uu: $o,Uv: $o] :
% 0.37/0.75 ( X
% 0.37/0.75 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( Xa2 != one_one_nat ) ) )
% 0.37/0.75 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( ~ ( ( Deg2 = Xa2 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 & ( case_o184042715313410164at_nat
% 0.37/0.75 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 @ ( produc6081775807080527818_nat_o
% 0.37/0.75 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.75 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 & ! [I3: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.37/0.75 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.37/0.75 & ( ( Mi3 = Ma3 )
% 0.37/0.75 => ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 & ( ( Mi3 != Ma3 )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.37/0.75 & ! [X4: nat] :
% 0.37/0.75 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 0.37/0.75 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.75 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.37/0.75 @ Mima2 ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % VEBT_internal.valid'.elims(1)
% 0.37/0.75 thf(fact_8852_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.75 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.37/0.75 => ( ( ? [Uu: $o,Uv: $o] :
% 0.37/0.75 ( X
% 0.37/0.75 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.75 => ( Xa2 != one_one_nat ) )
% 0.37/0.75 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.75 => ~ ( ( Deg2 = Xa2 )
% 0.37/0.75 & ! [X5: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 & ( case_o184042715313410164at_nat
% 0.37/0.75 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 @ ( produc6081775807080527818_nat_o
% 0.37/0.75 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.75 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 & ! [I3: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.37/0.75 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.37/0.75 & ( ( Mi3 = Ma3 )
% 0.37/0.75 => ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 & ( ( Mi3 != Ma3 )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.37/0.75 & ! [X4: nat] :
% 0.37/0.75 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 0.37/0.75 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.75 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.37/0.75 @ Mima2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % VEBT_internal.valid'.elims(2)
% 0.37/0.75 thf(fact_8853_finite__greaterThanAtMost__integer,axiom,
% 0.37/0.75 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 0.37/0.75
% 0.37/0.75 % finite_greaterThanAtMost_integer
% 0.37/0.75 thf(fact_8854_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 0.37/0.75 ! [L: code_integer,U: code_integer] :
% 0.37/0.75 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.37/0.75 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 0.37/0.75
% 0.37/0.75 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 0.37/0.75 thf(fact_8855_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 0.37/0.75 ! [Mima3: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 0.37/0.75 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima3 @ Deg @ TreeList @ Summary ) @ Deg3 )
% 0.37/0.75 = ( ( Deg = Deg3 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.75 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 & ( case_o184042715313410164at_nat
% 0.37/0.75 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X8 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 @ ( produc6081775807080527818_nat_o
% 0.37/0.75 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.75 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.37/0.75 & ! [I3: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X8 ) )
% 0.37/0.75 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.37/0.75 & ( ( Mi3 = Ma3 )
% 0.37/0.75 => ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 & ( ( Mi3 != Ma3 )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.37/0.75 & ! [X4: nat] :
% 0.37/0.75 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 0.37/0.75 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.75 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.37/0.75 @ Mima3 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % VEBT_internal.valid'.simps(2)
% 0.37/0.75 thf(fact_8856_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.75 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.37/0.75 => ( ( ? [Uu: $o,Uv: $o] :
% 0.37/0.75 ( X
% 0.37/0.75 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.75 => ( Xa2 = one_one_nat ) )
% 0.37/0.75 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.75 => ( ( Deg2 = Xa2 )
% 0.37/0.75 & ! [X3: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 & ( case_o184042715313410164at_nat
% 0.37/0.75 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 @ ( produc6081775807080527818_nat_o
% 0.37/0.75 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.75 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 & ! [I3: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.37/0.75 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.37/0.75 & ( ( Mi3 = Ma3 )
% 0.37/0.75 => ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 & ( ( Mi3 != Ma3 )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.37/0.75 & ! [X4: nat] :
% 0.37/0.75 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 0.37/0.75 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.75 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.37/0.75 @ Mima2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % VEBT_internal.valid'.elims(3)
% 0.37/0.75 thf(fact_8857_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.75 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.37/0.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.75 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 0.37/0.75 => ( Xa2 = one_one_nat ) ) )
% 0.37/0.75 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.37/0.75 => ( ( Deg2 = Xa2 )
% 0.37/0.75 & ! [X3: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 & ( case_o184042715313410164at_nat
% 0.37/0.75 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 @ ( produc6081775807080527818_nat_o
% 0.37/0.75 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.75 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 & ! [I3: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.37/0.75 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.37/0.75 & ( ( Mi3 = Ma3 )
% 0.37/0.75 => ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 & ( ( Mi3 != Ma3 )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.37/0.75 & ! [X4: nat] :
% 0.37/0.75 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 0.37/0.75 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.75 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.37/0.75 @ Mima2 ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % VEBT_internal.valid'.pelims(3)
% 0.37/0.75 thf(fact_8858_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.37/0.75 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.37/0.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.75 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 0.37/0.75 => ( Xa2 != one_one_nat ) ) )
% 0.37/0.75 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 0.37/0.75 => ~ ( ( Deg2 = Xa2 )
% 0.37/0.75 & ! [X5: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 & ( case_o184042715313410164at_nat
% 0.37/0.75 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 @ ( produc6081775807080527818_nat_o
% 0.37/0.75 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.75 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 & ! [I3: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.37/0.75 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.37/0.75 & ( ( Mi3 = Ma3 )
% 0.37/0.75 => ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 & ( ( Mi3 != Ma3 )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.37/0.75 & ! [X4: nat] :
% 0.37/0.75 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 0.37/0.75 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.75 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.37/0.75 @ Mima2 ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % VEBT_internal.valid'.pelims(2)
% 0.37/0.75 thf(fact_8859_Sup__real__def,axiom,
% 0.37/0.75 ( comple1385675409528146559p_real
% 0.37/0.75 = ( ^ [X8: set_real] :
% 0.37/0.75 ( ord_Least_real
% 0.37/0.75 @ ^ [Z2: real] :
% 0.37/0.75 ! [X4: real] :
% 0.37/0.75 ( ( member_real @ X4 @ X8 )
% 0.37/0.75 => ( ord_less_eq_real @ X4 @ Z2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Sup_real_def
% 0.37/0.75 thf(fact_8860_Sup__int__def,axiom,
% 0.37/0.75 ( complete_Sup_Sup_int
% 0.37/0.75 = ( ^ [X8: set_int] :
% 0.37/0.75 ( the_int
% 0.37/0.75 @ ^ [X4: int] :
% 0.37/0.75 ( ( member_int @ X4 @ X8 )
% 0.37/0.75 & ! [Y4: int] :
% 0.37/0.75 ( ( member_int @ Y4 @ X8 )
% 0.37/0.75 => ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Sup_int_def
% 0.37/0.75 thf(fact_8861_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.37/0.75 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.37/0.75 = Y )
% 0.37/0.75 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.37/0.75 => ( ! [Uu: $o,Uv: $o] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Leaf @ Uu @ Uv ) )
% 0.37/0.75 => ( ( Y
% 0.37/0.75 = ( Xa2 = one_one_nat ) )
% 0.37/0.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 0.37/0.75 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.37/0.75 ( ( X
% 0.37/0.75 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 0.37/0.75 => ( ( Y
% 0.37/0.75 = ( ( Deg2 = Xa2 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.37/0.75 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 & ( case_o184042715313410164at_nat
% 0.37/0.75 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 0.37/0.75 & ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 @ ( produc6081775807080527818_nat_o
% 0.37/0.75 @ ^ [Mi3: nat,Ma3: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.37/0.75 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 & ! [I3: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.37/0.75 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 0.37/0.75 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 0.37/0.75 & ( ( Mi3 = Ma3 )
% 0.37/0.75 => ! [X4: vEBT_VEBT] :
% 0.37/0.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.37/0.75 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 0.37/0.75 & ( ( Mi3 != Ma3 )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.37/0.75 & ! [X4: nat] :
% 0.37/0.75 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.37/0.75 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 0.37/0.75 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.37/0.75 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.37/0.75 @ Mima2 ) ) )
% 0.37/0.75 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % VEBT_internal.valid'.pelims(1)
% 0.37/0.75 thf(fact_8862_set__bits__int__def,axiom,
% 0.37/0.75 ( bit_bi6516823479961619367ts_int
% 0.37/0.75 = ( ^ [F5: nat > $o] :
% 0.37/0.75 ( if_int
% 0.37/0.75 @ ? [N6: nat] :
% 0.37/0.75 ! [M5: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ M5 )
% 0.37/0.75 => ( ( F5 @ M5 )
% 0.37/0.75 = ( F5 @ N6 ) ) )
% 0.37/0.75 @ ( bit_ri631733984087533419it_int
% 0.37/0.75 @ ( ord_Least_nat
% 0.37/0.75 @ ^ [N6: nat] :
% 0.37/0.75 ! [M5: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ M5 )
% 0.37/0.75 => ( ( F5 @ M5 )
% 0.37/0.75 = ( F5 @ N6 ) ) ) )
% 0.37/0.75 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.37/0.75 @ ( map_nat_o @ F5
% 0.37/0.75 @ ( upt @ zero_zero_nat
% 0.37/0.75 @ ( suc
% 0.37/0.75 @ ( ord_Least_nat
% 0.37/0.75 @ ^ [N6: nat] :
% 0.37/0.75 ! [M5: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ M5 )
% 0.37/0.75 => ( ( F5 @ M5 )
% 0.37/0.75 = ( F5 @ N6 ) ) ) ) ) ) ) ) )
% 0.37/0.75 @ zero_zero_int ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % set_bits_int_def
% 0.37/0.75 thf(fact_8863_set__bits__int__unfold_H,axiom,
% 0.37/0.75 ( bit_bi6516823479961619367ts_int
% 0.37/0.75 = ( ^ [F5: nat > $o] :
% 0.37/0.75 ( if_int
% 0.37/0.75 @ ? [N6: nat] :
% 0.37/0.75 ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ~ ( F5 @ N11 ) )
% 0.37/0.75 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.37/0.75 @ ( map_nat_o @ F5
% 0.37/0.75 @ ( upt @ zero_zero_nat
% 0.37/0.75 @ ( ord_Least_nat
% 0.37/0.75 @ ^ [N6: nat] :
% 0.37/0.75 ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ~ ( F5 @ N11 ) ) ) ) ) )
% 0.37/0.75 @ ( if_int
% 0.37/0.75 @ ? [N6: nat] :
% 0.37/0.75 ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ( F5 @ N11 ) )
% 0.37/0.75 @ ( bit_ri631733984087533419it_int
% 0.37/0.75 @ ( ord_Least_nat
% 0.37/0.75 @ ^ [N6: nat] :
% 0.37/0.75 ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ( F5 @ N11 ) ) )
% 0.37/0.75 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.37/0.75 @ ( append_o
% 0.37/0.75 @ ( map_nat_o @ F5
% 0.37/0.75 @ ( upt @ zero_zero_nat
% 0.37/0.75 @ ( ord_Least_nat
% 0.37/0.75 @ ^ [N6: nat] :
% 0.37/0.75 ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ( F5 @ N11 ) ) ) ) )
% 0.37/0.75 @ ( cons_o @ $true @ nil_o ) ) ) )
% 0.37/0.75 @ zero_zero_int ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % set_bits_int_unfold'
% 0.37/0.75 thf(fact_8864_bin__last__set__bits,axiom,
% 0.37/0.75 ! [F: nat > $o] :
% 0.37/0.75 ( ( bit_wf_set_bits_int @ F )
% 0.37/0.75 => ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_bi6516823479961619367ts_int @ F ) ) )
% 0.37/0.75 = ( F @ zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bin_last_set_bits
% 0.37/0.75 thf(fact_8865_wf__set__bits__int__Suc,axiom,
% 0.37/0.75 ! [F: nat > $o] :
% 0.37/0.75 ( ( bit_wf_set_bits_int
% 0.37/0.75 @ ^ [N6: nat] : ( F @ ( suc @ N6 ) ) )
% 0.37/0.75 = ( bit_wf_set_bits_int @ F ) ) ).
% 0.37/0.75
% 0.37/0.75 % wf_set_bits_int_Suc
% 0.37/0.75 thf(fact_8866_wf__set__bits__int__simps,axiom,
% 0.37/0.75 ( bit_wf_set_bits_int
% 0.37/0.75 = ( ^ [F5: nat > $o] :
% 0.37/0.75 ? [N6: nat] :
% 0.37/0.75 ( ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ~ ( F5 @ N11 ) )
% 0.37/0.75 | ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ( F5 @ N11 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % wf_set_bits_int_simps
% 0.37/0.75 thf(fact_8867_zeros,axiom,
% 0.37/0.75 ! [N: nat,F: nat > $o] :
% 0.37/0.75 ( ! [N5: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N @ N5 )
% 0.37/0.75 => ~ ( F @ N5 ) )
% 0.37/0.75 => ( bit_wf_set_bits_int @ F ) ) ).
% 0.37/0.75
% 0.37/0.75 % zeros
% 0.37/0.75 thf(fact_8868_wf__set__bits__int_Osimps,axiom,
% 0.37/0.75 ( bit_wf_set_bits_int
% 0.37/0.75 = ( ^ [F5: nat > $o] :
% 0.37/0.75 ( ? [N6: nat] :
% 0.37/0.75 ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ~ ( F5 @ N11 ) )
% 0.37/0.75 | ? [N6: nat] :
% 0.37/0.75 ! [N11: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N6 @ N11 )
% 0.37/0.75 => ( F5 @ N11 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % wf_set_bits_int.simps
% 0.37/0.75 thf(fact_8869_wf__set__bits__int_Ocases,axiom,
% 0.37/0.75 ! [F: nat > $o] :
% 0.37/0.75 ( ( bit_wf_set_bits_int @ F )
% 0.37/0.75 => ( ! [N2: nat] :
% 0.37/0.75 ~ ! [N4: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.37/0.75 => ~ ( F @ N4 ) )
% 0.37/0.75 => ~ ! [N2: nat] :
% 0.37/0.75 ~ ! [N4: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N2 @ N4 )
% 0.37/0.75 => ( F @ N4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % wf_set_bits_int.cases
% 0.37/0.75 thf(fact_8870_ones,axiom,
% 0.37/0.75 ! [N: nat,F: nat > $o] :
% 0.37/0.75 ( ! [N5: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N @ N5 )
% 0.37/0.75 => ( F @ N5 ) )
% 0.37/0.75 => ( bit_wf_set_bits_int @ F ) ) ).
% 0.37/0.75
% 0.37/0.75 % ones
% 0.37/0.75 thf(fact_8871_int__set__bits__unfold__BIT,axiom,
% 0.37/0.75 ! [F: nat > $o] :
% 0.37/0.75 ( ( bit_wf_set_bits_int @ F )
% 0.37/0.75 => ( ( bit_bi6516823479961619367ts_int @ F )
% 0.37/0.75 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( F @ zero_zero_nat ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_bi6516823479961619367ts_int @ ( comp_nat_o_nat @ F @ suc ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % int_set_bits_unfold_BIT
% 0.37/0.75 thf(fact_8872_bin__rest__set__bits,axiom,
% 0.37/0.75 ! [F: nat > $o] :
% 0.37/0.75 ( ( bit_wf_set_bits_int @ F )
% 0.37/0.75 => ( ( divide_divide_int @ ( bit_bi6516823479961619367ts_int @ F ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.37/0.75 = ( bit_bi6516823479961619367ts_int @ ( comp_nat_o_nat @ F @ suc ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bin_rest_set_bits
% 0.37/0.75 thf(fact_8873_less__eq__char__simp,axiom,
% 0.37/0.75 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o,C0: $o,C1: $o,C22: $o,C32: $o,C42: $o,C52: $o,C62: $o,C7: $o] :
% 0.37/0.75 ( ( ord_less_eq_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) @ ( char2 @ C0 @ C1 @ C22 @ C32 @ C42 @ C52 @ C62 @ C7 ) )
% 0.37/0.75 = ( ord_less_eq_nat
% 0.37/0.75 @ ( foldr_o_nat
% 0.37/0.75 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.75 @ ( cons_o @ B0 @ ( cons_o @ B1 @ ( cons_o @ B22 @ ( cons_o @ B32 @ ( cons_o @ B42 @ ( cons_o @ B52 @ ( cons_o @ B62 @ ( cons_o @ B72 @ nil_o ) ) ) ) ) ) ) )
% 0.37/0.75 @ zero_zero_nat )
% 0.37/0.75 @ ( foldr_o_nat
% 0.37/0.75 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.75 @ ( cons_o @ C0 @ ( cons_o @ C1 @ ( cons_o @ C22 @ ( cons_o @ C32 @ ( cons_o @ C42 @ ( cons_o @ C52 @ ( cons_o @ C62 @ ( cons_o @ C7 @ nil_o ) ) ) ) ) ) ) )
% 0.37/0.75 @ zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % less_eq_char_simp
% 0.37/0.75 thf(fact_8874_less__char__simp,axiom,
% 0.37/0.75 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o,C0: $o,C1: $o,C22: $o,C32: $o,C42: $o,C52: $o,C62: $o,C7: $o] :
% 0.37/0.75 ( ( ord_less_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) @ ( char2 @ C0 @ C1 @ C22 @ C32 @ C42 @ C52 @ C62 @ C7 ) )
% 0.37/0.75 = ( ord_less_nat
% 0.37/0.75 @ ( foldr_o_nat
% 0.37/0.75 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.75 @ ( cons_o @ B0 @ ( cons_o @ B1 @ ( cons_o @ B22 @ ( cons_o @ B32 @ ( cons_o @ B42 @ ( cons_o @ B52 @ ( cons_o @ B62 @ ( cons_o @ B72 @ nil_o ) ) ) ) ) ) ) )
% 0.37/0.75 @ zero_zero_nat )
% 0.37/0.75 @ ( foldr_o_nat
% 0.37/0.75 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.37/0.75 @ ( cons_o @ C0 @ ( cons_o @ C1 @ ( cons_o @ C22 @ ( cons_o @ C32 @ ( cons_o @ C42 @ ( cons_o @ C52 @ ( cons_o @ C62 @ ( cons_o @ C7 @ nil_o ) ) ) ) ) ) ) )
% 0.37/0.75 @ zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % less_char_simp
% 0.37/0.75 thf(fact_8875_card_Ocomp__fun__commute__on,axiom,
% 0.37/0.75 ( ( comp_nat_nat_nat @ suc @ suc )
% 0.37/0.75 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 0.37/0.75
% 0.37/0.75 % card.comp_fun_commute_on
% 0.37/0.75 thf(fact_8876_infinite__int__iff__infinite__nat__abs,axiom,
% 0.37/0.75 ! [S3: set_int] :
% 0.37/0.75 ( ( ~ ( finite_finite_int @ S3 ) )
% 0.37/0.75 = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S3 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % infinite_int_iff_infinite_nat_abs
% 0.37/0.75 thf(fact_8877_Code__Numeral_Onegative__def,axiom,
% 0.37/0.75 ( code_negative
% 0.37/0.75 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 0.37/0.75
% 0.37/0.75 % Code_Numeral.negative_def
% 0.37/0.75 thf(fact_8878_divmod__integer__eq__cases,axiom,
% 0.37/0.75 ( code_divmod_integer
% 0.37/0.75 = ( ^ [K3: code_integer,L4: code_integer] :
% 0.37/0.75 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.37/0.75 @ ( if_Pro6119634080678213985nteger @ ( L4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.37/0.75 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L4
% 0.37/0.75 @ ( if_Pro6119634080678213985nteger
% 0.37/0.75 @ ( ( sgn_sgn_Code_integer @ K3 )
% 0.37/0.75 = ( sgn_sgn_Code_integer @ L4 ) )
% 0.37/0.75 @ ( code_divmod_abs @ K3 @ L4 )
% 0.37/0.75 @ ( produc6916734918728496179nteger
% 0.37/0.75 @ ^ [R5: code_integer,S8: code_integer] : ( if_Pro6119634080678213985nteger @ ( S8 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L4 ) @ S8 ) ) )
% 0.37/0.75 @ ( code_divmod_abs @ K3 @ L4 ) ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % divmod_integer_eq_cases
% 0.37/0.75 thf(fact_8879_divmod__abs__code_I6_J,axiom,
% 0.37/0.75 ! [J: code_integer] :
% 0.37/0.75 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 0.37/0.75 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.37/0.75
% 0.37/0.75 % divmod_abs_code(6)
% 0.37/0.75 thf(fact_8880_divmod__abs__code_I5_J,axiom,
% 0.37/0.75 ! [J: code_integer] :
% 0.37/0.75 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 0.37/0.75 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % divmod_abs_code(5)
% 0.37/0.75 thf(fact_8881_divmod__integer__code,axiom,
% 0.37/0.75 ( code_divmod_integer
% 0.37/0.75 = ( ^ [K3: code_integer,L4: code_integer] :
% 0.37/0.75 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.37/0.75 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L4 )
% 0.37/0.75 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L4 )
% 0.37/0.75 @ ( produc6916734918728496179nteger
% 0.37/0.75 @ ^ [R5: code_integer,S8: code_integer] : ( if_Pro6119634080678213985nteger @ ( S8 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L4 @ S8 ) ) )
% 0.37/0.75 @ ( code_divmod_abs @ K3 @ L4 ) ) )
% 0.37/0.75 @ ( if_Pro6119634080678213985nteger @ ( L4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.37/0.75 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.37/0.75 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L4 )
% 0.37/0.75 @ ( produc6916734918728496179nteger
% 0.37/0.75 @ ^ [R5: code_integer,S8: code_integer] : ( if_Pro6119634080678213985nteger @ ( S8 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L4 ) @ S8 ) ) )
% 0.37/0.75 @ ( code_divmod_abs @ K3 @ L4 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % divmod_integer_code
% 0.37/0.75 thf(fact_8882_divmod__abs__def,axiom,
% 0.37/0.75 ( code_divmod_abs
% 0.37/0.75 = ( ^ [K3: code_integer,L4: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L4 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L4 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % divmod_abs_def
% 0.37/0.75 thf(fact_8883_bit__cut__integer__code,axiom,
% 0.37/0.75 ( code_bit_cut_integer
% 0.37/0.75 = ( ^ [K3: code_integer] :
% 0.37/0.75 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.37/0.75 @ ( produc9125791028180074456eger_o
% 0.37/0.75 @ ^ [R5: code_integer,S8: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S8 ) ) @ ( S8 = one_one_Code_integer ) )
% 0.37/0.75 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bit_cut_integer_code
% 0.37/0.75 thf(fact_8884_bit__cut__integer__def,axiom,
% 0.37/0.75 ( code_bit_cut_integer
% 0.37/0.75 = ( ^ [K3: code_integer] :
% 0.37/0.75 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.37/0.75 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bit_cut_integer_def
% 0.37/0.75 thf(fact_8885_len__num0,axiom,
% 0.37/0.75 ( type_l4264026598287037464l_num0
% 0.37/0.75 = ( ^ [Uu4: itself_Numeral_num0] : zero_zero_nat ) ) ).
% 0.37/0.75
% 0.37/0.75 % len_num0
% 0.37/0.75 thf(fact_8886_smod__int__compares_I3_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.75 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(3)
% 0.37/0.75 thf(fact_8887_smod__int__compares_I5_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.75 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A @ B ) @ ( uminus_uminus_int @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(5)
% 0.37/0.75 thf(fact_8888_smod__int__compares_I1_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.75 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A @ B ) @ B ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(1)
% 0.37/0.75 thf(fact_8889_smod__int__compares_I2_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.75 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(2)
% 0.37/0.75 thf(fact_8890_smod__int__compares_I4_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.75 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(4)
% 0.37/0.75 thf(fact_8891_smod__int__compares_I6_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.75 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(6)
% 0.37/0.75 thf(fact_8892_smod__int__compares_I7_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.75 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(7)
% 0.37/0.75 thf(fact_8893_smod__int__compares_I8_J,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.37/0.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.37/0.75 => ( ord_less_eq_int @ B @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_int_compares(8)
% 0.37/0.75 thf(fact_8894_smod__mod__positive,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.37/0.75 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.37/0.75 => ( ( signed6292675348222524329lo_int @ A @ B )
% 0.37/0.75 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % smod_mod_positive
% 0.37/0.75 thf(fact_8895_min__Suc__Suc,axiom,
% 0.37/0.75 ! [M: nat,N: nat] :
% 0.37/0.75 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.37/0.75 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % min_Suc_Suc
% 0.37/0.75 thf(fact_8896_min__0R,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( ord_min_nat @ N @ zero_zero_nat )
% 0.37/0.75 = zero_zero_nat ) ).
% 0.37/0.75
% 0.37/0.75 % min_0R
% 0.37/0.75 thf(fact_8897_min__0L,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( ord_min_nat @ zero_zero_nat @ N )
% 0.37/0.75 = zero_zero_nat ) ).
% 0.37/0.75
% 0.37/0.75 % min_0L
% 0.37/0.75 thf(fact_8898_min__Suc__gt_I2_J,axiom,
% 0.37/0.75 ! [A: nat,B: nat] :
% 0.37/0.75 ( ( ord_less_nat @ A @ B )
% 0.37/0.75 => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 0.37/0.75 = ( suc @ A ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % min_Suc_gt(2)
% 0.37/0.75 thf(fact_8899_min__Suc__gt_I1_J,axiom,
% 0.37/0.75 ! [A: nat,B: nat] :
% 0.37/0.75 ( ( ord_less_nat @ A @ B )
% 0.37/0.75 => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 0.37/0.75 = ( suc @ A ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % min_Suc_gt(1)
% 0.37/0.75 thf(fact_8900_nat__mult__min__left,axiom,
% 0.37/0.75 ! [M: nat,N: nat,Q3: nat] :
% 0.37/0.75 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 0.37/0.75 = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % nat_mult_min_left
% 0.37/0.75 thf(fact_8901_nat__mult__min__right,axiom,
% 0.37/0.75 ! [M: nat,N: nat,Q3: nat] :
% 0.37/0.75 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 0.37/0.75 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % nat_mult_min_right
% 0.37/0.75 thf(fact_8902_inf__nat__def,axiom,
% 0.37/0.75 inf_inf_nat = ord_min_nat ).
% 0.37/0.75
% 0.37/0.75 % inf_nat_def
% 0.37/0.75 thf(fact_8903_min__diff,axiom,
% 0.37/0.75 ! [M: nat,I: nat,N: nat] :
% 0.37/0.75 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 0.37/0.75 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 0.37/0.75
% 0.37/0.75 % min_diff
% 0.37/0.75 thf(fact_8904_int__of__integer__min,axiom,
% 0.37/0.75 ! [K: code_integer,L: code_integer] :
% 0.37/0.75 ( ( code_int_of_integer @ ( ord_min_Code_integer @ K @ L ) )
% 0.37/0.75 = ( ord_min_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % int_of_integer_min
% 0.37/0.75 thf(fact_8905_drop__bit__nonnegative__int__iff,axiom,
% 0.37/0.75 ! [N: nat,K: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 0.37/0.75 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_nonnegative_int_iff
% 0.37/0.75 thf(fact_8906_drop__bit__negative__int__iff,axiom,
% 0.37/0.75 ! [N: nat,K: int] :
% 0.37/0.75 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 0.37/0.75 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_negative_int_iff
% 0.37/0.75 thf(fact_8907_drop__bit__Suc__minus__bit0,axiom,
% 0.37/0.75 ! [N: nat,K: num] :
% 0.37/0.75 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.37/0.75 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_Suc_minus_bit0
% 0.37/0.75 thf(fact_8908_drop__bit__Suc__minus__bit1,axiom,
% 0.37/0.75 ! [N: nat,K: num] :
% 0.37/0.75 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.37/0.75 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_Suc_minus_bit1
% 0.37/0.75 thf(fact_8909_drop__bit__of__Suc__0,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.37/0.75 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_of_Suc_0
% 0.37/0.75 thf(fact_8910_drop__bit__integer_Oabs__eq,axiom,
% 0.37/0.75 ! [Xa2: nat,X: int] :
% 0.37/0.75 ( ( bit_se3928097537394005634nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 0.37/0.75 = ( code_integer_of_int @ ( bit_se8568078237143864401it_int @ Xa2 @ X ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_integer.abs_eq
% 0.37/0.75 thf(fact_8911_drop__bit__integer_Orep__eq,axiom,
% 0.37/0.75 ! [X: nat,Xa2: code_integer] :
% 0.37/0.75 ( ( code_int_of_integer @ ( bit_se3928097537394005634nteger @ X @ Xa2 ) )
% 0.37/0.75 = ( bit_se8568078237143864401it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_integer.rep_eq
% 0.37/0.75 thf(fact_8912_mask__nat__positive__iff,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.37/0.75 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % mask_nat_positive_iff
% 0.37/0.75 thf(fact_8913_push__bit__nonnegative__int__iff,axiom,
% 0.37/0.75 ! [N: nat,K: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 0.37/0.75 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_nonnegative_int_iff
% 0.37/0.75 thf(fact_8914_push__bit__negative__int__iff,axiom,
% 0.37/0.75 ! [N: nat,K: int] :
% 0.37/0.75 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 0.37/0.75 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_negative_int_iff
% 0.37/0.75 thf(fact_8915_push__bit__of__Suc__0,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_of_Suc_0
% 0.37/0.75 thf(fact_8916_bit__push__bit__iff__int,axiom,
% 0.37/0.75 ! [M: nat,K: int,N: nat] :
% 0.37/0.75 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 0.37/0.75 = ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.75 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bit_push_bit_iff_int
% 0.37/0.75 thf(fact_8917_not__mask__negative__int,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 0.37/0.75
% 0.37/0.75 % not_mask_negative_int
% 0.37/0.75 thf(fact_8918_mask__nonnegative__int,axiom,
% 0.37/0.75 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % mask_nonnegative_int
% 0.37/0.75 thf(fact_8919_less__eq__mask,axiom,
% 0.37/0.75 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % less_eq_mask
% 0.37/0.75 thf(fact_8920_mask__integer_Orep__eq,axiom,
% 0.37/0.75 ! [X: nat] :
% 0.37/0.75 ( ( code_int_of_integer @ ( bit_se2119862282449309892nteger @ X ) )
% 0.37/0.75 = ( bit_se2000444600071755411sk_int @ X ) ) ).
% 0.37/0.75
% 0.37/0.75 % mask_integer.rep_eq
% 0.37/0.75 thf(fact_8921_push__bit__integer_Orep__eq,axiom,
% 0.37/0.75 ! [X: nat,Xa2: code_integer] :
% 0.37/0.75 ( ( code_int_of_integer @ ( bit_se7788150548672797655nteger @ X @ Xa2 ) )
% 0.37/0.75 = ( bit_se545348938243370406it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_integer.rep_eq
% 0.37/0.75 thf(fact_8922_mask__integer_Oabs__eq,axiom,
% 0.37/0.75 ( bit_se2119862282449309892nteger
% 0.37/0.75 = ( ^ [X4: nat] : ( code_integer_of_int @ ( bit_se2000444600071755411sk_int @ X4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % mask_integer.abs_eq
% 0.37/0.75 thf(fact_8923_push__bit__integer_Oabs__eq,axiom,
% 0.37/0.75 ! [Xa2: nat,X: int] :
% 0.37/0.75 ( ( bit_se7788150548672797655nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 0.37/0.75 = ( code_integer_of_int @ ( bit_se545348938243370406it_int @ Xa2 @ X ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_integer.abs_eq
% 0.37/0.75 thf(fact_8924_less__mask,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.75 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % less_mask
% 0.37/0.75 thf(fact_8925_bit__push__bit__iff__nat,axiom,
% 0.37/0.75 ! [M: nat,Q3: nat,N: nat] :
% 0.37/0.75 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 0.37/0.75 = ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.75 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bit_push_bit_iff_nat
% 0.37/0.75 thf(fact_8926_Suc__mask__eq__exp,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % Suc_mask_eq_exp
% 0.37/0.75 thf(fact_8927_mask__nat__less__exp,axiom,
% 0.37/0.75 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % mask_nat_less_exp
% 0.37/0.75 thf(fact_8928_and__nonnegative__int__iff,axiom,
% 0.37/0.75 ! [K: int,L: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 0.37/0.75 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.37/0.75 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % and_nonnegative_int_iff
% 0.37/0.75 thf(fact_8929_and__negative__int__iff,axiom,
% 0.37/0.75 ! [K: int,L: int] :
% 0.37/0.75 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 0.37/0.75 = ( ( ord_less_int @ K @ zero_zero_int )
% 0.37/0.75 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % and_negative_int_iff
% 0.37/0.75 thf(fact_8930_AND__upper2_H_H,axiom,
% 0.37/0.75 ! [Y: int,Z: int,X: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( ( ord_less_int @ Y @ Z )
% 0.37/0.75 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % AND_upper2''
% 0.37/0.75 thf(fact_8931_AND__upper1_H_H,axiom,
% 0.37/0.75 ! [Y: int,Z: int,Ya: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( ( ord_less_int @ Y @ Z )
% 0.37/0.75 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % AND_upper1''
% 0.37/0.75 thf(fact_8932_and__less__eq,axiom,
% 0.37/0.75 ! [L: int,K: int] :
% 0.37/0.75 ( ( ord_less_int @ L @ zero_zero_int )
% 0.37/0.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 0.37/0.75
% 0.37/0.75 % and_less_eq
% 0.37/0.75 thf(fact_8933_AND__upper2_H,axiom,
% 0.37/0.75 ! [Y: int,Z: int,X: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( ( ord_less_eq_int @ Y @ Z )
% 0.37/0.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % AND_upper2'
% 0.37/0.75 thf(fact_8934_AND__upper1_H,axiom,
% 0.37/0.75 ! [Y: int,Z: int,Ya: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( ( ord_less_eq_int @ Y @ Z )
% 0.37/0.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % AND_upper1'
% 0.37/0.75 thf(fact_8935_AND__upper2,axiom,
% 0.37/0.75 ! [Y: int,X: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 0.37/0.75
% 0.37/0.75 % AND_upper2
% 0.37/0.75 thf(fact_8936_AND__upper1,axiom,
% 0.37/0.75 ! [X: int,Y: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 0.37/0.75
% 0.37/0.75 % AND_upper1
% 0.37/0.75 thf(fact_8937_AND__lower,axiom,
% 0.37/0.75 ! [X: int,Y: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.75 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % AND_lower
% 0.37/0.75 thf(fact_8938_drop__bit__int__code_I2_J,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ zero_zero_int )
% 0.37/0.75 = zero_zero_int ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_int_code(2)
% 0.37/0.75 thf(fact_8939_and__nat__numerals_I1_J,axiom,
% 0.37/0.75 ! [Y: num] :
% 0.37/0.75 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.37/0.75 = zero_zero_nat ) ).
% 0.37/0.75
% 0.37/0.75 % and_nat_numerals(1)
% 0.37/0.75 thf(fact_8940_and__nat__numerals_I3_J,axiom,
% 0.37/0.75 ! [X: num] :
% 0.37/0.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.75 = zero_zero_nat ) ).
% 0.37/0.75
% 0.37/0.75 % and_nat_numerals(3)
% 0.37/0.75 thf(fact_8941_and__nat__numerals_I4_J,axiom,
% 0.37/0.75 ! [X: num] :
% 0.37/0.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.37/0.75 = one_one_nat ) ).
% 0.37/0.75
% 0.37/0.75 % and_nat_numerals(4)
% 0.37/0.75 thf(fact_8942_and__nat__numerals_I2_J,axiom,
% 0.37/0.75 ! [Y: num] :
% 0.37/0.75 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.37/0.75 = one_one_nat ) ).
% 0.37/0.75
% 0.37/0.75 % and_nat_numerals(2)
% 0.37/0.75 thf(fact_8943_and__Suc__0__eq,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.37/0.75 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % and_Suc_0_eq
% 0.37/0.75 thf(fact_8944_Suc__0__and__eq,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.75 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Suc_0_and_eq
% 0.37/0.75 thf(fact_8945_and__integer_Orep__eq,axiom,
% 0.37/0.75 ! [X: code_integer,Xa2: code_integer] :
% 0.37/0.75 ( ( code_int_of_integer @ ( bit_se3949692690581998587nteger @ X @ Xa2 ) )
% 0.37/0.75 = ( bit_se725231765392027082nd_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % and_integer.rep_eq
% 0.37/0.75 thf(fact_8946_and__integer_Oabs__eq,axiom,
% 0.37/0.75 ! [Xa2: int,X: int] :
% 0.37/0.75 ( ( bit_se3949692690581998587nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.37/0.75 = ( code_integer_of_int @ ( bit_se725231765392027082nd_int @ Xa2 @ X ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % and_integer.abs_eq
% 0.37/0.75 thf(fact_8947_and__nat__unfold,axiom,
% 0.37/0.75 ( bit_se727722235901077358nd_nat
% 0.37/0.75 = ( ^ [M5: nat,N6: nat] :
% 0.37/0.75 ( if_nat
% 0.37/0.75 @ ( ( M5 = zero_zero_nat )
% 0.37/0.75 | ( N6 = zero_zero_nat ) )
% 0.37/0.75 @ zero_zero_nat
% 0.37/0.75 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % and_nat_unfold
% 0.37/0.75 thf(fact_8948_drop__bit__int__code_I1_J,axiom,
% 0.37/0.75 ! [I: int] :
% 0.37/0.75 ( ( bit_se8568078237143864401it_int @ zero_zero_nat @ I )
% 0.37/0.75 = I ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_int_code(1)
% 0.37/0.75 thf(fact_8949_push__bit__int__code_I1_J,axiom,
% 0.37/0.75 ! [I: int] :
% 0.37/0.75 ( ( bit_se545348938243370406it_int @ zero_zero_nat @ I )
% 0.37/0.75 = I ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_int_code(1)
% 0.37/0.75 thf(fact_8950_not__negative__int__iff,axiom,
% 0.37/0.75 ! [K: int] :
% 0.37/0.75 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 0.37/0.75 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 0.37/0.75
% 0.37/0.75 % not_negative_int_iff
% 0.37/0.75 thf(fact_8951_not__nonnegative__int__iff,axiom,
% 0.37/0.75 ! [K: int] :
% 0.37/0.75 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 0.37/0.75 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 0.37/0.75
% 0.37/0.75 % not_nonnegative_int_iff
% 0.37/0.75 thf(fact_8952_not__integer_Oabs__eq,axiom,
% 0.37/0.75 ! [X: int] :
% 0.37/0.75 ( ( bit_ri7632146776885996613nteger @ ( code_integer_of_int @ X ) )
% 0.37/0.75 = ( code_integer_of_int @ ( bit_ri7919022796975470100ot_int @ X ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % not_integer.abs_eq
% 0.37/0.75 thf(fact_8953_not__integer_Orep__eq,axiom,
% 0.37/0.75 ! [X: code_integer] :
% 0.37/0.75 ( ( code_int_of_integer @ ( bit_ri7632146776885996613nteger @ X ) )
% 0.37/0.75 = ( bit_ri7919022796975470100ot_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % not_integer.rep_eq
% 0.37/0.75 thf(fact_8954_shiftl__Suc__0,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( bit_Sh3965577149348748681tl_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % shiftl_Suc_0
% 0.37/0.75 thf(fact_8955_shiftr__Suc__0,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( bit_Sh2154871086232339855tr_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.37/0.75 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % shiftr_Suc_0
% 0.37/0.75 thf(fact_8956_not__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ bit_ri7919022796975470100ot_int
% 0.37/0.75 @ bit_ri7919022796975470100ot_int ) ).
% 0.37/0.75
% 0.37/0.75 % not_integer.rsp
% 0.37/0.75 thf(fact_8957_xor__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se6526347334894502574or_int
% 0.37/0.75 @ bit_se6526347334894502574or_int ) ).
% 0.37/0.75
% 0.37/0.75 % xor_integer.rsp
% 0.37/0.75 thf(fact_8958_less__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re3403563459893282935_int_o
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5089333283451836215nt_o_o
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 0.37/0.75 @ ord_less_int
% 0.37/0.75 @ ord_less_int ) ).
% 0.37/0.75
% 0.37/0.75 % less_integer.rsp
% 0.37/0.75 thf(fact_8959_less__eq__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re3403563459893282935_int_o
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5089333283451836215nt_o_o
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 0.37/0.75 @ ord_less_eq_int
% 0.37/0.75 @ ord_less_eq_int ) ).
% 0.37/0.75
% 0.37/0.75 % less_eq_integer.rsp
% 0.37/0.75 thf(fact_8960_minus__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ minus_minus_int
% 0.37/0.75 @ minus_minus_int ) ).
% 0.37/0.75
% 0.37/0.75 % minus_integer.rsp
% 0.37/0.75 thf(fact_8961_dup_Orsp,axiom,
% 0.37/0.75 ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
% 0.37/0.75 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).
% 0.37/0.75
% 0.37/0.75 % dup.rsp
% 0.37/0.75 thf(fact_8962_bit__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re3376528473927230327_nat_o
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat > $o,Z4: nat > $o] : ( Y6 = Z4 )
% 0.37/0.75 @ bit_se1146084159140164899it_int
% 0.37/0.75 @ bit_se1146084159140164899it_int ) ).
% 0.37/0.75
% 0.37/0.75 % bit_integer.rsp
% 0.37/0.75 thf(fact_8963_abs__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ abs_abs_int
% 0.37/0.75 @ abs_abs_int ) ).
% 0.37/0.75
% 0.37/0.75 % abs_integer.rsp
% 0.37/0.75 thf(fact_8964_sgn__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ sgn_sgn_int
% 0.37/0.75 @ sgn_sgn_int ) ).
% 0.37/0.75
% 0.37/0.75 % sgn_integer.rsp
% 0.37/0.75 thf(fact_8965_natural__of__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re3715656647883201625at_nat
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ nat2
% 0.37/0.75 @ nat2 ) ).
% 0.37/0.75
% 0.37/0.75 % natural_of_integer.rsp
% 0.37/0.75 thf(fact_8966_divide__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ divide_divide_int
% 0.37/0.75 @ divide_divide_int ) ).
% 0.37/0.75
% 0.37/0.75 % divide_integer.rsp
% 0.37/0.75 thf(fact_8967_modulo__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ modulo_modulo_int
% 0.37/0.75 @ modulo_modulo_int ) ).
% 0.37/0.75
% 0.37/0.75 % modulo_integer.rsp
% 0.37/0.75 thf(fact_8968_uminus__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ uminus_uminus_int
% 0.37/0.75 @ uminus_uminus_int ) ).
% 0.37/0.75
% 0.37/0.75 % uminus_integer.rsp
% 0.37/0.75 thf(fact_8969_plus__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ plus_plus_int
% 0.37/0.75 @ plus_plus_int ) ).
% 0.37/0.75
% 0.37/0.75 % plus_integer.rsp
% 0.37/0.75 thf(fact_8970_times__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ times_times_int
% 0.37/0.75 @ times_times_int ) ).
% 0.37/0.75
% 0.37/0.75 % times_integer.rsp
% 0.37/0.75 thf(fact_8971_or__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se1409905431419307370or_int
% 0.37/0.75 @ bit_se1409905431419307370or_int ) ).
% 0.37/0.75
% 0.37/0.75 % or_integer.rsp
% 0.37/0.75 thf(fact_8972_and__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re711492959462206631nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se725231765392027082nd_int
% 0.37/0.75 @ bit_se725231765392027082nd_int ) ).
% 0.37/0.75
% 0.37/0.75 % and_integer.rsp
% 0.37/0.75 thf(fact_8973_xor__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se6528837805403552850or_nat
% 0.37/0.75 @ bit_se6528837805403552850or_nat ) ).
% 0.37/0.75
% 0.37/0.75 % xor_natural.rsp
% 0.37/0.75 thf(fact_8974_drop__bit__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4785983289428654063nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se8568078237143864401it_int
% 0.37/0.75 @ bit_se8568078237143864401it_int ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_integer.rsp
% 0.37/0.75 thf(fact_8975_drop__bit__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se8570568707652914677it_nat
% 0.37/0.75 @ bit_se8570568707652914677it_nat ) ).
% 0.37/0.75
% 0.37/0.75 % drop_bit_natural.rsp
% 0.37/0.75 thf(fact_8976_take__bit__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4785983289428654063nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se2923211474154528505it_int
% 0.37/0.75 @ bit_se2923211474154528505it_int ) ).
% 0.37/0.75
% 0.37/0.75 % take_bit_integer.rsp
% 0.37/0.75 thf(fact_8977_take__bit__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se2925701944663578781it_nat
% 0.37/0.75 @ bit_se2925701944663578781it_nat ) ).
% 0.37/0.75
% 0.37/0.75 % take_bit_natural.rsp
% 0.37/0.75 thf(fact_8978_less__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re578469030762574527_nat_o
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4705727531993890431at_o_o
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 0.37/0.75 @ ord_less_nat
% 0.37/0.75 @ ord_less_nat ) ).
% 0.37/0.75
% 0.37/0.75 % less_natural.rsp
% 0.37/0.75 thf(fact_8979_less__eq__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re578469030762574527_nat_o
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4705727531993890431at_o_o
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 0.37/0.75 @ ord_less_eq_nat
% 0.37/0.75 @ ord_less_eq_nat ) ).
% 0.37/0.75
% 0.37/0.75 % less_eq_natural.rsp
% 0.37/0.75 thf(fact_8980_inj__on__diff__nat,axiom,
% 0.37/0.75 ! [N8: set_nat,K: nat] :
% 0.37/0.75 ( ! [N2: nat] :
% 0.37/0.75 ( ( member_nat @ N2 @ N8 )
% 0.37/0.75 => ( ord_less_eq_nat @ K @ N2 ) )
% 0.37/0.75 => ( inj_on_nat_nat
% 0.37/0.75 @ ^ [N6: nat] : ( minus_minus_nat @ N6 @ K )
% 0.37/0.75 @ N8 ) ) ).
% 0.37/0.75
% 0.37/0.75 % inj_on_diff_nat
% 0.37/0.75 thf(fact_8981_minus__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ minus_minus_nat
% 0.37/0.75 @ minus_minus_nat ) ).
% 0.37/0.75
% 0.37/0.75 % minus_natural.rsp
% 0.37/0.75 thf(fact_8982_sub_Orsp,axiom,
% 0.37/0.75 ( bNF_re8402795839162346335um_int
% 0.37/0.75 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re1822329894187522285nt_int
% 0.37/0.75 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ ^ [M5: num,N6: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) )
% 0.37/0.75 @ ^ [M5: num,N6: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % sub.rsp
% 0.37/0.75 thf(fact_8983_bit__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re578469030762574527_nat_o
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat > $o,Z4: nat > $o] : ( Y6 = Z4 )
% 0.37/0.75 @ bit_se1148574629649215175it_nat
% 0.37/0.75 @ bit_se1148574629649215175it_nat ) ).
% 0.37/0.75
% 0.37/0.75 % bit_natural.rsp
% 0.37/0.75 thf(fact_8984_unset__bit__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4785983289428654063nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se4203085406695923979it_int
% 0.37/0.75 @ bit_se4203085406695923979it_int ) ).
% 0.37/0.75
% 0.37/0.75 % unset_bit_integer.rsp
% 0.37/0.75 thf(fact_8985_flip__bit__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4785983289428654063nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se2159334234014336723it_int
% 0.37/0.75 @ bit_se2159334234014336723it_int ) ).
% 0.37/0.75
% 0.37/0.75 % flip_bit_integer.rsp
% 0.37/0.75 thf(fact_8986_inj__Suc,axiom,
% 0.37/0.75 ! [N8: set_nat] : ( inj_on_nat_nat @ suc @ N8 ) ).
% 0.37/0.75
% 0.37/0.75 % inj_Suc
% 0.37/0.75 thf(fact_8987_Suc_Orsp,axiom,
% 0.37/0.75 ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ suc
% 0.37/0.75 @ suc ) ).
% 0.37/0.75
% 0.37/0.75 % Suc.rsp
% 0.37/0.75 thf(fact_8988_divide__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ divide_divide_nat
% 0.37/0.75 @ divide_divide_nat ) ).
% 0.37/0.75
% 0.37/0.75 % divide_natural.rsp
% 0.37/0.75 thf(fact_8989_modulo__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ modulo_modulo_nat
% 0.37/0.75 @ modulo_modulo_nat ) ).
% 0.37/0.75
% 0.37/0.75 % modulo_natural.rsp
% 0.37/0.75 thf(fact_8990_Code__Numeral_Oset__bit__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4785983289428654063nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se7879613467334960850it_int
% 0.37/0.75 @ bit_se7879613467334960850it_int ) ).
% 0.37/0.75
% 0.37/0.75 % Code_Numeral.set_bit_integer.rsp
% 0.37/0.75 thf(fact_8991_plus__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ plus_plus_nat
% 0.37/0.75 @ plus_plus_nat ) ).
% 0.37/0.75
% 0.37/0.75 % plus_natural.rsp
% 0.37/0.75 thf(fact_8992_times__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ times_times_nat
% 0.37/0.75 @ times_times_nat ) ).
% 0.37/0.75
% 0.37/0.75 % times_natural.rsp
% 0.37/0.75 thf(fact_8993_or__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se1412395901928357646or_nat
% 0.37/0.75 @ bit_se1412395901928357646or_nat ) ).
% 0.37/0.75
% 0.37/0.75 % or_natural.rsp
% 0.37/0.75 thf(fact_8994_integer__of__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re6650684261131312217nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ semiri1314217659103216013at_int
% 0.37/0.75 @ semiri1314217659103216013at_int ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_natural.rsp
% 0.37/0.75 thf(fact_8995_inj__on__set__encode,axiom,
% 0.37/0.75 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 0.37/0.75
% 0.37/0.75 % inj_on_set_encode
% 0.37/0.75 thf(fact_8996_mask__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re6650684261131312217nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ bit_se2000444600071755411sk_int
% 0.37/0.75 @ bit_se2000444600071755411sk_int ) ).
% 0.37/0.75
% 0.37/0.75 % mask_integer.rsp
% 0.37/0.75 thf(fact_8997_mask__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ bit_se2002935070580805687sk_nat
% 0.37/0.75 @ bit_se2002935070580805687sk_nat ) ).
% 0.37/0.75
% 0.37/0.75 % mask_natural.rsp
% 0.37/0.75 thf(fact_8998_push__bit__integer_Orsp,axiom,
% 0.37/0.75 ( bNF_re4785983289428654063nt_int
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re4712519889275205905nt_int
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se545348938243370406it_int
% 0.37/0.75 @ bit_se545348938243370406it_int ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_integer.rsp
% 0.37/0.75 thf(fact_8999_push__bit__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se547839408752420682it_nat
% 0.37/0.75 @ bit_se547839408752420682it_nat ) ).
% 0.37/0.75
% 0.37/0.75 % push_bit_natural.rsp
% 0.37/0.75 thf(fact_9000_and__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se727722235901077358nd_nat
% 0.37/0.75 @ bit_se727722235901077358nd_nat ) ).
% 0.37/0.75
% 0.37/0.75 % and_natural.rsp
% 0.37/0.75 thf(fact_9001_summable__reindex,axiom,
% 0.37/0.75 ! [F: nat > real,G: nat > nat] :
% 0.37/0.75 ( ( summable_real @ F )
% 0.37/0.75 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.37/0.75 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.37/0.75 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % summable_reindex
% 0.37/0.75 thf(fact_9002_suminf__reindex__mono,axiom,
% 0.37/0.75 ! [F: nat > real,G: nat > nat] :
% 0.37/0.75 ( ( summable_real @ F )
% 0.37/0.75 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.37/0.75 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.37/0.75 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % suminf_reindex_mono
% 0.37/0.75 thf(fact_9003_suminf__reindex,axiom,
% 0.37/0.75 ! [F: nat > real,G: nat > nat] :
% 0.37/0.75 ( ( summable_real @ F )
% 0.37/0.75 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 0.37/0.75 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 0.37/0.75 => ( ! [X3: nat] :
% 0.37/0.75 ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 0.37/0.75 => ( ( F @ X3 )
% 0.37/0.75 = zero_zero_real ) )
% 0.37/0.75 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 0.37/0.75 = ( suminf_real @ F ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % suminf_reindex
% 0.37/0.75 thf(fact_9004_inj__sgn__power,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.75 => ( inj_on_real_real
% 0.37/0.75 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 0.37/0.75 @ top_top_set_real ) ) ).
% 0.37/0.75
% 0.37/0.75 % inj_sgn_power
% 0.37/0.75 thf(fact_9005_unset__bit__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se4205575877204974255it_nat
% 0.37/0.75 @ bit_se4205575877204974255it_nat ) ).
% 0.37/0.75
% 0.37/0.75 % unset_bit_natural.rsp
% 0.37/0.75 thf(fact_9006_flip__bit__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se2161824704523386999it_nat
% 0.37/0.75 @ bit_se2161824704523386999it_nat ) ).
% 0.37/0.75
% 0.37/0.75 % flip_bit_natural.rsp
% 0.37/0.75 thf(fact_9007_set__bit__natural_Orsp,axiom,
% 0.37/0.75 ( bNF_re1345281282404953727at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5653821019739307937at_nat
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 0.37/0.75 @ bit_se7882103937844011126it_nat
% 0.37/0.75 @ bit_se7882103937844011126it_nat ) ).
% 0.37/0.75
% 0.37/0.75 % set_bit_natural.rsp
% 0.37/0.75 thf(fact_9008_integer__of__num_I3_J,axiom,
% 0.37/0.75 ! [N: num] :
% 0.37/0.75 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 0.37/0.75 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_num(3)
% 0.37/0.75 thf(fact_9009_integer__of__num__def,axiom,
% 0.37/0.75 code_integer_of_num = numera6620942414471956472nteger ).
% 0.37/0.75
% 0.37/0.75 % integer_of_num_def
% 0.37/0.75 thf(fact_9010_integer__of__num__triv_I1_J,axiom,
% 0.37/0.75 ( ( code_integer_of_num @ one )
% 0.37/0.75 = one_one_Code_integer ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_num_triv(1)
% 0.37/0.75 thf(fact_9011_integer__of__num_I2_J,axiom,
% 0.37/0.75 ! [N: num] :
% 0.37/0.75 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 0.37/0.75 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_num(2)
% 0.37/0.75 thf(fact_9012_integer__of__num__triv_I2_J,axiom,
% 0.37/0.75 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 0.37/0.75 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_num_triv(2)
% 0.37/0.75 thf(fact_9013_hd__upt,axiom,
% 0.37/0.75 ! [I: nat,J: nat] :
% 0.37/0.75 ( ( ord_less_nat @ I @ J )
% 0.37/0.75 => ( ( hd_nat @ ( upt @ I @ J ) )
% 0.37/0.75 = I ) ) ).
% 0.37/0.75
% 0.37/0.75 % hd_upt
% 0.37/0.75 thf(fact_9014_Suc__0__div__numeral,axiom,
% 0.37/0.75 ! [K: num] :
% 0.37/0.75 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.37/0.75 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Suc_0_div_numeral
% 0.37/0.75 thf(fact_9015_fst__divmod__nat,axiom,
% 0.37/0.75 ! [M: nat,N: nat] :
% 0.37/0.75 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 0.37/0.75 = ( divide_divide_nat @ M @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % fst_divmod_nat
% 0.37/0.75 thf(fact_9016_fst__divmod__integer,axiom,
% 0.37/0.75 ! [K: code_integer,L: code_integer] :
% 0.37/0.75 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 0.37/0.75 = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 0.37/0.75
% 0.37/0.75 % fst_divmod_integer
% 0.37/0.75 thf(fact_9017_fst__divmod__abs,axiom,
% 0.37/0.75 ! [K: code_integer,L: code_integer] :
% 0.37/0.75 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 0.37/0.75 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % fst_divmod_abs
% 0.37/0.75 thf(fact_9018_bezw_Oelims,axiom,
% 0.37/0.75 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 0.37/0.75 ( ( ( bezw @ X @ Xa2 )
% 0.37/0.75 = Y )
% 0.37/0.75 => ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.37/0.75 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bezw.elims
% 0.37/0.75 thf(fact_9019_bezw_Osimps,axiom,
% 0.37/0.75 ( bezw
% 0.37/0.75 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bezw.simps
% 0.37/0.75 thf(fact_9020_bezw__non__0,axiom,
% 0.37/0.75 ! [Y: nat,X: nat] :
% 0.37/0.75 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 0.37/0.75 => ( ( bezw @ X @ Y )
% 0.37/0.75 = ( 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 ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bezw_non_0
% 0.37/0.75 thf(fact_9021_bezw_Opelims,axiom,
% 0.37/0.75 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 0.37/0.75 ( ( ( bezw @ X @ Xa2 )
% 0.37/0.75 = Y )
% 0.37/0.75 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.37/0.75 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.37/0.75 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( 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 ) ) ) ) ) ) ) )
% 0.37/0.75 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bezw.pelims
% 0.37/0.75 thf(fact_9022_snd__divmod__nat,axiom,
% 0.37/0.75 ! [M: nat,N: nat] :
% 0.37/0.75 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 0.37/0.75 = ( modulo_modulo_nat @ M @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % snd_divmod_nat
% 0.37/0.75 thf(fact_9023_snd__divmod__integer,axiom,
% 0.37/0.75 ! [K: code_integer,L: code_integer] :
% 0.37/0.75 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 0.37/0.75 = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 0.37/0.75
% 0.37/0.75 % snd_divmod_integer
% 0.37/0.75 thf(fact_9024_mod__pure,axiom,
% 0.37/0.75 ! [B: $o,H2: produc3658429121746597890et_nat] :
% 0.37/0.75 ( ( rep_assn @ ( pure_assn @ B ) @ H2 )
% 0.37/0.75 = ( ( ( produc8586169260539613262et_nat @ H2 )
% 0.37/0.75 = bot_bot_set_nat )
% 0.37/0.75 & B ) ) ).
% 0.37/0.75
% 0.37/0.75 % mod_pure
% 0.37/0.75 thf(fact_9025_snd__divmod__abs,axiom,
% 0.37/0.75 ! [K: code_integer,L: code_integer] :
% 0.37/0.75 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 0.37/0.75 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % snd_divmod_abs
% 0.37/0.75 thf(fact_9026_Suc__0__mod__numeral,axiom,
% 0.37/0.75 ! [K: num] :
% 0.37/0.75 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 0.37/0.75 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Suc_0_mod_numeral
% 0.37/0.75 thf(fact_9027_mod__emp,axiom,
% 0.37/0.75 ! [H2: produc3658429121746597890et_nat] :
% 0.37/0.75 ( ( rep_assn @ one_one_assn @ H2 )
% 0.37/0.75 = ( ( produc8586169260539613262et_nat @ H2 )
% 0.37/0.75 = bot_bot_set_nat ) ) ).
% 0.37/0.75
% 0.37/0.75 % mod_emp
% 0.37/0.75 thf(fact_9028_mod__star__trueE_H,axiom,
% 0.37/0.75 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 0.37/0.75 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 )
% 0.37/0.75 => ~ ! [H5: produc3658429121746597890et_nat] :
% 0.37/0.75 ( ( ( produc1824681642469235216et_nat @ H5 )
% 0.37/0.75 = ( produc1824681642469235216et_nat @ H2 ) )
% 0.37/0.75 => ( ( ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ H5 ) @ ( produc8586169260539613262et_nat @ H2 ) )
% 0.37/0.75 => ~ ( rep_assn @ P2 @ H5 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % mod_star_trueE'
% 0.37/0.75 thf(fact_9029_one__mod__minus__numeral,axiom,
% 0.37/0.75 ! [N: num] :
% 0.37/0.75 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.75 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % one_mod_minus_numeral
% 0.37/0.75 thf(fact_9030_minus__one__mod__numeral,axiom,
% 0.37/0.75 ! [N: num] :
% 0.37/0.75 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.75 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % minus_one_mod_numeral
% 0.37/0.75 thf(fact_9031_numeral__mod__minus__numeral,axiom,
% 0.37/0.75 ! [M: num,N: num] :
% 0.37/0.75 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.37/0.75 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % numeral_mod_minus_numeral
% 0.37/0.75 thf(fact_9032_minus__numeral__mod__numeral,axiom,
% 0.37/0.75 ! [M: num,N: num] :
% 0.37/0.75 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.37/0.75 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % minus_numeral_mod_numeral
% 0.37/0.75 thf(fact_9033_Divides_Oadjust__mod__def,axiom,
% 0.37/0.75 ( adjust_mod
% 0.37/0.75 = ( ^ [L4: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L4 @ R5 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Divides.adjust_mod_def
% 0.37/0.75 thf(fact_9034_normalize__def,axiom,
% 0.37/0.75 ( normalize
% 0.37/0.75 = ( ^ [P7: product_prod_int_int] :
% 0.37/0.75 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P7 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P7 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P7 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) )
% 0.37/0.75 @ ( if_Pro3027730157355071871nt_int
% 0.37/0.75 @ ( ( product_snd_int_int @ P7 )
% 0.37/0.75 = zero_zero_int )
% 0.37/0.75 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.37/0.75 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P7 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P7 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % normalize_def
% 0.37/0.75 thf(fact_9035_gcd__pos__int,axiom,
% 0.37/0.75 ! [M: int,N: int] :
% 0.37/0.75 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 0.37/0.75 = ( ( M != zero_zero_int )
% 0.37/0.75 | ( N != zero_zero_int ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_pos_int
% 0.37/0.75 thf(fact_9036_gcd__le1__int,axiom,
% 0.37/0.75 ! [A: int,B: int] :
% 0.37/0.75 ( ( ord_less_int @ zero_zero_int @ A )
% 0.37/0.75 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_le1_int
% 0.37/0.75 thf(fact_9037_gcd__le2__int,axiom,
% 0.37/0.75 ! [B: int,A: int] :
% 0.37/0.75 ( ( ord_less_int @ zero_zero_int @ B )
% 0.37/0.75 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_le2_int
% 0.37/0.75 thf(fact_9038_gcd__cases__int,axiom,
% 0.37/0.75 ! [X: int,Y: int,P2: int > $o] :
% 0.37/0.75 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.75 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( P2 @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 0.37/0.75 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.37/0.75 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.37/0.75 => ( P2 @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.37/0.75 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.37/0.75 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( P2 @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 0.37/0.75 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.37/0.75 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.37/0.75 => ( P2 @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.37/0.75 => ( P2 @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_cases_int
% 0.37/0.75 thf(fact_9039_gcd__ge__0__int,axiom,
% 0.37/0.75 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_ge_0_int
% 0.37/0.75 thf(fact_9040_gcd__unique__int,axiom,
% 0.37/0.75 ! [D: int,A: int,B: int] :
% 0.37/0.75 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 0.37/0.75 & ( dvd_dvd_int @ D @ A )
% 0.37/0.75 & ( dvd_dvd_int @ D @ B )
% 0.37/0.75 & ! [E3: int] :
% 0.37/0.75 ( ( ( dvd_dvd_int @ E3 @ A )
% 0.37/0.75 & ( dvd_dvd_int @ E3 @ B ) )
% 0.37/0.75 => ( dvd_dvd_int @ E3 @ D ) ) )
% 0.37/0.75 = ( D
% 0.37/0.75 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_unique_int
% 0.37/0.75 thf(fact_9041_gcd__non__0__int,axiom,
% 0.37/0.75 ! [Y: int,X: int] :
% 0.37/0.75 ( ( ord_less_int @ zero_zero_int @ Y )
% 0.37/0.75 => ( ( gcd_gcd_int @ X @ Y )
% 0.37/0.75 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_non_0_int
% 0.37/0.75 thf(fact_9042_integer__set__bit__code,axiom,
% 0.37/0.75 ( bits_integer_set_bit
% 0.37/0.75 = ( ^ [X4: code_integer,N6: code_integer,B7: $o] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi1878487536576149250nteger @ X4 @ N6 @ B7 ) @ ( if_Code_integer @ B7 @ ( bit_se1080825931792720795nteger @ X4 @ ( bit_se7788150548672797655nteger @ ( code_nat_of_integer @ N6 ) @ one_one_Code_integer ) ) @ ( bit_se3949692690581998587nteger @ X4 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ ( code_nat_of_integer @ N6 ) @ one_one_Code_integer ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_set_bit_code
% 0.37/0.75 thf(fact_9043_gcd__nat_Oeq__neutr__iff,axiom,
% 0.37/0.75 ! [A: nat,B: nat] :
% 0.37/0.75 ( ( ( gcd_gcd_nat @ A @ B )
% 0.37/0.75 = zero_zero_nat )
% 0.37/0.75 = ( ( A = zero_zero_nat )
% 0.37/0.75 & ( B = zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.eq_neutr_iff
% 0.37/0.75 thf(fact_9044_gcd__nat_Oleft__neutral,axiom,
% 0.37/0.75 ! [A: nat] :
% 0.37/0.75 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 0.37/0.75 = A ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.left_neutral
% 0.37/0.75 thf(fact_9045_gcd__nat_Oneutr__eq__iff,axiom,
% 0.37/0.75 ! [A: nat,B: nat] :
% 0.37/0.75 ( ( zero_zero_nat
% 0.37/0.75 = ( gcd_gcd_nat @ A @ B ) )
% 0.37/0.75 = ( ( A = zero_zero_nat )
% 0.37/0.75 & ( B = zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.neutr_eq_iff
% 0.37/0.75 thf(fact_9046_gcd__nat_Oright__neutral,axiom,
% 0.37/0.75 ! [A: nat] :
% 0.37/0.75 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 0.37/0.75 = A ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.right_neutral
% 0.37/0.75 thf(fact_9047_gcd__0__nat,axiom,
% 0.37/0.75 ! [X: nat] :
% 0.37/0.75 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_0_nat
% 0.37/0.75 thf(fact_9048_gcd__0__left__nat,axiom,
% 0.37/0.75 ! [X: nat] :
% 0.37/0.75 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_0_left_nat
% 0.37/0.75 thf(fact_9049_gcd__Suc__0,axiom,
% 0.37/0.75 ! [M: nat] :
% 0.37/0.75 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 0.37/0.75 = ( suc @ zero_zero_nat ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_Suc_0
% 0.37/0.75 thf(fact_9050_gcd__pos__nat,axiom,
% 0.37/0.75 ! [M: nat,N: nat] :
% 0.37/0.75 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 0.37/0.75 = ( ( M != zero_zero_nat )
% 0.37/0.75 | ( N != zero_zero_nat ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_pos_nat
% 0.37/0.75 thf(fact_9051_Gcd__in,axiom,
% 0.37/0.75 ! [A4: set_nat] :
% 0.37/0.75 ( ! [A3: nat,B3: nat] :
% 0.37/0.75 ( ( member_nat @ A3 @ A4 )
% 0.37/0.75 => ( ( member_nat @ B3 @ A4 )
% 0.37/0.75 => ( member_nat @ ( gcd_gcd_nat @ A3 @ B3 ) @ A4 ) ) )
% 0.37/0.75 => ( ( A4 != bot_bot_set_nat )
% 0.37/0.75 => ( member_nat @ ( gcd_Gcd_nat @ A4 ) @ A4 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % Gcd_in
% 0.37/0.75 thf(fact_9052_bezout__gcd__nat_H,axiom,
% 0.37/0.75 ! [B: nat,A: nat] :
% 0.37/0.75 ? [X3: nat,Y3: nat] :
% 0.37/0.75 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 0.37/0.75 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 0.37/0.75 = ( gcd_gcd_nat @ A @ B ) ) )
% 0.37/0.75 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 0.37/0.75 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 0.37/0.75 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bezout_gcd_nat'
% 0.37/0.75 thf(fact_9053_gcd__le2__nat,axiom,
% 0.37/0.75 ! [B: nat,A: nat] :
% 0.37/0.75 ( ( B != zero_zero_nat )
% 0.37/0.75 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_le2_nat
% 0.37/0.75 thf(fact_9054_gcd__le1__nat,axiom,
% 0.37/0.75 ! [A: nat,B: nat] :
% 0.37/0.75 ( ( A != zero_zero_nat )
% 0.37/0.75 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_le1_nat
% 0.37/0.75 thf(fact_9055_gcd__diff1__nat,axiom,
% 0.37/0.75 ! [N: nat,M: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ N @ M )
% 0.37/0.75 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.37/0.75 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_diff1_nat
% 0.37/0.75 thf(fact_9056_gcd__diff2__nat,axiom,
% 0.37/0.75 ! [M: nat,N: nat] :
% 0.37/0.75 ( ( ord_less_eq_nat @ M @ N )
% 0.37/0.75 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 0.37/0.75 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_diff2_nat
% 0.37/0.75 thf(fact_9057_bezout__nat,axiom,
% 0.37/0.75 ! [A: nat,B: nat] :
% 0.37/0.75 ( ( A != zero_zero_nat )
% 0.37/0.75 => ? [X3: nat,Y3: nat] :
% 0.37/0.75 ( ( times_times_nat @ A @ X3 )
% 0.37/0.75 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % bezout_nat
% 0.37/0.75 thf(fact_9058_gcd__nat_Oelims,axiom,
% 0.37/0.75 ! [X: nat,Xa2: nat,Y: nat] :
% 0.37/0.75 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 0.37/0.75 = Y )
% 0.37/0.75 => ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.75 => ( Y = X ) )
% 0.37/0.75 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.elims
% 0.37/0.75 thf(fact_9059_gcd__nat_Osimps,axiom,
% 0.37/0.75 ( gcd_gcd_nat
% 0.37/0.75 = ( ^ [X4: nat,Y4: nat] : ( if_nat @ ( Y4 = zero_zero_nat ) @ X4 @ ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.simps
% 0.37/0.75 thf(fact_9060_gcd__non__0__nat,axiom,
% 0.37/0.75 ! [Y: nat,X: nat] :
% 0.37/0.75 ( ( Y != zero_zero_nat )
% 0.37/0.75 => ( ( gcd_gcd_nat @ X @ Y )
% 0.37/0.75 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_non_0_nat
% 0.37/0.75 thf(fact_9061_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.37/0.75 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 0.37/0.75 @ ^ [M5: nat,N6: nat] :
% 0.37/0.75 ( ( dvd_dvd_nat @ M5 @ N6 )
% 0.37/0.75 & ( M5 != N6 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.semilattice_neutr_order_axioms
% 0.37/0.75 thf(fact_9062_gcd__is__Max__divisors__nat,axiom,
% 0.37/0.75 ! [N: nat,M: nat] :
% 0.37/0.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.37/0.75 => ( ( gcd_gcd_nat @ M @ N )
% 0.37/0.75 = ( lattic8265883725875713057ax_nat
% 0.37/0.75 @ ( collect_nat
% 0.37/0.75 @ ^ [D5: nat] :
% 0.37/0.75 ( ( dvd_dvd_nat @ D5 @ M )
% 0.37/0.75 & ( dvd_dvd_nat @ D5 @ N ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_is_Max_divisors_nat
% 0.37/0.75 thf(fact_9063_gcd__nat_Opelims,axiom,
% 0.37/0.75 ! [X: nat,Xa2: nat,Y: nat] :
% 0.37/0.75 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 0.37/0.75 = Y )
% 0.37/0.75 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.37/0.75 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.37/0.75 => ( Y = X ) )
% 0.37/0.75 & ( ( Xa2 != zero_zero_nat )
% 0.37/0.75 => ( Y
% 0.37/0.75 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 0.37/0.75 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % gcd_nat.pelims
% 0.37/0.75 thf(fact_9064_uint32__shiftl__def,axiom,
% 0.37/0.75 ( uint32_shiftl
% 0.37/0.75 = ( ^ [X4: uint32,N6: code_integer] :
% 0.37/0.75 ( if_uint32
% 0.37/0.75 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N6 ) )
% 0.37/0.75 @ ( undefi8952517107220742160uint32 @ bit_se5742574853984576102uint32 @ X4 @ N6 )
% 0.37/0.75 @ ( bit_se5742574853984576102uint32 @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_shiftl_def
% 0.37/0.75 thf(fact_9065_uint32__shiftr__def,axiom,
% 0.37/0.75 ( uint32_shiftr
% 0.37/0.75 = ( ^ [X4: uint32,N6: code_integer] :
% 0.37/0.75 ( if_uint32
% 0.37/0.75 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N6 ) )
% 0.37/0.75 @ ( undefi8952517107220742160uint32 @ bit_se3964402333458159761uint32 @ X4 @ N6 )
% 0.37/0.75 @ ( bit_se3964402333458159761uint32 @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_shiftr_def
% 0.37/0.75 thf(fact_9066_uint32__test__bit__def,axiom,
% 0.37/0.75 ( uint32_test_bit
% 0.37/0.75 = ( ^ [X4: uint32,N6: code_integer] :
% 0.37/0.75 ( ( ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 0.37/0.75 => ( undefi6981832269580975664eger_o @ bit_se5367290876889521763uint32 @ X4 @ N6 ) )
% 0.37/0.75 & ( ~ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 0.37/0.75 => ( bit_se5367290876889521763uint32 @ X4 @ ( code_nat_of_integer @ N6 ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_test_bit_def
% 0.37/0.75 thf(fact_9067_integer__set__bit__def,axiom,
% 0.37/0.75 ( bits_integer_set_bit
% 0.37/0.75 = ( ^ [X4: code_integer,N6: code_integer,B7: $o] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi1878487536576149250nteger @ X4 @ N6 @ B7 ) @ ( generi2397576812484419408nteger @ X4 @ ( code_nat_of_integer @ N6 ) @ B7 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_set_bit_def
% 0.37/0.75 thf(fact_9068_uint32__shiftr__code,axiom,
% 0.37/0.75 ! [N: code_integer,W2: uint32] :
% 0.37/0.75 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_shiftr @ W2 @ N ) )
% 0.37/0.75 = ( rep_uint32 @ ( undefi8952517107220742160uint32 @ bit_se3964402333458159761uint32 @ W2 @ N ) ) ) )
% 0.37/0.75 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_shiftr @ W2 @ N ) )
% 0.37/0.75 = ( bit_se5176125413884933531l_num1 @ ( code_nat_of_integer @ N ) @ ( rep_uint32 @ W2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_shiftr_code
% 0.37/0.75 thf(fact_9069_uint32_Oless__iff__word__of,axiom,
% 0.37/0.75 ( ord_less_uint32
% 0.37/0.75 = ( ^ [P7: uint32,Q8: uint32] : ( ord_le750835935415966154l_num1 @ ( rep_uint32 @ P7 ) @ ( rep_uint32 @ Q8 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32.less_iff_word_of
% 0.37/0.75 thf(fact_9070_less__uint32_Orep__eq,axiom,
% 0.37/0.75 ( ord_less_uint32
% 0.37/0.75 = ( ^ [X4: uint32,Xa4: uint32] : ( ord_le750835935415966154l_num1 @ ( rep_uint32 @ X4 ) @ ( rep_uint32 @ Xa4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % less_uint32.rep_eq
% 0.37/0.75 thf(fact_9071_uint32_Oless__eq__iff__word__of,axiom,
% 0.37/0.75 ( ord_less_eq_uint32
% 0.37/0.75 = ( ^ [P7: uint32,Q8: uint32] : ( ord_le3335648743751981014l_num1 @ ( rep_uint32 @ P7 ) @ ( rep_uint32 @ Q8 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32.less_eq_iff_word_of
% 0.37/0.75 thf(fact_9072_less__eq__uint32_Orep__eq,axiom,
% 0.37/0.75 ( ord_less_eq_uint32
% 0.37/0.75 = ( ^ [X4: uint32,Xa4: uint32] : ( ord_le3335648743751981014l_num1 @ ( rep_uint32 @ X4 ) @ ( rep_uint32 @ Xa4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % less_eq_uint32.rep_eq
% 0.37/0.75 thf(fact_9073_uint32__test__bit__code,axiom,
% 0.37/0.75 ( uint32_test_bit
% 0.37/0.75 = ( ^ [W3: uint32,N6: code_integer] :
% 0.37/0.75 ( ( ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 0.37/0.75 => ( undefi6981832269580975664eger_o @ bit_se5367290876889521763uint32 @ W3 @ N6 ) )
% 0.37/0.75 & ( ~ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 0.37/0.75 => ( bit_se6859397288646540909l_num1 @ ( rep_uint32 @ W3 ) @ ( code_nat_of_integer @ N6 ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_test_bit_code
% 0.37/0.75 thf(fact_9074_uint32__shiftl__code,axiom,
% 0.37/0.75 ! [N: code_integer,W2: uint32] :
% 0.37/0.75 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_shiftl @ W2 @ N ) )
% 0.37/0.75 = ( rep_uint32 @ ( undefi8952517107220742160uint32 @ bit_se5742574853984576102uint32 @ W2 @ N ) ) ) )
% 0.37/0.75 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_shiftl @ W2 @ N ) )
% 0.37/0.75 = ( bit_se837345729053750000l_num1 @ ( code_nat_of_integer @ N ) @ ( rep_uint32 @ W2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_shiftl_code
% 0.37/0.75 thf(fact_9075_integer__shiftl__def,axiom,
% 0.37/0.75 ( bits_integer_shiftl
% 0.37/0.75 = ( ^ [X4: code_integer,N6: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi8133104259855420269nteger @ X4 @ N6 ) @ ( bit_se7788150548672797655nteger @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_shiftl_def
% 0.37/0.75 thf(fact_9076_less__eq__uint32_Orsp,axiom,
% 0.37/0.75 ( bNF_re7364608769721783435num1_o
% 0.37/0.75 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5013357767504289739m1_o_o
% 0.37/0.75 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 0.37/0.75 @ ord_le3335648743751981014l_num1
% 0.37/0.75 @ ord_le3335648743751981014l_num1 ) ).
% 0.37/0.75
% 0.37/0.75 % less_eq_uint32.rsp
% 0.37/0.75 thf(fact_9077_less__uint32_Orsp,axiom,
% 0.37/0.75 ( bNF_re7364608769721783435num1_o
% 0.37/0.75 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 0.37/0.75 @ ( bNF_re5013357767504289739m1_o_o
% 0.37/0.75 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 0.37/0.75 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 0.37/0.75 @ ord_le750835935415966154l_num1
% 0.37/0.75 @ ord_le750835935415966154l_num1 ) ).
% 0.37/0.75
% 0.37/0.75 % less_uint32.rsp
% 0.37/0.75 thf(fact_9078_uint32__set__bit__code,axiom,
% 0.37/0.75 ! [N: code_integer,W2: uint32,B: $o] :
% 0.37/0.75 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_set_bit @ W2 @ N @ B ) )
% 0.37/0.75 = ( rep_uint32 @ ( undefi8537048349889504752uint32 @ generi1993664874377053279uint32 @ W2 @ N @ B ) ) ) )
% 0.37/0.75 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_set_bit @ W2 @ N @ B ) )
% 0.37/0.75 = ( generi5268133209446125161l_num1 @ ( rep_uint32 @ W2 ) @ ( code_nat_of_integer @ N ) @ B ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_set_bit_code
% 0.37/0.75 thf(fact_9079_uint32__set__bit__def,axiom,
% 0.37/0.75 ( uint32_set_bit
% 0.37/0.75 = ( ^ [X4: uint32,N6: code_integer,B7: $o] :
% 0.37/0.75 ( if_uint32
% 0.37/0.75 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 0.37/0.75 @ ( undefi8537048349889504752uint32 @ generi1993664874377053279uint32 @ X4 @ N6 @ B7 )
% 0.37/0.75 @ ( generi1993664874377053279uint32 @ X4 @ ( code_nat_of_integer @ N6 ) @ B7 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_set_bit_def
% 0.37/0.75 thf(fact_9080_integer__shiftr__def,axiom,
% 0.37/0.75 ( bits_integer_shiftr
% 0.37/0.75 = ( ^ [X4: code_integer,N6: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi8133104259855420269nteger @ X4 @ N6 ) @ ( bit_se3928097537394005634nteger @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_shiftr_def
% 0.37/0.75 thf(fact_9081_uint32__divmod__code,axiom,
% 0.37/0.75 ( uint32_divmod
% 0.37/0.75 = ( ^ [X4: uint32,Y4: uint32] : ( if_Pro1135515155860407935uint32 @ ( ord_less_eq_uint32 @ ( numera9087168376688890119uint32 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ Y4 ) @ ( if_Pro1135515155860407935uint32 @ ( ord_less_uint32 @ X4 @ Y4 ) @ ( produc1400373151660368625uint32 @ zero_zero_uint32 @ X4 ) @ ( produc1400373151660368625uint32 @ one_one_uint32 @ ( minus_minus_uint32 @ X4 @ Y4 ) ) ) @ ( if_Pro1135515155860407935uint32 @ ( Y4 = zero_zero_uint32 ) @ ( produc1400373151660368625uint32 @ ( div0_uint32 @ X4 ) @ ( mod0_uint32 @ X4 ) ) @ ( if_Pro1135515155860407935uint32 @ ( ord_less_eq_uint32 @ Y4 @ ( minus_minus_uint32 @ X4 @ ( times_times_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ Y4 ) ) ) @ ( produc1400373151660368625uint32 @ ( plus_plus_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ one_one_uint32 ) @ ( minus_minus_uint32 @ ( minus_minus_uint32 @ X4 @ ( times_times_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ Y4 ) ) @ Y4 ) ) @ ( produc1400373151660368625uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ ( minus_minus_uint32 @ X4 @ ( times_times_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ Y4 ) ) ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_divmod_code
% 0.37/0.75 thf(fact_9082_uint32_Oset__bits__aux__code,axiom,
% 0.37/0.75 ( set_bits_aux_uint32
% 0.37/0.75 = ( ^ [F5: nat > $o,N6: nat,W3: uint32] : ( if_uint32 @ ( N6 = zero_zero_nat ) @ W3 @ ( set_bits_aux_uint32 @ F5 @ ( minus_minus_nat @ N6 @ one_one_nat ) @ ( bit_se2966626333419230250uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ W3 ) @ ( if_uint32 @ ( F5 @ ( minus_minus_nat @ N6 @ one_one_nat ) ) @ one_one_uint32 @ zero_zero_uint32 ) ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32.set_bits_aux_code
% 0.37/0.75 thf(fact_9083_shiftr__uint32__code,axiom,
% 0.37/0.75 ( bit_se3964402333458159761uint32
% 0.37/0.75 = ( ^ [N6: nat,X4: uint32] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_shiftr @ X4 @ ( code_integer_of_nat @ N6 ) ) @ zero_zero_uint32 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % shiftr_uint32_code
% 0.37/0.75 thf(fact_9084_nat__of__integer__integer__of__nat,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( code_nat_of_integer @ ( code_integer_of_nat @ N ) )
% 0.37/0.75 = N ) ).
% 0.37/0.75
% 0.37/0.75 % nat_of_integer_integer_of_nat
% 0.37/0.75 thf(fact_9085_integer__of__nat_Orep__eq,axiom,
% 0.37/0.75 ! [X: nat] :
% 0.37/0.75 ( ( code_int_of_integer @ ( code_integer_of_nat @ X ) )
% 0.37/0.75 = ( semiri1314217659103216013at_int @ X ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_nat.rep_eq
% 0.37/0.75 thf(fact_9086_int__of__integer__integer__of__nat,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ( ( code_int_of_integer @ ( code_integer_of_nat @ N ) )
% 0.37/0.75 = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % int_of_integer_integer_of_nat
% 0.37/0.75 thf(fact_9087_integer__of__nat__0,axiom,
% 0.37/0.75 ( ( code_integer_of_nat @ zero_zero_nat )
% 0.37/0.75 = zero_z3403309356797280102nteger ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_nat_0
% 0.37/0.75 thf(fact_9088_integer__of__nat__1,axiom,
% 0.37/0.75 ( ( code_integer_of_nat @ one_one_nat )
% 0.37/0.75 = one_one_Code_integer ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_nat_1
% 0.37/0.75 thf(fact_9089_integer__of__nat__less__0__conv,axiom,
% 0.37/0.75 ! [N: nat] :
% 0.37/0.75 ~ ( ord_le6747313008572928689nteger @ ( code_integer_of_nat @ N ) @ zero_z3403309356797280102nteger ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_nat_less_0_conv
% 0.37/0.75 thf(fact_9090_integer__of__nat__eq__of__nat,axiom,
% 0.37/0.75 code_integer_of_nat = semiri4939895301339042750nteger ).
% 0.37/0.75
% 0.37/0.75 % integer_of_nat_eq_of_nat
% 0.37/0.75 thf(fact_9091_integer__of__nat_Oabs__eq,axiom,
% 0.37/0.75 ( code_integer_of_nat
% 0.37/0.75 = ( ^ [X4: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_nat.abs_eq
% 0.37/0.75 thf(fact_9092_integer__of__nat__numeral,axiom,
% 0.37/0.75 ! [N: num] :
% 0.37/0.75 ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 0.37/0.75 = ( numera6620942414471956472nteger @ N ) ) ).
% 0.37/0.75
% 0.37/0.75 % integer_of_nat_numeral
% 0.37/0.75 thf(fact_9093_test__bit__uint32__code,axiom,
% 0.37/0.75 ( bit_se5367290876889521763uint32
% 0.37/0.75 = ( ^ [X4: uint32,N6: nat] :
% 0.37/0.75 ( ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) )
% 0.37/0.75 & ( uint32_test_bit @ X4 @ ( code_integer_of_nat @ N6 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % test_bit_uint32_code
% 0.37/0.75 thf(fact_9094_set__bit__uint32__code,axiom,
% 0.37/0.75 ( generi1993664874377053279uint32
% 0.37/0.75 = ( ^ [X4: uint32,N6: nat,B7: $o] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_set_bit @ X4 @ ( code_integer_of_nat @ N6 ) @ B7 ) @ X4 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % set_bit_uint32_code
% 0.37/0.75 thf(fact_9095_shiftl__uint32__code,axiom,
% 0.37/0.75 ( bit_se5742574853984576102uint32
% 0.37/0.75 = ( ^ [N6: nat,X4: uint32] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_shiftl @ X4 @ ( code_integer_of_nat @ N6 ) ) @ zero_zero_uint32 ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % shiftl_uint32_code
% 0.37/0.75 thf(fact_9096_sshiftr__uint32__code,axiom,
% 0.37/0.75 ( signed489701013188660438uint32
% 0.37/0.75 = ( ^ [N6: nat,X4: uint32] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_sshiftr @ X4 @ ( code_integer_of_nat @ N6 ) ) @ ( if_uint32 @ ( bit_se5367290876889521763uint32 @ X4 @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ zero_zero_uint32 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % sshiftr_uint32_code
% 0.37/0.75 thf(fact_9097_uint32__sshiftr__def,axiom,
% 0.37/0.75 ( uint32_sshiftr
% 0.37/0.75 = ( ^ [X4: uint32,N6: code_integer] :
% 0.37/0.75 ( if_uint32
% 0.37/0.75 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N6 ) )
% 0.37/0.75 @ ( undefi7330133036835070352uint32 @ signed489701013188660438uint32 @ N6 @ X4 )
% 0.37/0.75 @ ( signed489701013188660438uint32 @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_sshiftr_def
% 0.37/0.75 thf(fact_9098_uint32__sshiftr__code,axiom,
% 0.37/0.75 ! [N: code_integer,W2: uint32] :
% 0.37/0.75 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_sshiftr @ W2 @ N ) )
% 0.37/0.75 = ( rep_uint32 @ ( undefi7330133036835070352uint32 @ signed489701013188660438uint32 @ N @ W2 ) ) ) )
% 0.37/0.75 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 0.37/0.75 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 0.37/0.75 => ( ( rep_uint32 @ ( uint32_sshiftr @ W2 @ N ) )
% 0.37/0.75 = ( signed5000768011106662067l_num1 @ ( code_nat_of_integer @ N ) @ ( rep_uint32 @ W2 ) ) ) ) ) ).
% 0.37/0.75
% 0.37/0.75 % uint32_sshiftr_code
% 0.37/0.75
% 0.37/0.75 % Helper facts (45)
% 0.37/0.75 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.37/0.75 ! [X: int,Y: int] :
% 0.37/0.75 ( ( if_int @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.37/0.75 ! [X: int,Y: int] :
% 0.37/0.75 ( ( if_int @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.37/0.75 ! [X: nat,Y: nat] :
% 0.37/0.75 ( ( if_nat @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.37/0.75 ! [X: nat,Y: nat] :
% 0.37/0.75 ( ( if_nat @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.37/0.75 ! [X: num,Y: num] :
% 0.37/0.75 ( ( if_num @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.37/0.75 ! [X: num,Y: num] :
% 0.37/0.75 ( ( if_num @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.37/0.75 ! [X: rat,Y: rat] :
% 0.37/0.75 ( ( if_rat @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.37/0.75 ! [X: rat,Y: rat] :
% 0.37/0.75 ( ( if_rat @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.37/0.75 ! [X: real,Y: real] :
% 0.37/0.75 ( ( if_real @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.37/0.75 ! [X: real,Y: real] :
% 0.37/0.75 ( ( if_real @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Uint32__Ouint32_T,axiom,
% 0.37/0.75 ! [X: uint32,Y: uint32] :
% 0.37/0.75 ( ( if_uint32 @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Uint32__Ouint32_T,axiom,
% 0.37/0.75 ! [X: uint32,Y: uint32] :
% 0.37/0.75 ( ( if_uint32 @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 0.37/0.75 ! [X: assn,Y: assn] :
% 0.37/0.75 ( ( if_assn @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 0.37/0.75 ! [X: assn,Y: assn] :
% 0.37/0.75 ( ( if_assn @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.37/0.75 ! [X: complex,Y: complex] :
% 0.37/0.75 ( ( if_complex @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.37/0.75 ! [X: complex,Y: complex] :
% 0.37/0.75 ( ( if_complex @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.37/0.75 ! [X: code_integer,Y: code_integer] :
% 0.37/0.75 ( ( if_Code_integer @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.37/0.75 ! [X: code_integer,Y: code_integer] :
% 0.37/0.75 ( ( if_Code_integer @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.37/0.75 ! [X: set_int,Y: set_int] :
% 0.37/0.75 ( ( if_set_int @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.37/0.75 ! [X: set_int,Y: set_int] :
% 0.37/0.75 ( ( if_set_int @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.75 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.37/0.75 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.37/0.75 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.37/0.75 ! [X: list_int,Y: list_int] :
% 0.37/0.75 ( ( if_list_int @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.37/0.75 ! [X: list_int,Y: list_int] :
% 0.37/0.75 ( ( if_list_int @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.37/0.75 ! [X: list_nat,Y: list_nat] :
% 0.37/0.75 ( ( if_list_nat @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.37/0.75 ! [X: list_nat,Y: list_nat] :
% 0.37/0.75 ( ( if_list_nat @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.37/0.75 ! [X: option_nat,Y: option_nat] :
% 0.37/0.75 ( ( if_option_nat @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.37/0.75 ! [X: option_nat,Y: option_nat] :
% 0.37/0.75 ( ( if_option_nat @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 0.37/0.75 ! [X: option_set_o,Y: option_set_o] :
% 0.37/0.75 ( ( if_option_set_o @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 0.37/0.75 ! [X: option_set_o,Y: option_set_o] :
% 0.37/0.75 ( ( if_option_set_o @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 0.37/0.75 ! [X: option_set_int,Y: option_set_int] :
% 0.37/0.75 ( ( if_option_set_int @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 0.37/0.75 ! [X: option_set_int,Y: option_set_int] :
% 0.37/0.75 ( ( if_option_set_int @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 0.37/0.75 ! [X: option_set_nat,Y: option_set_nat] :
% 0.37/0.75 ( ( if_option_set_nat @ $false @ X @ Y )
% 0.37/0.75 = Y ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 0.37/0.75 ! [X: option_set_nat,Y: option_set_nat] :
% 0.37/0.75 ( ( if_option_set_nat @ $true @ X @ Y )
% 0.37/0.75 = X ) ).
% 0.37/0.75
% 0.37/0.75 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
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% 0.37/0.75
% 0.37/0.75 % Conjectures (6)
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% 0.37/0.75 thf(conj_4,hypothesis,
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% 0.37/0.75
% 0.37/0.75 thf(conj_5,conjecture,
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% 0.37/0.75
% 0.37/0.75 %------------------------------------------------------------------------------
% 0.37/0.75 ------------------------
% 9.61/3.53 ---- Embedded in THF ---
% 9.61/3.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 9.61/3.53 %%% Generated on Fri Feb 27 18:59:23 EST 2026
% 9.61/3.53 %%% using '$$dhol' embedding, version 1.3.0.
% 9.61/3.53 %%% Logic specification used:
% 9.61/3.53 %%% thf(spec, logic, $$dhol).
% 9.61/3.53
% 9.61/3.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2DTF8220.p
% See solution above
% 9.61/3.57 ------------------------
% 13.71/7.65 ---- Cleaned THF ---
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% 13.71/7.65
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% 13.71/7.65 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
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% 13.71/7.65 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint_001t__Int__Oint,type,
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% 13.71/7.65 thf(sy_c_Binomial_Obinomial,type,
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% 13.71/7.65 thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Int__Oint,type,
% 13.71/7.65 complete_Sup_Sup_int: set_int > int ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Real__Oreal,type,
% 13.71/7.65 comple1385675409528146559p_real: set_real > real ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Complex_Ocomplex_OComplex,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Deriv_Ohas__field__derivative_001t__Real__Oreal,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Oadjust__div,type,
% 13.71/7.65 adjust_div: product_prod_int_int > int ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Oadjust__mod,type,
% 13.71/7.65 adjust_mod: int > int > int ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Odivmod__nat,type,
% 13.71/7.65 divmod_nat: nat > nat > product_prod_nat_nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Oeucl__rel__int,type,
% 13.71/7.65 eucl_rel_int: int > int > product_prod_int_int > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 13.71/7.65 unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 13.71/7.65 unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 13.71/7.65 unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 13.71/7.65 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 13.71/7.65 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 13.71/7.65 inverse_inverse_real: real > real ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 13.71/7.65 at_top_real: filter_real ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 13.71/7.65 eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 13.71/7.65 eventually_real: ( real > $o ) > filter_real > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 13.71/7.65 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 13.71/7.65 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 13.71/7.65 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_OFpow_001_Eo,type,
% 13.71/7.65 finite_Fpow_o: set_o > set_set_o ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_OFpow_001t__Code____Numeral__Ointeger,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_OFpow_001t__Complex__Ocomplex,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_OFpow_001t__Int__Oint,type,
% 13.71/7.65 finite_Fpow_int: set_int > set_set_int ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_OFpow_001t__Nat__Onat,type,
% 13.71/7.65 finite_Fpow_nat: set_nat > set_set_nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_OFpow_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.65 finite_Fpow_set_nat: set_set_nat > set_set_set_nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Code____Numeral__Ointeger,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 13.71/7.65 finite_card_int: set_int > nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_I_Eo_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Int__Oint_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Real__Oreal_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__String__Oliteral_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Num__Onum,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Numeral____Type__Onum0,type,
% 13.71/7.65 finite6454714172617411596l_num0: set_Numeral_num0 > nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 13.71/7.65 finite410649719033368117t_unit: set_Product_unit > nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Rat__Orat,type,
% 13.71/7.65 finite_card_rat: set_rat > nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Real__Oreal,type,
% 13.71/7.65 finite_card_real: set_real > nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__String__Oliteral,type,
% 13.71/7.65 finite_card_literal: set_literal > nat ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ocard_001t__VEBT____Definitions__OVEBT,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Code____Numeral__Ointeger,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Real__Oreal_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 13.71/7.65
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_I_Eo_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Real__Oreal_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__String__Oliteral,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 13.71/7.65 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 13.71/7.65 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001_Eo_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Real__Oreal_001t__Nat__Onat,type,
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% 13.71/7.65
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Oinj__on_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
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% 13.71/7.65
% 13.71/7.65 thf(sy_c_GCD_Obezw,type,
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% 13.71/7.65
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% 13.71/7.66 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_If_001t__Rat__Orat,type,
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% 13.71/7.66 thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
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% 13.71/7.66 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
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% 13.71/7.66 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
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% 13.71/7.66 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.66 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
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% 13.71/7.66 thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
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% 13.71/7.66 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
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% 13.71/7.66 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001_Eo,type,
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% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Num__Onum,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Rat__Orat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMin_001_Eo,type,
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% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMin_001t__Code____Numeral__Ointeger,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMin_001t__Nat__Onat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMin_001t__Num__Onum,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMin_001t__Rat__Orat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Olinorder__class_OMin_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001_Eo_001t__Rat__Orat,type,
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% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001_Eo_001t__Real__Oreal,type,
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% 13.71/7.66
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% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Int__Oint_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Nat__Onat_001t__Rat__Orat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Nat__Onat_001t__Real__Oreal,type,
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__Real__Oreal_001t__Rat__Orat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__VEBT____Definitions__OVEBT_001t__Num__Onum,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Lattices__Big_Oord__class_Oarg__min__on_001t__VEBT____Definitions__OVEBT_001t__Rat__Orat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oappend_001_Eo,type,
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% 13.71/7.66 thf(sy_c_List_Oappend_001t__Int__Oint,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Obutlast_001_Eo,type,
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Obutlast_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Obutlast_001t__VEBT____BuildupMemImp__OVEBTi,type,
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oconcat_001_Eo,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oconcat_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oconcat_001t__VEBT____Definitions__OVEBT,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ocount__list_001_Eo,type,
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% 13.71/7.66
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ocount__list_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ocount__list_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ocount__list_001t__VEBT____Definitions__OVEBT,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Odistinct_001_Eo,type,
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
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% 13.71/7.66
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% 13.71/7.66
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% 13.71/7.66 thf(sy_c_List_Odistinct_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.66 thf(sy_c_List_Oenumerate_001_Eo,type,
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% 13.71/7.66 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
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% 13.71/7.66 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oenumerate_001t__Real__Oreal,type,
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% 13.71/7.66 thf(sy_c_List_Oenumerate_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 enumerate_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_P2320588648998582380_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oenumerate_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
% 13.71/7.66 filter_nat2: ( nat > $o ) > list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Assertions__Oassn_001t__Assertions__Oassn,type,
% 13.71/7.66 foldl_assn_assn: ( assn > assn > assn ) > assn > list_assn > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Int__Oint_001t__Int__Oint,type,
% 13.71/7.66 foldl_int_int: ( int > int > int ) > int > list_int > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001_Eo,type,
% 13.71/7.66 foldl_nat_o: ( nat > $o > nat ) > nat > list_o > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__Nat__Onat,type,
% 13.71/7.66 foldl_nat_nat: ( nat > nat > nat ) > nat > list_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__Real__Oreal,type,
% 13.71/7.66 foldl_nat_real: ( nat > real > nat ) > nat > list_real > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 foldl_nat_VEBT_VEBT: ( nat > vEBT_VEBT > nat ) > nat > list_VEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Rat__Orat_001t__Rat__Orat,type,
% 13.71/7.66 foldl_rat_rat: ( rat > rat > rat ) > rat > list_rat > rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Real__Oreal_001t__Real__Oreal,type,
% 13.71/7.66 foldl_real_real: ( real > real > real ) > real > list_real > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldl_001t__Uint32__Ouint32_001t__Uint32__Ouint32,type,
% 13.71/7.66 foldl_uint32_uint32: ( uint32 > uint32 > uint32 ) > uint32 > list_uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldr_001_Eo_001t__Nat__Onat,type,
% 13.71/7.66 foldr_o_nat: ( $o > nat > nat ) > list_o > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldr_001t__Nat__Onat_001t__Nat__Onat,type,
% 13.71/7.66 foldr_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Nat__Onat,type,
% 13.71/7.66 foldr_real_nat: ( real > nat > nat ) > list_real > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldr_001t__Real__Oreal_001t__Real__Oreal,type,
% 13.71/7.66 foldr_real_real: ( real > real > real ) > list_real > real > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ofoldr_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 13.71/7.66 foldr_VEBT_VEBT_nat: ( vEBT_VEBT > nat > nat ) > list_VEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olast_001_Eo,type,
% 13.71/7.66 last_o: list_o > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olast_001t__Int__Oint,type,
% 13.71/7.66 last_int: list_int > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 13.71/7.66 last_nat: list_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olast_001t__Real__Oreal,type,
% 13.71/7.66 last_real: list_real > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olast_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 last_VEBT_VEBTi: list_VEBT_VEBTi > vEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olast_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 last_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olenlex_001_Eo,type,
% 13.71/7.66 lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olenlex_001t__Int__Oint,type,
% 13.71/7.66 lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olenlex_001t__Nat__Onat,type,
% 13.71/7.66 lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olenlex_001t__Real__Oreal,type,
% 13.71/7.66 lenlex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olenlex_001t__Uint32__Ouint32,type,
% 13.71/7.66 lenlex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olenlex_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olex_001_Eo,type,
% 13.71/7.66 lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olex_001t__Int__Oint,type,
% 13.71/7.66 lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 13.71/7.66 lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olex_001t__Real__Oreal,type,
% 13.71/7.66 lex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olex_001t__Uint32__Ouint32,type,
% 13.71/7.66 lex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olex_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 lex_VEBT_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr4797120415438012619_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olex_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001_Eo,type,
% 13.71/7.66 linord3142498349692569832_set_o: set_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 linord2324613341767563021nteger: set_Code_integer > list_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Int__Oint,type,
% 13.71/7.66 linord2612477271533052124et_int: set_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 13.71/7.66 linord2614967742042102400et_nat: set_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Num__Onum,type,
% 13.71/7.66 linord8395671565052656842et_num: set_num > list_num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Rat__Orat,type,
% 13.71/7.66 linord1979837681955606664et_rat: set_rat > list_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Real__Oreal,type,
% 13.71/7.66 linord4252657396651189596t_real: set_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__String__Oliteral,type,
% 13.71/7.66 linord2913955441264437540iteral: set_literal > list_literal ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 13.71/7.66 cons_o: $o > list_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 cons_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 13.71/7.66 cons_int: int > list_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 13.71/7.66 cons_nat: nat > list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 13.71/7.66 cons_num: num > list_num > list_num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 13.71/7.66 cons_P8766293264717362397od_o_o: product_prod_o_o > list_P4002435161011370285od_o_o > list_P4002435161011370285od_o_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 13.71/7.66 cons_P1455986808126089405_o_int: product_prod_o_int > list_P3795440434834930179_o_int > list_P3795440434834930179_o_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 13.71/7.66 cons_P5633837827635286113_o_nat: product_prod_o_nat > list_P6285523579766656935_o_nat > list_P6285523579766656935_o_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_M_Eo_J,type,
% 13.71/7.66 cons_P7321330006258091179_int_o: product_prod_int_o > list_P5087981734274514673_int_o > list_P5087981734274514673_int_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 13.71/7.66 cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Nat__Onat_J,type,
% 13.71/7.66 cons_P7512249878480867347nt_nat: product_prod_int_nat > list_P8198026277950538467nt_nat > list_P8198026277950538467nt_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 13.71/7.66 cons_P9142372351690779143_nat_o: product_prod_nat_o > list_P7333126701944960589_nat_o > list_P7333126701944960589_nat_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 13.71/7.66 cons_P2335045147070616083at_int: product_prod_nat_int > list_P3521021558325789923at_int > list_P3521021558325789923at_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 13.71/7.66 cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Uint32__Ouint32_Mt__Uint32__Ouint32_J,type,
% 13.71/7.66 cons_P3149448846263281007uint32: produc827990862158126777uint32 > list_P3069071885182933823uint32 > list_P3069071885182933823uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Rat__Orat,type,
% 13.71/7.66 cons_rat: rat > list_rat > list_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Real__Oreal,type,
% 13.71/7.66 cons_real: real > list_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__Uint32__Ouint32,type,
% 13.71/7.66 cons_uint32: uint32 > list_uint32 > list_uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 cons_VEBT_VEBTi: vEBT_VEBTi > list_VEBT_VEBTi > list_VEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_OCons_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_ONil_001_Eo,type,
% 13.71/7.66 nil_o: list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 13.71/7.66 nil_int: list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 13.71/7.66 nil_nat: list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 13.71/7.66 hd_nat: list_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001_Eo,type,
% 13.71/7.66 map_nat_o: ( nat > $o ) > list_nat > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 13.71/7.66 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Omap_001t__Product____Type__Oprod_I_Eo_M_Eo_J_001_Eo,type,
% 13.71/7.66 map_Pr7541730621154948341_o_o_o: ( product_prod_o_o > $o ) > list_P4002435161011370285od_o_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 13.71/7.66 map_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 13.71/7.66 map_VEBT_VEBT_real: ( vEBT_VEBT > real ) > list_VEBT_VEBT > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 13.71/7.66 set_o2: list_o > set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 set_Code_integer2: list_Code_integer > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 13.71/7.66 set_complex2: list_complex > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 13.71/7.66 set_int2: list_int > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 13.71/7.66 set_list_o2: list_list_o > set_list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 13.71/7.66 set_list_int2: list_list_int > set_list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 13.71/7.66 set_list_nat2: list_list_nat > set_list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Real__Oreal_J,type,
% 13.71/7.66 set_list_real2: list_list_real > set_list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 13.71/7.66 set_nat2: list_nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Num__Onum,type,
% 13.71/7.66 set_num2: list_num > set_num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Oset_001t__Rat__Orat,type,
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% 13.71/7.66
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% 13.71/7.66
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
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% 13.71/7.66 thf(sy_c_List_Olist__update_001_Eo,type,
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% 13.71/7.66
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% 13.71/7.66
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% 13.71/7.66
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% 13.71/7.66 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
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% 13.71/7.66 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
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% 13.71/7.66 nth_Pr3433448822664029129i_real: list_P8536626330812492744i_real > nat > produc6680258955013199682i_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__VEBT____BuildupMemImp__OVEBTi_J,type,
% 13.71/7.66 nth_Pr6329974346453275474_VEBTi: list_P785718909624839377_VEBTi > nat > produc3777764054643897931_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 nth_Pr8725177398587324397T_VEBT: list_P5988454224134618948T_VEBT > nat > produc2810682830582626868T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__Rat__Orat,type,
% 13.71/7.66 nth_rat: list_rat > nat > rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 13.71/7.66 nth_real: list_real > nat > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 nth_set_nat: list_set_nat > nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__Uint32__Ouint32,type,
% 13.71/7.66 nth_uint32: list_uint32 > nat > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 nth_VEBT_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001_Eo,type,
% 13.71/7.66 remove1_o: $o > list_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 remove1_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001t__Int__Oint,type,
% 13.71/7.66 remove1_int: int > list_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001t__Nat__Onat,type,
% 13.71/7.66 remove1_nat: nat > list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001t__Num__Onum,type,
% 13.71/7.66 remove1_num: num > list_num > list_num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001t__Rat__Orat,type,
% 13.71/7.66 remove1_rat: rat > list_rat > list_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001t__Real__Oreal,type,
% 13.71/7.66 remove1_real: real > list_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oremove1_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 remove1_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_OremoveAll_001_Eo,type,
% 13.71/7.66 removeAll_o: $o > list_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_OremoveAll_001t__Int__Oint,type,
% 13.71/7.66 removeAll_int: int > list_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_OremoveAll_001t__Nat__Onat,type,
% 13.71/7.66 removeAll_nat: nat > list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_OremoveAll_001t__Real__Oreal,type,
% 13.71/7.66 removeAll_real: real > list_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_OremoveAll_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 removeAll_set_nat: set_nat > list_set_nat > list_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_OremoveAll_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 removeAll_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Orotate1_001_Eo,type,
% 13.71/7.66 rotate1_o: list_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 13.71/7.66 rotate1_nat: list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Orotate1_001t__Real__Oreal,type,
% 13.71/7.66 rotate1_real: list_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001_Eo,type,
% 13.71/7.66 sorted_wrt_o: ( $o > $o > $o ) > list_o > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 sorted710888440204495920nteger: ( code_integer > code_integer > $o ) > list_Code_integer > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 13.71/7.66 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 13.71/7.66 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__Num__Onum,type,
% 13.71/7.66 sorted_wrt_num: ( num > num > $o ) > list_num > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__Rat__Orat,type,
% 13.71/7.66 sorted_wrt_rat: ( rat > rat > $o ) > list_rat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__Real__Oreal,type,
% 13.71/7.66 sorted_wrt_real: ( real > real > $o ) > list_real > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__String__Oliteral,type,
% 13.71/7.66 sorted_wrt_literal: ( literal > literal > $o ) > list_literal > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 sorted9206477368072086664_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi > $o ) > list_VEBT_VEBTi > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osorted__wrt_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 sorted_wrt_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > list_VEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osubseqs_001_Eo,type,
% 13.71/7.66 subseqs_o: list_o > list_list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 13.71/7.66 subseqs_int: list_int > list_list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 13.71/7.66 subseqs_nat: list_nat > list_list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osubseqs_001t__Real__Oreal,type,
% 13.71/7.66 subseqs_real: list_real > list_list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Osubseqs_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001_Eo,type,
% 13.71/7.66 take_o: nat > list_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__Int__Oint,type,
% 13.71/7.66 take_int: nat > list_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 13.71/7.66 take_nat: nat > list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__Num__Onum,type,
% 13.71/7.66 take_num: nat > list_num > list_num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__Rat__Orat,type,
% 13.71/7.66 take_rat: nat > list_rat > list_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__Real__Oreal,type,
% 13.71/7.66 take_real: nat > list_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 take_set_nat: nat > list_set_nat > list_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__Uint32__Ouint32,type,
% 13.71/7.66 take_uint32: nat > list_uint32 > list_uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 take_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_VEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oupt,type,
% 13.71/7.66 upt: nat > nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oupto,type,
% 13.71/7.66 upto: int > int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oupto__aux,type,
% 13.71/7.66 upto_aux: int > int > list_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Oupto__rel,type,
% 13.71/7.66 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 13.71/7.66 zip_Pr8136144321567152340et_nat: list_P7985473006766602707_nat_o > list_P2321686559999237006et_nat > list_P362550909693114634et_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 13.71/7.66 zip_Pr7134870689397686104et_nat: list_P7985473006766602707_nat_o > list_P9062070895058802706et_nat > list_P2321686559999237006et_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001_Eo_001_Eo,type,
% 13.71/7.66 zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 13.71/7.66 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001_Eo_001t__Nat__Onat,type,
% 13.71/7.66 zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001_Eo_001t__Real__Oreal,type,
% 13.71/7.66 zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Int__Oint_001_Eo,type,
% 13.71/7.66 zip_int_o: list_int > list_o > list_P5087981734274514673_int_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 13.71/7.66 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Nat__Onat,type,
% 13.71/7.66 zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Real__Oreal,type,
% 13.71/7.66 zip_int_real: list_int > list_real > list_P6863124054624500543t_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Int__Oint_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 zip_int_VEBT_VEBTi: list_int > list_VEBT_VEBTi > list_P4447955379000644808_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 zip_int_VEBT_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Nat__Onat_001_Eo,type,
% 13.71/7.66 zip_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Int__Oint,type,
% 13.71/7.66 zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 13.71/7.66 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Real__Oreal_001_Eo,type,
% 13.71/7.66 zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Int__Oint,type,
% 13.71/7.66 zip_real_int: list_real > list_int > list_P4344331454722006975al_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Nat__Onat,type,
% 13.71/7.66 zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Real__Oreal,type,
% 13.71/7.66 zip_real_real: list_real > list_real > list_P8689742595348180415l_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__Uint32__Ouint32_001t__Uint32__Ouint32,type,
% 13.71/7.66 zip_uint32_uint32: list_uint32 > list_uint32 > list_P3069071885182933823uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001_Eo,type,
% 13.71/7.66 zip_VEBT_VEBTi_o: list_VEBT_VEBTi > list_o > list_P8833571063612306856EBTi_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
% 13.71/7.66 zip_VEBT_VEBTi_int: list_VEBT_VEBTi > list_int > list_P7392757774524453448Ti_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001t__Real__Oreal,type,
% 13.71/7.66 zip_VEBT_VEBTi_real: list_VEBT_VEBTi > list_real > list_P8536626330812492744i_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 zip_VE793581609497812771_VEBTi: list_VEBT_VEBTi > list_VEBT_VEBTi > list_P785718909624839377_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 zip_VE7413257051550508102T_VEBT: list_VEBT_VEBTi > list_VEBT_VEBT > list_P5988454224134618948T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 13.71/7.66 zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 13.71/7.66 zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 13.71/7.66 zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 13.71/7.66 zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 zip_VE6444338338598820466_VEBTi: list_VEBT_VEBT > list_VEBT_VEBTi > list_P735349106241217576_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Obijective_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 13.71/7.66 biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Obijective_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 13.71/7.66 biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Obijective_001t__Int__Oint_001t__Int__Oint,type,
% 13.71/7.66 bijective_int_int: set_Pr958786334691620121nt_int > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Obijective_001t__Nat__Onat_001t__Nat__Onat,type,
% 13.71/7.66 bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Obijective_001t__Uint32__Ouint32_001t__Uint32__Ouint32,type,
% 13.71/7.66 biject2923219584331114343uint32: set_Pr1773385645901665561uint32 > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Odflt__None__set_001_Eo,type,
% 13.71/7.66 dflt_None_set_o: set_o > option_set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Odflt__None__set_001t__Int__Oint,type,
% 13.71/7.66 dflt_None_set_int: set_int > option_set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Odflt__None__set_001t__Nat__Onat,type,
% 13.71/7.66 dflt_None_set_nat: set_nat > option_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Omergesort__remdups_001_Eo,type,
% 13.71/7.66 mergesort_remdups_o: list_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Omergesort__remdups_001t__Int__Oint,type,
% 13.71/7.66 merges1654122896337280797ps_int: list_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Omergesort__remdups_001t__Nat__Onat,type,
% 13.71/7.66 merges1656613366846331073ps_nat: list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Omergesort__remdups_001t__Num__Onum,type,
% 13.71/7.66 merges7437317189856885515ps_num: list_num > list_num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Omergesort__remdups_001t__Rat__Orat,type,
% 13.71/7.66 merges1021483306759835337ps_rat: list_rat > list_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Omergesort__remdups_001t__Real__Oreal,type,
% 13.71/7.66 merges7559785487730971421s_real: list_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Oslice_001_Eo,type,
% 13.71/7.66 slice_o: nat > nat > list_o > list_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Oslice_001t__Int__Oint,type,
% 13.71/7.66 slice_int: nat > nat > list_int > list_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Oslice_001t__Nat__Onat,type,
% 13.71/7.66 slice_nat: nat > nat > list_nat > list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Oslice_001t__Real__Oreal,type,
% 13.71/7.66 slice_real: nat > nat > list_real > list_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Oslice_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 slice_VEBT_VEBTi: nat > nat > list_VEBT_VEBTi > list_VEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Oslice_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 slice_VEBT_VEBT: nat > nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Othe__default_001t__Nat__Onat,type,
% 13.71/7.66 the_default_nat: nat > option_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Othe__default_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 13.71/7.66 the_de3812365490807259288at_nat: product_prod_nat_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Othe__default_001t__Set__Oset_I_Eo_J,type,
% 13.71/7.66 the_default_set_o: set_o > option_set_o > set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Othe__default_001t__Set__Oset_It__Int__Oint_J,type,
% 13.71/7.66 the_default_set_int: set_int > option_set_int > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Misc_Othe__default_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 the_default_set_nat: set_nat > option_set_nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_OSuc,type,
% 13.71/7.66 suc: nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 13.71/7.66 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 semiri4939895301339042750nteger: nat > code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 13.71/7.66 semiri1314217659103216013at_int: nat > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 13.71/7.66 semiri1316708129612266289at_nat: nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 13.71/7.66 semiri681578069525770553at_rat: nat > rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 13.71/7.66 semiri5074537144036343181t_real: nat > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Uint32__Ouint32,type,
% 13.71/7.66 semiri2565882477558803405uint32: nat > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 13.71/7.66 size_size_list_o: list_o > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 13.71/7.66 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 13.71/7.66 size_s3451745648224563538omplex: list_complex > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 13.71/7.66 size_size_list_int: list_int > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 13.71/7.66 size_s2710708370519433104list_o: list_list_o > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 13.71/7.66 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Real__Oreal_J_J,type,
% 13.71/7.66 size_s6660260683639930848t_real: list_list_real > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 13.71/7.66 size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 13.71/7.66 size_size_list_nat: list_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 13.71/7.66 size_size_list_num: list_num > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Real__Oreal_J_J,type,
% 13.71/7.66 size_s2624279037499656343o_real: list_P5232166724548748803o_real > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 13.71/7.66 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_M_Eo_J_J,type,
% 13.71/7.66 size_s987546567493390085real_o: list_P3595434254542482545real_o > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J_J,type,
% 13.71/7.66 size_s1877336372972134351al_nat: list_P6834414599653733731al_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 13.71/7.66 size_s3932428310213730859l_real: list_P8689742595348180415l_real > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Real__Oreal_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 13.71/7.66 size_s3289364478449617953T_VEBT: list_P877281246627933069T_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 13.71/7.66 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 13.71/7.66 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J_J,type,
% 13.71/7.66 size_s5035110155006384947T_real: list_P2623026923184700063T_real > nat ).
% 13.71/7.66
% 13.71/7.66 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,
% 13.71/7.66 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Rat__Orat_J,type,
% 13.71/7.66 size_size_list_rat: list_rat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 13.71/7.66 size_size_list_real: list_real > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 13.71/7.66 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__String__Oliteral_J,type,
% 13.71/7.66 size_s2501651207091587910iteral: list_literal > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Uint32__Ouint32_J,type,
% 13.71/7.66 size_s4844771616002835472uint32: list_uint32 > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____BuildupMemImp__OVEBTi_J,type,
% 13.71/7.66 size_s7982070591426661849_VEBTi: list_VEBT_VEBTi > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 13.71/7.66 size_size_num: num > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 13.71/7.66 size_size_option_nat: option_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 13.71/7.66 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 size_size_VEBT_VEBTi: vEBT_VEBTi > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 13.71/7.66 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 13.71/7.66 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 13.71/7.66 nat_set_decode: nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 13.71/7.66 nat_set_encode: set_nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Nat__Bijection_Otriangle,type,
% 13.71/7.66 nat_triangle: nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_NthRoot_Oroot,type,
% 13.71/7.66 root: nat > real > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_NthRoot_Osqrt,type,
% 13.71/7.66 sqrt: real > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_OBitM,type,
% 13.71/7.66 bitM: num > num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oinc,type,
% 13.71/7.66 inc: num > num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 13.71/7.66 neg_nu3811975205180677377ec_int: int > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 13.71/7.66 neg_nu3179335615603231917ec_rat: rat > rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 13.71/7.66 neg_nu6075765906172075777c_real: real > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Uint32__Ouint32,type,
% 13.71/7.66 neg_nu965353292909893953uint32: uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 13.71/7.66 neg_nu5851722552734809277nc_int: int > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 13.71/7.66 neg_nu5219082963157363817nc_rat: rat > rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 13.71/7.66 neg_nu8295874005876285629c_real: real > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Uint32__Ouint32,type,
% 13.71/7.66 neg_nu4269007558841261821uint32: uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onum_OBit0,type,
% 13.71/7.66 bit0: num > num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onum_OBit1,type,
% 13.71/7.66 bit1: num > num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onum_OOne,type,
% 13.71/7.66 one: num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onum_Osize__num,type,
% 13.71/7.66 size_num: num > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 numera6620942414471956472nteger: num > code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 13.71/7.66 numera1916890842035813515d_enat: num > extended_enat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 13.71/7.66 numeral_numeral_int: num > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 13.71/7.66 numeral_numeral_nat: num > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 13.71/7.66 numeral_numeral_real: num > real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Uint32__Ouint32,type,
% 13.71/7.66 numera9087168376688890119uint32: num > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
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% 13.71/7.66
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% 13.71/7.66 thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
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% 13.71/7.66 thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
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% 13.71/7.66 thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
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% 13.71/7.66
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% 13.71/7.66 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
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% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 13.71/7.66 image_948535463418740880er_int: ( code_integer > int ) > set_Code_integer > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 13.71/7.66 image_951025933927791156er_nat: ( code_integer > nat ) > set_Code_integer > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 13.71/7.66 image_315895873841295420er_rat: ( code_integer > rat ) > set_Code_integer > set_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Code____Numeral__Ointeger_001t__Real__Oreal,type,
% 13.71/7.66 image_7738145705984076560r_real: ( code_integer > real ) > set_Code_integer > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Complex__Ocomplex_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 image_1994230757181692690nteger: ( complex > code_integer ) > set_complex > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 13.71/7.66 image_1468599708987790691omplex: ( complex > complex ) > set_complex > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 13.71/7.66 image_complex_int: ( complex > int ) > set_complex > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 13.71/7.66 image_complex_nat: ( complex > nat ) > set_complex > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Complex__Ocomplex_001t__Rat__Orat,type,
% 13.71/7.66 image_complex_rat: ( complex > rat ) > set_complex > set_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 13.71/7.66 image_complex_real: ( complex > real ) > set_complex > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Complex__Ocomplex_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 image_932796090930683071T_VEBT: ( complex > vEBT_VEBT ) > set_complex > set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001_Eo,type,
% 13.71/7.66 image_int_o: ( int > $o ) > set_int > set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 image_1587234942943678608nteger: ( int > code_integer ) > set_int > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Complex__Ocomplex,type,
% 13.71/7.66 image_int_complex: ( int > complex ) > set_int > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 13.71/7.66 image_int_int: ( int > int ) > set_int > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
% 13.71/7.66 image_int_nat: ( int > nat ) > set_int > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Real__Oreal,type,
% 13.71/7.66 image_int_real: ( int > real ) > set_int > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__String__Oliteral,type,
% 13.71/7.66 image_int_literal: ( int > literal ) > set_int > set_literal ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 image_int_VEBT_VEBT: ( int > vEBT_VEBT ) > set_int > set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__List__Olist_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
% 13.71/7.66 image_list_o_set_o: ( list_o > set_o ) > set_list_o > set_set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__List__Olist_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
% 13.71/7.66 image_3606813740839090725et_int: ( list_int > set_int ) > set_list_int > set_set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 13.71/7.66 image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__List__Olist_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 image_1775855109352712557et_nat: ( list_nat > set_nat ) > set_list_nat > set_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__List__Olist_It__Real__Oreal_J_001t__Set__Oset_It__Real__Oreal_J,type,
% 13.71/7.66 image_6239767680843085477t_real: ( list_real > set_real ) > set_list_real > set_set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__List__Olist_It__VEBT____Definitions__OVEBT_J_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 image_6463372868993444447T_VEBT: ( list_VEBT_VEBT > set_VEBT_VEBT ) > set_list_VEBT_VEBT > set_set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001_Eo,type,
% 13.71/7.66 image_nat_o: ( nat > $o ) > set_nat > set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 image_1215581382706833972nteger: ( nat > code_integer ) > set_nat > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 13.71/7.66 image_nat_complex: ( nat > complex ) > set_nat > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 13.71/7.66 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 13.71/7.66 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Rat__Orat,type,
% 13.71/7.66 image_nat_rat: ( nat > rat ) > set_nat > set_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 13.71/7.66 image_nat_real: ( nat > real ) > set_nat > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Oliteral,type,
% 13.71/7.66 image_nat_literal: ( nat > literal ) > set_nat > set_literal ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 image_nat_VEBT_VEBTi: ( nat > vEBT_VEBTi ) > set_nat > set_VEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 image_nat_VEBT_VEBT: ( nat > vEBT_VEBT ) > set_nat > set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Rat__Orat_001t__Rat__Orat,type,
% 13.71/7.66 image_rat_rat: ( rat > rat ) > set_rat > set_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 image_4958697645175560720nteger: ( real > code_integer ) > set_real > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 13.71/7.66 image_real_complex: ( real > complex ) > set_real > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Int__Oint,type,
% 13.71/7.66 image_real_int: ( real > int ) > set_real > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Nat__Onat,type,
% 13.71/7.66 image_real_nat: ( real > nat ) > set_real > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 13.71/7.66 image_real_real: ( real > real ) > set_real > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 image_real_VEBT_VEBT: ( real > vEBT_VEBT ) > set_real > set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_I_Eo_J_001t__Set__Oset_I_Eo_J,type,
% 13.71/7.66 image_set_o_set_o: ( set_o > set_o ) > set_set_o > set_set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
% 13.71/7.66 image_524474410958335435et_int: ( set_int > set_int ) > set_set_int > set_set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 image_4702325430467532143et_nat: ( set_int > set_nat ) > set_set_int > set_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 13.71/7.66 image_set_nat_int: ( set_nat > int ) > set_set_nat > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 13.71/7.66 image_set_nat_nat: ( set_nat > nat ) > set_set_nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Int__Oint_J,type,
% 13.71/7.66 image_3739036796817536367et_int: ( set_nat > set_int ) > set_set_nat > set_set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 image_7916887816326733075et_nat: ( set_nat > set_nat ) > set_set_nat > set_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 13.71/7.66 image_6725021117256019401et_nat: ( set_nat > set_set_nat ) > set_set_nat > set_set_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Real__Oreal_J_001t__Set__Oset_It__Real__Oreal_J,type,
% 13.71/7.66 image_2436557299294012491t_real: ( set_real > set_real ) > set_set_real > set_set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 13.71/7.66 image_7884819252390400639et_nat: ( set_set_nat > set_set_nat ) > set_set_set_nat > set_set_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 image_1661326939266726661T_VEBT: ( set_VEBT_VEBT > set_VEBT_VEBT ) > set_set_VEBT_VEBT > set_set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__String__Oliteral_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 image_4442872163159017964nteger: ( literal > code_integer ) > set_literal > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__String__Oliteral_001t__Complex__Ocomplex,type,
% 13.71/7.66 image_5274195009022015549omplex: ( literal > complex ) > set_literal > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__String__Oliteral_001t__Nat__Onat,type,
% 13.71/7.66 image_literal_nat: ( literal > nat ) > set_literal > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__String__Oliteral_001t__String__Oliteral,type,
% 13.71/7.66 image_8195128725298311301iteral: ( literal > literal ) > set_literal > set_literal ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__Uint32__Ouint32_001t__Uint32__Ouint32,type,
% 13.71/7.66 image_uint32_uint32: ( uint32 > uint32 ) > set_uint32 > set_uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
% 13.71/7.66 image_VEBT_VEBTi_int: ( vEBT_VEBTi > int ) > set_VEBT_VEBTi > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 13.71/7.66 image_VEBT_VEBTi_nat: ( vEBT_VEBTi > nat ) > set_VEBT_VEBTi > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____BuildupMemImp__OVEBTi_001t__Real__Oreal,type,
% 13.71/7.66 image_6202559892754154600i_real: ( vEBT_VEBTi > real ) > set_VEBT_VEBTi > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 image_7547481670047419768T_VEBT: ( vEBT_VEBTi > vEBT_VEBT ) > set_VEBT_VEBTi > set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 13.71/7.66 image_VEBT_VEBT_o: ( vEBT_VEBT > $o ) > set_VEBT_VEBT > set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 image_2092689629700589388nteger: ( vEBT_VEBT > code_integer ) > set_VEBT_VEBT > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Complex__Ocomplex,type,
% 13.71/7.66 image_3793382806556112285omplex: ( vEBT_VEBT > complex ) > set_VEBT_VEBT > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 13.71/7.66 image_VEBT_VEBT_int: ( vEBT_VEBT > int ) > set_VEBT_VEBT > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 13.71/7.66 image_VEBT_VEBT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 13.71/7.66 image_VEBT_VEBT_real: ( vEBT_VEBT > real ) > set_VEBT_VEBT > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oimage_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 image_3375948659692109573T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > set_VEBT_VEBT > set_VEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001_Eo,type,
% 13.71/7.66 insert_o: $o > set_o > set_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Code____Numeral__Ointeger,type,
% 13.71/7.66 insert_Code_integer: code_integer > set_Code_integer > set_Code_integer ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 13.71/7.66 insert_complex: complex > set_complex > set_complex ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 13.71/7.66 insert_int: int > set_int > set_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
% 13.71/7.66 insert_list_nat: list_nat > set_list_nat > set_list_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 13.71/7.66 insert_nat: nat > set_nat > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 13.71/7.66 insert_num: num > set_num > set_num ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 13.71/7.66 insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 13.71/7.66 insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 13.71/7.66 insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Uint32__Ouint32_Mt__Uint32__Ouint32_J,type,
% 13.71/7.66 insert4454361187789264009uint32: produc827990862158126777uint32 > set_Pr1773385645901665561uint32 > set_Pr1773385645901665561uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 insert494605675473494903T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > set_Pr6192946355708809607T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 13.71/7.66 insert_rat: rat > set_rat > set_rat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 13.71/7.66 insert_real: real > set_real > set_real ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__String__Oliteral,type,
% 13.71/7.66 insert_literal: literal > set_literal > set_literal ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Set_Oinsert_001t__Uint32__Ouint32,type,
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% 13.71/7.66 thf(sy_c_Set_Oremove_001t__Nat__Onat,type,
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% 13.71/7.66 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
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% 13.71/7.66
% 13.71/7.66 thf(sy_c_Transitive__Closure_Otrancl_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 transi8906537157094044885T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr6192946355708809607T_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Type__Length_Olen0__class_Olen__of_001t__Numeral____Type__Onum0,type,
% 13.71/7.66 type_l4264026598287037464l_num0: itself_Numeral_num0 > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Typedef_Otype__definition_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 13.71/7.66 type_d8366093980585677751er_int: ( code_integer > int ) > ( int > code_integer ) > set_int > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Odiv0__uint32,type,
% 13.71/7.66 div0_uint32: uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Omod0__uint32,type,
% 13.71/7.66 mod0_uint32: uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Oset__bits__aux__uint32,type,
% 13.71/7.66 set_bits_aux_uint32: ( nat > $o ) > nat > uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Osigned__drop__bit__uint32,type,
% 13.71/7.66 signed489701013188660438uint32: nat > uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32_ORep__uint32,type,
% 13.71/7.66 rep_uint32: uint32 > word_N3645301735248828278l_num1 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32__divmod,type,
% 13.71/7.66 uint32_divmod: uint32 > uint32 > produc827990862158126777uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32__sdiv,type,
% 13.71/7.66 uint32_sdiv: uint32 > uint32 > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32__set__bit,type,
% 13.71/7.66 uint32_set_bit: uint32 > code_integer > $o > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32__shiftl,type,
% 13.71/7.66 uint32_shiftl: uint32 > code_integer > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32__shiftr,type,
% 13.71/7.66 uint32_shiftr: uint32 > code_integer > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32__sshiftr,type,
% 13.71/7.66 uint32_sshiftr: uint32 > code_integer > uint32 ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_Uint32_Ouint32__test__bit,type,
% 13.71/7.66 uint32_test_bit: uint32 > code_integer > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t,type,
% 13.71/7.66 vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H,type,
% 13.71/7.66 vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H__rel,type,
% 13.71/7.66 vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t__rel,type,
% 13.71/7.66 vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t,type,
% 13.71/7.66 vEBT_T_m_a_x_t: vEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t__rel,type,
% 13.71/7.66 vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 13.71/7.66 vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 13.71/7.66 vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 13.71/7.66 vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 13.71/7.66 vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l,type,
% 13.71/7.66 vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l__rel,type,
% 13.71/7.66 vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t,type,
% 13.71/7.66 vEBT_T_m_i_n_t: vEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t__rel,type,
% 13.71/7.66 vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d,type,
% 13.71/7.66 vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H,type,
% 13.71/7.66 vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H__rel,type,
% 13.71/7.66 vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d__rel,type,
% 13.71/7.66 vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c,type,
% 13.71/7.66 vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H,type,
% 13.71/7.66 vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H__rel,type,
% 13.71/7.66 vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c__rel,type,
% 13.71/7.66 vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi,type,
% 13.71/7.66 vEBT_V441764108873111860ildupi: nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi_H,type,
% 13.71/7.66 vEBT_V9176841429113362141ildupi: nat > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi_H__rel,type,
% 13.71/7.66 vEBT_V3352910403632780892pi_rel: nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OT__vebt__buildupi__rel,type,
% 13.71/7.66 vEBT_V2957053500504383685pi_rel: nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb,type,
% 13.71/7.66 vEBT_VEBT_Tb: nat > int ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb_H,type,
% 13.71/7.66 vEBT_VEBT_Tb2: nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb_H__rel,type,
% 13.71/7.66 vEBT_VEBT_Tb_rel: nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OTb__rel,type,
% 13.71/7.66 vEBT_VEBT_Tb_rel2: nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ohighi,type,
% 13.71/7.66 vEBT_VEBT_highi: nat > nat > heap_Time_Heap_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Olowi,type,
% 13.71/7.66 vEBT_VEBT_lowi: nat > nat > heap_Time_Heap_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_OminNulli,type,
% 13.71/7.66 vEBT_VEBT_minNulli: vEBT_VEBTi > heap_Time_Heap_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__buildupi_H,type,
% 13.71/7.66 vEBT_V739175172307565963ildupi: nat > heap_T8145700208782473153_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__inserti_H,type,
% 13.71/7.66 vEBT_V3964819847710782039nserti: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBT__internal_Ovebt__memberi_H,type,
% 13.71/7.66 vEBT_V854960066525838166emberi: vEBT_VEBT > vEBT_VEBTi > nat > heap_Time_Heap_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_OLeafi,type,
% 13.71/7.66 vEBT_Leafi: $o > $o > vEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_ONodei,type,
% 13.71/7.66 vEBT_Nodei: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > vEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_OVEBTi_Osize__VEBTi,type,
% 13.71/7.66 vEBT_size_VEBTi: vEBT_VEBTi > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw,type,
% 13.71/7.66 vEBT_vebt_assn_raw: vEBT_VEBT > vEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__assn__raw__rel,type,
% 13.71/7.66 vEBT_v8524038756793281170aw_rel: produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__buildupi,type,
% 13.71/7.66 vEBT_vebt_buildupi: nat > heap_T8145700208782473153_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__inserti,type,
% 13.71/7.66 vEBT_vebt_inserti: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__maxti,type,
% 13.71/7.66 vEBT_vebt_maxti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__maxti__rel,type,
% 13.71/7.66 vEBT_vebt_maxti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__memberi,type,
% 13.71/7.66 vEBT_vebt_memberi: vEBT_VEBTi > nat > heap_Time_Heap_o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__minti,type,
% 13.71/7.66 vEBT_vebt_minti: vEBT_VEBTi > heap_T2636463487746394924on_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__BuildupMemImp_Ovebt__minti__rel,type,
% 13.71/7.66 vEBT_vebt_minti_rel: vEBT_VEBTi > vEBT_VEBTi > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 13.71/7.66 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 13.71/7.66 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 13.71/7.66 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 13.71/7.66 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 13.71/7.66 vEBT_VEBT_high: nat > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 13.71/7.66 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 13.71/7.66 vEBT_VEBT_low: nat > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 13.71/7.66 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 13.71/7.66 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 13.71/7.66 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 13.71/7.66 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 13.71/7.66 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 13.71/7.66 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 13.71/7.66 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 13.71/7.66 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 13.71/7.66 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 13.71/7.66 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__DelImperative_OVEBT__internal_Ovebt__deletei_H,type,
% 13.71/7.66 vEBT_V1365221501068881998eletei: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__DelImperative_Ovebt__deletei,type,
% 13.71/7.66 vEBT_vebt_deletei: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e,type,
% 13.71/7.66 vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__DeleteBounds_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e__rel,type,
% 13.71/7.66 vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__DeleteBounds_OVEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H,type,
% 13.71/7.66 vEBT_V1232361888498592333_e_t_e: vEBT_VEBT > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__DeleteBounds_OVEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H__rel,type,
% 13.71/7.66 vEBT_V6368547301243506412_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 13.71/7.66 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 13.71/7.66 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 13.71/7.66 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 13.71/7.66 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H,type,
% 13.71/7.66 vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__InsertCorrectness_OVEBT__internal_Oinsert_H__rel,type,
% 13.71/7.66 vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 13.71/7.66 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 13.71/7.66 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Intf__Imperative_Ovebt__assn,type,
% 13.71/7.66 vEBT_Intf_vebt_assn: nat > set_nat > vEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001_Eo_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L6286945158656146733_VEBTi: set_nat > ( $o > vEBT_VEBTi > assn ) > list_o > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L1319876754960170684T_VEBT: set_nat > ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001_Eo,type,
% 13.71/7.66 vEBT_L3563379889750563018_int_o: set_nat > ( int > $o > assn ) > list_int > list_o > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Int__Oint,type,
% 13.71/7.66 vEBT_L8888932350013902202nt_int: set_nat > ( int > int > assn ) > list_int > list_int > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Nat__Onat,type,
% 13.71/7.66 vEBT_L8891422820522952478nt_nat: set_nat > ( int > nat > assn ) > list_int > list_nat > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__Real__Oreal,type,
% 13.71/7.66 vEBT_L7077748017936769786t_real: set_nat > ( int > real > assn ) > list_int > list_real > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L114188773329725699_VEBTi: set_nat > ( int > vEBT_VEBTi > assn ) > list_int > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L2018189785592951398T_VEBT: set_nat > ( int > vEBT_VEBT > assn ) > list_int > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L7489483478785760935_VEBTi: set_nat > ( nat > vEBT_VEBTi > assn ) > list_nat > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L8511957252848910786T_VEBT: set_nat > ( nat > vEBT_VEBT > assn ) > list_nat > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L7851252805511451907_VEBTi: set_nat > ( real > vEBT_VEBTi > assn ) > list_real > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L3095048238742455910T_VEBT: set_nat > ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001_Eo,type,
% 13.71/7.66 vEBT_L3328983362619735041EBTi_o: set_nat > ( vEBT_VEBTi > $o > assn ) > list_VEBT_VEBTi > list_o > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
% 13.71/7.66 vEBT_L2806540629473551875Ti_int: set_nat > ( vEBT_VEBTi > int > assn ) > list_VEBT_VEBTi > list_int > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 13.71/7.66 vEBT_L2809031099982602151Ti_nat: set_nat > ( vEBT_VEBTi > nat > assn ) > list_VEBT_VEBTi > list_nat > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Real__Oreal,type,
% 13.71/7.66 vEBT_L7728200936804140803i_real: set_nat > ( vEBT_VEBTi > real > assn ) > list_VEBT_VEBTi > list_real > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L886525131989349516_VEBTi: set_nat > ( vEBT_VEBTi > vEBT_VEBTi > assn ) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L2497118539674116125T_VEBT: set_nat > ( vEBT_VEBTi > vEBT_VEBT > assn ) > list_VEBT_VEBTi > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 13.71/7.66 vEBT_L8650695023172932196BT_nat: set_nat > ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L1528199826722428489_VEBTi: set_nat > ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_OlistI__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L3204528365124325536T_VEBT: set_nat > ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__Real__Oreal,type,
% 13.71/7.66 vEBT_L4725278957065240257o_real: ( $o > real > assn ) > list_o > list_real > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L1750719106661372127T_VEBT: ( $o > vEBT_VEBT > assn ) > list_o > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Int__Oint,type,
% 13.71/7.66 vEBT_L74593716426352029nt_int: ( int > int > assn ) > list_int > list_int > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__Nat__Onat,type,
% 13.71/7.66 vEBT_L77084186935402305nt_nat: ( int > nat > assn ) > list_int > list_nat > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L6235239671944049190_VEBTi: ( int > vEBT_VEBTi > assn ) > list_int > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Int__Oint_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L1664421287176695555T_VEBT: ( int > vEBT_VEBT > assn ) > list_int > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001t__Real__Oreal,type,
% 13.71/7.66 vEBT_L6102073776069194049t_real: ( nat > real > assn ) > list_nat > list_real > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L8158188754432654943T_VEBT: ( nat > vEBT_VEBT > assn ) > list_nat > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001_Eo,type,
% 13.71/7.66 vEBT_L6234343332106409831real_o: ( real > $o > assn ) > list_real > list_o > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__Real__Oreal,type,
% 13.71/7.66 vEBT_L1930518968523514909l_real: ( real > real > assn ) > list_real > list_real > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L4595930785310033027T_VEBT: ( real > vEBT_VEBT > assn ) > list_real > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Int__Oint,type,
% 13.71/7.66 vEBT_L8927591528087875366Ti_int: ( vEBT_VEBTi > int > assn ) > list_VEBT_VEBTi > list_int > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__Nat__Onat,type,
% 13.71/7.66 vEBT_L8930081998596925642Ti_nat: ( vEBT_VEBTi > nat > assn ) > list_VEBT_VEBTi > list_nat > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L1891944875198410415_VEBTi: ( vEBT_VEBTi > vEBT_VEBTi > assn ) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____BuildupMemImp__OVEBTi_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L7265847600308530106T_VEBT: ( vEBT_VEBTi > vEBT_VEBT > assn ) > list_VEBT_VEBTi > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 13.71/7.66 vEBT_L7489408758114837031VEBT_o: ( vEBT_VEBT > $o > assn ) > list_VEBT_VEBT > list_o > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 13.71/7.66 vEBT_L8296926524756676353BT_nat: ( vEBT_VEBT > nat > assn ) > list_VEBT_VEBT > list_nat > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 13.71/7.66 vEBT_L5781919052683127133T_real: ( vEBT_VEBT > real > assn ) > list_VEBT_VEBT > list_real > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 vEBT_L6296928887356842470_VEBTi: ( vEBT_VEBT > vEBT_VEBTi > assn ) > list_VEBT_VEBT > list_VEBT_VEBTi > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__List__Assn_Olist__assn_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 vEBT_L1279224858307276611T_VEBT: ( vEBT_VEBT > vEBT_VEBT > assn ) > list_VEBT_VEBT > list_VEBT_VEBT > assn ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 13.71/7.66 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 13.71/7.66 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 13.71/7.66 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 13.71/7.66 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 13.71/7.66 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 13.71/7.66 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 13.71/7.66 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 13.71/7.66 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 13.71/7.66 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 13.71/7.66 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 13.71/7.66 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 13.71/7.66 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 13.71/7.66 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 13.71/7.66 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 13.71/7.66 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 13.71/7.66 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 13.71/7.66 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 13.71/7.66 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 13.71/7.66 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 13.71/7.66 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 13.71/7.66 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 13.71/7.66 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d,type,
% 13.71/7.66 vEBT_V8646137997579335489_i_l_d: nat > nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_VEBT__Space_OVEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p,type,
% 13.71/7.66 vEBT_V8346862874174094_d_u_p: nat > nat ).
% 13.71/7.66
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% 13.71/7.66 thf(sy_c_member_001t__Product____Type__Oprod_It__Uint32__Ouint32_Mt__Uint32__Ouint32_J,type,
% 13.71/7.66 member8027108493173000802uint32: produc827990862158126777uint32 > set_Pr1773385645901665561uint32 > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____BuildupMemImp__OVEBTi_Mt__VEBT____BuildupMemImp__OVEBTi_J,type,
% 13.71/7.66 member660371905731732212_VEBTi: produc3777764054643897931_VEBTi > set_Pr2227491710730465451_VEBTi > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 13.71/7.66 member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 13.71/7.66 member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 13.71/7.66 member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J,type,
% 13.71/7.66 member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Rat__Orat,type,
% 13.71/7.66 member_rat: rat > set_rat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Real__Oreal,type,
% 13.71/7.66 member_real: real > set_real > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Set__Oset_I_Eo_J,type,
% 13.71/7.66 member_set_o: set_o > set_set_o > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 13.71/7.66 member_set_int: set_int > set_set_int > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 13.71/7.66 member_set_nat: set_nat > set_set_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Set__Oset_It__Real__Oreal_J,type,
% 13.71/7.66 member_set_real: set_real > set_set_real > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 13.71/7.66 member_set_set_nat: set_set_nat > set_set_set_nat > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 13.71/7.66 member_set_VEBT_VEBT: set_VEBT_VEBT > set_set_VEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__String__Oliteral,type,
% 13.71/7.66 member_literal: literal > set_literal > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__Uint32__Ouint32,type,
% 13.71/7.66 member_uint32: uint32 > set_uint32 > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__VEBT____BuildupMemImp__OVEBTi,type,
% 13.71/7.66 member_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 13.71/7.66 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_a,type,
% 13.71/7.66 a: heap_e7401611519738050253t_unit ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_b,type,
% 13.71/7.66 b: set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_n,type,
% 13.71/7.66 n: nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_r,type,
% 13.71/7.66 r: vEBT_VEBTi ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_s,type,
% 13.71/7.66 s: set_nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_t,type,
% 13.71/7.66 t: vEBT_VEBT ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_x,type,
% 13.71/7.66 x: nat ).
% 13.71/7.66
% 13.71/7.66 thf(sy_v_xa,type,
% 13.71/7.66 xa: nat ).
% 13.71/7.66
% 13.71/7.66 thf(fact_0_invar__vebt__delete,axiom,
% 13.71/7.66 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.66 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_1_set__vebt__equal,axiom,
% 13.71/7.67 ! [T_1: vEBT_VEBT,N: nat,T_2: vEBT_VEBT] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T_1 @ N )
% 13.71/7.67 => ( ( vEBT_invar_vebt @ T_2 @ N )
% 13.71/7.67 => ( ( T_1 = T_2 )
% 13.71/7.67 = ( ( vEBT_set_vebt @ T_1 )
% 13.71/7.67 = ( vEBT_set_vebt @ T_2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_2_unique__tree,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,S: vEBT_VEBT] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_invar_vebt @ S @ N )
% 13.71/7.67 => ( ( ( vEBT_set_vebt @ T )
% 13.71/7.67 = ( vEBT_set_vebt @ S ) )
% 13.71/7.67 => ( S = T ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_3_insert_H__pres__valid,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( vEBT_invar_vebt @ ( vEBT_VEBT_insert @ T @ X ) @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_4_perIT__concat,axiom,
% 13.71/7.67 ! [S: vEBT_VEBT,T: vEBT_VEBT,U: vEBT_VEBT] :
% 13.71/7.67 ( ( vEBT_V6289311342943941716sTrans @ S @ T )
% 13.71/7.67 => ( ( vEBT_V6289311342943941716sTrans @ T @ U )
% 13.71/7.67 => ( vEBT_V6289311342943941716sTrans @ S @ U ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_5_set__vebt__set__vebt_H__valid,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_set_vebt @ T )
% 13.71/7.67 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_6_uniquetree,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,S: vEBT_VEBT] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_invar_vebt @ S @ N )
% 13.71/7.67 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 13.71/7.67 = ( vEBT_VEBT_set_vebt @ S ) )
% 13.71/7.67 => ( S = T ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_7_Rep__assn__inject,axiom,
% 13.71/7.67 ! [X: assn,Y: assn] :
% 13.71/7.67 ( ( ( rep_assn @ X )
% 13.71/7.67 = ( rep_assn @ Y ) )
% 13.71/7.67 = ( X = Y ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_8_prod_Oinject,axiom,
% 13.71/7.67 ! [X1: uint32,X2: uint32,Y1: uint32,Y2: uint32] :
% 13.71/7.67 ( ( ( produc1400373151660368625uint32 @ X1 @ X2 )
% 13.71/7.67 = ( produc1400373151660368625uint32 @ Y1 @ Y2 ) )
% 13.71/7.67 = ( ( X1 = Y1 )
% 13.71/7.67 & ( X2 = Y2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_9_prod_Oinject,axiom,
% 13.71/7.67 ! [X1: nat,X2: nat,Y1: nat,Y2: nat] :
% 13.71/7.67 ( ( ( product_Pair_nat_nat @ X1 @ X2 )
% 13.71/7.67 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 13.71/7.67 = ( ( X1 = Y1 )
% 13.71/7.67 & ( X2 = Y2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_10_prod_Oinject,axiom,
% 13.71/7.67 ! [X1: int,X2: int,Y1: int,Y2: int] :
% 13.71/7.67 ( ( ( product_Pair_int_int @ X1 @ X2 )
% 13.71/7.67 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 13.71/7.67 = ( ( X1 = Y1 )
% 13.71/7.67 & ( X2 = Y2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_11_prod_Oinject,axiom,
% 13.71/7.67 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 13.71/7.67 ( ( ( produc5001842942810119800et_nat @ X1 @ X2 )
% 13.71/7.67 = ( produc5001842942810119800et_nat @ Y1 @ Y2 ) )
% 13.71/7.67 = ( ( X1 = Y1 )
% 13.71/7.67 & ( X2 = Y2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_12_prod_Oinject,axiom,
% 13.71/7.67 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 13.71/7.67 ( ( ( produc2245416461498447860et_nat @ X1 @ X2 )
% 13.71/7.67 = ( produc2245416461498447860et_nat @ Y1 @ Y2 ) )
% 13.71/7.67 = ( ( X1 = Y1 )
% 13.71/7.67 & ( X2 = Y2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_13_old_Oprod_Oinject,axiom,
% 13.71/7.67 ! [A: uint32,B: uint32,A2: uint32,B2: uint32] :
% 13.71/7.67 ( ( ( produc1400373151660368625uint32 @ A @ B )
% 13.71/7.67 = ( produc1400373151660368625uint32 @ A2 @ B2 ) )
% 13.71/7.67 = ( ( A = A2 )
% 13.71/7.67 & ( B = B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_14_old_Oprod_Oinject,axiom,
% 13.71/7.67 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 13.71/7.67 ( ( ( product_Pair_nat_nat @ A @ B )
% 13.71/7.67 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 13.71/7.67 = ( ( A = A2 )
% 13.71/7.67 & ( B = B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_15_old_Oprod_Oinject,axiom,
% 13.71/7.67 ! [A: int,B: int,A2: int,B2: int] :
% 13.71/7.67 ( ( ( product_Pair_int_int @ A @ B )
% 13.71/7.67 = ( product_Pair_int_int @ A2 @ B2 ) )
% 13.71/7.67 = ( ( A = A2 )
% 13.71/7.67 & ( B = B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_16_old_Oprod_Oinject,axiom,
% 13.71/7.67 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 13.71/7.67 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 13.71/7.67 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 13.71/7.67 = ( ( A = A2 )
% 13.71/7.67 & ( B = B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_17_old_Oprod_Oinject,axiom,
% 13.71/7.67 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 13.71/7.67 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 13.71/7.67 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 13.71/7.67 = ( ( A = A2 )
% 13.71/7.67 & ( B = B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_18_valid__eq,axiom,
% 13.71/7.67 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 13.71/7.67
% 13.71/7.67 thf(fact_19_valid__eq1,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,D: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ D )
% 13.71/7.67 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_20_valid__eq2,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,D: nat] :
% 13.71/7.67 ( ( vEBT_VEBT_valid @ T @ D )
% 13.71/7.67 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_21_set__vebt__member,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_vebt_member @ T @ X )
% 13.71/7.67 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_22_dele__member__cont__corr,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 13.71/7.67 = ( ( X != Y )
% 13.71/7.67 & ( vEBT_vebt_member @ T @ Y ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_23_dele__bmo__cont__corr,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 13.71/7.67 = ( ( X != Y )
% 13.71/7.67 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_24_valid__member__both__member__options,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 13.71/7.67 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_25_both__member__options__equiv__member,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 13.71/7.67 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_26_times__assn__raw_Ocases,axiom,
% 13.71/7.67 ! [X: produc2732055786443039994et_nat] :
% 13.71/7.67 ~ ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.71/7.67 ( X
% 13.71/7.67 != ( produc2245416461498447860et_nat @ P @ ( produc5001842942810119800et_nat @ Q @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_27_prod__induct4,axiom,
% 13.71/7.67 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 13.71/7.67 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D2: set_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D2 ) ) ) )
% 13.71/7.67 => ( P2 @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_28_prod__induct3,axiom,
% 13.71/7.67 ! [P2: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 13.71/7.67 ( ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) )
% 13.71/7.67 => ( P2 @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_29_prod__induct3,axiom,
% 13.71/7.67 ! [P2: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 13.71/7.67 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) )
% 13.71/7.67 => ( P2 @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_30_prod__cases4,axiom,
% 13.71/7.67 ! [Y: produc2732055786443039994et_nat] :
% 13.71/7.67 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: heap_e7401611519738050253t_unit,D2: set_nat] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ ( produc7507926704131184380et_nat @ C @ D2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_31_prod__cases3,axiom,
% 13.71/7.67 ! [Y: produc3925858234332021118et_nat] :
% 13.71/7.67 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: heap_e7401611519738050253t_unit,C: set_nat] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( produc5001842942810119800et_nat @ A3 @ ( produc7507926704131184380et_nat @ B3 @ C ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_32_prod__cases3,axiom,
% 13.71/7.67 ! [Y: produc2732055786443039994et_nat] :
% 13.71/7.67 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat > $o,C: produc3658429121746597890et_nat] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( produc2245416461498447860et_nat @ A3 @ ( produc5001842942810119800et_nat @ B3 @ C ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_33_Pair__inject,axiom,
% 13.71/7.67 ! [A: uint32,B: uint32,A2: uint32,B2: uint32] :
% 13.71/7.67 ( ( ( produc1400373151660368625uint32 @ A @ B )
% 13.71/7.67 = ( produc1400373151660368625uint32 @ A2 @ B2 ) )
% 13.71/7.67 => ~ ( ( A = A2 )
% 13.71/7.67 => ( B != B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_34_Pair__inject,axiom,
% 13.71/7.67 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 13.71/7.67 ( ( ( product_Pair_nat_nat @ A @ B )
% 13.71/7.67 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 13.71/7.67 => ~ ( ( A = A2 )
% 13.71/7.67 => ( B != B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_35_Pair__inject,axiom,
% 13.71/7.67 ! [A: int,B: int,A2: int,B2: int] :
% 13.71/7.67 ( ( ( product_Pair_int_int @ A @ B )
% 13.71/7.67 = ( product_Pair_int_int @ A2 @ B2 ) )
% 13.71/7.67 => ~ ( ( A = A2 )
% 13.71/7.67 => ( B != B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_36_Pair__inject,axiom,
% 13.71/7.67 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 13.71/7.67 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 13.71/7.67 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 13.71/7.67 => ~ ( ( A = A2 )
% 13.71/7.67 => ( B != B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_37_Pair__inject,axiom,
% 13.71/7.67 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 13.71/7.67 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 13.71/7.67 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 13.71/7.67 => ~ ( ( A = A2 )
% 13.71/7.67 => ( B != B2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_38_prod__cases,axiom,
% 13.71/7.67 ! [P2: produc827990862158126777uint32 > $o,P3: produc827990862158126777uint32] :
% 13.71/7.67 ( ! [A3: uint32,B3: uint32] : ( P2 @ ( produc1400373151660368625uint32 @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ P3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_39_prod__cases,axiom,
% 13.71/7.67 ! [P2: product_prod_nat_nat > $o,P3: product_prod_nat_nat] :
% 13.71/7.67 ( ! [A3: nat,B3: nat] : ( P2 @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ P3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_40_prod__cases,axiom,
% 13.71/7.67 ! [P2: product_prod_int_int > $o,P3: product_prod_int_int] :
% 13.71/7.67 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ P3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_41_prod__cases,axiom,
% 13.71/7.67 ! [P2: produc3925858234332021118et_nat > $o,P3: produc3925858234332021118et_nat] :
% 13.71/7.67 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] : ( P2 @ ( produc5001842942810119800et_nat @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ P3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_42_prod__cases,axiom,
% 13.71/7.67 ! [P2: produc2732055786443039994et_nat > $o,P3: produc2732055786443039994et_nat] :
% 13.71/7.67 ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] : ( P2 @ ( produc2245416461498447860et_nat @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ P3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_43_surj__pair,axiom,
% 13.71/7.67 ! [P3: produc827990862158126777uint32] :
% 13.71/7.67 ? [X3: uint32,Y3: uint32] :
% 13.71/7.67 ( P3
% 13.71/7.67 = ( produc1400373151660368625uint32 @ X3 @ Y3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_44_surj__pair,axiom,
% 13.71/7.67 ! [P3: product_prod_nat_nat] :
% 13.71/7.67 ? [X3: nat,Y3: nat] :
% 13.71/7.67 ( P3
% 13.71/7.67 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_45_surj__pair,axiom,
% 13.71/7.67 ! [P3: product_prod_int_int] :
% 13.71/7.67 ? [X3: int,Y3: int] :
% 13.71/7.67 ( P3
% 13.71/7.67 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_46_surj__pair,axiom,
% 13.71/7.67 ! [P3: produc3925858234332021118et_nat] :
% 13.71/7.67 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 13.71/7.67 ( P3
% 13.71/7.67 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_47_surj__pair,axiom,
% 13.71/7.67 ! [P3: produc2732055786443039994et_nat] :
% 13.71/7.67 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 13.71/7.67 ( P3
% 13.71/7.67 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_48_old_Oprod_Oexhaust,axiom,
% 13.71/7.67 ! [Y: produc827990862158126777uint32] :
% 13.71/7.67 ~ ! [A3: uint32,B3: uint32] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( produc1400373151660368625uint32 @ A3 @ B3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_49_old_Oprod_Oexhaust,axiom,
% 13.71/7.67 ! [Y: product_prod_nat_nat] :
% 13.71/7.67 ~ ! [A3: nat,B3: nat] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_50_old_Oprod_Oexhaust,axiom,
% 13.71/7.67 ! [Y: product_prod_int_int] :
% 13.71/7.67 ~ ! [A3: int,B3: int] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_51_old_Oprod_Oexhaust,axiom,
% 13.71/7.67 ! [Y: produc3925858234332021118et_nat] :
% 13.71/7.67 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( produc5001842942810119800et_nat @ A3 @ B3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_52_old_Oprod_Oexhaust,axiom,
% 13.71/7.67 ! [Y: produc2732055786443039994et_nat] :
% 13.71/7.67 ~ ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( produc2245416461498447860et_nat @ A3 @ B3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_53_one__assn__raw_Ocases,axiom,
% 13.71/7.67 ! [X: produc3658429121746597890et_nat] :
% 13.71/7.67 ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.71/7.67 ( X
% 13.71/7.67 != ( produc7507926704131184380et_nat @ H @ As ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_54_set__vebt__finite,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_55_mem__Collect__eq,axiom,
% 13.71/7.67 ! [A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.71/7.67 ( ( member_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P2 ) )
% 13.71/7.67 = ( P2 @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_56_mem__Collect__eq,axiom,
% 13.71/7.67 ! [A: real,P2: real > $o] :
% 13.71/7.67 ( ( member_real @ A @ ( collect_real @ P2 ) )
% 13.71/7.67 = ( P2 @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_57_mem__Collect__eq,axiom,
% 13.71/7.67 ! [A: complex,P2: complex > $o] :
% 13.71/7.67 ( ( member_complex @ A @ ( collect_complex @ P2 ) )
% 13.71/7.67 = ( P2 @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_58_mem__Collect__eq,axiom,
% 13.71/7.67 ! [A: list_nat,P2: list_nat > $o] :
% 13.71/7.67 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 13.71/7.67 = ( P2 @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_59_mem__Collect__eq,axiom,
% 13.71/7.67 ! [A: set_nat,P2: set_nat > $o] :
% 13.71/7.67 ( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 13.71/7.67 = ( P2 @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_60_mem__Collect__eq,axiom,
% 13.71/7.67 ! [A: nat,P2: nat > $o] :
% 13.71/7.67 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 13.71/7.67 = ( P2 @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_61_mem__Collect__eq,axiom,
% 13.71/7.67 ! [A: int,P2: int > $o] :
% 13.71/7.67 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 13.71/7.67 = ( P2 @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_62_Collect__mem__eq,axiom,
% 13.71/7.67 ! [A4: set_VEBT_VEBT] :
% 13.71/7.67 ( ( collect_VEBT_VEBT
% 13.71/7.67 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A4 ) )
% 13.71/7.67 = A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_63_Collect__mem__eq,axiom,
% 13.71/7.67 ! [A4: set_real] :
% 13.71/7.67 ( ( collect_real
% 13.71/7.67 @ ^ [X4: real] : ( member_real @ X4 @ A4 ) )
% 13.71/7.67 = A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_64_Collect__mem__eq,axiom,
% 13.71/7.67 ! [A4: set_complex] :
% 13.71/7.67 ( ( collect_complex
% 13.71/7.67 @ ^ [X4: complex] : ( member_complex @ X4 @ A4 ) )
% 13.71/7.67 = A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_65_Collect__mem__eq,axiom,
% 13.71/7.67 ! [A4: set_list_nat] :
% 13.71/7.67 ( ( collect_list_nat
% 13.71/7.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A4 ) )
% 13.71/7.67 = A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_66_Collect__mem__eq,axiom,
% 13.71/7.67 ! [A4: set_set_nat] :
% 13.71/7.67 ( ( collect_set_nat
% 13.71/7.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 13.71/7.67 = A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_67_Collect__mem__eq,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ( collect_nat
% 13.71/7.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 13.71/7.67 = A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_68_Collect__mem__eq,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ( collect_int
% 13.71/7.67 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 13.71/7.67 = A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_69_Collect__cong,axiom,
% 13.71/7.67 ! [P2: complex > $o,Q2: complex > $o] :
% 13.71/7.67 ( ! [X3: complex] :
% 13.71/7.67 ( ( P2 @ X3 )
% 13.71/7.67 = ( Q2 @ X3 ) )
% 13.71/7.67 => ( ( collect_complex @ P2 )
% 13.71/7.67 = ( collect_complex @ Q2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_70_Collect__cong,axiom,
% 13.71/7.67 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 13.71/7.67 ( ! [X3: list_nat] :
% 13.71/7.67 ( ( P2 @ X3 )
% 13.71/7.67 = ( Q2 @ X3 ) )
% 13.71/7.67 => ( ( collect_list_nat @ P2 )
% 13.71/7.67 = ( collect_list_nat @ Q2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_71_Collect__cong,axiom,
% 13.71/7.67 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 13.71/7.67 ( ! [X3: set_nat] :
% 13.71/7.67 ( ( P2 @ X3 )
% 13.71/7.67 = ( Q2 @ X3 ) )
% 13.71/7.67 => ( ( collect_set_nat @ P2 )
% 13.71/7.67 = ( collect_set_nat @ Q2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_72_Collect__cong,axiom,
% 13.71/7.67 ! [P2: nat > $o,Q2: nat > $o] :
% 13.71/7.67 ( ! [X3: nat] :
% 13.71/7.67 ( ( P2 @ X3 )
% 13.71/7.67 = ( Q2 @ X3 ) )
% 13.71/7.67 => ( ( collect_nat @ P2 )
% 13.71/7.67 = ( collect_nat @ Q2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_73_Collect__cong,axiom,
% 13.71/7.67 ! [P2: int > $o,Q2: int > $o] :
% 13.71/7.67 ( ! [X3: int] :
% 13.71/7.67 ( ( P2 @ X3 )
% 13.71/7.67 = ( Q2 @ X3 ) )
% 13.71/7.67 => ( ( collect_int @ P2 )
% 13.71/7.67 = ( collect_int @ Q2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_74_VEBT__internal_OperInsTrans_Ointros_I1_J,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT] : ( vEBT_V6289311342943941716sTrans @ T @ T ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_75_valid__tree__deg__neq__0,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT] :
% 13.71/7.67 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_76_valid__0__not,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT] :
% 13.71/7.67 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_77_min__Null__member,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,X: nat] :
% 13.71/7.67 ( ( vEBT_VEBT_minNull @ T )
% 13.71/7.67 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_78_not__min__Null__member,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT] :
% 13.71/7.67 ( ~ ( vEBT_VEBT_minNull @ T )
% 13.71/7.67 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_79_deg__deg__n,axiom,
% 13.71/7.67 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 13.71/7.67 => ( Deg = N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_80_ssubst__Pair__rhs,axiom,
% 13.71/7.67 ! [R: uint32,S: uint32,R2: set_Pr1773385645901665561uint32,S2: uint32] :
% 13.71/7.67 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ R @ S ) @ R2 )
% 13.71/7.67 => ( ( S2 = S )
% 13.71/7.67 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ R @ S2 ) @ R2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_81_ssubst__Pair__rhs,axiom,
% 13.71/7.67 ! [R: nat,S: nat,R2: set_Pr1261947904930325089at_nat,S2: nat] :
% 13.71/7.67 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S ) @ R2 )
% 13.71/7.67 => ( ( S2 = S )
% 13.71/7.67 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R @ S2 ) @ R2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_82_ssubst__Pair__rhs,axiom,
% 13.71/7.67 ! [R: int,S: int,R2: set_Pr958786334691620121nt_int,S2: int] :
% 13.71/7.67 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S ) @ R2 )
% 13.71/7.67 => ( ( S2 = S )
% 13.71/7.67 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ R @ S2 ) @ R2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_83_ssubst__Pair__rhs,axiom,
% 13.71/7.67 ! [R: produc3658429121746597890et_nat > $o,S: produc3658429121746597890et_nat,R2: set_Pr3286484037609594932et_nat,S2: produc3658429121746597890et_nat] :
% 13.71/7.67 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R @ S ) @ R2 )
% 13.71/7.67 => ( ( S2 = S )
% 13.71/7.67 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R @ S2 ) @ R2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_84_ssubst__Pair__rhs,axiom,
% 13.71/7.67 ! [R: produc3658429121746597890et_nat > $o,S: produc3925858234332021118et_nat,R2: set_Pr8536935166611901872et_nat,S2: produc3925858234332021118et_nat] :
% 13.71/7.67 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R @ S ) @ R2 )
% 13.71/7.67 => ( ( S2 = S )
% 13.71/7.67 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R @ S2 ) @ R2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_85_bex2I,axiom,
% 13.71/7.67 ! [A: uint32,B: uint32,S3: set_Pr1773385645901665561uint32,P2: uint32 > uint32 > $o] :
% 13.71/7.67 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ S3 )
% 13.71/7.67 => ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ S3 )
% 13.71/7.67 => ( P2 @ A @ B ) )
% 13.71/7.67 => ? [A3: uint32,B3: uint32] :
% 13.71/7.67 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A3 @ B3 ) @ S3 )
% 13.71/7.67 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_86_bex2I,axiom,
% 13.71/7.67 ! [A: nat,B: nat,S3: set_Pr1261947904930325089at_nat,P2: nat > nat > $o] :
% 13.71/7.67 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S3 )
% 13.71/7.67 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S3 )
% 13.71/7.67 => ( P2 @ A @ B ) )
% 13.71/7.67 => ? [A3: nat,B3: nat] :
% 13.71/7.67 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ S3 )
% 13.71/7.67 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_87_bex2I,axiom,
% 13.71/7.67 ! [A: int,B: int,S3: set_Pr958786334691620121nt_int,P2: int > int > $o] :
% 13.71/7.67 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S3 )
% 13.71/7.67 => ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ S3 )
% 13.71/7.67 => ( P2 @ A @ B ) )
% 13.71/7.67 => ? [A3: int,B3: int] :
% 13.71/7.67 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ S3 )
% 13.71/7.67 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_88_bex2I,axiom,
% 13.71/7.67 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S3: set_Pr3286484037609594932et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 13.71/7.67 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S3 )
% 13.71/7.67 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S3 )
% 13.71/7.67 => ( P2 @ A @ B ) )
% 13.71/7.67 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 13.71/7.67 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A3 @ B3 ) @ S3 )
% 13.71/7.67 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_89_bex2I,axiom,
% 13.71/7.67 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S3: set_Pr8536935166611901872et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 13.71/7.67 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S3 )
% 13.71/7.67 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S3 )
% 13.71/7.67 => ( P2 @ A @ B ) )
% 13.71/7.67 => ? [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 13.71/7.67 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A3 @ B3 ) @ S3 )
% 13.71/7.67 & ( P2 @ A3 @ B3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_90_set__vebt__minNull,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ( vEBT_VEBT_minNull @ T )
% 13.71/7.67 = ( ( vEBT_set_vebt @ T )
% 13.71/7.67 = bot_bot_set_nat ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_91_VEBT_Oinject_I1_J,axiom,
% 13.71/7.67 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 13.71/7.67 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 13.71/7.67 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 13.71/7.67 = ( ( X11 = Y11 )
% 13.71/7.67 & ( X12 = Y12 )
% 13.71/7.67 & ( X13 = Y13 )
% 13.71/7.67 & ( X14 = Y14 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_92_deg__not__0,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,N: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.67 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_93_deg__SUcn__Node,axiom,
% 13.71/7.67 ! [Tree: vEBT_VEBT,N: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 13.71/7.67 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.71/7.67 ( Tree
% 13.71/7.67 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_94_Leaf__0__not,axiom,
% 13.71/7.67 ! [A: $o,B: $o] :
% 13.71/7.67 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_95_divides__aux__eq,axiom,
% 13.71/7.67 ! [Q3: nat,R: nat] :
% 13.71/7.67 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R ) )
% 13.71/7.67 = ( R = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_96_divides__aux__eq,axiom,
% 13.71/7.67 ! [Q3: int,R: int] :
% 13.71/7.67 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.71/7.67 = ( R = zero_zero_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_97_zero__natural_Orsp,axiom,
% 13.71/7.67 zero_zero_nat = zero_zero_nat ).
% 13.71/7.67
% 13.71/7.67 thf(fact_98_VEBT_Oinject_I2_J,axiom,
% 13.71/7.67 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 13.71/7.67 ( ( ( vEBT_Leaf @ X21 @ X22 )
% 13.71/7.67 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 13.71/7.67 = ( ( X21 = Y21 )
% 13.71/7.67 & ( X22 = Y22 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_99_not__gr__zero,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 13.71/7.67 = ( N = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_100_succ__none__empty,axiom,
% 13.71/7.67 ! [Xs: set_nat,A: nat] :
% 13.71/7.67 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A @ X_1 )
% 13.71/7.67 => ( ( finite_finite_nat @ Xs )
% 13.71/7.67 => ~ ? [X5: nat] :
% 13.71/7.67 ( ( member_nat @ X5 @ Xs )
% 13.71/7.67 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_101_pred__none__empty,axiom,
% 13.71/7.67 ! [Xs: set_nat,A: nat] :
% 13.71/7.67 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A @ X_1 )
% 13.71/7.67 => ( ( finite_finite_nat @ Xs )
% 13.71/7.67 => ~ ? [X5: nat] :
% 13.71/7.67 ( ( member_nat @ X5 @ Xs )
% 13.71/7.67 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_102_memb__imp__not__empty,axiom,
% 13.71/7.67 ! [X: vEBT_VEBT,S3: set_VEBT_VEBT] :
% 13.71/7.67 ( ( member_VEBT_VEBT @ X @ S3 )
% 13.71/7.67 => ( S3 != bot_bo8194388402131092736T_VEBT ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_103_memb__imp__not__empty,axiom,
% 13.71/7.67 ! [X: real,S3: set_real] :
% 13.71/7.67 ( ( member_real @ X @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_real ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_104_memb__imp__not__empty,axiom,
% 13.71/7.67 ! [X: set_nat,S3: set_set_nat] :
% 13.71/7.67 ( ( member_set_nat @ X @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_105_memb__imp__not__empty,axiom,
% 13.71/7.67 ! [X: nat,S3: set_nat] :
% 13.71/7.67 ( ( member_nat @ X @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_106_memb__imp__not__empty,axiom,
% 13.71/7.67 ! [X: int,S3: set_int] :
% 13.71/7.67 ( ( member_int @ X @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_107_memb__imp__not__empty,axiom,
% 13.71/7.67 ! [X: $o,S3: set_o] :
% 13.71/7.67 ( ( member_o @ X @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_108_set__notEmptyE,axiom,
% 13.71/7.67 ! [S3: set_VEBT_VEBT] :
% 13.71/7.67 ( ( S3 != bot_bo8194388402131092736T_VEBT )
% 13.71/7.67 => ~ ! [X3: vEBT_VEBT] :
% 13.71/7.67 ~ ( member_VEBT_VEBT @ X3 @ S3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_109_set__notEmptyE,axiom,
% 13.71/7.67 ! [S3: set_real] :
% 13.71/7.67 ( ( S3 != bot_bot_set_real )
% 13.71/7.67 => ~ ! [X3: real] :
% 13.71/7.67 ~ ( member_real @ X3 @ S3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_110_set__notEmptyE,axiom,
% 13.71/7.67 ! [S3: set_set_nat] :
% 13.71/7.67 ( ( S3 != bot_bot_set_set_nat )
% 13.71/7.67 => ~ ! [X3: set_nat] :
% 13.71/7.67 ~ ( member_set_nat @ X3 @ S3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_111_set__notEmptyE,axiom,
% 13.71/7.67 ! [S3: set_nat] :
% 13.71/7.67 ( ( S3 != bot_bot_set_nat )
% 13.71/7.67 => ~ ! [X3: nat] :
% 13.71/7.67 ~ ( member_nat @ X3 @ S3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_112_set__notEmptyE,axiom,
% 13.71/7.67 ! [S3: set_int] :
% 13.71/7.67 ( ( S3 != bot_bot_set_int )
% 13.71/7.67 => ~ ! [X3: int] :
% 13.71/7.67 ~ ( member_int @ X3 @ S3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_113_set__notEmptyE,axiom,
% 13.71/7.67 ! [S3: set_o] :
% 13.71/7.67 ( ( S3 != bot_bot_set_o )
% 13.71/7.67 => ~ ! [X3: $o] :
% 13.71/7.67 ~ ( member_o @ X3 @ S3 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_114_gr__zeroI,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( N != zero_zero_nat )
% 13.71/7.67 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_115_not__less__zero,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_116_gr__implies__not__zero,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( N != zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_117_zero__less__iff__neq__zero,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.67 = ( N != zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_118_VEBT_Odistinct_I1_J,axiom,
% 13.71/7.67 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 13.71/7.67 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 13.71/7.67 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_119_VEBT_Oexhaust,axiom,
% 13.71/7.67 ! [Y: vEBT_VEBT] :
% 13.71/7.67 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 13.71/7.67 => ~ ! [X212: $o,X222: $o] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_120_finite_OemptyI,axiom,
% 13.71/7.67 finite3207457112153483333omplex @ bot_bot_set_complex ).
% 13.71/7.67
% 13.71/7.67 thf(fact_121_finite_OemptyI,axiom,
% 13.71/7.67 finite6017078050557962740nteger @ bot_bo3990330152332043303nteger ).
% 13.71/7.67
% 13.71/7.67 thf(fact_122_finite_OemptyI,axiom,
% 13.71/7.67 finite_finite_nat @ bot_bot_set_nat ).
% 13.71/7.67
% 13.71/7.67 thf(fact_123_finite_OemptyI,axiom,
% 13.71/7.67 finite_finite_int @ bot_bot_set_int ).
% 13.71/7.67
% 13.71/7.67 thf(fact_124_finite_OemptyI,axiom,
% 13.71/7.67 finite_finite_o @ bot_bot_set_o ).
% 13.71/7.67
% 13.71/7.67 thf(fact_125_infinite__imp__nonempty,axiom,
% 13.71/7.67 ! [S3: set_complex] :
% 13.71/7.67 ( ~ ( finite3207457112153483333omplex @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_complex ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_126_infinite__imp__nonempty,axiom,
% 13.71/7.67 ! [S3: set_Code_integer] :
% 13.71/7.67 ( ~ ( finite6017078050557962740nteger @ S3 )
% 13.71/7.67 => ( S3 != bot_bo3990330152332043303nteger ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_127_infinite__imp__nonempty,axiom,
% 13.71/7.67 ! [S3: set_nat] :
% 13.71/7.67 ( ~ ( finite_finite_nat @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_128_infinite__imp__nonempty,axiom,
% 13.71/7.67 ! [S3: set_int] :
% 13.71/7.67 ( ~ ( finite_finite_int @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_129_infinite__imp__nonempty,axiom,
% 13.71/7.67 ! [S3: set_o] :
% 13.71/7.67 ( ~ ( finite_finite_o @ S3 )
% 13.71/7.67 => ( S3 != bot_bot_set_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_130_VEBT__internal_Onaive__member_Ocases,axiom,
% 13.71/7.67 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.67 ( ! [A3: $o,B3: $o,X3: nat] :
% 13.71/7.67 ( X
% 13.71/7.67 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 13.71/7.67 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 13.71/7.67 ( X
% 13.71/7.67 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) )
% 13.71/7.67 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT,X3: nat] :
% 13.71/7.67 ( X
% 13.71/7.67 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ X3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_131_invar__vebt_Ointros_I1_J,axiom,
% 13.71/7.67 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_132_mod__h__bot__indep,axiom,
% 13.71/7.67 ! [P2: assn,H2: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 13.71/7.67 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.71/7.67 = ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_133_zero__reorient,axiom,
% 13.71/7.67 ! [X: uint32] :
% 13.71/7.67 ( ( zero_zero_uint32 = X )
% 13.71/7.67 = ( X = zero_zero_uint32 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_134_zero__reorient,axiom,
% 13.71/7.67 ! [X: real] :
% 13.71/7.67 ( ( zero_zero_real = X )
% 13.71/7.67 = ( X = zero_zero_real ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_135_zero__reorient,axiom,
% 13.71/7.67 ! [X: rat] :
% 13.71/7.67 ( ( zero_zero_rat = X )
% 13.71/7.67 = ( X = zero_zero_rat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_136_zero__reorient,axiom,
% 13.71/7.67 ! [X: nat] :
% 13.71/7.67 ( ( zero_zero_nat = X )
% 13.71/7.67 = ( X = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_137_zero__reorient,axiom,
% 13.71/7.67 ! [X: int] :
% 13.71/7.67 ( ( zero_zero_int = X )
% 13.71/7.67 = ( X = zero_zero_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_138_zero__less__Suc,axiom,
% 13.71/7.67 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_139_less__Suc0,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 13.71/7.67 = ( N = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_140_bot__nat__0_Onot__eq__extremum,axiom,
% 13.71/7.67 ! [A: nat] :
% 13.71/7.67 ( ( A != zero_zero_nat )
% 13.71/7.67 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_141_neq0__conv,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( N != zero_zero_nat )
% 13.71/7.67 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_142_less__nat__zero__code,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_143_lessI,axiom,
% 13.71/7.67 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_144_Suc__mono,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_145_Suc__less__eq,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 13.71/7.67 = ( ord_less_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_146_vebt__delete_Osimps_I2_J,axiom,
% 13.71/7.67 ! [A: $o,B: $o] :
% 13.71/7.67 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 13.71/7.67 = ( vEBT_Leaf @ A @ $false ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_147_invar__vebt__buildup,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N )
% 13.71/7.67 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_148_buildup__gives__valid,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.67 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_149_T__vebt__buildupi__gq__0,axiom,
% 13.71/7.67 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_150_set__vebt__buildup,axiom,
% 13.71/7.67 ! [I: nat] :
% 13.71/7.67 ( ( vEBT_set_vebt @ ( vEBT_vebt_buildup @ I ) )
% 13.71/7.67 = bot_bot_set_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_151_buildup__gives__empty,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 13.71/7.67 = bot_bot_set_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_152_old_Onat_Oinject,axiom,
% 13.71/7.67 ! [Nat: nat,Nat2: nat] :
% 13.71/7.67 ( ( ( suc @ Nat )
% 13.71/7.67 = ( suc @ Nat2 ) )
% 13.71/7.67 = ( Nat = Nat2 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_153_nat_Oinject,axiom,
% 13.71/7.67 ! [X2: nat,Y2: nat] :
% 13.71/7.67 ( ( ( suc @ X2 )
% 13.71/7.67 = ( suc @ Y2 ) )
% 13.71/7.67 = ( X2 = Y2 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_154_obtain__set__pred,axiom,
% 13.71/7.67 ! [Z: nat,X: nat,A4: set_nat] :
% 13.71/7.67 ( ( ord_less_nat @ Z @ X )
% 13.71/7.67 => ( ( vEBT_VEBT_min_in_set @ A4 @ Z )
% 13.71/7.67 => ( ( finite_finite_nat @ A4 )
% 13.71/7.67 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A4 @ X @ X_1 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_155_obtain__set__succ,axiom,
% 13.71/7.67 ! [X: nat,Z: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.67 ( ( ord_less_nat @ X @ Z )
% 13.71/7.67 => ( ( vEBT_VEBT_max_in_set @ A4 @ Z )
% 13.71/7.67 => ( ( finite_finite_nat @ B4 )
% 13.71/7.67 => ( ( A4 = B4 )
% 13.71/7.67 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A4 @ X @ X_1 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_156_finite__psubset__induct,axiom,
% 13.71/7.67 ! [A4: set_nat,P2: set_nat > $o] :
% 13.71/7.67 ( ( finite_finite_nat @ A4 )
% 13.71/7.67 => ( ! [A5: set_nat] :
% 13.71/7.67 ( ( finite_finite_nat @ A5 )
% 13.71/7.67 => ( ! [B5: set_nat] :
% 13.71/7.67 ( ( ord_less_set_nat @ B5 @ A5 )
% 13.71/7.67 => ( P2 @ B5 ) )
% 13.71/7.67 => ( P2 @ A5 ) ) )
% 13.71/7.67 => ( P2 @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_157_finite__psubset__induct,axiom,
% 13.71/7.67 ! [A4: set_int,P2: set_int > $o] :
% 13.71/7.67 ( ( finite_finite_int @ A4 )
% 13.71/7.67 => ( ! [A5: set_int] :
% 13.71/7.67 ( ( finite_finite_int @ A5 )
% 13.71/7.67 => ( ! [B5: set_int] :
% 13.71/7.67 ( ( ord_less_set_int @ B5 @ A5 )
% 13.71/7.67 => ( P2 @ B5 ) )
% 13.71/7.67 => ( P2 @ A5 ) ) )
% 13.71/7.67 => ( P2 @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_158_finite__psubset__induct,axiom,
% 13.71/7.67 ! [A4: set_complex,P2: set_complex > $o] :
% 13.71/7.67 ( ( finite3207457112153483333omplex @ A4 )
% 13.71/7.67 => ( ! [A5: set_complex] :
% 13.71/7.67 ( ( finite3207457112153483333omplex @ A5 )
% 13.71/7.67 => ( ! [B5: set_complex] :
% 13.71/7.67 ( ( ord_less_set_complex @ B5 @ A5 )
% 13.71/7.67 => ( P2 @ B5 ) )
% 13.71/7.67 => ( P2 @ A5 ) ) )
% 13.71/7.67 => ( P2 @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_159_finite__psubset__induct,axiom,
% 13.71/7.67 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.67 => ( ! [A5: set_Code_integer] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ A5 )
% 13.71/7.67 => ( ! [B5: set_Code_integer] :
% 13.71/7.67 ( ( ord_le1307284697595431911nteger @ B5 @ A5 )
% 13.71/7.67 => ( P2 @ B5 ) )
% 13.71/7.67 => ( P2 @ A5 ) ) )
% 13.71/7.67 => ( P2 @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_160_vebt__buildup_Osimps_I1_J,axiom,
% 13.71/7.67 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 13.71/7.67 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_161_n__not__Suc__n,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( N
% 13.71/7.67 != ( suc @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_162_Suc__inject,axiom,
% 13.71/7.67 ! [X: nat,Y: nat] :
% 13.71/7.67 ( ( ( suc @ X )
% 13.71/7.67 = ( suc @ Y ) )
% 13.71/7.67 => ( X = Y ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_163_linorder__neqE__nat,axiom,
% 13.71/7.67 ! [X: nat,Y: nat] :
% 13.71/7.67 ( ( X != Y )
% 13.71/7.67 => ( ~ ( ord_less_nat @ X @ Y )
% 13.71/7.67 => ( ord_less_nat @ Y @ X ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_164_infinite__descent,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ! [N2: nat] :
% 13.71/7.67 ( ~ ( P2 @ N2 )
% 13.71/7.67 => ? [M2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M2 @ N2 )
% 13.71/7.67 & ~ ( P2 @ M2 ) ) )
% 13.71/7.67 => ( P2 @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_165_nat__less__induct,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ! [N2: nat] :
% 13.71/7.67 ( ! [M2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M2 @ N2 )
% 13.71/7.67 => ( P2 @ M2 ) )
% 13.71/7.67 => ( P2 @ N2 ) )
% 13.71/7.67 => ( P2 @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_166_less__irrefl__nat,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ~ ( ord_less_nat @ N @ N ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_167_less__not__refl3,axiom,
% 13.71/7.67 ! [S: nat,T: nat] :
% 13.71/7.67 ( ( ord_less_nat @ S @ T )
% 13.71/7.67 => ( S != T ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_168_less__not__refl2,axiom,
% 13.71/7.67 ! [N: nat,M: nat] :
% 13.71/7.67 ( ( ord_less_nat @ N @ M )
% 13.71/7.67 => ( M != N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_169_less__not__refl,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ~ ( ord_less_nat @ N @ N ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_170_nat__neq__iff,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( M != N )
% 13.71/7.67 = ( ( ord_less_nat @ M @ N )
% 13.71/7.67 | ( ord_less_nat @ N @ M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_171_vebt__buildup_Osimps_I2_J,axiom,
% 13.71/7.67 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 13.71/7.67 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_172_not0__implies__Suc,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( N != zero_zero_nat )
% 13.71/7.67 => ? [M3: nat] :
% 13.71/7.67 ( N
% 13.71/7.67 = ( suc @ M3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_173_Zero__not__Suc,axiom,
% 13.71/7.67 ! [M: nat] :
% 13.71/7.67 ( zero_zero_nat
% 13.71/7.67 != ( suc @ M ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_174_Zero__neq__Suc,axiom,
% 13.71/7.67 ! [M: nat] :
% 13.71/7.67 ( zero_zero_nat
% 13.71/7.67 != ( suc @ M ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_175_Suc__neq__Zero,axiom,
% 13.71/7.67 ! [M: nat] :
% 13.71/7.67 ( ( suc @ M )
% 13.71/7.67 != zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_176_zero__induct,axiom,
% 13.71/7.67 ! [P2: nat > $o,K: nat] :
% 13.71/7.67 ( ( P2 @ K )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ( P2 @ ( suc @ N2 ) )
% 13.71/7.67 => ( P2 @ N2 ) )
% 13.71/7.67 => ( P2 @ zero_zero_nat ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_177_diff__induct,axiom,
% 13.71/7.67 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 13.71/7.67 ( ! [X3: nat] : ( P2 @ X3 @ zero_zero_nat )
% 13.71/7.67 => ( ! [Y3: nat] : ( P2 @ zero_zero_nat @ ( suc @ Y3 ) )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( P2 @ X3 @ Y3 )
% 13.71/7.67 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 13.71/7.67 => ( P2 @ M @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_178_nat__induct,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ( P2 @ zero_zero_nat )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ( P2 @ N2 )
% 13.71/7.67 => ( P2 @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( P2 @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_179_old_Onat_Oexhaust,axiom,
% 13.71/7.67 ! [Y: nat] :
% 13.71/7.67 ( ( Y != zero_zero_nat )
% 13.71/7.67 => ~ ! [Nat3: nat] :
% 13.71/7.67 ( Y
% 13.71/7.67 != ( suc @ Nat3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_180_nat_OdiscI,axiom,
% 13.71/7.67 ! [Nat: nat,X2: nat] :
% 13.71/7.67 ( ( Nat
% 13.71/7.67 = ( suc @ X2 ) )
% 13.71/7.67 => ( Nat != zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_181_old_Onat_Odistinct_I1_J,axiom,
% 13.71/7.67 ! [Nat2: nat] :
% 13.71/7.67 ( zero_zero_nat
% 13.71/7.67 != ( suc @ Nat2 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_182_old_Onat_Odistinct_I2_J,axiom,
% 13.71/7.67 ! [Nat2: nat] :
% 13.71/7.67 ( ( suc @ Nat2 )
% 13.71/7.67 != zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_183_nat_Odistinct_I1_J,axiom,
% 13.71/7.67 ! [X2: nat] :
% 13.71/7.67 ( zero_zero_nat
% 13.71/7.67 != ( suc @ X2 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_184_not__less__less__Suc__eq,axiom,
% 13.71/7.67 ! [N: nat,M: nat] :
% 13.71/7.67 ( ~ ( ord_less_nat @ N @ M )
% 13.71/7.67 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 13.71/7.67 = ( N = M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_185_strict__inc__induct,axiom,
% 13.71/7.67 ! [I: nat,J: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ord_less_nat @ I @ J )
% 13.71/7.67 => ( ! [I2: nat] :
% 13.71/7.67 ( ( J
% 13.71/7.67 = ( suc @ I2 ) )
% 13.71/7.67 => ( P2 @ I2 ) )
% 13.71/7.67 => ( ! [I2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I2 @ J )
% 13.71/7.67 => ( ( P2 @ ( suc @ I2 ) )
% 13.71/7.67 => ( P2 @ I2 ) ) )
% 13.71/7.67 => ( P2 @ I ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_186_less__Suc__induct,axiom,
% 13.71/7.67 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 13.71/7.67 ( ( ord_less_nat @ I @ J )
% 13.71/7.67 => ( ! [I2: nat] : ( P2 @ I2 @ ( suc @ I2 ) )
% 13.71/7.67 => ( ! [I2: nat,J2: nat,K2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I2 @ J2 )
% 13.71/7.67 => ( ( ord_less_nat @ J2 @ K2 )
% 13.71/7.67 => ( ( P2 @ I2 @ J2 )
% 13.71/7.67 => ( ( P2 @ J2 @ K2 )
% 13.71/7.67 => ( P2 @ I2 @ K2 ) ) ) ) )
% 13.71/7.67 => ( P2 @ I @ J ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_187_less__trans__Suc,axiom,
% 13.71/7.67 ! [I: nat,J: nat,K: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I @ J )
% 13.71/7.67 => ( ( ord_less_nat @ J @ K )
% 13.71/7.67 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_188_Suc__less__SucD,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 13.71/7.67 => ( ord_less_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_189_less__antisym,axiom,
% 13.71/7.67 ! [N: nat,M: nat] :
% 13.71/7.67 ( ~ ( ord_less_nat @ N @ M )
% 13.71/7.67 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 13.71/7.67 => ( M = N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_190_Suc__less__eq2,axiom,
% 13.71/7.67 ! [N: nat,M: nat] :
% 13.71/7.67 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 13.71/7.67 = ( ? [M4: nat] :
% 13.71/7.67 ( ( M
% 13.71/7.67 = ( suc @ M4 ) )
% 13.71/7.67 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_191_Nat_OAll__less__Suc,axiom,
% 13.71/7.67 ! [N: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 13.71/7.67 => ( P2 @ I3 ) ) )
% 13.71/7.67 = ( ( P2 @ N )
% 13.71/7.67 & ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ N )
% 13.71/7.67 => ( P2 @ I3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_192_not__less__eq,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ~ ( ord_less_nat @ M @ N ) )
% 13.71/7.67 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_193_less__Suc__eq,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 13.71/7.67 = ( ( ord_less_nat @ M @ N )
% 13.71/7.67 | ( M = N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_194_Ex__less__Suc,axiom,
% 13.71/7.67 ! [N: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ? [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 13.71/7.67 & ( P2 @ I3 ) ) )
% 13.71/7.67 = ( ( P2 @ N )
% 13.71/7.67 | ? [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ N )
% 13.71/7.67 & ( P2 @ I3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_195_less__SucI,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_196_less__SucE,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 13.71/7.67 => ( ~ ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( M = N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_197_Suc__lessI,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( ( ( suc @ M )
% 13.71/7.67 != N )
% 13.71/7.67 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_198_Suc__lessE,axiom,
% 13.71/7.67 ! [I: nat,K: nat] :
% 13.71/7.67 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 13.71/7.67 => ~ ! [J2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I @ J2 )
% 13.71/7.67 => ( K
% 13.71/7.67 != ( suc @ J2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_199_Suc__lessD,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 13.71/7.67 => ( ord_less_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_200_Nat_OlessE,axiom,
% 13.71/7.67 ! [I: nat,K: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I @ K )
% 13.71/7.67 => ( ( K
% 13.71/7.67 != ( suc @ I ) )
% 13.71/7.67 => ~ ! [J2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I @ J2 )
% 13.71/7.67 => ( K
% 13.71/7.67 != ( suc @ J2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_201_infinite__descent0,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ( P2 @ zero_zero_nat )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 13.71/7.67 => ( ~ ( P2 @ N2 )
% 13.71/7.67 => ? [M2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M2 @ N2 )
% 13.71/7.67 & ~ ( P2 @ M2 ) ) ) )
% 13.71/7.67 => ( P2 @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_202_gr__implies__not0,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( N != zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_203_less__zeroE,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_204_not__less0,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_205_not__gr0,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 13.71/7.67 = ( N = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_206_gr0I,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( N != zero_zero_nat )
% 13.71/7.67 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_207_bot__nat__0_Oextremum__strict,axiom,
% 13.71/7.67 ! [A: nat] :
% 13.71/7.67 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_208_lift__Suc__mono__less__iff,axiom,
% 13.71/7.67 ! [F: nat > real,N: nat,M: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 13.71/7.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_209_lift__Suc__mono__less__iff,axiom,
% 13.71/7.67 ! [F: nat > rat,N: nat,M: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 13.71/7.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_210_lift__Suc__mono__less__iff,axiom,
% 13.71/7.67 ! [F: nat > num,N: nat,M: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 13.71/7.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_211_lift__Suc__mono__less__iff,axiom,
% 13.71/7.67 ! [F: nat > nat,N: nat,M: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 13.71/7.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_212_lift__Suc__mono__less__iff,axiom,
% 13.71/7.67 ! [F: nat > int,N: nat,M: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 13.71/7.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_213_lift__Suc__mono__less,axiom,
% 13.71/7.67 ! [F: nat > real,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_real @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_214_lift__Suc__mono__less,axiom,
% 13.71/7.67 ! [F: nat > rat,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_215_lift__Suc__mono__less,axiom,
% 13.71/7.67 ! [F: nat > num,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_216_lift__Suc__mono__less,axiom,
% 13.71/7.67 ! [F: nat > nat,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_217_lift__Suc__mono__less,axiom,
% 13.71/7.67 ! [F: nat > int,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_218_Ex__less__Suc2,axiom,
% 13.71/7.67 ! [N: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ? [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 13.71/7.67 & ( P2 @ I3 ) ) )
% 13.71/7.67 = ( ( P2 @ zero_zero_nat )
% 13.71/7.67 | ? [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ N )
% 13.71/7.67 & ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_219_gr0__conv__Suc,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.67 = ( ? [M5: nat] :
% 13.71/7.67 ( N
% 13.71/7.67 = ( suc @ M5 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_220_All__less__Suc2,axiom,
% 13.71/7.67 ! [N: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 13.71/7.67 => ( P2 @ I3 ) ) )
% 13.71/7.67 = ( ( P2 @ zero_zero_nat )
% 13.71/7.67 & ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ N )
% 13.71/7.67 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_221_gr0__implies__Suc,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.67 => ? [M3: nat] :
% 13.71/7.67 ( N
% 13.71/7.67 = ( suc @ M3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_222_less__Suc__eq__0__disj,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 13.71/7.67 = ( ( M = zero_zero_nat )
% 13.71/7.67 | ? [J3: nat] :
% 13.71/7.67 ( ( M
% 13.71/7.67 = ( suc @ J3 ) )
% 13.71/7.67 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_223_vebt__delete_Osimps_I3_J,axiom,
% 13.71/7.67 ! [A: $o,B: $o,N: nat] :
% 13.71/7.67 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 13.71/7.67 = ( vEBT_Leaf @ A @ B ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_224_vebt__delete_Osimps_I1_J,axiom,
% 13.71/7.67 ! [A: $o,B: $o] :
% 13.71/7.67 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 13.71/7.67 = ( vEBT_Leaf @ $false @ B ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_225_succ__member,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 13.71/7.67 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 13.71/7.67 = ( ( vEBT_vebt_member @ T @ Y )
% 13.71/7.67 & ( ord_less_nat @ X @ Y )
% 13.71/7.67 & ! [Z2: nat] :
% 13.71/7.67 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 13.71/7.67 & ( ord_less_nat @ X @ Z2 ) )
% 13.71/7.67 => ( ord_less_eq_nat @ Y @ Z2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_226_pred__member,axiom,
% 13.71/7.67 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 13.71/7.67 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 13.71/7.67 = ( ( vEBT_vebt_member @ T @ Y )
% 13.71/7.67 & ( ord_less_nat @ Y @ X )
% 13.71/7.67 & ! [Z2: nat] :
% 13.71/7.67 ( ( ( vEBT_vebt_member @ T @ Z2 )
% 13.71/7.67 & ( ord_less_nat @ Z2 @ X ) )
% 13.71/7.67 => ( ord_less_eq_nat @ Z2 @ Y ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_227_buildup__nothing__in__leaf,axiom,
% 13.71/7.67 ! [N: nat,X: nat] :
% 13.71/7.67 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_228_VEBT__internal_OT__vebt__buildupi_Osimps_I2_J,axiom,
% 13.71/7.67 ( ( vEBT_V441764108873111860ildupi @ ( suc @ zero_zero_nat ) )
% 13.71/7.67 = ( suc @ zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_229_VEBT__internal_OT__vebt__buildupi_Osimps_I1_J,axiom,
% 13.71/7.67 ( ( vEBT_V441764108873111860ildupi @ zero_zero_nat )
% 13.71/7.67 = ( suc @ zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_230_VEBT__internal_Oinsert_H_Ocases,axiom,
% 13.71/7.67 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.67 ( ! [A3: $o,B3: $o,X3: nat] :
% 13.71/7.67 ( X
% 13.71/7.67 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 13.71/7.67 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.67 ( X
% 13.71/7.67 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ X3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_231_forall__finite_I3_J,axiom,
% 13.71/7.67 ! [X: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ ( suc @ X ) ) )
% 13.71/7.67 => ( P2 @ I3 ) ) )
% 13.71/7.67 = ( ( P2 @ zero_zero_nat )
% 13.71/7.67 & ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ X ) )
% 13.71/7.67 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_232_forall__finite_I2_J,axiom,
% 13.71/7.67 ! [P2: nat > $o] :
% 13.71/7.67 ( ( ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ zero_zero_nat ) )
% 13.71/7.67 => ( P2 @ I3 ) ) )
% 13.71/7.67 = ( P2 @ zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_233_Comparator__Generator_OAll__less__Suc,axiom,
% 13.71/7.67 ! [X: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ ( suc @ X ) )
% 13.71/7.67 => ( P2 @ I3 ) ) )
% 13.71/7.67 = ( ( P2 @ zero_zero_nat )
% 13.71/7.67 & ! [I3: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I3 @ X )
% 13.71/7.67 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_234_infinite__growing,axiom,
% 13.71/7.67 ! [X6: set_Code_integer] :
% 13.71/7.67 ( ( X6 != bot_bo3990330152332043303nteger )
% 13.71/7.67 => ( ! [X3: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ X3 @ X6 )
% 13.71/7.67 => ? [Xa: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ Xa @ X6 )
% 13.71/7.67 & ( ord_le6747313008572928689nteger @ X3 @ Xa ) ) )
% 13.71/7.67 => ~ ( finite6017078050557962740nteger @ X6 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_235_infinite__growing,axiom,
% 13.71/7.67 ! [X6: set_o] :
% 13.71/7.67 ( ( X6 != bot_bot_set_o )
% 13.71/7.67 => ( ! [X3: $o] :
% 13.71/7.67 ( ( member_o @ X3 @ X6 )
% 13.71/7.67 => ? [Xa: $o] :
% 13.71/7.67 ( ( member_o @ Xa @ X6 )
% 13.71/7.67 & ( ord_less_o @ X3 @ Xa ) ) )
% 13.71/7.67 => ~ ( finite_finite_o @ X6 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_236_infinite__growing,axiom,
% 13.71/7.67 ! [X6: set_real] :
% 13.71/7.67 ( ( X6 != bot_bot_set_real )
% 13.71/7.67 => ( ! [X3: real] :
% 13.71/7.67 ( ( member_real @ X3 @ X6 )
% 13.71/7.67 => ? [Xa: real] :
% 13.71/7.67 ( ( member_real @ Xa @ X6 )
% 13.71/7.67 & ( ord_less_real @ X3 @ Xa ) ) )
% 13.71/7.67 => ~ ( finite_finite_real @ X6 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_237_infinite__growing,axiom,
% 13.71/7.67 ! [X6: set_rat] :
% 13.71/7.67 ( ( X6 != bot_bot_set_rat )
% 13.71/7.67 => ( ! [X3: rat] :
% 13.71/7.67 ( ( member_rat @ X3 @ X6 )
% 13.71/7.67 => ? [Xa: rat] :
% 13.71/7.67 ( ( member_rat @ Xa @ X6 )
% 13.71/7.67 & ( ord_less_rat @ X3 @ Xa ) ) )
% 13.71/7.67 => ~ ( finite_finite_rat @ X6 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_238_infinite__growing,axiom,
% 13.71/7.67 ! [X6: set_num] :
% 13.71/7.67 ( ( X6 != bot_bot_set_num )
% 13.71/7.67 => ( ! [X3: num] :
% 13.71/7.67 ( ( member_num @ X3 @ X6 )
% 13.71/7.67 => ? [Xa: num] :
% 13.71/7.67 ( ( member_num @ Xa @ X6 )
% 13.71/7.67 & ( ord_less_num @ X3 @ Xa ) ) )
% 13.71/7.67 => ~ ( finite_finite_num @ X6 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_239_infinite__growing,axiom,
% 13.71/7.67 ! [X6: set_nat] :
% 13.71/7.67 ( ( X6 != bot_bot_set_nat )
% 13.71/7.67 => ( ! [X3: nat] :
% 13.71/7.67 ( ( member_nat @ X3 @ X6 )
% 13.71/7.67 => ? [Xa: nat] :
% 13.71/7.67 ( ( member_nat @ Xa @ X6 )
% 13.71/7.67 & ( ord_less_nat @ X3 @ Xa ) ) )
% 13.71/7.67 => ~ ( finite_finite_nat @ X6 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_240_infinite__growing,axiom,
% 13.71/7.67 ! [X6: set_int] :
% 13.71/7.67 ( ( X6 != bot_bot_set_int )
% 13.71/7.67 => ( ! [X3: int] :
% 13.71/7.67 ( ( member_int @ X3 @ X6 )
% 13.71/7.67 => ? [Xa: int] :
% 13.71/7.67 ( ( member_int @ Xa @ X6 )
% 13.71/7.67 & ( ord_less_int @ X3 @ Xa ) ) )
% 13.71/7.67 => ~ ( finite_finite_int @ X6 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_241_ex__min__if__finite,axiom,
% 13.71/7.67 ! [S3: set_Code_integer] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ S3 )
% 13.71/7.67 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.71/7.67 => ? [X3: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ X3 @ S3 )
% 13.71/7.67 & ~ ? [Xa: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ Xa @ S3 )
% 13.71/7.67 & ( ord_le6747313008572928689nteger @ Xa @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_242_ex__min__if__finite,axiom,
% 13.71/7.67 ! [S3: set_o] :
% 13.71/7.67 ( ( finite_finite_o @ S3 )
% 13.71/7.67 => ( ( S3 != bot_bot_set_o )
% 13.71/7.67 => ? [X3: $o] :
% 13.71/7.67 ( ( member_o @ X3 @ S3 )
% 13.71/7.67 & ~ ? [Xa: $o] :
% 13.71/7.67 ( ( member_o @ Xa @ S3 )
% 13.71/7.67 & ( ord_less_o @ Xa @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_243_ex__min__if__finite,axiom,
% 13.71/7.67 ! [S3: set_real] :
% 13.71/7.67 ( ( finite_finite_real @ S3 )
% 13.71/7.67 => ( ( S3 != bot_bot_set_real )
% 13.71/7.67 => ? [X3: real] :
% 13.71/7.67 ( ( member_real @ X3 @ S3 )
% 13.71/7.67 & ~ ? [Xa: real] :
% 13.71/7.67 ( ( member_real @ Xa @ S3 )
% 13.71/7.67 & ( ord_less_real @ Xa @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_244_ex__min__if__finite,axiom,
% 13.71/7.67 ! [S3: set_rat] :
% 13.71/7.67 ( ( finite_finite_rat @ S3 )
% 13.71/7.67 => ( ( S3 != bot_bot_set_rat )
% 13.71/7.67 => ? [X3: rat] :
% 13.71/7.67 ( ( member_rat @ X3 @ S3 )
% 13.71/7.67 & ~ ? [Xa: rat] :
% 13.71/7.67 ( ( member_rat @ Xa @ S3 )
% 13.71/7.67 & ( ord_less_rat @ Xa @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_245_ex__min__if__finite,axiom,
% 13.71/7.67 ! [S3: set_num] :
% 13.71/7.67 ( ( finite_finite_num @ S3 )
% 13.71/7.67 => ( ( S3 != bot_bot_set_num )
% 13.71/7.67 => ? [X3: num] :
% 13.71/7.67 ( ( member_num @ X3 @ S3 )
% 13.71/7.67 & ~ ? [Xa: num] :
% 13.71/7.67 ( ( member_num @ Xa @ S3 )
% 13.71/7.67 & ( ord_less_num @ Xa @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_246_ex__min__if__finite,axiom,
% 13.71/7.67 ! [S3: set_nat] :
% 13.71/7.67 ( ( finite_finite_nat @ S3 )
% 13.71/7.67 => ( ( S3 != bot_bot_set_nat )
% 13.71/7.67 => ? [X3: nat] :
% 13.71/7.67 ( ( member_nat @ X3 @ S3 )
% 13.71/7.67 & ~ ? [Xa: nat] :
% 13.71/7.67 ( ( member_nat @ Xa @ S3 )
% 13.71/7.67 & ( ord_less_nat @ Xa @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_247_ex__min__if__finite,axiom,
% 13.71/7.67 ! [S3: set_int] :
% 13.71/7.67 ( ( finite_finite_int @ S3 )
% 13.71/7.67 => ( ( S3 != bot_bot_set_int )
% 13.71/7.67 => ? [X3: int] :
% 13.71/7.67 ( ( member_int @ X3 @ S3 )
% 13.71/7.67 & ~ ? [Xa: int] :
% 13.71/7.67 ( ( member_int @ Xa @ S3 )
% 13.71/7.67 & ( ord_less_int @ Xa @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_248_empty__Collect__eq,axiom,
% 13.71/7.67 ! [P2: complex > $o] :
% 13.71/7.67 ( ( bot_bot_set_complex
% 13.71/7.67 = ( collect_complex @ P2 ) )
% 13.71/7.67 = ( ! [X4: complex] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_249_empty__Collect__eq,axiom,
% 13.71/7.67 ! [P2: list_nat > $o] :
% 13.71/7.67 ( ( bot_bot_set_list_nat
% 13.71/7.67 = ( collect_list_nat @ P2 ) )
% 13.71/7.67 = ( ! [X4: list_nat] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_250_empty__Collect__eq,axiom,
% 13.71/7.67 ! [P2: set_nat > $o] :
% 13.71/7.67 ( ( bot_bot_set_set_nat
% 13.71/7.67 = ( collect_set_nat @ P2 ) )
% 13.71/7.67 = ( ! [X4: set_nat] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_251_empty__Collect__eq,axiom,
% 13.71/7.67 ! [P2: nat > $o] :
% 13.71/7.67 ( ( bot_bot_set_nat
% 13.71/7.67 = ( collect_nat @ P2 ) )
% 13.71/7.67 = ( ! [X4: nat] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_252_empty__Collect__eq,axiom,
% 13.71/7.67 ! [P2: int > $o] :
% 13.71/7.67 ( ( bot_bot_set_int
% 13.71/7.67 = ( collect_int @ P2 ) )
% 13.71/7.67 = ( ! [X4: int] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_253_empty__Collect__eq,axiom,
% 13.71/7.67 ! [P2: $o > $o] :
% 13.71/7.67 ( ( bot_bot_set_o
% 13.71/7.67 = ( collect_o @ P2 ) )
% 13.71/7.67 = ( ! [X4: $o] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_254_max__in__set__def,axiom,
% 13.71/7.67 ( vEBT_VEBT_max_in_set
% 13.71/7.67 = ( ^ [Xs2: set_nat,X4: nat] :
% 13.71/7.67 ( ( member_nat @ X4 @ Xs2 )
% 13.71/7.67 & ! [Y4: nat] :
% 13.71/7.67 ( ( member_nat @ Y4 @ Xs2 )
% 13.71/7.67 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_255_min__in__set__def,axiom,
% 13.71/7.67 ( vEBT_VEBT_min_in_set
% 13.71/7.67 = ( ^ [Xs2: set_nat,X4: nat] :
% 13.71/7.67 ( ( member_nat @ X4 @ Xs2 )
% 13.71/7.67 & ! [Y4: nat] :
% 13.71/7.67 ( ( member_nat @ Y4 @ Xs2 )
% 13.71/7.67 => ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_256_empty__iff,axiom,
% 13.71/7.67 ! [C2: vEBT_VEBT] :
% 13.71/7.67 ~ ( member_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_257_empty__iff,axiom,
% 13.71/7.67 ! [C2: real] :
% 13.71/7.67 ~ ( member_real @ C2 @ bot_bot_set_real ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_258_empty__iff,axiom,
% 13.71/7.67 ! [C2: set_nat] :
% 13.71/7.67 ~ ( member_set_nat @ C2 @ bot_bot_set_set_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_259_empty__iff,axiom,
% 13.71/7.67 ! [C2: nat] :
% 13.71/7.67 ~ ( member_nat @ C2 @ bot_bot_set_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_260_empty__iff,axiom,
% 13.71/7.67 ! [C2: int] :
% 13.71/7.67 ~ ( member_int @ C2 @ bot_bot_set_int ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_261_empty__iff,axiom,
% 13.71/7.67 ! [C2: $o] :
% 13.71/7.67 ~ ( member_o @ C2 @ bot_bot_set_o ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_262_all__not__in__conv,axiom,
% 13.71/7.67 ! [A4: set_VEBT_VEBT] :
% 13.71/7.67 ( ( ! [X4: vEBT_VEBT] :
% 13.71/7.67 ~ ( member_VEBT_VEBT @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 = bot_bo8194388402131092736T_VEBT ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_263_all__not__in__conv,axiom,
% 13.71/7.67 ! [A4: set_real] :
% 13.71/7.67 ( ( ! [X4: real] :
% 13.71/7.67 ~ ( member_real @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 = bot_bot_set_real ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_264_all__not__in__conv,axiom,
% 13.71/7.67 ! [A4: set_set_nat] :
% 13.71/7.67 ( ( ! [X4: set_nat] :
% 13.71/7.67 ~ ( member_set_nat @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 = bot_bot_set_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_265_all__not__in__conv,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ( ! [X4: nat] :
% 13.71/7.67 ~ ( member_nat @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 = bot_bot_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_266_all__not__in__conv,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ( ! [X4: int] :
% 13.71/7.67 ~ ( member_int @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 = bot_bot_set_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_267_all__not__in__conv,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ( ( ! [X4: $o] :
% 13.71/7.67 ~ ( member_o @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 = bot_bot_set_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_268_Collect__empty__eq,axiom,
% 13.71/7.67 ! [P2: complex > $o] :
% 13.71/7.67 ( ( ( collect_complex @ P2 )
% 13.71/7.67 = bot_bot_set_complex )
% 13.71/7.67 = ( ! [X4: complex] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_269_Collect__empty__eq,axiom,
% 13.71/7.67 ! [P2: list_nat > $o] :
% 13.71/7.67 ( ( ( collect_list_nat @ P2 )
% 13.71/7.67 = bot_bot_set_list_nat )
% 13.71/7.67 = ( ! [X4: list_nat] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_270_Collect__empty__eq,axiom,
% 13.71/7.67 ! [P2: set_nat > $o] :
% 13.71/7.67 ( ( ( collect_set_nat @ P2 )
% 13.71/7.67 = bot_bot_set_set_nat )
% 13.71/7.67 = ( ! [X4: set_nat] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_271_Collect__empty__eq,axiom,
% 13.71/7.67 ! [P2: nat > $o] :
% 13.71/7.67 ( ( ( collect_nat @ P2 )
% 13.71/7.67 = bot_bot_set_nat )
% 13.71/7.67 = ( ! [X4: nat] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_272_Collect__empty__eq,axiom,
% 13.71/7.67 ! [P2: int > $o] :
% 13.71/7.67 ( ( ( collect_int @ P2 )
% 13.71/7.67 = bot_bot_set_int )
% 13.71/7.67 = ( ! [X4: int] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_273_Collect__empty__eq,axiom,
% 13.71/7.67 ! [P2: $o > $o] :
% 13.71/7.67 ( ( ( collect_o @ P2 )
% 13.71/7.67 = bot_bot_set_o )
% 13.71/7.67 = ( ! [X4: $o] :
% 13.71/7.67 ~ ( P2 @ X4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_274_le__zero__eq,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 13.71/7.67 = ( N = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_275_Suc__le__mono,axiom,
% 13.71/7.67 ! [N: nat,M: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 13.71/7.67 = ( ord_less_eq_nat @ N @ M ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_276_bot__nat__0_Oextremum,axiom,
% 13.71/7.67 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_277_le0,axiom,
% 13.71/7.67 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_278_psubsetD,axiom,
% 13.71/7.67 ! [A4: set_nat,B4: set_nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_set_nat @ A4 @ B4 )
% 13.71/7.67 => ( ( member_nat @ C2 @ A4 )
% 13.71/7.67 => ( member_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_279_psubsetD,axiom,
% 13.71/7.67 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,C2: vEBT_VEBT] :
% 13.71/7.67 ( ( ord_le3480810397992357184T_VEBT @ A4 @ B4 )
% 13.71/7.67 => ( ( member_VEBT_VEBT @ C2 @ A4 )
% 13.71/7.67 => ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_280_psubsetD,axiom,
% 13.71/7.67 ! [A4: set_real,B4: set_real,C2: real] :
% 13.71/7.67 ( ( ord_less_set_real @ A4 @ B4 )
% 13.71/7.67 => ( ( member_real @ C2 @ A4 )
% 13.71/7.67 => ( member_real @ C2 @ B4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_281_psubsetD,axiom,
% 13.71/7.67 ! [A4: set_int,B4: set_int,C2: int] :
% 13.71/7.67 ( ( ord_less_set_int @ A4 @ B4 )
% 13.71/7.67 => ( ( member_int @ C2 @ A4 )
% 13.71/7.67 => ( member_int @ C2 @ B4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_282_psubsetD,axiom,
% 13.71/7.67 ! [A4: set_set_nat,B4: set_set_nat,C2: set_nat] :
% 13.71/7.67 ( ( ord_less_set_set_nat @ A4 @ B4 )
% 13.71/7.67 => ( ( member_set_nat @ C2 @ A4 )
% 13.71/7.67 => ( member_set_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_283_Nat_Oex__has__greatest__nat,axiom,
% 13.71/7.67 ! [P2: nat > $o,K: nat,B: nat] :
% 13.71/7.67 ( ( P2 @ K )
% 13.71/7.67 => ( ! [Y3: nat] :
% 13.71/7.67 ( ( P2 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ Y3 @ B ) )
% 13.71/7.67 => ? [X3: nat] :
% 13.71/7.67 ( ( P2 @ X3 )
% 13.71/7.67 & ! [Y5: nat] :
% 13.71/7.67 ( ( P2 @ Y5 )
% 13.71/7.67 => ( ord_less_eq_nat @ Y5 @ X3 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_284_nat__le__linear,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 | ( ord_less_eq_nat @ N @ M ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_285_le__antisym,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ M )
% 13.71/7.67 => ( M = N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_286_eq__imp__le,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( M = N )
% 13.71/7.67 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_287_le__trans,axiom,
% 13.71/7.67 ! [I: nat,J: nat,K: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ I @ J )
% 13.71/7.67 => ( ( ord_less_eq_nat @ J @ K )
% 13.71/7.67 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_288_le__refl,axiom,
% 13.71/7.67 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_289_ord__eq__le__eq__trans,axiom,
% 13.71/7.67 ! [A: set_int,B: set_int,C2: set_int,D: set_int] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ B @ C2 )
% 13.71/7.67 => ( ( C2 = D )
% 13.71/7.67 => ( ord_less_eq_set_int @ A @ D ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_290_ord__eq__le__eq__trans,axiom,
% 13.71/7.67 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ( C2 = D )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ D ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_291_ord__eq__le__eq__trans,axiom,
% 13.71/7.67 ! [A: num,B: num,C2: num,D: num] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ( C2 = D )
% 13.71/7.67 => ( ord_less_eq_num @ A @ D ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_292_ord__eq__le__eq__trans,axiom,
% 13.71/7.67 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.67 => ( ( C2 = D )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ D ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_293_ord__eq__le__eq__trans,axiom,
% 13.71/7.67 ! [A: int,B: int,C2: int,D: int] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_int @ B @ C2 )
% 13.71/7.67 => ( ( C2 = D )
% 13.71/7.67 => ( ord_less_eq_int @ A @ D ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_294_lift__Suc__antimono__le,axiom,
% 13.71/7.67 ! [F: nat > set_int,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_295_lift__Suc__antimono__le,axiom,
% 13.71/7.67 ! [F: nat > rat,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_296_lift__Suc__antimono__le,axiom,
% 13.71/7.67 ! [F: nat > num,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_297_lift__Suc__antimono__le,axiom,
% 13.71/7.67 ! [F: nat > nat,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_298_lift__Suc__antimono__le,axiom,
% 13.71/7.67 ! [F: nat > int,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_299_lift__Suc__mono__le,axiom,
% 13.71/7.67 ! [F: nat > set_int,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_300_lift__Suc__mono__le,axiom,
% 13.71/7.67 ! [F: nat > rat,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_301_lift__Suc__mono__le,axiom,
% 13.71/7.67 ! [F: nat > num,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_302_lift__Suc__mono__le,axiom,
% 13.71/7.67 ! [F: nat > nat,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_303_lift__Suc__mono__le,axiom,
% 13.71/7.67 ! [F: nat > int,N: nat,N3: nat] :
% 13.71/7.67 ( ! [N2: nat] : ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ N @ N3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_304_zero__le,axiom,
% 13.71/7.67 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_305_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_real,A: real] :
% 13.71/7.67 ( ( finite_finite_real @ A4 )
% 13.71/7.67 => ( ( member_real @ A @ A4 )
% 13.71/7.67 => ? [X3: real] :
% 13.71/7.67 ( ( member_real @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_real @ A @ X3 )
% 13.71/7.67 & ! [Xa: real] :
% 13.71/7.67 ( ( member_real @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_real @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_306_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_set_nat,A: set_nat] :
% 13.71/7.67 ( ( finite1152437895449049373et_nat @ A4 )
% 13.71/7.67 => ( ( member_set_nat @ A @ A4 )
% 13.71/7.67 => ? [X3: set_nat] :
% 13.71/7.67 ( ( member_set_nat @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_set_nat @ A @ X3 )
% 13.71/7.67 & ! [Xa: set_nat] :
% 13.71/7.67 ( ( member_set_nat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_307_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_Code_integer,A: code_integer] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.67 => ( ( member_Code_integer @ A @ A4 )
% 13.71/7.67 => ? [X3: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ X3 @ A4 )
% 13.71/7.67 & ( ord_le3102999989581377725nteger @ A @ X3 )
% 13.71/7.67 & ! [Xa: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_308_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_set_int,A: set_int] :
% 13.71/7.67 ( ( finite6197958912794628473et_int @ A4 )
% 13.71/7.67 => ( ( member_set_int @ A @ A4 )
% 13.71/7.67 => ? [X3: set_int] :
% 13.71/7.67 ( ( member_set_int @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_set_int @ A @ X3 )
% 13.71/7.67 & ! [Xa: set_int] :
% 13.71/7.67 ( ( member_set_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_309_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_rat,A: rat] :
% 13.71/7.67 ( ( finite_finite_rat @ A4 )
% 13.71/7.67 => ( ( member_rat @ A @ A4 )
% 13.71/7.67 => ? [X3: rat] :
% 13.71/7.67 ( ( member_rat @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_rat @ A @ X3 )
% 13.71/7.67 & ! [Xa: rat] :
% 13.71/7.67 ( ( member_rat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_310_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_num,A: num] :
% 13.71/7.67 ( ( finite_finite_num @ A4 )
% 13.71/7.67 => ( ( member_num @ A @ A4 )
% 13.71/7.67 => ? [X3: num] :
% 13.71/7.67 ( ( member_num @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_num @ A @ X3 )
% 13.71/7.67 & ! [Xa: num] :
% 13.71/7.67 ( ( member_num @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_num @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_311_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_nat,A: nat] :
% 13.71/7.67 ( ( finite_finite_nat @ A4 )
% 13.71/7.67 => ( ( member_nat @ A @ A4 )
% 13.71/7.67 => ? [X3: nat] :
% 13.71/7.67 ( ( member_nat @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_nat @ A @ X3 )
% 13.71/7.67 & ! [Xa: nat] :
% 13.71/7.67 ( ( member_nat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_312_finite__has__maximal2,axiom,
% 13.71/7.67 ! [A4: set_int,A: int] :
% 13.71/7.67 ( ( finite_finite_int @ A4 )
% 13.71/7.67 => ( ( member_int @ A @ A4 )
% 13.71/7.67 => ? [X3: int] :
% 13.71/7.67 ( ( member_int @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_int @ A @ X3 )
% 13.71/7.67 & ! [Xa: int] :
% 13.71/7.67 ( ( member_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_int @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_313_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_real,A: real] :
% 13.71/7.67 ( ( finite_finite_real @ A4 )
% 13.71/7.67 => ( ( member_real @ A @ A4 )
% 13.71/7.67 => ? [X3: real] :
% 13.71/7.67 ( ( member_real @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_real @ X3 @ A )
% 13.71/7.67 & ! [Xa: real] :
% 13.71/7.67 ( ( member_real @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_real @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_314_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_set_nat,A: set_nat] :
% 13.71/7.67 ( ( finite1152437895449049373et_nat @ A4 )
% 13.71/7.67 => ( ( member_set_nat @ A @ A4 )
% 13.71/7.67 => ? [X3: set_nat] :
% 13.71/7.67 ( ( member_set_nat @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_set_nat @ X3 @ A )
% 13.71/7.67 & ! [Xa: set_nat] :
% 13.71/7.67 ( ( member_set_nat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_315_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_Code_integer,A: code_integer] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.67 => ( ( member_Code_integer @ A @ A4 )
% 13.71/7.67 => ? [X3: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ X3 @ A4 )
% 13.71/7.67 & ( ord_le3102999989581377725nteger @ X3 @ A )
% 13.71/7.67 & ! [Xa: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_le3102999989581377725nteger @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_316_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_set_int,A: set_int] :
% 13.71/7.67 ( ( finite6197958912794628473et_int @ A4 )
% 13.71/7.67 => ( ( member_set_int @ A @ A4 )
% 13.71/7.67 => ? [X3: set_int] :
% 13.71/7.67 ( ( member_set_int @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_set_int @ X3 @ A )
% 13.71/7.67 & ! [Xa: set_int] :
% 13.71/7.67 ( ( member_set_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_317_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_rat,A: rat] :
% 13.71/7.67 ( ( finite_finite_rat @ A4 )
% 13.71/7.67 => ( ( member_rat @ A @ A4 )
% 13.71/7.67 => ? [X3: rat] :
% 13.71/7.67 ( ( member_rat @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_rat @ X3 @ A )
% 13.71/7.67 & ! [Xa: rat] :
% 13.71/7.67 ( ( member_rat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_318_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_num,A: num] :
% 13.71/7.67 ( ( finite_finite_num @ A4 )
% 13.71/7.67 => ( ( member_num @ A @ A4 )
% 13.71/7.67 => ? [X3: num] :
% 13.71/7.67 ( ( member_num @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_num @ X3 @ A )
% 13.71/7.67 & ! [Xa: num] :
% 13.71/7.67 ( ( member_num @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_num @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_319_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_nat,A: nat] :
% 13.71/7.67 ( ( finite_finite_nat @ A4 )
% 13.71/7.67 => ( ( member_nat @ A @ A4 )
% 13.71/7.67 => ? [X3: nat] :
% 13.71/7.67 ( ( member_nat @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_nat @ X3 @ A )
% 13.71/7.67 & ! [Xa: nat] :
% 13.71/7.67 ( ( member_nat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_320_finite__has__minimal2,axiom,
% 13.71/7.67 ! [A4: set_int,A: int] :
% 13.71/7.67 ( ( finite_finite_int @ A4 )
% 13.71/7.67 => ( ( member_int @ A @ A4 )
% 13.71/7.67 => ? [X3: int] :
% 13.71/7.67 ( ( member_int @ X3 @ A4 )
% 13.71/7.67 & ( ord_less_eq_int @ X3 @ A )
% 13.71/7.67 & ! [Xa: int] :
% 13.71/7.67 ( ( member_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_int @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_321_Suc__leD,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 13.71/7.67 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_322_le__SucE,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 13.71/7.67 => ( ~ ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( M
% 13.71/7.67 = ( suc @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_323_le__SucI,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_324_Suc__le__D,axiom,
% 13.71/7.67 ! [N: nat,M6: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ ( suc @ N ) @ M6 )
% 13.71/7.67 => ? [M3: nat] :
% 13.71/7.67 ( M6
% 13.71/7.67 = ( suc @ M3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_325_le__Suc__eq,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 13.71/7.67 = ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 | ( M
% 13.71/7.67 = ( suc @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_326_Suc__n__not__le__n,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_327_not__less__eq__eq,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 13.71/7.67 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_328_full__nat__induct,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ! [N2: nat] :
% 13.71/7.67 ( ! [M2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N2 )
% 13.71/7.67 => ( P2 @ M2 ) )
% 13.71/7.67 => ( P2 @ N2 ) )
% 13.71/7.67 => ( P2 @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_329_nat__induct__at__least,axiom,
% 13.71/7.67 ! [M: nat,N: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( ( P2 @ M )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N2 )
% 13.71/7.67 => ( ( P2 @ N2 )
% 13.71/7.67 => ( P2 @ ( suc @ N2 ) ) ) )
% 13.71/7.67 => ( P2 @ N ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_330_transitive__stepwise__le,axiom,
% 13.71/7.67 ! [M: nat,N: nat,R2: nat > nat > $o] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 13.71/7.67 ( ( R2 @ X3 @ Y3 )
% 13.71/7.67 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.67 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.67 => ( ! [N2: nat] : ( R2 @ N2 @ ( suc @ N2 ) )
% 13.71/7.67 => ( R2 @ M @ N ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_331_less__eq__nat_Osimps_I1_J,axiom,
% 13.71/7.67 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_332_bot__nat__0_Oextremum__unique,axiom,
% 13.71/7.67 ! [A: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 13.71/7.67 = ( A = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_333_bot__nat__0_Oextremum__uniqueI,axiom,
% 13.71/7.67 ! [A: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 13.71/7.67 => ( A = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_334_le__0__eq,axiom,
% 13.71/7.67 ! [N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 13.71/7.67 = ( N = zero_zero_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_335_exists__leI,axiom,
% 13.71/7.67 ! [N: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ! [N4: nat] :
% 13.71/7.67 ( ( ord_less_nat @ N4 @ N )
% 13.71/7.67 => ~ ( P2 @ N4 ) )
% 13.71/7.67 => ( P2 @ N ) )
% 13.71/7.67 => ? [N5: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ N5 @ N )
% 13.71/7.67 & ( P2 @ N5 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_336_nat__less__le,axiom,
% 13.71/7.67 ( ord_less_nat
% 13.71/7.67 = ( ^ [M5: nat,N6: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M5 @ N6 )
% 13.71/7.67 & ( M5 != N6 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_337_less__imp__le__nat,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_338_le__eq__less__or__eq,axiom,
% 13.71/7.67 ( ord_less_eq_nat
% 13.71/7.67 = ( ^ [M5: nat,N6: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M5 @ N6 )
% 13.71/7.67 | ( M5 = N6 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_339_less__or__eq__imp__le,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ( ord_less_nat @ M @ N )
% 13.71/7.67 | ( M = N ) )
% 13.71/7.67 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_340_le__neq__implies__less,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( ( M != N )
% 13.71/7.67 => ( ord_less_nat @ M @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_341_less__mono__imp__le__mono,axiom,
% 13.71/7.67 ! [F: nat > nat,I: nat,J: nat] :
% 13.71/7.67 ( ! [I2: nat,J2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I2 @ J2 )
% 13.71/7.67 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ I @ J )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_342_finite__has__minimal,axiom,
% 13.71/7.67 ! [A4: set_Code_integer] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.71/7.67 => ? [X3: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_le3102999989581377725nteger @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_343_finite__has__minimal,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ( ( finite_finite_o @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_o )
% 13.71/7.67 => ? [X3: $o] :
% 13.71/7.67 ( ( member_o @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: $o] :
% 13.71/7.67 ( ( member_o @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_o @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_344_finite__has__minimal,axiom,
% 13.71/7.67 ! [A4: set_set_int] :
% 13.71/7.67 ( ( finite6197958912794628473et_int @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_set_int )
% 13.71/7.67 => ? [X3: set_int] :
% 13.71/7.67 ( ( member_set_int @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: set_int] :
% 13.71/7.67 ( ( member_set_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_345_finite__has__minimal,axiom,
% 13.71/7.67 ! [A4: set_rat] :
% 13.71/7.67 ( ( finite_finite_rat @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_rat )
% 13.71/7.67 => ? [X3: rat] :
% 13.71/7.67 ( ( member_rat @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: rat] :
% 13.71/7.67 ( ( member_rat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_346_finite__has__minimal,axiom,
% 13.71/7.67 ! [A4: set_num] :
% 13.71/7.67 ( ( finite_finite_num @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_num )
% 13.71/7.67 => ? [X3: num] :
% 13.71/7.67 ( ( member_num @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: num] :
% 13.71/7.67 ( ( member_num @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_num @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_347_finite__has__minimal,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ( finite_finite_nat @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_nat )
% 13.71/7.67 => ? [X3: nat] :
% 13.71/7.67 ( ( member_nat @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: nat] :
% 13.71/7.67 ( ( member_nat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_348_finite__has__minimal,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ( finite_finite_int @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_int )
% 13.71/7.67 => ? [X3: int] :
% 13.71/7.67 ( ( member_int @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: int] :
% 13.71/7.67 ( ( member_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_int @ Xa @ X3 )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_349_finite__has__maximal,axiom,
% 13.71/7.67 ! [A4: set_Code_integer] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.71/7.67 => ? [X3: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: code_integer] :
% 13.71/7.67 ( ( member_Code_integer @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_350_finite__has__maximal,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ( ( finite_finite_o @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_o )
% 13.71/7.67 => ? [X3: $o] :
% 13.71/7.67 ( ( member_o @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: $o] :
% 13.71/7.67 ( ( member_o @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_o @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_351_finite__has__maximal,axiom,
% 13.71/7.67 ! [A4: set_set_int] :
% 13.71/7.67 ( ( finite6197958912794628473et_int @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_set_int )
% 13.71/7.67 => ? [X3: set_int] :
% 13.71/7.67 ( ( member_set_int @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: set_int] :
% 13.71/7.67 ( ( member_set_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_352_finite__has__maximal,axiom,
% 13.71/7.67 ! [A4: set_rat] :
% 13.71/7.67 ( ( finite_finite_rat @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_rat )
% 13.71/7.67 => ? [X3: rat] :
% 13.71/7.67 ( ( member_rat @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: rat] :
% 13.71/7.67 ( ( member_rat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_353_finite__has__maximal,axiom,
% 13.71/7.67 ! [A4: set_num] :
% 13.71/7.67 ( ( finite_finite_num @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_num )
% 13.71/7.67 => ? [X3: num] :
% 13.71/7.67 ( ( member_num @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: num] :
% 13.71/7.67 ( ( member_num @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_num @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_354_finite__has__maximal,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ( finite_finite_nat @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_nat )
% 13.71/7.67 => ? [X3: nat] :
% 13.71/7.67 ( ( member_nat @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: nat] :
% 13.71/7.67 ( ( member_nat @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_355_finite__has__maximal,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ( finite_finite_int @ A4 )
% 13.71/7.67 => ( ( A4 != bot_bot_set_int )
% 13.71/7.67 => ? [X3: int] :
% 13.71/7.67 ( ( member_int @ X3 @ A4 )
% 13.71/7.67 & ! [Xa: int] :
% 13.71/7.67 ( ( member_int @ Xa @ A4 )
% 13.71/7.67 => ( ( ord_less_eq_int @ X3 @ Xa )
% 13.71/7.67 => ( X3 = Xa ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_356_nat__compl__induct,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ( P2 @ zero_zero_nat )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ! [Nn: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ Nn @ N2 )
% 13.71/7.67 => ( P2 @ Nn ) )
% 13.71/7.67 => ( P2 @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( P2 @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_357_nat__compl__induct_H,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ( P2 @ zero_zero_nat )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ! [Nn: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ Nn @ N2 )
% 13.71/7.67 => ( P2 @ Nn ) )
% 13.71/7.67 => ( P2 @ ( suc @ N2 ) ) )
% 13.71/7.67 => ( P2 @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_358_nat__in__between__eq_I1_J,axiom,
% 13.71/7.67 ! [A: nat,B: nat] :
% 13.71/7.67 ( ( ( ord_less_nat @ A @ B )
% 13.71/7.67 & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 13.71/7.67 = ( B
% 13.71/7.67 = ( suc @ A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_359_nat__in__between__eq_I2_J,axiom,
% 13.71/7.67 ! [A: nat,B: nat] :
% 13.71/7.67 ( ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 13.71/7.67 = ( B = A ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_360_Suc__leI,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ N )
% 13.71/7.67 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_361_Suc__le__eq,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 13.71/7.67 = ( ord_less_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_362_dec__induct,axiom,
% 13.71/7.67 ! [I: nat,J: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ord_less_eq_nat @ I @ J )
% 13.71/7.67 => ( ( P2 @ I )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ I @ N2 )
% 13.71/7.67 => ( ( ord_less_nat @ N2 @ J )
% 13.71/7.67 => ( ( P2 @ N2 )
% 13.71/7.67 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 13.71/7.67 => ( P2 @ J ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_363_inc__induct,axiom,
% 13.71/7.67 ! [I: nat,J: nat,P2: nat > $o] :
% 13.71/7.67 ( ( ord_less_eq_nat @ I @ J )
% 13.71/7.67 => ( ( P2 @ J )
% 13.71/7.67 => ( ! [N2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ I @ N2 )
% 13.71/7.67 => ( ( ord_less_nat @ N2 @ J )
% 13.71/7.67 => ( ( P2 @ ( suc @ N2 ) )
% 13.71/7.67 => ( P2 @ N2 ) ) ) )
% 13.71/7.67 => ( P2 @ I ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_364_Suc__le__lessD,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 13.71/7.67 => ( ord_less_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_365_le__less__Suc__eq,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 13.71/7.67 = ( N = M ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_366_less__Suc__eq__le,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 13.71/7.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_367_less__eq__Suc__le,axiom,
% 13.71/7.67 ( ord_less_nat
% 13.71/7.67 = ( ^ [N6: nat] : ( ord_less_eq_nat @ ( suc @ N6 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_368_le__imp__less__Suc,axiom,
% 13.71/7.67 ! [M: nat,N: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.67 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_369_ex__least__nat__le,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ( P2 @ N )
% 13.71/7.67 => ( ~ ( P2 @ zero_zero_nat )
% 13.71/7.67 => ? [K2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ K2 @ N )
% 13.71/7.67 & ! [I4: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I4 @ K2 )
% 13.71/7.67 => ~ ( P2 @ I4 ) )
% 13.71/7.67 & ( P2 @ K2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_370_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 13.71/7.67 ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 13.71/7.67 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_371_ex__least__nat__less,axiom,
% 13.71/7.67 ! [P2: nat > $o,N: nat] :
% 13.71/7.67 ( ( P2 @ N )
% 13.71/7.67 => ( ~ ( P2 @ zero_zero_nat )
% 13.71/7.67 => ? [K2: nat] :
% 13.71/7.67 ( ( ord_less_nat @ K2 @ N )
% 13.71/7.67 & ! [I4: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ I4 @ K2 )
% 13.71/7.67 => ~ ( P2 @ I4 ) )
% 13.71/7.67 & ( P2 @ ( suc @ K2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_372_emptyE,axiom,
% 13.71/7.67 ! [A: vEBT_VEBT] :
% 13.71/7.67 ~ ( member_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_373_emptyE,axiom,
% 13.71/7.67 ! [A: real] :
% 13.71/7.67 ~ ( member_real @ A @ bot_bot_set_real ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_374_emptyE,axiom,
% 13.71/7.67 ! [A: set_nat] :
% 13.71/7.67 ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_375_emptyE,axiom,
% 13.71/7.67 ! [A: nat] :
% 13.71/7.67 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_376_emptyE,axiom,
% 13.71/7.67 ! [A: int] :
% 13.71/7.67 ~ ( member_int @ A @ bot_bot_set_int ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_377_emptyE,axiom,
% 13.71/7.67 ! [A: $o] :
% 13.71/7.67 ~ ( member_o @ A @ bot_bot_set_o ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_378_equals0D,axiom,
% 13.71/7.67 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT] :
% 13.71/7.67 ( ( A4 = bot_bo8194388402131092736T_VEBT )
% 13.71/7.67 => ~ ( member_VEBT_VEBT @ A @ A4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_379_equals0D,axiom,
% 13.71/7.67 ! [A4: set_real,A: real] :
% 13.71/7.67 ( ( A4 = bot_bot_set_real )
% 13.71/7.67 => ~ ( member_real @ A @ A4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_380_equals0D,axiom,
% 13.71/7.67 ! [A4: set_set_nat,A: set_nat] :
% 13.71/7.67 ( ( A4 = bot_bot_set_set_nat )
% 13.71/7.67 => ~ ( member_set_nat @ A @ A4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_381_equals0D,axiom,
% 13.71/7.67 ! [A4: set_nat,A: nat] :
% 13.71/7.67 ( ( A4 = bot_bot_set_nat )
% 13.71/7.67 => ~ ( member_nat @ A @ A4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_382_equals0D,axiom,
% 13.71/7.67 ! [A4: set_int,A: int] :
% 13.71/7.67 ( ( A4 = bot_bot_set_int )
% 13.71/7.67 => ~ ( member_int @ A @ A4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_383_equals0D,axiom,
% 13.71/7.67 ! [A4: set_o,A: $o] :
% 13.71/7.67 ( ( A4 = bot_bot_set_o )
% 13.71/7.67 => ~ ( member_o @ A @ A4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_384_equals0I,axiom,
% 13.71/7.67 ! [A4: set_VEBT_VEBT] :
% 13.71/7.67 ( ! [Y3: vEBT_VEBT] :
% 13.71/7.67 ~ ( member_VEBT_VEBT @ Y3 @ A4 )
% 13.71/7.67 => ( A4 = bot_bo8194388402131092736T_VEBT ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_385_equals0I,axiom,
% 13.71/7.67 ! [A4: set_real] :
% 13.71/7.67 ( ! [Y3: real] :
% 13.71/7.67 ~ ( member_real @ Y3 @ A4 )
% 13.71/7.67 => ( A4 = bot_bot_set_real ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_386_equals0I,axiom,
% 13.71/7.67 ! [A4: set_set_nat] :
% 13.71/7.67 ( ! [Y3: set_nat] :
% 13.71/7.67 ~ ( member_set_nat @ Y3 @ A4 )
% 13.71/7.67 => ( A4 = bot_bot_set_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_387_equals0I,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ! [Y3: nat] :
% 13.71/7.67 ~ ( member_nat @ Y3 @ A4 )
% 13.71/7.67 => ( A4 = bot_bot_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_388_equals0I,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ! [Y3: int] :
% 13.71/7.67 ~ ( member_int @ Y3 @ A4 )
% 13.71/7.67 => ( A4 = bot_bot_set_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_389_equals0I,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ( ! [Y3: $o] :
% 13.71/7.67 ~ ( member_o @ Y3 @ A4 )
% 13.71/7.67 => ( A4 = bot_bot_set_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_390_ex__in__conv,axiom,
% 13.71/7.67 ! [A4: set_VEBT_VEBT] :
% 13.71/7.67 ( ( ? [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 != bot_bo8194388402131092736T_VEBT ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_391_ex__in__conv,axiom,
% 13.71/7.67 ! [A4: set_real] :
% 13.71/7.67 ( ( ? [X4: real] : ( member_real @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 != bot_bot_set_real ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_392_ex__in__conv,axiom,
% 13.71/7.67 ! [A4: set_set_nat] :
% 13.71/7.67 ( ( ? [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 != bot_bot_set_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_393_ex__in__conv,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ( ? [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 != bot_bot_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_394_ex__in__conv,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ( ? [X4: int] : ( member_int @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 != bot_bot_set_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_395_ex__in__conv,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ( ( ? [X4: $o] : ( member_o @ X4 @ A4 ) )
% 13.71/7.67 = ( A4 != bot_bot_set_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_396_not__psubset__empty,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ~ ( ord_less_set_nat @ A4 @ bot_bot_set_nat ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_397_not__psubset__empty,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ~ ( ord_less_set_int @ A4 @ bot_bot_set_int ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_398_not__psubset__empty,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ~ ( ord_less_set_o @ A4 @ bot_bot_set_o ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_399_forall__finite_I1_J,axiom,
% 13.71/7.67 ! [P2: nat > $o,I4: nat] :
% 13.71/7.67 ( ( ord_less_nat @ I4 @ zero_zero_nat )
% 13.71/7.67 => ( P2 @ I4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_400_member__valid__both__member__options,axiom,
% 13.71/7.67 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.67 ( ( vEBT_invar_vebt @ Tree @ N )
% 13.71/7.67 => ( ( vEBT_vebt_member @ Tree @ X )
% 13.71/7.67 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 13.71/7.67 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_401_both__member__options__def,axiom,
% 13.71/7.67 ( vEBT_V8194947554948674370ptions
% 13.71/7.67 = ( ^ [T2: vEBT_VEBT,X4: nat] :
% 13.71/7.67 ( ( vEBT_V5719532721284313246member @ T2 @ X4 )
% 13.71/7.67 | ( vEBT_VEBT_membermima @ T2 @ X4 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_402_is__succ__in__set__def,axiom,
% 13.71/7.67 ( vEBT_is_succ_in_set
% 13.71/7.67 = ( ^ [Xs2: set_nat,X4: nat,Y4: nat] :
% 13.71/7.67 ( ( member_nat @ Y4 @ Xs2 )
% 13.71/7.67 & ( ord_less_nat @ X4 @ Y4 )
% 13.71/7.67 & ! [Z2: nat] :
% 13.71/7.67 ( ( member_nat @ Z2 @ Xs2 )
% 13.71/7.67 => ( ( ord_less_nat @ X4 @ Z2 )
% 13.71/7.67 => ( ord_less_eq_nat @ Y4 @ Z2 ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_403_is__pred__in__set__def,axiom,
% 13.71/7.67 ( vEBT_is_pred_in_set
% 13.71/7.67 = ( ^ [Xs2: set_nat,X4: nat,Y4: nat] :
% 13.71/7.67 ( ( member_nat @ Y4 @ Xs2 )
% 13.71/7.67 & ( ord_less_nat @ Y4 @ X4 )
% 13.71/7.67 & ! [Z2: nat] :
% 13.71/7.67 ( ( member_nat @ Z2 @ Xs2 )
% 13.71/7.67 => ( ( ord_less_nat @ Z2 @ X4 )
% 13.71/7.67 => ( ord_less_eq_nat @ Z2 @ Y4 ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_404_order__refl,axiom,
% 13.71/7.67 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_405_order__refl,axiom,
% 13.71/7.67 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_406_order__refl,axiom,
% 13.71/7.67 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_407_order__refl,axiom,
% 13.71/7.67 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_408_order__refl,axiom,
% 13.71/7.67 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_409_dual__order_Orefl,axiom,
% 13.71/7.67 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_410_dual__order_Orefl,axiom,
% 13.71/7.67 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_411_dual__order_Orefl,axiom,
% 13.71/7.67 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_412_dual__order_Orefl,axiom,
% 13.71/7.67 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_413_dual__order_Orefl,axiom,
% 13.71/7.67 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_414_buildup__nothing__in__min__max,axiom,
% 13.71/7.67 ! [N: nat,X: nat] :
% 13.71/7.67 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_415_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 13.71/7.67 ! [Uu2: $o] :
% 13.71/7.67 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu2 @ $true ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_416_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 13.71/7.67 ! [Uv2: $o] :
% 13.71/7.67 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv2 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_417_empty__subsetI,axiom,
% 13.71/7.67 ! [A4: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_418_empty__subsetI,axiom,
% 13.71/7.67 ! [A4: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_419_empty__subsetI,axiom,
% 13.71/7.67 ! [A4: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A4 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_420_subset__empty,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat )
% 13.71/7.67 = ( A4 = bot_bot_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_421_subset__empty,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ( ( ord_less_eq_set_o @ A4 @ bot_bot_set_o )
% 13.71/7.67 = ( A4 = bot_bot_set_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_422_subset__empty,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A4 @ bot_bot_set_int )
% 13.71/7.67 = ( A4 = bot_bot_set_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_423_psubsetI,axiom,
% 13.71/7.67 ! [A4: set_int,B4: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.67 => ( ( A4 != B4 )
% 13.71/7.67 => ( ord_less_set_int @ A4 @ B4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_424_bot__set__def,axiom,
% 13.71/7.67 ( bot_bot_set_complex
% 13.71/7.67 = ( collect_complex @ bot_bot_complex_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_425_bot__set__def,axiom,
% 13.71/7.67 ( bot_bot_set_list_nat
% 13.71/7.67 = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_426_bot__set__def,axiom,
% 13.71/7.67 ( bot_bot_set_set_nat
% 13.71/7.67 = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_427_bot__set__def,axiom,
% 13.71/7.67 ( bot_bot_set_nat
% 13.71/7.67 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_428_bot__set__def,axiom,
% 13.71/7.67 ( bot_bot_set_int
% 13.71/7.67 = ( collect_int @ bot_bot_int_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_429_bot__set__def,axiom,
% 13.71/7.67 ( bot_bot_set_o
% 13.71/7.67 = ( collect_o @ bot_bot_o_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_430_bot__nat__def,axiom,
% 13.71/7.67 bot_bot_nat = zero_zero_nat ).
% 13.71/7.67
% 13.71/7.67 thf(fact_431_subset__emptyI,axiom,
% 13.71/7.67 ! [A4: set_VEBT_VEBT] :
% 13.71/7.67 ( ! [X3: vEBT_VEBT] :
% 13.71/7.67 ~ ( member_VEBT_VEBT @ X3 @ A4 )
% 13.71/7.67 => ( ord_le4337996190870823476T_VEBT @ A4 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_432_subset__emptyI,axiom,
% 13.71/7.67 ! [A4: set_real] :
% 13.71/7.67 ( ! [X3: real] :
% 13.71/7.67 ~ ( member_real @ X3 @ A4 )
% 13.71/7.67 => ( ord_less_eq_set_real @ A4 @ bot_bot_set_real ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_433_subset__emptyI,axiom,
% 13.71/7.67 ! [A4: set_set_nat] :
% 13.71/7.67 ( ! [X3: set_nat] :
% 13.71/7.67 ~ ( member_set_nat @ X3 @ A4 )
% 13.71/7.67 => ( ord_le6893508408891458716et_nat @ A4 @ bot_bot_set_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_434_subset__emptyI,axiom,
% 13.71/7.67 ! [A4: set_nat] :
% 13.71/7.67 ( ! [X3: nat] :
% 13.71/7.67 ~ ( member_nat @ X3 @ A4 )
% 13.71/7.67 => ( ord_less_eq_set_nat @ A4 @ bot_bot_set_nat ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_435_subset__emptyI,axiom,
% 13.71/7.67 ! [A4: set_o] :
% 13.71/7.67 ( ! [X3: $o] :
% 13.71/7.67 ~ ( member_o @ X3 @ A4 )
% 13.71/7.67 => ( ord_less_eq_set_o @ A4 @ bot_bot_set_o ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_436_subset__emptyI,axiom,
% 13.71/7.67 ! [A4: set_int] :
% 13.71/7.67 ( ! [X3: int] :
% 13.71/7.67 ~ ( member_int @ X3 @ A4 )
% 13.71/7.67 => ( ord_less_eq_set_int @ A4 @ bot_bot_set_int ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_437_rev__finite__subset,axiom,
% 13.71/7.67 ! [B4: set_nat,A4: set_nat] :
% 13.71/7.67 ( ( finite_finite_nat @ B4 )
% 13.71/7.67 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.71/7.67 => ( finite_finite_nat @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_438_rev__finite__subset,axiom,
% 13.71/7.67 ! [B4: set_complex,A4: set_complex] :
% 13.71/7.67 ( ( finite3207457112153483333omplex @ B4 )
% 13.71/7.67 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.71/7.67 => ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_439_rev__finite__subset,axiom,
% 13.71/7.67 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.71/7.67 ( ( finite6017078050557962740nteger @ B4 )
% 13.71/7.67 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.71/7.67 => ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_440_rev__finite__subset,axiom,
% 13.71/7.67 ! [B4: set_int,A4: set_int] :
% 13.71/7.67 ( ( finite_finite_int @ B4 )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.67 => ( finite_finite_int @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_441_infinite__super,axiom,
% 13.71/7.67 ! [S3: set_nat,T3: set_nat] :
% 13.71/7.67 ( ( ord_less_eq_set_nat @ S3 @ T3 )
% 13.71/7.67 => ( ~ ( finite_finite_nat @ S3 )
% 13.71/7.67 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_442_infinite__super,axiom,
% 13.71/7.67 ! [S3: set_complex,T3: set_complex] :
% 13.71/7.67 ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.71/7.67 => ( ~ ( finite3207457112153483333omplex @ S3 )
% 13.71/7.67 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_443_infinite__super,axiom,
% 13.71/7.67 ! [S3: set_Code_integer,T3: set_Code_integer] :
% 13.71/7.67 ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.71/7.67 => ( ~ ( finite6017078050557962740nteger @ S3 )
% 13.71/7.67 => ~ ( finite6017078050557962740nteger @ T3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_444_infinite__super,axiom,
% 13.71/7.67 ! [S3: set_int,T3: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ S3 @ T3 )
% 13.71/7.67 => ( ~ ( finite_finite_int @ S3 )
% 13.71/7.67 => ~ ( finite_finite_int @ T3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_445_finite__subset,axiom,
% 13.71/7.67 ! [A4: set_nat,B4: set_nat] :
% 13.71/7.67 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.71/7.67 => ( ( finite_finite_nat @ B4 )
% 13.71/7.67 => ( finite_finite_nat @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_446_finite__subset,axiom,
% 13.71/7.67 ! [A4: set_complex,B4: set_complex] :
% 13.71/7.67 ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.71/7.67 => ( ( finite3207457112153483333omplex @ B4 )
% 13.71/7.67 => ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_447_finite__subset,axiom,
% 13.71/7.67 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.71/7.67 ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.71/7.67 => ( ( finite6017078050557962740nteger @ B4 )
% 13.71/7.67 => ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_448_finite__subset,axiom,
% 13.71/7.67 ! [A4: set_int,B4: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.67 => ( ( finite_finite_int @ B4 )
% 13.71/7.67 => ( finite_finite_int @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_449_mod__false,axiom,
% 13.71/7.67 ! [H2: produc3658429121746597890et_nat] :
% 13.71/7.67 ~ ( rep_assn @ bot_bot_assn @ H2 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_450_subset__iff__psubset__eq,axiom,
% 13.71/7.67 ( ord_less_eq_set_int
% 13.71/7.67 = ( ^ [A6: set_int,B6: set_int] :
% 13.71/7.67 ( ( ord_less_set_int @ A6 @ B6 )
% 13.71/7.67 | ( A6 = B6 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_451_subset__psubset__trans,axiom,
% 13.71/7.67 ! [A4: set_int,B4: set_int,C3: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.67 => ( ( ord_less_set_int @ B4 @ C3 )
% 13.71/7.67 => ( ord_less_set_int @ A4 @ C3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_452_subset__not__subset__eq,axiom,
% 13.71/7.67 ( ord_less_set_int
% 13.71/7.67 = ( ^ [A6: set_int,B6: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 13.71/7.67 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_453_psubset__subset__trans,axiom,
% 13.71/7.67 ! [A4: set_int,B4: set_int,C3: set_int] :
% 13.71/7.67 ( ( ord_less_set_int @ A4 @ B4 )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ B4 @ C3 )
% 13.71/7.67 => ( ord_less_set_int @ A4 @ C3 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_454_psubset__imp__subset,axiom,
% 13.71/7.67 ! [A4: set_int,B4: set_int] :
% 13.71/7.67 ( ( ord_less_set_int @ A4 @ B4 )
% 13.71/7.67 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_455_psubset__eq,axiom,
% 13.71/7.67 ( ord_less_set_int
% 13.71/7.67 = ( ^ [A6: set_int,B6: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 13.71/7.67 & ( A6 != B6 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_456_psubsetE,axiom,
% 13.71/7.67 ! [A4: set_int,B4: set_int] :
% 13.71/7.67 ( ( ord_less_set_int @ A4 @ B4 )
% 13.71/7.67 => ~ ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.67 => ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_457_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 13.71/7.67 ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 13.71/7.67 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_458_order__antisym__conv,axiom,
% 13.71/7.67 ! [Y: set_int,X: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ Y @ X )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ X @ Y )
% 13.71/7.67 = ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_459_order__antisym__conv,axiom,
% 13.71/7.67 ! [Y: rat,X: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ Y @ X )
% 13.71/7.67 => ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.67 = ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_460_order__antisym__conv,axiom,
% 13.71/7.67 ! [Y: num,X: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ Y @ X )
% 13.71/7.67 => ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.67 = ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_461_order__antisym__conv,axiom,
% 13.71/7.67 ! [Y: nat,X: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ Y @ X )
% 13.71/7.67 => ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.67 = ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_462_order__antisym__conv,axiom,
% 13.71/7.67 ! [Y: int,X: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ Y @ X )
% 13.71/7.67 => ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.67 = ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_463_linorder__le__cases,axiom,
% 13.71/7.67 ! [X: rat,Y: rat] :
% 13.71/7.67 ( ~ ( ord_less_eq_rat @ X @ Y )
% 13.71/7.67 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_464_linorder__le__cases,axiom,
% 13.71/7.67 ! [X: num,Y: num] :
% 13.71/7.67 ( ~ ( ord_less_eq_num @ X @ Y )
% 13.71/7.67 => ( ord_less_eq_num @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_465_linorder__le__cases,axiom,
% 13.71/7.67 ! [X: nat,Y: nat] :
% 13.71/7.67 ( ~ ( ord_less_eq_nat @ X @ Y )
% 13.71/7.67 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_466_linorder__le__cases,axiom,
% 13.71/7.67 ! [X: int,Y: int] :
% 13.71/7.67 ( ~ ( ord_less_eq_int @ X @ Y )
% 13.71/7.67 => ( ord_less_eq_int @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_467_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_468_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_469_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_470_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_471_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_472_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_473_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_474_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_475_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_476_ord__le__eq__subst,axiom,
% 13.71/7.67 ! [A: nat,B: nat,F: nat > num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( ( ( F @ B )
% 13.71/7.67 = C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_477_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_478_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_479_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_480_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_481_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: rat,F: num > rat,B: num,C2: num] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_482_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: num,F: num > num,B: num,C2: num] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_483_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: nat,F: num > nat,B: num,C2: num] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_484_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: int,F: num > int,B: num,C2: num] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_485_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_486_ord__eq__le__subst,axiom,
% 13.71/7.67 ! [A: num,F: nat > num,B: nat,C2: nat] :
% 13.71/7.67 ( ( A
% 13.71/7.67 = ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_487_linorder__linear,axiom,
% 13.71/7.67 ! [X: rat,Y: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.67 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_488_linorder__linear,axiom,
% 13.71/7.67 ! [X: num,Y: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.67 | ( ord_less_eq_num @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_489_linorder__linear,axiom,
% 13.71/7.67 ! [X: nat,Y: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.67 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_490_linorder__linear,axiom,
% 13.71/7.67 ! [X: int,Y: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.67 | ( ord_less_eq_int @ Y @ X ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_491_order__eq__refl,axiom,
% 13.71/7.67 ! [X: set_int,Y: set_int] :
% 13.71/7.67 ( ( X = Y )
% 13.71/7.67 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_492_order__eq__refl,axiom,
% 13.71/7.67 ! [X: rat,Y: rat] :
% 13.71/7.67 ( ( X = Y )
% 13.71/7.67 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_493_order__eq__refl,axiom,
% 13.71/7.67 ! [X: num,Y: num] :
% 13.71/7.67 ( ( X = Y )
% 13.71/7.67 => ( ord_less_eq_num @ X @ Y ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_494_order__eq__refl,axiom,
% 13.71/7.67 ! [X: nat,Y: nat] :
% 13.71/7.67 ( ( X = Y )
% 13.71/7.67 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_495_order__eq__refl,axiom,
% 13.71/7.67 ! [X: int,Y: int] :
% 13.71/7.67 ( ( X = Y )
% 13.71/7.67 => ( ord_less_eq_int @ X @ Y ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_496_order__subst2,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_497_order__subst2,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_498_order__subst2,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_499_order__subst2,axiom,
% 13.71/7.67 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_500_order__subst2,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_501_order__subst2,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_502_order__subst2,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_nat @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_503_order__subst2,axiom,
% 13.71/7.67 ! [A: num,B: num,F: num > int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_504_order__subst2,axiom,
% 13.71/7.67 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_505_order__subst2,axiom,
% 13.71/7.67 ! [A: nat,B: nat,F: nat > num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_num @ ( F @ B ) @ C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_506_order__subst1,axiom,
% 13.71/7.67 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_507_order__subst1,axiom,
% 13.71/7.67 ! [A: rat,F: num > rat,B: num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_508_order__subst1,axiom,
% 13.71/7.67 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_509_order__subst1,axiom,
% 13.71/7.67 ! [A: rat,F: int > rat,B: int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_int @ B @ C2 )
% 13.71/7.67 => ( ! [X3: int,Y3: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_510_order__subst1,axiom,
% 13.71/7.67 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_511_order__subst1,axiom,
% 13.71/7.67 ! [A: num,F: num > num,B: num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_512_order__subst1,axiom,
% 13.71/7.67 ! [A: num,F: nat > num,B: nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_513_order__subst1,axiom,
% 13.71/7.67 ! [A: num,F: int > num,B: int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_int @ B @ C2 )
% 13.71/7.67 => ( ! [X3: int,Y3: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_514_order__subst1,axiom,
% 13.71/7.67 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_515_order__subst1,axiom,
% 13.71/7.67 ! [A: nat,F: num > nat,B: num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ! [X3: num,Y3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_516_Orderings_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: set_int,B7: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A7 @ B7 )
% 13.71/7.67 & ( ord_less_eq_set_int @ B7 @ A7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_517_Orderings_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: rat,B7: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A7 @ B7 )
% 13.71/7.67 & ( ord_less_eq_rat @ B7 @ A7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_518_Orderings_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: num,B7: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A7 @ B7 )
% 13.71/7.67 & ( ord_less_eq_num @ B7 @ A7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_519_Orderings_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: nat,B7: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A7 @ B7 )
% 13.71/7.67 & ( ord_less_eq_nat @ B7 @ A7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_520_Orderings_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: int,B7: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ A7 @ B7 )
% 13.71/7.67 & ( ord_less_eq_int @ B7 @ A7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_521_antisym,axiom,
% 13.71/7.67 ! [A: set_int,B: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ B @ A )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_522_antisym,axiom,
% 13.71/7.67 ! [A: rat,B: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ A )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_523_antisym,axiom,
% 13.71/7.67 ! [A: num,B: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ A )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_524_antisym,axiom,
% 13.71/7.67 ! [A: nat,B: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ A )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_525_antisym,axiom,
% 13.71/7.67 ! [A: int,B: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_int @ B @ A )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_526_dual__order_Otrans,axiom,
% 13.71/7.67 ! [B: set_int,A: set_int,C2: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ C2 @ B )
% 13.71/7.67 => ( ord_less_eq_set_int @ C2 @ A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_527_dual__order_Otrans,axiom,
% 13.71/7.67 ! [B: rat,A: rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_rat @ C2 @ B )
% 13.71/7.67 => ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_528_dual__order_Otrans,axiom,
% 13.71/7.67 ! [B: num,A: num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_num @ C2 @ B )
% 13.71/7.67 => ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_529_dual__order_Otrans,axiom,
% 13.71/7.67 ! [B: nat,A: nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_nat @ C2 @ B )
% 13.71/7.67 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_530_dual__order_Otrans,axiom,
% 13.71/7.67 ! [B: int,A: int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_int @ C2 @ B )
% 13.71/7.67 => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_531_dual__order_Oantisym,axiom,
% 13.71/7.67 ! [B: set_int,A: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ A @ B )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_532_dual__order_Oantisym,axiom,
% 13.71/7.67 ! [B: rat,A: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_533_dual__order_Oantisym,axiom,
% 13.71/7.67 ! [B: num,A: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_534_dual__order_Oantisym,axiom,
% 13.71/7.67 ! [B: nat,A: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_535_dual__order_Oantisym,axiom,
% 13.71/7.67 ! [B: int,A: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ B @ A )
% 13.71/7.67 => ( ( ord_less_eq_int @ A @ B )
% 13.71/7.67 => ( A = B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_536_dual__order_Oeq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: set_int,B7: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ B7 @ A7 )
% 13.71/7.67 & ( ord_less_eq_set_int @ A7 @ B7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_537_dual__order_Oeq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: rat,B7: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ B7 @ A7 )
% 13.71/7.67 & ( ord_less_eq_rat @ A7 @ B7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_538_dual__order_Oeq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: num,B7: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ B7 @ A7 )
% 13.71/7.67 & ( ord_less_eq_num @ A7 @ B7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_539_dual__order_Oeq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: nat,B7: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ B7 @ A7 )
% 13.71/7.67 & ( ord_less_eq_nat @ A7 @ B7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_540_dual__order_Oeq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [A7: int,B7: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ B7 @ A7 )
% 13.71/7.67 & ( ord_less_eq_int @ A7 @ B7 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_541_linorder__wlog,axiom,
% 13.71/7.67 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 13.71/7.67 ( ! [A3: rat,B3: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A3 @ B3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( ! [A3: rat,B3: rat] :
% 13.71/7.67 ( ( P2 @ B3 @ A3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ A @ B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_542_linorder__wlog,axiom,
% 13.71/7.67 ! [P2: num > num > $o,A: num,B: num] :
% 13.71/7.67 ( ! [A3: num,B3: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A3 @ B3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( ! [A3: num,B3: num] :
% 13.71/7.67 ( ( P2 @ B3 @ A3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ A @ B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_543_linorder__wlog,axiom,
% 13.71/7.67 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 13.71/7.67 ( ! [A3: nat,B3: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A3 @ B3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( ! [A3: nat,B3: nat] :
% 13.71/7.67 ( ( P2 @ B3 @ A3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ A @ B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_544_linorder__wlog,axiom,
% 13.71/7.67 ! [P2: int > int > $o,A: int,B: int] :
% 13.71/7.67 ( ! [A3: int,B3: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ A3 @ B3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( ! [A3: int,B3: int] :
% 13.71/7.67 ( ( P2 @ B3 @ A3 )
% 13.71/7.67 => ( P2 @ A3 @ B3 ) )
% 13.71/7.67 => ( P2 @ A @ B ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_545_order__trans,axiom,
% 13.71/7.67 ! [X: set_int,Y: set_int,Z: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ Y @ Z )
% 13.71/7.67 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_546_order__trans,axiom,
% 13.71/7.67 ! [X: rat,Y: rat,Z: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_rat @ Y @ Z )
% 13.71/7.67 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_547_order__trans,axiom,
% 13.71/7.67 ! [X: num,Y: num,Z: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_num @ Y @ Z )
% 13.71/7.67 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_548_order__trans,axiom,
% 13.71/7.67 ! [X: nat,Y: nat,Z: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_nat @ Y @ Z )
% 13.71/7.67 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_549_order__trans,axiom,
% 13.71/7.67 ! [X: int,Y: int,Z: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_int @ Y @ Z )
% 13.71/7.67 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_550_order_Otrans,axiom,
% 13.71/7.67 ! [A: set_int,B: set_int,C2: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_551_order_Otrans,axiom,
% 13.71/7.67 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_552_order_Otrans,axiom,
% 13.71/7.67 ! [A: num,B: num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_553_order_Otrans,axiom,
% 13.71/7.67 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_554_order_Otrans,axiom,
% 13.71/7.67 ! [A: int,B: int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ A @ B )
% 13.71/7.67 => ( ( ord_less_eq_int @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_555_order__antisym,axiom,
% 13.71/7.67 ! [X: set_int,Y: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ Y @ X )
% 13.71/7.67 => ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_556_order__antisym,axiom,
% 13.71/7.67 ! [X: rat,Y: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_rat @ Y @ X )
% 13.71/7.67 => ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_557_order__antisym,axiom,
% 13.71/7.67 ! [X: num,Y: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_num @ Y @ X )
% 13.71/7.67 => ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_558_order__antisym,axiom,
% 13.71/7.67 ! [X: nat,Y: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_nat @ Y @ X )
% 13.71/7.67 => ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_559_order__antisym,axiom,
% 13.71/7.67 ! [X: int,Y: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.67 => ( ( ord_less_eq_int @ Y @ X )
% 13.71/7.67 => ( X = Y ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_560_ord__le__eq__trans,axiom,
% 13.71/7.67 ! [A: set_int,B: set_int,C2: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ A @ B )
% 13.71/7.67 => ( ( B = C2 )
% 13.71/7.67 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_561_ord__le__eq__trans,axiom,
% 13.71/7.67 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.67 => ( ( B = C2 )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_562_ord__le__eq__trans,axiom,
% 13.71/7.67 ! [A: num,B: num,C2: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.67 => ( ( B = C2 )
% 13.71/7.67 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_563_ord__le__eq__trans,axiom,
% 13.71/7.67 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.67 => ( ( B = C2 )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_564_ord__le__eq__trans,axiom,
% 13.71/7.67 ! [A: int,B: int,C2: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ A @ B )
% 13.71/7.67 => ( ( B = C2 )
% 13.71/7.67 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_565_ord__eq__le__trans,axiom,
% 13.71/7.67 ! [A: set_int,B: set_int,C2: set_int] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_set_int @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_set_int @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_566_ord__eq__le__trans,axiom,
% 13.71/7.67 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_567_ord__eq__le__trans,axiom,
% 13.71/7.67 ! [A: num,B: num,C2: num] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_568_ord__eq__le__trans,axiom,
% 13.71/7.67 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_569_ord__eq__le__trans,axiom,
% 13.71/7.67 ! [A: int,B: int,C2: int] :
% 13.71/7.67 ( ( A = B )
% 13.71/7.67 => ( ( ord_less_eq_int @ B @ C2 )
% 13.71/7.67 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_570_order__class_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [X4: set_int,Y4: set_int] :
% 13.71/7.67 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 13.71/7.67 & ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_571_order__class_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [X4: rat,Y4: rat] :
% 13.71/7.67 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 13.71/7.67 & ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_572_order__class_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [X4: num,Y4: num] :
% 13.71/7.67 ( ( ord_less_eq_num @ X4 @ Y4 )
% 13.71/7.67 & ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_573_order__class_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [X4: nat,Y4: nat] :
% 13.71/7.67 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 13.71/7.67 & ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_574_order__class_Oorder__eq__iff,axiom,
% 13.71/7.67 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.71/7.67 = ( ^ [X4: int,Y4: int] :
% 13.71/7.67 ( ( ord_less_eq_int @ X4 @ Y4 )
% 13.71/7.67 & ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_575_le__cases3,axiom,
% 13.71/7.67 ! [X: rat,Y: rat,Z: rat] :
% 13.71/7.67 ( ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_rat @ Y @ X )
% 13.71/7.67 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_rat @ X @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 13.71/7.67 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 13.71/7.67 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 13.71/7.67 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 13.71/7.67 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_576_le__cases3,axiom,
% 13.71/7.67 ! [X: num,Y: num,Z: num] :
% 13.71/7.67 ( ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_num @ Y @ X )
% 13.71/7.67 => ~ ( ord_less_eq_num @ X @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_num @ X @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 13.71/7.67 => ( ( ( ord_less_eq_num @ Z @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_num @ Y @ X ) )
% 13.71/7.67 => ( ( ( ord_less_eq_num @ Y @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_num @ Z @ X ) )
% 13.71/7.67 => ~ ( ( ord_less_eq_num @ Z @ X )
% 13.71/7.67 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_577_le__cases3,axiom,
% 13.71/7.67 ! [X: nat,Y: nat,Z: nat] :
% 13.71/7.67 ( ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_nat @ Y @ X )
% 13.71/7.67 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_nat @ X @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 13.71/7.67 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 13.71/7.67 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 13.71/7.67 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 13.71/7.67 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_578_le__cases3,axiom,
% 13.71/7.67 ! [X: int,Y: int,Z: int] :
% 13.71/7.67 ( ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_int @ Y @ X )
% 13.71/7.67 => ~ ( ord_less_eq_int @ X @ Z ) )
% 13.71/7.67 => ( ( ( ord_less_eq_int @ X @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 13.71/7.67 => ( ( ( ord_less_eq_int @ Z @ Y )
% 13.71/7.67 => ~ ( ord_less_eq_int @ Y @ X ) )
% 13.71/7.67 => ( ( ( ord_less_eq_int @ Y @ Z )
% 13.71/7.67 => ~ ( ord_less_eq_int @ Z @ X ) )
% 13.71/7.67 => ~ ( ( ord_less_eq_int @ Z @ X )
% 13.71/7.67 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_579_nle__le,axiom,
% 13.71/7.67 ! [A: rat,B: rat] :
% 13.71/7.67 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 13.71/7.67 = ( ( ord_less_eq_rat @ B @ A )
% 13.71/7.67 & ( B != A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_580_nle__le,axiom,
% 13.71/7.67 ! [A: num,B: num] :
% 13.71/7.67 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 13.71/7.67 = ( ( ord_less_eq_num @ B @ A )
% 13.71/7.67 & ( B != A ) ) ) ).
% 13.71/7.67
% 13.71/7.67 thf(fact_581_nle__le,axiom,
% 13.71/7.67 ! [A: nat,B: nat] :
% 13.71/7.67 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 13.71/7.67 = ( ( ord_less_eq_nat @ B @ A )
% 13.71/7.67 & ( B != A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_582_nle__le,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 13.71/7.68 = ( ( ord_less_eq_int @ B @ A )
% 13.71/7.68 & ( B != A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_583_order__less__imp__not__less,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_584_order__less__imp__not__less,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_585_order__less__imp__not__less,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_586_order__less__imp__not__less,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_587_order__less__imp__not__less,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_588_order__less__imp__not__eq2,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( Y != X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_589_order__less__imp__not__eq2,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( Y != X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_590_order__less__imp__not__eq2,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( Y != X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_591_order__less__imp__not__eq2,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( Y != X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_592_order__less__imp__not__eq2,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( Y != X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_593_order__less__imp__not__eq,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_594_order__less__imp__not__eq,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_595_order__less__imp__not__eq,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_596_order__less__imp__not__eq,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_597_order__less__imp__not__eq,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_598_linorder__less__linear,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 | ( X = Y )
% 13.71/7.68 | ( ord_less_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_599_linorder__less__linear,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 | ( X = Y )
% 13.71/7.68 | ( ord_less_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_600_linorder__less__linear,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 | ( X = Y )
% 13.71/7.68 | ( ord_less_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_601_linorder__less__linear,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 | ( X = Y )
% 13.71/7.68 | ( ord_less_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_602_linorder__less__linear,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 | ( X = Y )
% 13.71/7.68 | ( ord_less_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_603_order__less__imp__triv,axiom,
% 13.71/7.68 ! [X: real,Y: real,P2: $o] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ( ord_less_real @ Y @ X )
% 13.71/7.68 => P2 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_604_order__less__imp__triv,axiom,
% 13.71/7.68 ! [X: rat,Y: rat,P2: $o] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_rat @ Y @ X )
% 13.71/7.68 => P2 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_605_order__less__imp__triv,axiom,
% 13.71/7.68 ! [X: num,Y: num,P2: $o] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ( ord_less_num @ Y @ X )
% 13.71/7.68 => P2 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_606_order__less__imp__triv,axiom,
% 13.71/7.68 ! [X: nat,Y: nat,P2: $o] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_nat @ Y @ X )
% 13.71/7.68 => P2 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_607_order__less__imp__triv,axiom,
% 13.71/7.68 ! [X: int,Y: int,P2: $o] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_int @ Y @ X )
% 13.71/7.68 => P2 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_608_order__less__not__sym,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_609_order__less__not__sym,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_610_order__less__not__sym,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_611_order__less__not__sym,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_612_order__less__not__sym,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_613_order__less__subst2,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_614_order__less__subst2,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_615_order__less__subst2,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > num,C2: num] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_616_order__less__subst2,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_617_order__less__subst2,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > int,C2: int] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_618_order__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_619_order__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_620_order__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_621_order__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_622_order__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_623_order__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: real > real,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_624_order__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_625_order__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: num > real,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_626_order__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: nat > real,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_nat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_627_order__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: int > real,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_int @ B @ C2 )
% 13.71/7.68 => ( ! [X3: int,Y3: int] :
% 13.71/7.68 ( ( ord_less_int @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_628_order__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: real > rat,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_629_order__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_630_order__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: num > rat,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_631_order__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_nat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_632_order__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: int > rat,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_int @ B @ C2 )
% 13.71/7.68 => ( ! [X3: int,Y3: int] :
% 13.71/7.68 ( ( ord_less_int @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_633_order__less__irrefl,axiom,
% 13.71/7.68 ! [X: real] :
% 13.71/7.68 ~ ( ord_less_real @ X @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_634_order__less__irrefl,axiom,
% 13.71/7.68 ! [X: rat] :
% 13.71/7.68 ~ ( ord_less_rat @ X @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_635_order__less__irrefl,axiom,
% 13.71/7.68 ! [X: num] :
% 13.71/7.68 ~ ( ord_less_num @ X @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_636_order__less__irrefl,axiom,
% 13.71/7.68 ! [X: nat] :
% 13.71/7.68 ~ ( ord_less_nat @ X @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_637_order__less__irrefl,axiom,
% 13.71/7.68 ! [X: int] :
% 13.71/7.68 ~ ( ord_less_int @ X @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_638_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_639_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_640_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > num,C2: num] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_641_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_642_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > int,C2: int] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_643_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_644_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_645_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_646_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_647_ord__less__eq__subst,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ( F @ B )
% 13.71/7.68 = C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_648_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: real,F: real > real,B: real,C2: real] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_649_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: rat,F: real > rat,B: real,C2: real] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_650_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: num,F: real > num,B: real,C2: real] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_651_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: nat,F: real > nat,B: real,C2: real] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_652_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: int,F: real > int,B: real,C2: real] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_653_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_654_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_655_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_656_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_657_ord__eq__less__subst,axiom,
% 13.71/7.68 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 13.71/7.68 ( ( A
% 13.71/7.68 = ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_658_order__less__trans,axiom,
% 13.71/7.68 ! [X: real,Y: real,Z: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ( ord_less_real @ Y @ Z )
% 13.71/7.68 => ( ord_less_real @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_659_order__less__trans,axiom,
% 13.71/7.68 ! [X: rat,Y: rat,Z: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_rat @ Y @ Z )
% 13.71/7.68 => ( ord_less_rat @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_660_order__less__trans,axiom,
% 13.71/7.68 ! [X: num,Y: num,Z: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ( ord_less_num @ Y @ Z )
% 13.71/7.68 => ( ord_less_num @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_661_order__less__trans,axiom,
% 13.71/7.68 ! [X: nat,Y: nat,Z: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_nat @ Y @ Z )
% 13.71/7.68 => ( ord_less_nat @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_662_order__less__trans,axiom,
% 13.71/7.68 ! [X: int,Y: int,Z: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_int @ Y @ Z )
% 13.71/7.68 => ( ord_less_int @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_663_order__less__asym_H,axiom,
% 13.71/7.68 ! [A: real,B: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ~ ( ord_less_real @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_664_order__less__asym_H,axiom,
% 13.71/7.68 ! [A: rat,B: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ~ ( ord_less_rat @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_665_order__less__asym_H,axiom,
% 13.71/7.68 ! [A: num,B: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ~ ( ord_less_num @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_666_order__less__asym_H,axiom,
% 13.71/7.68 ! [A: nat,B: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ~ ( ord_less_nat @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_667_order__less__asym_H,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ~ ( ord_less_int @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_668_linorder__neq__iff,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 = ( ( ord_less_real @ X @ Y )
% 13.71/7.68 | ( ord_less_real @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_669_linorder__neq__iff,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 = ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 | ( ord_less_rat @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_670_linorder__neq__iff,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 = ( ( ord_less_num @ X @ Y )
% 13.71/7.68 | ( ord_less_num @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_671_linorder__neq__iff,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 = ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 | ( ord_less_nat @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_672_linorder__neq__iff,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 = ( ( ord_less_int @ X @ Y )
% 13.71/7.68 | ( ord_less_int @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_673_order__less__asym,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_674_order__less__asym,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_675_order__less__asym,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_676_order__less__asym,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_677_order__less__asym,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ~ ( ord_less_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_678_linorder__neqE,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ord_less_real @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_679_linorder__neqE,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ord_less_rat @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_680_linorder__neqE,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ord_less_num @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_681_linorder__neqE,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ord_less_nat @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_682_linorder__neqE,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ord_less_int @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_683_dual__order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [B: real,A: real] :
% 13.71/7.68 ( ( ord_less_real @ B @ A )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_684_dual__order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [B: rat,A: rat] :
% 13.71/7.68 ( ( ord_less_rat @ B @ A )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_685_dual__order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [B: num,A: num] :
% 13.71/7.68 ( ( ord_less_num @ B @ A )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_686_dual__order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [B: nat,A: nat] :
% 13.71/7.68 ( ( ord_less_nat @ B @ A )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_687_dual__order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [B: int,A: int] :
% 13.71/7.68 ( ( ord_less_int @ B @ A )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_688_order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [A: real,B: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_689_order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [A: rat,B: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_690_order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [A: num,B: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_691_order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [A: nat,B: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_692_order_Ostrict__implies__not__eq,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( A != B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_693_dual__order_Ostrict__trans,axiom,
% 13.71/7.68 ! [B: real,A: real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ B @ A )
% 13.71/7.68 => ( ( ord_less_real @ C2 @ B )
% 13.71/7.68 => ( ord_less_real @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_694_dual__order_Ostrict__trans,axiom,
% 13.71/7.68 ! [B: rat,A: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ B @ A )
% 13.71/7.68 => ( ( ord_less_rat @ C2 @ B )
% 13.71/7.68 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_695_dual__order_Ostrict__trans,axiom,
% 13.71/7.68 ! [B: num,A: num,C2: num] :
% 13.71/7.68 ( ( ord_less_num @ B @ A )
% 13.71/7.68 => ( ( ord_less_num @ C2 @ B )
% 13.71/7.68 => ( ord_less_num @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_696_dual__order_Ostrict__trans,axiom,
% 13.71/7.68 ! [B: nat,A: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_nat @ B @ A )
% 13.71/7.68 => ( ( ord_less_nat @ C2 @ B )
% 13.71/7.68 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_697_dual__order_Ostrict__trans,axiom,
% 13.71/7.68 ! [B: int,A: int,C2: int] :
% 13.71/7.68 ( ( ord_less_int @ B @ A )
% 13.71/7.68 => ( ( ord_less_int @ C2 @ B )
% 13.71/7.68 => ( ord_less_int @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_698_not__less__iff__gr__or__eq,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ~ ( ord_less_real @ X @ Y ) )
% 13.71/7.68 = ( ( ord_less_real @ Y @ X )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_699_not__less__iff__gr__or__eq,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 13.71/7.68 = ( ( ord_less_rat @ Y @ X )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_700_not__less__iff__gr__or__eq,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ~ ( ord_less_num @ X @ Y ) )
% 13.71/7.68 = ( ( ord_less_num @ Y @ X )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_701_not__less__iff__gr__or__eq,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 13.71/7.68 = ( ( ord_less_nat @ Y @ X )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_702_not__less__iff__gr__or__eq,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ~ ( ord_less_int @ X @ Y ) )
% 13.71/7.68 = ( ( ord_less_int @ Y @ X )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_703_order_Ostrict__trans,axiom,
% 13.71/7.68 ! [A: real,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ord_less_real @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_704_order_Ostrict__trans,axiom,
% 13.71/7.68 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_705_order_Ostrict__trans,axiom,
% 13.71/7.68 ! [A: num,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_num @ B @ C2 )
% 13.71/7.68 => ( ord_less_num @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_706_order_Ostrict__trans,axiom,
% 13.71/7.68 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( ( ord_less_nat @ B @ C2 )
% 13.71/7.68 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_707_order_Ostrict__trans,axiom,
% 13.71/7.68 ! [A: int,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( ( ord_less_int @ B @ C2 )
% 13.71/7.68 => ( ord_less_int @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_708_linorder__less__wlog,axiom,
% 13.71/7.68 ! [P2: real > real > $o,A: real,B: real] :
% 13.71/7.68 ( ! [A3: real,B3: real] :
% 13.71/7.68 ( ( ord_less_real @ A3 @ B3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( ! [A3: real] : ( P2 @ A3 @ A3 )
% 13.71/7.68 => ( ! [A3: real,B3: real] :
% 13.71/7.68 ( ( P2 @ B3 @ A3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( P2 @ A @ B ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_709_linorder__less__wlog,axiom,
% 13.71/7.68 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 13.71/7.68 ( ! [A3: rat,B3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A3 @ B3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( ! [A3: rat] : ( P2 @ A3 @ A3 )
% 13.71/7.68 => ( ! [A3: rat,B3: rat] :
% 13.71/7.68 ( ( P2 @ B3 @ A3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( P2 @ A @ B ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_710_linorder__less__wlog,axiom,
% 13.71/7.68 ! [P2: num > num > $o,A: num,B: num] :
% 13.71/7.68 ( ! [A3: num,B3: num] :
% 13.71/7.68 ( ( ord_less_num @ A3 @ B3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( ! [A3: num] : ( P2 @ A3 @ A3 )
% 13.71/7.68 => ( ! [A3: num,B3: num] :
% 13.71/7.68 ( ( P2 @ B3 @ A3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( P2 @ A @ B ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_711_linorder__less__wlog,axiom,
% 13.71/7.68 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 13.71/7.68 ( ! [A3: nat,B3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A3 @ B3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( ! [A3: nat] : ( P2 @ A3 @ A3 )
% 13.71/7.68 => ( ! [A3: nat,B3: nat] :
% 13.71/7.68 ( ( P2 @ B3 @ A3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( P2 @ A @ B ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_712_linorder__less__wlog,axiom,
% 13.71/7.68 ! [P2: int > int > $o,A: int,B: int] :
% 13.71/7.68 ( ! [A3: int,B3: int] :
% 13.71/7.68 ( ( ord_less_int @ A3 @ B3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( ! [A3: int] : ( P2 @ A3 @ A3 )
% 13.71/7.68 => ( ! [A3: int,B3: int] :
% 13.71/7.68 ( ( P2 @ B3 @ A3 )
% 13.71/7.68 => ( P2 @ A3 @ B3 ) )
% 13.71/7.68 => ( P2 @ A @ B ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_713_exists__least__iff,axiom,
% 13.71/7.68 ( ( ^ [P4: nat > $o] :
% 13.71/7.68 ? [X7: nat] : ( P4 @ X7 ) )
% 13.71/7.68 = ( ^ [P5: nat > $o] :
% 13.71/7.68 ? [N6: nat] :
% 13.71/7.68 ( ( P5 @ N6 )
% 13.71/7.68 & ! [M5: nat] :
% 13.71/7.68 ( ( ord_less_nat @ M5 @ N6 )
% 13.71/7.68 => ~ ( P5 @ M5 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_714_dual__order_Oirrefl,axiom,
% 13.71/7.68 ! [A: real] :
% 13.71/7.68 ~ ( ord_less_real @ A @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_715_dual__order_Oirrefl,axiom,
% 13.71/7.68 ! [A: rat] :
% 13.71/7.68 ~ ( ord_less_rat @ A @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_716_dual__order_Oirrefl,axiom,
% 13.71/7.68 ! [A: num] :
% 13.71/7.68 ~ ( ord_less_num @ A @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_717_dual__order_Oirrefl,axiom,
% 13.71/7.68 ! [A: nat] :
% 13.71/7.68 ~ ( ord_less_nat @ A @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_718_dual__order_Oirrefl,axiom,
% 13.71/7.68 ! [A: int] :
% 13.71/7.68 ~ ( ord_less_int @ A @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_719_dual__order_Oasym,axiom,
% 13.71/7.68 ! [B: real,A: real] :
% 13.71/7.68 ( ( ord_less_real @ B @ A )
% 13.71/7.68 => ~ ( ord_less_real @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_720_dual__order_Oasym,axiom,
% 13.71/7.68 ! [B: rat,A: rat] :
% 13.71/7.68 ( ( ord_less_rat @ B @ A )
% 13.71/7.68 => ~ ( ord_less_rat @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_721_dual__order_Oasym,axiom,
% 13.71/7.68 ! [B: num,A: num] :
% 13.71/7.68 ( ( ord_less_num @ B @ A )
% 13.71/7.68 => ~ ( ord_less_num @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_722_dual__order_Oasym,axiom,
% 13.71/7.68 ! [B: nat,A: nat] :
% 13.71/7.68 ( ( ord_less_nat @ B @ A )
% 13.71/7.68 => ~ ( ord_less_nat @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_723_dual__order_Oasym,axiom,
% 13.71/7.68 ! [B: int,A: int] :
% 13.71/7.68 ( ( ord_less_int @ B @ A )
% 13.71/7.68 => ~ ( ord_less_int @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_724_linorder__cases,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ~ ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ( X != Y )
% 13.71/7.68 => ( ord_less_real @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_725_linorder__cases,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ~ ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ( X != Y )
% 13.71/7.68 => ( ord_less_rat @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_726_linorder__cases,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ~ ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ( X != Y )
% 13.71/7.68 => ( ord_less_num @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_727_linorder__cases,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ~ ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ( X != Y )
% 13.71/7.68 => ( ord_less_nat @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_728_linorder__cases,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ~ ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ( X != Y )
% 13.71/7.68 => ( ord_less_int @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_729_antisym__conv3,axiom,
% 13.71/7.68 ! [Y: real,X: real] :
% 13.71/7.68 ( ~ ( ord_less_real @ Y @ X )
% 13.71/7.68 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_730_antisym__conv3,axiom,
% 13.71/7.68 ! [Y: rat,X: rat] :
% 13.71/7.68 ( ~ ( ord_less_rat @ Y @ X )
% 13.71/7.68 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_731_antisym__conv3,axiom,
% 13.71/7.68 ! [Y: num,X: num] :
% 13.71/7.68 ( ~ ( ord_less_num @ Y @ X )
% 13.71/7.68 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_732_antisym__conv3,axiom,
% 13.71/7.68 ! [Y: nat,X: nat] :
% 13.71/7.68 ( ~ ( ord_less_nat @ Y @ X )
% 13.71/7.68 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_733_antisym__conv3,axiom,
% 13.71/7.68 ! [Y: int,X: int] :
% 13.71/7.68 ( ~ ( ord_less_int @ Y @ X )
% 13.71/7.68 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_734_less__induct,axiom,
% 13.71/7.68 ! [P2: nat > $o,A: nat] :
% 13.71/7.68 ( ! [X3: nat] :
% 13.71/7.68 ( ! [Y5: nat] :
% 13.71/7.68 ( ( ord_less_nat @ Y5 @ X3 )
% 13.71/7.68 => ( P2 @ Y5 ) )
% 13.71/7.68 => ( P2 @ X3 ) )
% 13.71/7.68 => ( P2 @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_735_ord__less__eq__trans,axiom,
% 13.71/7.68 ! [A: real,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( B = C2 )
% 13.71/7.68 => ( ord_less_real @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_736_ord__less__eq__trans,axiom,
% 13.71/7.68 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( B = C2 )
% 13.71/7.68 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_737_ord__less__eq__trans,axiom,
% 13.71/7.68 ! [A: num,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ( ( B = C2 )
% 13.71/7.68 => ( ord_less_num @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_738_ord__less__eq__trans,axiom,
% 13.71/7.68 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( ( B = C2 )
% 13.71/7.68 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_739_ord__less__eq__trans,axiom,
% 13.71/7.68 ! [A: int,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( ( B = C2 )
% 13.71/7.68 => ( ord_less_int @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_740_ord__eq__less__trans,axiom,
% 13.71/7.68 ! [A: real,B: real,C2: real] :
% 13.71/7.68 ( ( A = B )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ord_less_real @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_741_ord__eq__less__trans,axiom,
% 13.71/7.68 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( A = B )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_742_ord__eq__less__trans,axiom,
% 13.71/7.68 ! [A: num,B: num,C2: num] :
% 13.71/7.68 ( ( A = B )
% 13.71/7.68 => ( ( ord_less_num @ B @ C2 )
% 13.71/7.68 => ( ord_less_num @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_743_ord__eq__less__trans,axiom,
% 13.71/7.68 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.68 ( ( A = B )
% 13.71/7.68 => ( ( ord_less_nat @ B @ C2 )
% 13.71/7.68 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_744_ord__eq__less__trans,axiom,
% 13.71/7.68 ! [A: int,B: int,C2: int] :
% 13.71/7.68 ( ( A = B )
% 13.71/7.68 => ( ( ord_less_int @ B @ C2 )
% 13.71/7.68 => ( ord_less_int @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_745_order_Oasym,axiom,
% 13.71/7.68 ! [A: real,B: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ~ ( ord_less_real @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_746_order_Oasym,axiom,
% 13.71/7.68 ! [A: rat,B: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ~ ( ord_less_rat @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_747_order_Oasym,axiom,
% 13.71/7.68 ! [A: num,B: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ~ ( ord_less_num @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_748_order_Oasym,axiom,
% 13.71/7.68 ! [A: nat,B: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ~ ( ord_less_nat @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_749_order_Oasym,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ~ ( ord_less_int @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_750_less__imp__neq,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_751_less__imp__neq,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_752_less__imp__neq,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_753_less__imp__neq,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_754_less__imp__neq,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( X != Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_755_dense,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ? [Z3: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Z3 )
% 13.71/7.68 & ( ord_less_real @ Z3 @ Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_756_dense,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ? [Z3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Z3 )
% 13.71/7.68 & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_757_gt__ex,axiom,
% 13.71/7.68 ! [X: real] :
% 13.71/7.68 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_758_gt__ex,axiom,
% 13.71/7.68 ! [X: rat] :
% 13.71/7.68 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_759_gt__ex,axiom,
% 13.71/7.68 ! [X: nat] :
% 13.71/7.68 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_760_gt__ex,axiom,
% 13.71/7.68 ! [X: int] :
% 13.71/7.68 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_761_lt__ex,axiom,
% 13.71/7.68 ! [X: real] :
% 13.71/7.68 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_762_lt__ex,axiom,
% 13.71/7.68 ! [X: rat] :
% 13.71/7.68 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_763_lt__ex,axiom,
% 13.71/7.68 ! [X: int] :
% 13.71/7.68 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_764_order__le__imp__less__or__eq,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ X @ Y )
% 13.71/7.68 => ( ( ord_less_real @ X @ Y )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_765_order__le__imp__less__or__eq,axiom,
% 13.71/7.68 ! [X: set_int,Y: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_set_int @ X @ Y )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_766_order__le__imp__less__or__eq,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_767_order__le__imp__less__or__eq,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.68 => ( ( ord_less_num @ X @ Y )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_768_order__le__imp__less__or__eq,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_769_order__le__imp__less__or__eq,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_int @ X @ Y )
% 13.71/7.68 | ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_770_linorder__le__less__linear,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ X @ Y )
% 13.71/7.68 | ( ord_less_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_771_linorder__le__less__linear,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.68 | ( ord_less_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_772_linorder__le__less__linear,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.68 | ( ord_less_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_773_linorder__le__less__linear,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.68 | ( ord_less_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_774_linorder__le__less__linear,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.68 | ( ord_less_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_775_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_776_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_777_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: num,B: num,F: num > real,C2: real] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_778_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: nat,B: nat,F: nat > real,C2: real] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_779_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: int,B: int,F: int > real,C2: real] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: int,Y3: int] :
% 13.71/7.68 ( ( ord_less_int @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_780_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: real,B: real,F: real > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_781_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_782_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: num,B: num,F: num > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_783_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: nat,B: nat,F: nat > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_784_order__less__le__subst2,axiom,
% 13.71/7.68 ! [A: int,B: int,F: int > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: int,Y3: int] :
% 13.71/7.68 ( ( ord_less_int @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_785_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_786_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_787_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: num,F: rat > num,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_num @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_788_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: nat,F: rat > nat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_789_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: int,F: rat > int,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_int @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_790_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: real,F: num > real,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_791_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: num > rat,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_792_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: num,F: num > num,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_793_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: nat,F: num > nat,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_nat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_794_order__less__le__subst1,axiom,
% 13.71/7.68 ! [A: int,F: num > int,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_int @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_795_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > real,C2: real] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_796_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_797_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > num,C2: num] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_798_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_799_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,F: rat > int,C2: int] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_800_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: num,B: num,F: num > real,C2: real] :
% 13.71/7.68 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_801_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: num,B: num,F: num > rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_rat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_802_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: num,B: num,F: num > num,C2: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_num @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_num @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_803_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: num,B: num,F: num > nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_nat @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_nat @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_804_order__le__less__subst2,axiom,
% 13.71/7.68 ! [A: num,B: num,F: num > int,C2: int] :
% 13.71/7.68 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_805_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: real > real,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_806_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: rat > real,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_807_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: num > real,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_808_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: nat > real,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_nat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_809_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: real,F: int > real,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_int @ B @ C2 )
% 13.71/7.68 => ( ! [X3: int,Y3: int] :
% 13.71/7.68 ( ( ord_less_int @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_real @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_810_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: real > rat,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ! [X3: real,Y3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_811_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: rat > rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: rat,Y3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_812_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: num > rat,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_num @ B @ C2 )
% 13.71/7.68 => ( ! [X3: num,Y3: num] :
% 13.71/7.68 ( ( ord_less_num @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_813_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: nat > rat,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_nat @ B @ C2 )
% 13.71/7.68 => ( ! [X3: nat,Y3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_814_order__le__less__subst1,axiom,
% 13.71/7.68 ! [A: rat,F: int > rat,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 13.71/7.68 => ( ( ord_less_int @ B @ C2 )
% 13.71/7.68 => ( ! [X3: int,Y3: int] :
% 13.71/7.68 ( ( ord_less_int @ X3 @ Y3 )
% 13.71/7.68 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 13.71/7.68 => ( ord_less_rat @ A @ ( F @ C2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_815_order__less__le__trans,axiom,
% 13.71/7.68 ! [X: real,Y: real,Z: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_real @ Y @ Z )
% 13.71/7.68 => ( ord_less_real @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_816_order__less__le__trans,axiom,
% 13.71/7.68 ! [X: set_int,Y: set_int,Z: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_set_int @ Y @ Z )
% 13.71/7.68 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_817_order__less__le__trans,axiom,
% 13.71/7.68 ! [X: rat,Y: rat,Z: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_rat @ Y @ Z )
% 13.71/7.68 => ( ord_less_rat @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_818_order__less__le__trans,axiom,
% 13.71/7.68 ! [X: num,Y: num,Z: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_num @ Y @ Z )
% 13.71/7.68 => ( ord_less_num @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_819_order__less__le__trans,axiom,
% 13.71/7.68 ! [X: nat,Y: nat,Z: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_nat @ Y @ Z )
% 13.71/7.68 => ( ord_less_nat @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_820_order__less__le__trans,axiom,
% 13.71/7.68 ! [X: int,Y: int,Z: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_int @ Y @ Z )
% 13.71/7.68 => ( ord_less_int @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_821_order__le__less__trans,axiom,
% 13.71/7.68 ! [X: real,Y: real,Z: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ X @ Y )
% 13.71/7.68 => ( ( ord_less_real @ Y @ Z )
% 13.71/7.68 => ( ord_less_real @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_822_order__le__less__trans,axiom,
% 13.71/7.68 ! [X: set_int,Y: set_int,Z: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_set_int @ Y @ Z )
% 13.71/7.68 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_823_order__le__less__trans,axiom,
% 13.71/7.68 ! [X: rat,Y: rat,Z: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_rat @ Y @ Z )
% 13.71/7.68 => ( ord_less_rat @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_824_order__le__less__trans,axiom,
% 13.71/7.68 ! [X: num,Y: num,Z: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.68 => ( ( ord_less_num @ Y @ Z )
% 13.71/7.68 => ( ord_less_num @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_825_order__le__less__trans,axiom,
% 13.71/7.68 ! [X: nat,Y: nat,Z: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_nat @ Y @ Z )
% 13.71/7.68 => ( ord_less_nat @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_826_order__le__less__trans,axiom,
% 13.71/7.68 ! [X: int,Y: int,Z: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_int @ Y @ Z )
% 13.71/7.68 => ( ord_less_int @ X @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_827_order__neq__le__trans,axiom,
% 13.71/7.68 ! [A: real,B: real] :
% 13.71/7.68 ( ( A != B )
% 13.71/7.68 => ( ( ord_less_eq_real @ A @ B )
% 13.71/7.68 => ( ord_less_real @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_828_order__neq__le__trans,axiom,
% 13.71/7.68 ! [A: set_int,B: set_int] :
% 13.71/7.68 ( ( A != B )
% 13.71/7.68 => ( ( ord_less_eq_set_int @ A @ B )
% 13.71/7.68 => ( ord_less_set_int @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_829_order__neq__le__trans,axiom,
% 13.71/7.68 ! [A: rat,B: rat] :
% 13.71/7.68 ( ( A != B )
% 13.71/7.68 => ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ord_less_rat @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_830_order__neq__le__trans,axiom,
% 13.71/7.68 ! [A: num,B: num] :
% 13.71/7.68 ( ( A != B )
% 13.71/7.68 => ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ord_less_num @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_831_order__neq__le__trans,axiom,
% 13.71/7.68 ! [A: nat,B: nat] :
% 13.71/7.68 ( ( A != B )
% 13.71/7.68 => ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.68 => ( ord_less_nat @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_832_order__neq__le__trans,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( A != B )
% 13.71/7.68 => ( ( ord_less_eq_int @ A @ B )
% 13.71/7.68 => ( ord_less_int @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_833_order__le__neq__trans,axiom,
% 13.71/7.68 ! [A: real,B: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ B )
% 13.71/7.68 => ( ( A != B )
% 13.71/7.68 => ( ord_less_real @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_834_order__le__neq__trans,axiom,
% 13.71/7.68 ! [A: set_int,B: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A @ B )
% 13.71/7.68 => ( ( A != B )
% 13.71/7.68 => ( ord_less_set_int @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_835_order__le__neq__trans,axiom,
% 13.71/7.68 ! [A: rat,B: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ( A != B )
% 13.71/7.68 => ( ord_less_rat @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_836_order__le__neq__trans,axiom,
% 13.71/7.68 ! [A: num,B: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ( A != B )
% 13.71/7.68 => ( ord_less_num @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_837_order__le__neq__trans,axiom,
% 13.71/7.68 ! [A: nat,B: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.68 => ( ( A != B )
% 13.71/7.68 => ( ord_less_nat @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_838_order__le__neq__trans,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ A @ B )
% 13.71/7.68 => ( ( A != B )
% 13.71/7.68 => ( ord_less_int @ A @ B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_839_order__less__imp__le,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_real @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_840_order__less__imp__le,axiom,
% 13.71/7.68 ! [X: set_int,Y: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_841_order__less__imp__le,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_842_order__less__imp__le,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_num @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_843_order__less__imp__le,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_844_order__less__imp__le,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_int @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_845_linorder__not__less,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ~ ( ord_less_real @ X @ Y ) )
% 13.71/7.68 = ( ord_less_eq_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_846_linorder__not__less,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 13.71/7.68 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_847_linorder__not__less,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ~ ( ord_less_num @ X @ Y ) )
% 13.71/7.68 = ( ord_less_eq_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_848_linorder__not__less,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 13.71/7.68 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_849_linorder__not__less,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ~ ( ord_less_int @ X @ Y ) )
% 13.71/7.68 = ( ord_less_eq_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_850_linorder__not__le,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 13.71/7.68 = ( ord_less_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_851_linorder__not__le,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 13.71/7.68 = ( ord_less_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_852_linorder__not__le,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 13.71/7.68 = ( ord_less_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_853_linorder__not__le,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 13.71/7.68 = ( ord_less_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_854_linorder__not__le,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 13.71/7.68 = ( ord_less_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_855_order__less__le,axiom,
% 13.71/7.68 ( ord_less_real
% 13.71/7.68 = ( ^ [X4: real,Y4: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ X4 @ Y4 )
% 13.71/7.68 & ( X4 != Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_856_order__less__le,axiom,
% 13.71/7.68 ( ord_less_set_int
% 13.71/7.68 = ( ^ [X4: set_int,Y4: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 13.71/7.68 & ( X4 != Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_857_order__less__le,axiom,
% 13.71/7.68 ( ord_less_rat
% 13.71/7.68 = ( ^ [X4: rat,Y4: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 13.71/7.68 & ( X4 != Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_858_order__less__le,axiom,
% 13.71/7.68 ( ord_less_num
% 13.71/7.68 = ( ^ [X4: num,Y4: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X4 @ Y4 )
% 13.71/7.68 & ( X4 != Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_859_order__less__le,axiom,
% 13.71/7.68 ( ord_less_nat
% 13.71/7.68 = ( ^ [X4: nat,Y4: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 13.71/7.68 & ( X4 != Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_860_order__less__le,axiom,
% 13.71/7.68 ( ord_less_int
% 13.71/7.68 = ( ^ [X4: int,Y4: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ X4 @ Y4 )
% 13.71/7.68 & ( X4 != Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_861_order__le__less,axiom,
% 13.71/7.68 ( ord_less_eq_real
% 13.71/7.68 = ( ^ [X4: real,Y4: real] :
% 13.71/7.68 ( ( ord_less_real @ X4 @ Y4 )
% 13.71/7.68 | ( X4 = Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_862_order__le__less,axiom,
% 13.71/7.68 ( ord_less_eq_set_int
% 13.71/7.68 = ( ^ [X4: set_int,Y4: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ X4 @ Y4 )
% 13.71/7.68 | ( X4 = Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_863_order__le__less,axiom,
% 13.71/7.68 ( ord_less_eq_rat
% 13.71/7.68 = ( ^ [X4: rat,Y4: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X4 @ Y4 )
% 13.71/7.68 | ( X4 = Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_864_order__le__less,axiom,
% 13.71/7.68 ( ord_less_eq_num
% 13.71/7.68 = ( ^ [X4: num,Y4: num] :
% 13.71/7.68 ( ( ord_less_num @ X4 @ Y4 )
% 13.71/7.68 | ( X4 = Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_865_order__le__less,axiom,
% 13.71/7.68 ( ord_less_eq_nat
% 13.71/7.68 = ( ^ [X4: nat,Y4: nat] :
% 13.71/7.68 ( ( ord_less_nat @ X4 @ Y4 )
% 13.71/7.68 | ( X4 = Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_866_order__le__less,axiom,
% 13.71/7.68 ( ord_less_eq_int
% 13.71/7.68 = ( ^ [X4: int,Y4: int] :
% 13.71/7.68 ( ( ord_less_int @ X4 @ Y4 )
% 13.71/7.68 | ( X4 = Y4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_867_dual__order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [B: real,A: real] :
% 13.71/7.68 ( ( ord_less_real @ B @ A )
% 13.71/7.68 => ( ord_less_eq_real @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_868_dual__order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [B: set_int,A: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ B @ A )
% 13.71/7.68 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_869_dual__order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [B: rat,A: rat] :
% 13.71/7.68 ( ( ord_less_rat @ B @ A )
% 13.71/7.68 => ( ord_less_eq_rat @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_870_dual__order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [B: num,A: num] :
% 13.71/7.68 ( ( ord_less_num @ B @ A )
% 13.71/7.68 => ( ord_less_eq_num @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_871_dual__order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [B: nat,A: nat] :
% 13.71/7.68 ( ( ord_less_nat @ B @ A )
% 13.71/7.68 => ( ord_less_eq_nat @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_872_dual__order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [B: int,A: int] :
% 13.71/7.68 ( ( ord_less_int @ B @ A )
% 13.71/7.68 => ( ord_less_eq_int @ B @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_873_order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [A: real,B: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ord_less_eq_real @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_874_order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [A: set_int,B: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ A @ B )
% 13.71/7.68 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_875_order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [A: rat,B: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ord_less_eq_rat @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_876_order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [A: num,B: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ( ord_less_eq_num @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_877_order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [A: nat,B: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( ord_less_eq_nat @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_878_order_Ostrict__implies__order,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( ord_less_eq_int @ A @ B ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_879_dual__order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_real
% 13.71/7.68 = ( ^ [B7: real,A7: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ B7 @ A7 )
% 13.71/7.68 & ~ ( ord_less_eq_real @ A7 @ B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_880_dual__order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_set_int
% 13.71/7.68 = ( ^ [B7: set_int,A7: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ B7 @ A7 )
% 13.71/7.68 & ~ ( ord_less_eq_set_int @ A7 @ B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_881_dual__order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_rat
% 13.71/7.68 = ( ^ [B7: rat,A7: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ B7 @ A7 )
% 13.71/7.68 & ~ ( ord_less_eq_rat @ A7 @ B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_882_dual__order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_num
% 13.71/7.68 = ( ^ [B7: num,A7: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ B7 @ A7 )
% 13.71/7.68 & ~ ( ord_less_eq_num @ A7 @ B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_883_dual__order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_nat
% 13.71/7.68 = ( ^ [B7: nat,A7: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ B7 @ A7 )
% 13.71/7.68 & ~ ( ord_less_eq_nat @ A7 @ B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_884_dual__order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_int
% 13.71/7.68 = ( ^ [B7: int,A7: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ B7 @ A7 )
% 13.71/7.68 & ~ ( ord_less_eq_int @ A7 @ B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_885_dual__order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [B: real,A: real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ B @ A )
% 13.71/7.68 => ( ( ord_less_eq_real @ C2 @ B )
% 13.71/7.68 => ( ord_less_real @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_886_dual__order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [B: set_int,A: set_int,C2: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ B @ A )
% 13.71/7.68 => ( ( ord_less_eq_set_int @ C2 @ B )
% 13.71/7.68 => ( ord_less_set_int @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_887_dual__order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [B: rat,A: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ B @ A )
% 13.71/7.68 => ( ( ord_less_eq_rat @ C2 @ B )
% 13.71/7.68 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_888_dual__order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [B: num,A: num,C2: num] :
% 13.71/7.68 ( ( ord_less_num @ B @ A )
% 13.71/7.68 => ( ( ord_less_eq_num @ C2 @ B )
% 13.71/7.68 => ( ord_less_num @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_889_dual__order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [B: nat,A: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_nat @ B @ A )
% 13.71/7.68 => ( ( ord_less_eq_nat @ C2 @ B )
% 13.71/7.68 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_890_dual__order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [B: int,A: int,C2: int] :
% 13.71/7.68 ( ( ord_less_int @ B @ A )
% 13.71/7.68 => ( ( ord_less_eq_int @ C2 @ B )
% 13.71/7.68 => ( ord_less_int @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_891_dual__order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [B: real,A: real,C2: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ B @ A )
% 13.71/7.68 => ( ( ord_less_real @ C2 @ B )
% 13.71/7.68 => ( ord_less_real @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_892_dual__order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [B: set_int,A: set_int,C2: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ B @ A )
% 13.71/7.68 => ( ( ord_less_set_int @ C2 @ B )
% 13.71/7.68 => ( ord_less_set_int @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_893_dual__order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [B: rat,A: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ B @ A )
% 13.71/7.68 => ( ( ord_less_rat @ C2 @ B )
% 13.71/7.68 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_894_dual__order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [B: num,A: num,C2: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ B @ A )
% 13.71/7.68 => ( ( ord_less_num @ C2 @ B )
% 13.71/7.68 => ( ord_less_num @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_895_dual__order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [B: nat,A: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ B @ A )
% 13.71/7.68 => ( ( ord_less_nat @ C2 @ B )
% 13.71/7.68 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_896_dual__order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [B: int,A: int,C2: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ B @ A )
% 13.71/7.68 => ( ( ord_less_int @ C2 @ B )
% 13.71/7.68 => ( ord_less_int @ C2 @ A ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_897_dual__order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_real
% 13.71/7.68 = ( ^ [B7: real,A7: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ B7 @ A7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_898_dual__order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_set_int
% 13.71/7.68 = ( ^ [B7: set_int,A7: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ B7 @ A7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_899_dual__order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_rat
% 13.71/7.68 = ( ^ [B7: rat,A7: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ B7 @ A7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_900_dual__order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_num
% 13.71/7.68 = ( ^ [B7: num,A7: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ B7 @ A7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_901_dual__order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_nat
% 13.71/7.68 = ( ^ [B7: nat,A7: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ B7 @ A7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_902_dual__order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_int
% 13.71/7.68 = ( ^ [B7: int,A7: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ B7 @ A7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_903_dual__order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_real
% 13.71/7.68 = ( ^ [B7: real,A7: real] :
% 13.71/7.68 ( ( ord_less_real @ B7 @ A7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_904_dual__order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_set_int
% 13.71/7.68 = ( ^ [B7: set_int,A7: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ B7 @ A7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_905_dual__order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_rat
% 13.71/7.68 = ( ^ [B7: rat,A7: rat] :
% 13.71/7.68 ( ( ord_less_rat @ B7 @ A7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_906_dual__order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_num
% 13.71/7.68 = ( ^ [B7: num,A7: num] :
% 13.71/7.68 ( ( ord_less_num @ B7 @ A7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_907_dual__order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_nat
% 13.71/7.68 = ( ^ [B7: nat,A7: nat] :
% 13.71/7.68 ( ( ord_less_nat @ B7 @ A7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_908_dual__order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_int
% 13.71/7.68 = ( ^ [B7: int,A7: int] :
% 13.71/7.68 ( ( ord_less_int @ B7 @ A7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_909_dense__le__bounded,axiom,
% 13.71/7.68 ! [X: real,Y: real,Z: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ! [W: real] :
% 13.71/7.68 ( ( ord_less_real @ X @ W )
% 13.71/7.68 => ( ( ord_less_real @ W @ Y )
% 13.71/7.68 => ( ord_less_eq_real @ W @ Z ) ) )
% 13.71/7.68 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_910_dense__le__bounded,axiom,
% 13.71/7.68 ! [X: rat,Y: rat,Z: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ! [W: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X @ W )
% 13.71/7.68 => ( ( ord_less_rat @ W @ Y )
% 13.71/7.68 => ( ord_less_eq_rat @ W @ Z ) ) )
% 13.71/7.68 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_911_dense__ge__bounded,axiom,
% 13.71/7.68 ! [Z: real,X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_real @ Z @ X )
% 13.71/7.68 => ( ! [W: real] :
% 13.71/7.68 ( ( ord_less_real @ Z @ W )
% 13.71/7.68 => ( ( ord_less_real @ W @ X )
% 13.71/7.68 => ( ord_less_eq_real @ Y @ W ) ) )
% 13.71/7.68 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_912_dense__ge__bounded,axiom,
% 13.71/7.68 ! [Z: rat,X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_rat @ Z @ X )
% 13.71/7.68 => ( ! [W: rat] :
% 13.71/7.68 ( ( ord_less_rat @ Z @ W )
% 13.71/7.68 => ( ( ord_less_rat @ W @ X )
% 13.71/7.68 => ( ord_less_eq_rat @ Y @ W ) ) )
% 13.71/7.68 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_913_order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_real
% 13.71/7.68 = ( ^ [A7: real,B7: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ A7 @ B7 )
% 13.71/7.68 & ~ ( ord_less_eq_real @ B7 @ A7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_914_order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_set_int
% 13.71/7.68 = ( ^ [A7: set_int,B7: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A7 @ B7 )
% 13.71/7.68 & ~ ( ord_less_eq_set_int @ B7 @ A7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_915_order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_rat
% 13.71/7.68 = ( ^ [A7: rat,B7: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A7 @ B7 )
% 13.71/7.68 & ~ ( ord_less_eq_rat @ B7 @ A7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_916_order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_num
% 13.71/7.68 = ( ^ [A7: num,B7: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ A7 @ B7 )
% 13.71/7.68 & ~ ( ord_less_eq_num @ B7 @ A7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_917_order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_nat
% 13.71/7.68 = ( ^ [A7: nat,B7: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ A7 @ B7 )
% 13.71/7.68 & ~ ( ord_less_eq_nat @ B7 @ A7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_918_order_Ostrict__iff__not,axiom,
% 13.71/7.68 ( ord_less_int
% 13.71/7.68 = ( ^ [A7: int,B7: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ A7 @ B7 )
% 13.71/7.68 & ~ ( ord_less_eq_int @ B7 @ A7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_919_order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [A: real,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_real @ B @ C2 )
% 13.71/7.68 => ( ord_less_real @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_920_order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [A: set_int,B: set_int,C2: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_set_int @ B @ C2 )
% 13.71/7.68 => ( ord_less_set_int @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_921_order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.71/7.68 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_922_order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [A: num,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_num @ B @ C2 )
% 13.71/7.68 => ( ord_less_num @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_923_order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.68 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_924_order_Ostrict__trans2,axiom,
% 13.71/7.68 ! [A: int,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( ( ord_less_eq_int @ B @ C2 )
% 13.71/7.68 => ( ord_less_int @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_925_order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [A: real,B: real,C2: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ B )
% 13.71/7.68 => ( ( ord_less_real @ B @ C2 )
% 13.71/7.68 => ( ord_less_real @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_926_order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [A: set_int,B: set_int,C2: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A @ B )
% 13.71/7.68 => ( ( ord_less_set_int @ B @ C2 )
% 13.71/7.68 => ( ord_less_set_int @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_927_order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 => ( ( ord_less_rat @ B @ C2 )
% 13.71/7.68 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_928_order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [A: num,B: num,C2: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ A @ B )
% 13.71/7.68 => ( ( ord_less_num @ B @ C2 )
% 13.71/7.68 => ( ord_less_num @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_929_order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ A @ B )
% 13.71/7.68 => ( ( ord_less_nat @ B @ C2 )
% 13.71/7.68 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_930_order_Ostrict__trans1,axiom,
% 13.71/7.68 ! [A: int,B: int,C2: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ A @ B )
% 13.71/7.68 => ( ( ord_less_int @ B @ C2 )
% 13.71/7.68 => ( ord_less_int @ A @ C2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_931_order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_real
% 13.71/7.68 = ( ^ [A7: real,B7: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ A7 @ B7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_932_order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_set_int
% 13.71/7.68 = ( ^ [A7: set_int,B7: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A7 @ B7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_933_order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_rat
% 13.71/7.68 = ( ^ [A7: rat,B7: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ A7 @ B7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_934_order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_num
% 13.71/7.68 = ( ^ [A7: num,B7: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ A7 @ B7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_935_order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_nat
% 13.71/7.68 = ( ^ [A7: nat,B7: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ A7 @ B7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_936_order_Ostrict__iff__order,axiom,
% 13.71/7.68 ( ord_less_int
% 13.71/7.68 = ( ^ [A7: int,B7: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ A7 @ B7 )
% 13.71/7.68 & ( A7 != B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_937_order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_real
% 13.71/7.68 = ( ^ [A7: real,B7: real] :
% 13.71/7.68 ( ( ord_less_real @ A7 @ B7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_938_order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_set_int
% 13.71/7.68 = ( ^ [A7: set_int,B7: set_int] :
% 13.71/7.68 ( ( ord_less_set_int @ A7 @ B7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_939_order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_rat
% 13.71/7.68 = ( ^ [A7: rat,B7: rat] :
% 13.71/7.68 ( ( ord_less_rat @ A7 @ B7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_940_order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_num
% 13.71/7.68 = ( ^ [A7: num,B7: num] :
% 13.71/7.68 ( ( ord_less_num @ A7 @ B7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_941_order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_nat
% 13.71/7.68 = ( ^ [A7: nat,B7: nat] :
% 13.71/7.68 ( ( ord_less_nat @ A7 @ B7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_942_order_Oorder__iff__strict,axiom,
% 13.71/7.68 ( ord_less_eq_int
% 13.71/7.68 = ( ^ [A7: int,B7: int] :
% 13.71/7.68 ( ( ord_less_int @ A7 @ B7 )
% 13.71/7.68 | ( A7 = B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_943_not__le__imp__less,axiom,
% 13.71/7.68 ! [Y: real,X: real] :
% 13.71/7.68 ( ~ ( ord_less_eq_real @ Y @ X )
% 13.71/7.68 => ( ord_less_real @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_944_not__le__imp__less,axiom,
% 13.71/7.68 ! [Y: rat,X: rat] :
% 13.71/7.68 ( ~ ( ord_less_eq_rat @ Y @ X )
% 13.71/7.68 => ( ord_less_rat @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_945_not__le__imp__less,axiom,
% 13.71/7.68 ! [Y: num,X: num] :
% 13.71/7.68 ( ~ ( ord_less_eq_num @ Y @ X )
% 13.71/7.68 => ( ord_less_num @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_946_not__le__imp__less,axiom,
% 13.71/7.68 ! [Y: nat,X: nat] :
% 13.71/7.68 ( ~ ( ord_less_eq_nat @ Y @ X )
% 13.71/7.68 => ( ord_less_nat @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_947_not__le__imp__less,axiom,
% 13.71/7.68 ! [Y: int,X: int] :
% 13.71/7.68 ( ~ ( ord_less_eq_int @ Y @ X )
% 13.71/7.68 => ( ord_less_int @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_948_less__le__not__le,axiom,
% 13.71/7.68 ( ord_less_real
% 13.71/7.68 = ( ^ [X4: real,Y4: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ X4 @ Y4 )
% 13.71/7.68 & ~ ( ord_less_eq_real @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_949_less__le__not__le,axiom,
% 13.71/7.68 ( ord_less_set_int
% 13.71/7.68 = ( ^ [X4: set_int,Y4: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 13.71/7.68 & ~ ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_950_less__le__not__le,axiom,
% 13.71/7.68 ( ord_less_rat
% 13.71/7.68 = ( ^ [X4: rat,Y4: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 13.71/7.68 & ~ ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_951_less__le__not__le,axiom,
% 13.71/7.68 ( ord_less_num
% 13.71/7.68 = ( ^ [X4: num,Y4: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X4 @ Y4 )
% 13.71/7.68 & ~ ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_952_less__le__not__le,axiom,
% 13.71/7.68 ( ord_less_nat
% 13.71/7.68 = ( ^ [X4: nat,Y4: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 13.71/7.68 & ~ ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_953_less__le__not__le,axiom,
% 13.71/7.68 ( ord_less_int
% 13.71/7.68 = ( ^ [X4: int,Y4: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ X4 @ Y4 )
% 13.71/7.68 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_954_dense__le,axiom,
% 13.71/7.68 ! [Y: real,Z: real] :
% 13.71/7.68 ( ! [X3: real] :
% 13.71/7.68 ( ( ord_less_real @ X3 @ Y )
% 13.71/7.68 => ( ord_less_eq_real @ X3 @ Z ) )
% 13.71/7.68 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_955_dense__le,axiom,
% 13.71/7.68 ! [Y: rat,Z: rat] :
% 13.71/7.68 ( ! [X3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ X3 @ Y )
% 13.71/7.68 => ( ord_less_eq_rat @ X3 @ Z ) )
% 13.71/7.68 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_956_dense__ge,axiom,
% 13.71/7.68 ! [Z: real,Y: real] :
% 13.71/7.68 ( ! [X3: real] :
% 13.71/7.68 ( ( ord_less_real @ Z @ X3 )
% 13.71/7.68 => ( ord_less_eq_real @ Y @ X3 ) )
% 13.71/7.68 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_957_dense__ge,axiom,
% 13.71/7.68 ! [Z: rat,Y: rat] :
% 13.71/7.68 ( ! [X3: rat] :
% 13.71/7.68 ( ( ord_less_rat @ Z @ X3 )
% 13.71/7.68 => ( ord_less_eq_rat @ Y @ X3 ) )
% 13.71/7.68 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_958_antisym__conv2,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ X @ Y )
% 13.71/7.68 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_959_antisym__conv2,axiom,
% 13.71/7.68 ! [X: set_int,Y: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ X @ Y )
% 13.71/7.68 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_960_antisym__conv2,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.68 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_961_antisym__conv2,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.68 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_962_antisym__conv2,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.68 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_963_antisym__conv2,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.68 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_964_antisym__conv1,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ~ ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_real @ X @ Y )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_965_antisym__conv1,axiom,
% 13.71/7.68 ! [X: set_int,Y: set_int] :
% 13.71/7.68 ( ~ ( ord_less_set_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_set_int @ X @ Y )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_966_antisym__conv1,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ~ ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_rat @ X @ Y )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_967_antisym__conv1,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ~ ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_num @ X @ Y )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_968_antisym__conv1,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ~ ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_nat @ X @ Y )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_969_antisym__conv1,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ~ ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ( ord_less_eq_int @ X @ Y )
% 13.71/7.68 = ( X = Y ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_970_nless__le,axiom,
% 13.71/7.68 ! [A: real,B: real] :
% 13.71/7.68 ( ( ~ ( ord_less_real @ A @ B ) )
% 13.71/7.68 = ( ~ ( ord_less_eq_real @ A @ B )
% 13.71/7.68 | ( A = B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_971_nless__le,axiom,
% 13.71/7.68 ! [A: set_int,B: set_int] :
% 13.71/7.68 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 13.71/7.68 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 13.71/7.68 | ( A = B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_972_nless__le,axiom,
% 13.71/7.68 ! [A: rat,B: rat] :
% 13.71/7.68 ( ( ~ ( ord_less_rat @ A @ B ) )
% 13.71/7.68 = ( ~ ( ord_less_eq_rat @ A @ B )
% 13.71/7.68 | ( A = B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_973_nless__le,axiom,
% 13.71/7.68 ! [A: num,B: num] :
% 13.71/7.68 ( ( ~ ( ord_less_num @ A @ B ) )
% 13.71/7.68 = ( ~ ( ord_less_eq_num @ A @ B )
% 13.71/7.68 | ( A = B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_974_nless__le,axiom,
% 13.71/7.68 ! [A: nat,B: nat] :
% 13.71/7.68 ( ( ~ ( ord_less_nat @ A @ B ) )
% 13.71/7.68 = ( ~ ( ord_less_eq_nat @ A @ B )
% 13.71/7.68 | ( A = B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_975_nless__le,axiom,
% 13.71/7.68 ! [A: int,B: int] :
% 13.71/7.68 ( ( ~ ( ord_less_int @ A @ B ) )
% 13.71/7.68 = ( ~ ( ord_less_eq_int @ A @ B )
% 13.71/7.68 | ( A = B ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_976_leI,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ~ ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_real @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_977_leI,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ~ ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_978_leI,axiom,
% 13.71/7.68 ! [X: num,Y: num] :
% 13.71/7.68 ( ~ ( ord_less_num @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_num @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_979_leI,axiom,
% 13.71/7.68 ! [X: nat,Y: nat] :
% 13.71/7.68 ( ~ ( ord_less_nat @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_980_leI,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ~ ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ord_less_eq_int @ Y @ X ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_981_leD,axiom,
% 13.71/7.68 ! [Y: real,X: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ Y @ X )
% 13.71/7.68 => ~ ( ord_less_real @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_982_leD,axiom,
% 13.71/7.68 ! [Y: set_int,X: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ Y @ X )
% 13.71/7.68 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_983_leD,axiom,
% 13.71/7.68 ! [Y: rat,X: rat] :
% 13.71/7.68 ( ( ord_less_eq_rat @ Y @ X )
% 13.71/7.68 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_984_leD,axiom,
% 13.71/7.68 ! [Y: num,X: num] :
% 13.71/7.68 ( ( ord_less_eq_num @ Y @ X )
% 13.71/7.68 => ~ ( ord_less_num @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_985_leD,axiom,
% 13.71/7.68 ! [Y: nat,X: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ Y @ X )
% 13.71/7.68 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_986_leD,axiom,
% 13.71/7.68 ! [Y: int,X: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ Y @ X )
% 13.71/7.68 => ~ ( ord_less_int @ X @ Y ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_987_bot_Oextremum__uniqueI,axiom,
% 13.71/7.68 ! [A: set_nat] :
% 13.71/7.68 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 13.71/7.68 => ( A = bot_bot_set_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_988_bot_Oextremum__uniqueI,axiom,
% 13.71/7.68 ! [A: assn] :
% 13.71/7.68 ( ( ord_less_eq_assn @ A @ bot_bot_assn )
% 13.71/7.68 => ( A = bot_bot_assn ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_989_bot_Oextremum__uniqueI,axiom,
% 13.71/7.68 ! [A: set_o] :
% 13.71/7.68 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 13.71/7.68 => ( A = bot_bot_set_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_990_bot_Oextremum__uniqueI,axiom,
% 13.71/7.68 ! [A: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 13.71/7.68 => ( A = bot_bot_set_int ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_991_bot_Oextremum__uniqueI,axiom,
% 13.71/7.68 ! [A: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 13.71/7.68 => ( A = bot_bot_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_992_bot_Oextremum__unique,axiom,
% 13.71/7.68 ! [A: set_nat] :
% 13.71/7.68 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 13.71/7.68 = ( A = bot_bot_set_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_993_bot_Oextremum__unique,axiom,
% 13.71/7.68 ! [A: assn] :
% 13.71/7.68 ( ( ord_less_eq_assn @ A @ bot_bot_assn )
% 13.71/7.68 = ( A = bot_bot_assn ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_994_bot_Oextremum__unique,axiom,
% 13.71/7.68 ! [A: set_o] :
% 13.71/7.68 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 13.71/7.68 = ( A = bot_bot_set_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_995_bot_Oextremum__unique,axiom,
% 13.71/7.68 ! [A: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 13.71/7.68 = ( A = bot_bot_set_int ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_996_bot_Oextremum__unique,axiom,
% 13.71/7.68 ! [A: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 13.71/7.68 = ( A = bot_bot_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_997_bot_Oextremum,axiom,
% 13.71/7.68 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_998_bot_Oextremum,axiom,
% 13.71/7.68 ! [A: assn] : ( ord_less_eq_assn @ bot_bot_assn @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_999_bot_Oextremum,axiom,
% 13.71/7.68 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1000_bot_Oextremum,axiom,
% 13.71/7.68 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1001_bot_Oextremum,axiom,
% 13.71/7.68 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1002_bot_Onot__eq__extremum,axiom,
% 13.71/7.68 ! [A: set_nat] :
% 13.71/7.68 ( ( A != bot_bot_set_nat )
% 13.71/7.68 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1003_bot_Onot__eq__extremum,axiom,
% 13.71/7.68 ! [A: assn] :
% 13.71/7.68 ( ( A != bot_bot_assn )
% 13.71/7.68 = ( ord_less_assn @ bot_bot_assn @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1004_bot_Onot__eq__extremum,axiom,
% 13.71/7.68 ! [A: set_int] :
% 13.71/7.68 ( ( A != bot_bot_set_int )
% 13.71/7.68 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1005_bot_Onot__eq__extremum,axiom,
% 13.71/7.68 ! [A: set_o] :
% 13.71/7.68 ( ( A != bot_bot_set_o )
% 13.71/7.68 = ( ord_less_set_o @ bot_bot_set_o @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1006_bot_Onot__eq__extremum,axiom,
% 13.71/7.68 ! [A: nat] :
% 13.71/7.68 ( ( A != bot_bot_nat )
% 13.71/7.68 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1007_bot_Oextremum__strict,axiom,
% 13.71/7.68 ! [A: set_nat] :
% 13.71/7.68 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1008_bot_Oextremum__strict,axiom,
% 13.71/7.68 ! [A: assn] :
% 13.71/7.68 ~ ( ord_less_assn @ A @ bot_bot_assn ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1009_bot_Oextremum__strict,axiom,
% 13.71/7.68 ! [A: set_int] :
% 13.71/7.68 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1010_bot_Oextremum__strict,axiom,
% 13.71/7.68 ! [A: set_o] :
% 13.71/7.68 ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1011_bot_Oextremum__strict,axiom,
% 13.71/7.68 ! [A: nat] :
% 13.71/7.68 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1012_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 13.71/7.68 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1013_deg1Leaf,axiom,
% 13.71/7.68 ! [T: vEBT_VEBT] :
% 13.71/7.68 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 13.71/7.68 = ( ? [A7: $o,B7: $o] :
% 13.71/7.68 ( T
% 13.71/7.68 = ( vEBT_Leaf @ A7 @ B7 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1014_deg__1__Leaf,axiom,
% 13.71/7.68 ! [T: vEBT_VEBT] :
% 13.71/7.68 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 13.71/7.68 => ? [A3: $o,B3: $o] :
% 13.71/7.68 ( T
% 13.71/7.68 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1015_deg__1__Leafy,axiom,
% 13.71/7.68 ! [T: vEBT_VEBT,N: nat] :
% 13.71/7.68 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.68 => ( ( N = one_one_nat )
% 13.71/7.68 => ? [A3: $o,B3: $o] :
% 13.71/7.68 ( T
% 13.71/7.68 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1016_finite__nat__set__iff__bounded__le,axiom,
% 13.71/7.68 ( finite_finite_nat
% 13.71/7.68 = ( ^ [N7: set_nat] :
% 13.71/7.68 ? [M5: nat] :
% 13.71/7.68 ! [X4: nat] :
% 13.71/7.68 ( ( member_nat @ X4 @ N7 )
% 13.71/7.68 => ( ord_less_eq_nat @ X4 @ M5 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1017_infinite__nat__iff__unbounded__le,axiom,
% 13.71/7.68 ! [S3: set_nat] :
% 13.71/7.68 ( ( ~ ( finite_finite_nat @ S3 ) )
% 13.71/7.68 = ( ! [M5: nat] :
% 13.71/7.68 ? [N6: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ M5 @ N6 )
% 13.71/7.68 & ( member_nat @ N6 @ S3 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1018_finite__nat__set__iff__bounded,axiom,
% 13.71/7.68 ( finite_finite_nat
% 13.71/7.68 = ( ^ [N7: set_nat] :
% 13.71/7.68 ? [M5: nat] :
% 13.71/7.68 ! [X4: nat] :
% 13.71/7.68 ( ( member_nat @ X4 @ N7 )
% 13.71/7.68 => ( ord_less_nat @ X4 @ M5 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1019_infinite__nat__iff__unbounded,axiom,
% 13.71/7.68 ! [S3: set_nat] :
% 13.71/7.68 ( ( ~ ( finite_finite_nat @ S3 ) )
% 13.71/7.68 = ( ! [M5: nat] :
% 13.71/7.68 ? [N6: nat] :
% 13.71/7.68 ( ( ord_less_nat @ M5 @ N6 )
% 13.71/7.68 & ( member_nat @ N6 @ S3 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1020_bounded__nat__set__is__finite,axiom,
% 13.71/7.68 ! [N8: set_nat,N: nat] :
% 13.71/7.68 ( ! [X3: nat] :
% 13.71/7.68 ( ( member_nat @ X3 @ N8 )
% 13.71/7.68 => ( ord_less_nat @ X3 @ N ) )
% 13.71/7.68 => ( finite_finite_nat @ N8 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1021_unbounded__k__infinite,axiom,
% 13.71/7.68 ! [K: nat,S3: set_nat] :
% 13.71/7.68 ( ! [M3: nat] :
% 13.71/7.68 ( ( ord_less_nat @ K @ M3 )
% 13.71/7.68 => ? [N9: nat] :
% 13.71/7.68 ( ( ord_less_nat @ M3 @ N9 )
% 13.71/7.68 & ( member_nat @ N9 @ S3 ) ) )
% 13.71/7.68 => ~ ( finite_finite_nat @ S3 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1022_VEBT__internal_Oheight_Ocases,axiom,
% 13.71/7.68 ! [X: vEBT_VEBT] :
% 13.71/7.68 ( ! [A3: $o,B3: $o] :
% 13.71/7.68 ( X
% 13.71/7.68 != ( vEBT_Leaf @ A3 @ B3 ) )
% 13.71/7.68 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.71/7.68 ( X
% 13.71/7.68 != ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1023_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_complex,F: complex > real] :
% 13.71/7.68 ( ( finite3207457112153483333omplex @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_complex )
% 13.71/7.68 => ~ ? [X5: complex] :
% 13.71/7.68 ( ( member_complex @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic8794016678065449205x_real @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1024_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_Code_integer,F: code_integer > real] :
% 13.71/7.68 ( ( finite6017078050557962740nteger @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.71/7.68 => ~ ? [X5: code_integer] :
% 13.71/7.68 ( ( member_Code_integer @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic2659822949269061924r_real @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1025_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_nat,F: nat > real] :
% 13.71/7.68 ( ( finite_finite_nat @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_nat )
% 13.71/7.68 => ~ ? [X5: nat] :
% 13.71/7.68 ( ( member_nat @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic488527866317076247t_real @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1026_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_int,F: int > real] :
% 13.71/7.68 ( ( finite_finite_int @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_int )
% 13.71/7.68 => ~ ? [X5: int] :
% 13.71/7.68 ( ( member_int @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic2675449441010098035t_real @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1027_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_o,F: $o > real] :
% 13.71/7.68 ( ( finite_finite_o @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_o )
% 13.71/7.68 => ~ ? [X5: $o] :
% 13.71/7.68 ( ( member_o @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_real @ ( F @ X5 ) @ ( F @ ( lattic8697145971487455083o_real @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1028_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_complex,F: complex > rat] :
% 13.71/7.68 ( ( finite3207457112153483333omplex @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_complex )
% 13.71/7.68 => ~ ? [X5: complex] :
% 13.71/7.68 ( ( member_complex @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1029_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_Code_integer,F: code_integer > rat] :
% 13.71/7.68 ( ( finite6017078050557962740nteger @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.71/7.68 => ~ ? [X5: code_integer] :
% 13.71/7.68 ( ( member_Code_integer @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic5439806495466278992er_rat @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1030_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_nat,F: nat > rat] :
% 13.71/7.68 ( ( finite_finite_nat @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_nat )
% 13.71/7.68 => ~ ? [X5: nat] :
% 13.71/7.68 ( ( member_nat @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic6811802900495863747at_rat @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1031_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_int,F: int > rat] :
% 13.71/7.68 ( ( finite_finite_int @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_int )
% 13.71/7.68 => ~ ? [X5: int] :
% 13.71/7.68 ( ( member_int @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1032_arg__min__if__finite_I2_J,axiom,
% 13.71/7.68 ! [S3: set_o,F: $o > rat] :
% 13.71/7.68 ( ( finite_finite_o @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_o )
% 13.71/7.68 => ~ ? [X5: $o] :
% 13.71/7.68 ( ( member_o @ X5 @ S3 )
% 13.71/7.68 & ( ord_less_rat @ ( F @ X5 ) @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S3 ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1033_subsetI,axiom,
% 13.71/7.68 ! [A4: set_nat,B4: set_nat] :
% 13.71/7.68 ( ! [X3: nat] :
% 13.71/7.68 ( ( member_nat @ X3 @ A4 )
% 13.71/7.68 => ( member_nat @ X3 @ B4 ) )
% 13.71/7.68 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1034_subsetI,axiom,
% 13.71/7.68 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.68 ( ! [X3: vEBT_VEBT] :
% 13.71/7.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.71/7.68 => ( member_VEBT_VEBT @ X3 @ B4 ) )
% 13.71/7.68 => ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1035_subsetI,axiom,
% 13.71/7.68 ! [A4: set_real,B4: set_real] :
% 13.71/7.68 ( ! [X3: real] :
% 13.71/7.68 ( ( member_real @ X3 @ A4 )
% 13.71/7.68 => ( member_real @ X3 @ B4 ) )
% 13.71/7.68 => ( ord_less_eq_set_real @ A4 @ B4 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1036_subsetI,axiom,
% 13.71/7.68 ! [A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.68 ( ! [X3: set_nat] :
% 13.71/7.68 ( ( member_set_nat @ X3 @ A4 )
% 13.71/7.68 => ( member_set_nat @ X3 @ B4 ) )
% 13.71/7.68 => ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1037_subsetI,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int] :
% 13.71/7.68 ( ! [X3: int] :
% 13.71/7.68 ( ( member_int @ X3 @ A4 )
% 13.71/7.68 => ( member_int @ X3 @ B4 ) )
% 13.71/7.68 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1038_subset__antisym,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.68 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.71/7.68 => ( A4 = B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1039_less__one,axiom,
% 13.71/7.68 ! [N: nat] :
% 13.71/7.68 ( ( ord_less_nat @ N @ one_one_nat )
% 13.71/7.68 = ( N = zero_zero_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1040_subset__Collect__conv,axiom,
% 13.71/7.68 ! [S3: set_complex,P2: complex > $o] :
% 13.71/7.68 ( ( ord_le211207098394363844omplex @ S3 @ ( collect_complex @ P2 ) )
% 13.71/7.68 = ( ! [X4: complex] :
% 13.71/7.68 ( ( member_complex @ X4 @ S3 )
% 13.71/7.68 => ( P2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1041_subset__Collect__conv,axiom,
% 13.71/7.68 ! [S3: set_list_nat,P2: list_nat > $o] :
% 13.71/7.68 ( ( ord_le6045566169113846134st_nat @ S3 @ ( collect_list_nat @ P2 ) )
% 13.71/7.68 = ( ! [X4: list_nat] :
% 13.71/7.68 ( ( member_list_nat @ X4 @ S3 )
% 13.71/7.68 => ( P2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1042_subset__Collect__conv,axiom,
% 13.71/7.68 ! [S3: set_set_nat,P2: set_nat > $o] :
% 13.71/7.68 ( ( ord_le6893508408891458716et_nat @ S3 @ ( collect_set_nat @ P2 ) )
% 13.71/7.68 = ( ! [X4: set_nat] :
% 13.71/7.68 ( ( member_set_nat @ X4 @ S3 )
% 13.71/7.68 => ( P2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1043_subset__Collect__conv,axiom,
% 13.71/7.68 ! [S3: set_nat,P2: nat > $o] :
% 13.71/7.68 ( ( ord_less_eq_set_nat @ S3 @ ( collect_nat @ P2 ) )
% 13.71/7.68 = ( ! [X4: nat] :
% 13.71/7.68 ( ( member_nat @ X4 @ S3 )
% 13.71/7.68 => ( P2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1044_subset__Collect__conv,axiom,
% 13.71/7.68 ! [S3: set_int,P2: int > $o] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ S3 @ ( collect_int @ P2 ) )
% 13.71/7.68 = ( ! [X4: int] :
% 13.71/7.68 ( ( member_int @ X4 @ S3 )
% 13.71/7.68 => ( P2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1045_in__mono,axiom,
% 13.71/7.68 ! [A4: set_nat,B4: set_nat,X: nat] :
% 13.71/7.68 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.71/7.68 => ( ( member_nat @ X @ A4 )
% 13.71/7.68 => ( member_nat @ X @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1046_in__mono,axiom,
% 13.71/7.68 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.71/7.68 ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.71/7.68 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.71/7.68 => ( member_VEBT_VEBT @ X @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1047_in__mono,axiom,
% 13.71/7.68 ! [A4: set_real,B4: set_real,X: real] :
% 13.71/7.68 ( ( ord_less_eq_set_real @ A4 @ B4 )
% 13.71/7.68 => ( ( member_real @ X @ A4 )
% 13.71/7.68 => ( member_real @ X @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1048_in__mono,axiom,
% 13.71/7.68 ! [A4: set_set_nat,B4: set_set_nat,X: set_nat] :
% 13.71/7.68 ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 13.71/7.68 => ( ( member_set_nat @ X @ A4 )
% 13.71/7.68 => ( member_set_nat @ X @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1049_in__mono,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int,X: int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.68 => ( ( member_int @ X @ A4 )
% 13.71/7.68 => ( member_int @ X @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1050_subsetD,axiom,
% 13.71/7.68 ! [A4: set_nat,B4: set_nat,C2: nat] :
% 13.71/7.68 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.71/7.68 => ( ( member_nat @ C2 @ A4 )
% 13.71/7.68 => ( member_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1051_subsetD,axiom,
% 13.71/7.68 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,C2: vEBT_VEBT] :
% 13.71/7.68 ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.71/7.68 => ( ( member_VEBT_VEBT @ C2 @ A4 )
% 13.71/7.68 => ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1052_subsetD,axiom,
% 13.71/7.68 ! [A4: set_real,B4: set_real,C2: real] :
% 13.71/7.68 ( ( ord_less_eq_set_real @ A4 @ B4 )
% 13.71/7.68 => ( ( member_real @ C2 @ A4 )
% 13.71/7.68 => ( member_real @ C2 @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1053_subsetD,axiom,
% 13.71/7.68 ! [A4: set_set_nat,B4: set_set_nat,C2: set_nat] :
% 13.71/7.68 ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 13.71/7.68 => ( ( member_set_nat @ C2 @ A4 )
% 13.71/7.68 => ( member_set_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1054_subsetD,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int,C2: int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.68 => ( ( member_int @ C2 @ A4 )
% 13.71/7.68 => ( member_int @ C2 @ B4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1055_equalityE,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int] :
% 13.71/7.68 ( ( A4 = B4 )
% 13.71/7.68 => ~ ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.68 => ~ ( ord_less_eq_set_int @ B4 @ A4 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1056_subset__eq,axiom,
% 13.71/7.68 ( ord_less_eq_set_nat
% 13.71/7.68 = ( ^ [A6: set_nat,B6: set_nat] :
% 13.71/7.68 ! [X4: nat] :
% 13.71/7.68 ( ( member_nat @ X4 @ A6 )
% 13.71/7.68 => ( member_nat @ X4 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1057_subset__eq,axiom,
% 13.71/7.68 ( ord_le4337996190870823476T_VEBT
% 13.71/7.68 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.71/7.68 ! [X4: vEBT_VEBT] :
% 13.71/7.68 ( ( member_VEBT_VEBT @ X4 @ A6 )
% 13.71/7.68 => ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1058_subset__eq,axiom,
% 13.71/7.68 ( ord_less_eq_set_real
% 13.71/7.68 = ( ^ [A6: set_real,B6: set_real] :
% 13.71/7.68 ! [X4: real] :
% 13.71/7.68 ( ( member_real @ X4 @ A6 )
% 13.71/7.68 => ( member_real @ X4 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1059_subset__eq,axiom,
% 13.71/7.68 ( ord_le6893508408891458716et_nat
% 13.71/7.68 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 13.71/7.68 ! [X4: set_nat] :
% 13.71/7.68 ( ( member_set_nat @ X4 @ A6 )
% 13.71/7.68 => ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1060_subset__eq,axiom,
% 13.71/7.68 ( ord_less_eq_set_int
% 13.71/7.68 = ( ^ [A6: set_int,B6: set_int] :
% 13.71/7.68 ! [X4: int] :
% 13.71/7.68 ( ( member_int @ X4 @ A6 )
% 13.71/7.68 => ( member_int @ X4 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1061_equalityD1,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int] :
% 13.71/7.68 ( ( A4 = B4 )
% 13.71/7.68 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1062_Set_OequalityD2,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int] :
% 13.71/7.68 ( ( A4 = B4 )
% 13.71/7.68 => ( ord_less_eq_set_int @ B4 @ A4 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1063_subset__iff,axiom,
% 13.71/7.68 ( ord_less_eq_set_nat
% 13.71/7.68 = ( ^ [A6: set_nat,B6: set_nat] :
% 13.71/7.68 ! [T2: nat] :
% 13.71/7.68 ( ( member_nat @ T2 @ A6 )
% 13.71/7.68 => ( member_nat @ T2 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1064_subset__iff,axiom,
% 13.71/7.68 ( ord_le4337996190870823476T_VEBT
% 13.71/7.68 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.71/7.68 ! [T2: vEBT_VEBT] :
% 13.71/7.68 ( ( member_VEBT_VEBT @ T2 @ A6 )
% 13.71/7.68 => ( member_VEBT_VEBT @ T2 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1065_subset__iff,axiom,
% 13.71/7.68 ( ord_less_eq_set_real
% 13.71/7.68 = ( ^ [A6: set_real,B6: set_real] :
% 13.71/7.68 ! [T2: real] :
% 13.71/7.68 ( ( member_real @ T2 @ A6 )
% 13.71/7.68 => ( member_real @ T2 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1066_subset__iff,axiom,
% 13.71/7.68 ( ord_le6893508408891458716et_nat
% 13.71/7.68 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 13.71/7.68 ! [T2: set_nat] :
% 13.71/7.68 ( ( member_set_nat @ T2 @ A6 )
% 13.71/7.68 => ( member_set_nat @ T2 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1067_subset__iff,axiom,
% 13.71/7.68 ( ord_less_eq_set_int
% 13.71/7.68 = ( ^ [A6: set_int,B6: set_int] :
% 13.71/7.68 ! [T2: int] :
% 13.71/7.68 ( ( member_int @ T2 @ A6 )
% 13.71/7.68 => ( member_int @ T2 @ B6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1068_subset__refl,axiom,
% 13.71/7.68 ! [A4: set_int] : ( ord_less_eq_set_int @ A4 @ A4 ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1069_Collect__mono,axiom,
% 13.71/7.68 ! [P2: complex > $o,Q2: complex > $o] :
% 13.71/7.68 ( ! [X3: complex] :
% 13.71/7.68 ( ( P2 @ X3 )
% 13.71/7.68 => ( Q2 @ X3 ) )
% 13.71/7.68 => ( ord_le211207098394363844omplex @ ( collect_complex @ P2 ) @ ( collect_complex @ Q2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1070_Collect__mono,axiom,
% 13.71/7.68 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 13.71/7.68 ( ! [X3: list_nat] :
% 13.71/7.68 ( ( P2 @ X3 )
% 13.71/7.68 => ( Q2 @ X3 ) )
% 13.71/7.68 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1071_Collect__mono,axiom,
% 13.71/7.68 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 13.71/7.68 ( ! [X3: set_nat] :
% 13.71/7.68 ( ( P2 @ X3 )
% 13.71/7.68 => ( Q2 @ X3 ) )
% 13.71/7.68 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1072_Collect__mono,axiom,
% 13.71/7.68 ! [P2: nat > $o,Q2: nat > $o] :
% 13.71/7.68 ( ! [X3: nat] :
% 13.71/7.68 ( ( P2 @ X3 )
% 13.71/7.68 => ( Q2 @ X3 ) )
% 13.71/7.68 => ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1073_Collect__mono,axiom,
% 13.71/7.68 ! [P2: int > $o,Q2: int > $o] :
% 13.71/7.68 ( ! [X3: int] :
% 13.71/7.68 ( ( P2 @ X3 )
% 13.71/7.68 => ( Q2 @ X3 ) )
% 13.71/7.68 => ( ord_less_eq_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1074_subset__trans,axiom,
% 13.71/7.68 ! [A4: set_int,B4: set_int,C3: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.68 => ( ( ord_less_eq_set_int @ B4 @ C3 )
% 13.71/7.68 => ( ord_less_eq_set_int @ A4 @ C3 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1075_set__eq__subset,axiom,
% 13.71/7.68 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 13.71/7.68 = ( ^ [A6: set_int,B6: set_int] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 13.71/7.68 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1076_Collect__mono__iff,axiom,
% 13.71/7.68 ! [P2: complex > $o,Q2: complex > $o] :
% 13.71/7.68 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P2 ) @ ( collect_complex @ Q2 ) )
% 13.71/7.68 = ( ! [X4: complex] :
% 13.71/7.68 ( ( P2 @ X4 )
% 13.71/7.68 => ( Q2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1077_Collect__mono__iff,axiom,
% 13.71/7.68 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 13.71/7.68 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P2 ) @ ( collect_list_nat @ Q2 ) )
% 13.71/7.68 = ( ! [X4: list_nat] :
% 13.71/7.68 ( ( P2 @ X4 )
% 13.71/7.68 => ( Q2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1078_Collect__mono__iff,axiom,
% 13.71/7.68 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 13.71/7.68 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P2 ) @ ( collect_set_nat @ Q2 ) )
% 13.71/7.68 = ( ! [X4: set_nat] :
% 13.71/7.68 ( ( P2 @ X4 )
% 13.71/7.68 => ( Q2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1079_Collect__mono__iff,axiom,
% 13.71/7.68 ! [P2: nat > $o,Q2: nat > $o] :
% 13.71/7.68 ( ( ord_less_eq_set_nat @ ( collect_nat @ P2 ) @ ( collect_nat @ Q2 ) )
% 13.71/7.68 = ( ! [X4: nat] :
% 13.71/7.68 ( ( P2 @ X4 )
% 13.71/7.68 => ( Q2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1080_Collect__mono__iff,axiom,
% 13.71/7.68 ! [P2: int > $o,Q2: int > $o] :
% 13.71/7.68 ( ( ord_less_eq_set_int @ ( collect_int @ P2 ) @ ( collect_int @ Q2 ) )
% 13.71/7.68 = ( ! [X4: int] :
% 13.71/7.68 ( ( P2 @ X4 )
% 13.71/7.68 => ( Q2 @ X4 ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1081_one__reorient,axiom,
% 13.71/7.68 ! [X: uint32] :
% 13.71/7.68 ( ( one_one_uint32 = X )
% 13.71/7.68 = ( X = one_one_uint32 ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1082_one__reorient,axiom,
% 13.71/7.68 ! [X: real] :
% 13.71/7.68 ( ( one_one_real = X )
% 13.71/7.68 = ( X = one_one_real ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1083_one__reorient,axiom,
% 13.71/7.68 ! [X: rat] :
% 13.71/7.68 ( ( one_one_rat = X )
% 13.71/7.68 = ( X = one_one_rat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1084_one__reorient,axiom,
% 13.71/7.68 ! [X: nat] :
% 13.71/7.68 ( ( one_one_nat = X )
% 13.71/7.68 = ( X = one_one_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1085_one__reorient,axiom,
% 13.71/7.68 ! [X: int] :
% 13.71/7.68 ( ( one_one_int = X )
% 13.71/7.68 = ( X = one_one_int ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1086_one__natural_Orsp,axiom,
% 13.71/7.68 one_one_nat = one_one_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1087_One__nat__def,axiom,
% 13.71/7.68 ( one_one_nat
% 13.71/7.68 = ( suc @ zero_zero_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1088_nat__geq__1__eq__neqz,axiom,
% 13.71/7.68 ! [X: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 13.71/7.68 = ( X != zero_zero_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1089_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 13.71/7.68 ! [Uu2: $o,Uv2: $o,D: nat] :
% 13.71/7.68 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D )
% 13.71/7.68 = ( D = one_one_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1090_nat__induct__non__zero,axiom,
% 13.71/7.68 ! [N: nat,P2: nat > $o] :
% 13.71/7.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.68 => ( ( P2 @ one_one_nat )
% 13.71/7.68 => ( ! [N2: nat] :
% 13.71/7.68 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 13.71/7.68 => ( ( P2 @ N2 )
% 13.71/7.68 => ( P2 @ ( suc @ N2 ) ) ) )
% 13.71/7.68 => ( P2 @ N ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1091_bounded__Max__nat,axiom,
% 13.71/7.68 ! [P2: nat > $o,X: nat,M7: nat] :
% 13.71/7.68 ( ( P2 @ X )
% 13.71/7.68 => ( ! [X3: nat] :
% 13.71/7.68 ( ( P2 @ X3 )
% 13.71/7.68 => ( ord_less_eq_nat @ X3 @ M7 ) )
% 13.71/7.68 => ~ ! [M3: nat] :
% 13.71/7.68 ( ( P2 @ M3 )
% 13.71/7.68 => ~ ! [X5: nat] :
% 13.71/7.68 ( ( P2 @ X5 )
% 13.71/7.68 => ( ord_less_eq_nat @ X5 @ M3 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1092_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 13.71/7.68 ! [A: $o,B: $o,X: nat] :
% 13.71/7.68 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.71/7.68 = ( ( ( X = zero_zero_nat )
% 13.71/7.68 => A )
% 13.71/7.68 & ( ( X != zero_zero_nat )
% 13.71/7.68 => ( ( ( X = one_one_nat )
% 13.71/7.68 => B )
% 13.71/7.68 & ( X = one_one_nat ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1093_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_VEBT_VEBT,R2: vEBT_VEBT > vEBT_VEBT > $o] :
% 13.71/7.68 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.71/7.68 => ( ! [X3: vEBT_VEBT] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: vEBT_VEBT,Y3: vEBT_VEBT,Z3: vEBT_VEBT] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: vEBT_VEBT] :
% 13.71/7.68 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: vEBT_VEBT] :
% 13.71/7.68 ( ( member_VEBT_VEBT @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1094_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_real,R2: real > real > $o] :
% 13.71/7.68 ( ( finite_finite_real @ A4 )
% 13.71/7.68 => ( ! [X3: real] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: real,Y3: real,Z3: real] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: real] :
% 13.71/7.68 ( ( member_real @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: real] :
% 13.71/7.68 ( ( member_real @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bot_set_real ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1095_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_set_nat,R2: set_nat > set_nat > $o] :
% 13.71/7.68 ( ( finite1152437895449049373et_nat @ A4 )
% 13.71/7.68 => ( ! [X3: set_nat] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: set_nat,Y3: set_nat,Z3: set_nat] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: set_nat] :
% 13.71/7.68 ( ( member_set_nat @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: set_nat] :
% 13.71/7.68 ( ( member_set_nat @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bot_set_set_nat ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1096_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_complex,R2: complex > complex > $o] :
% 13.71/7.68 ( ( finite3207457112153483333omplex @ A4 )
% 13.71/7.68 => ( ! [X3: complex] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: complex,Y3: complex,Z3: complex] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: complex] :
% 13.71/7.68 ( ( member_complex @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: complex] :
% 13.71/7.68 ( ( member_complex @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bot_set_complex ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1097_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_Code_integer,R2: code_integer > code_integer > $o] :
% 13.71/7.68 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.68 => ( ! [X3: code_integer] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: code_integer,Y3: code_integer,Z3: code_integer] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: code_integer] :
% 13.71/7.68 ( ( member_Code_integer @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: code_integer] :
% 13.71/7.68 ( ( member_Code_integer @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1098_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_nat,R2: nat > nat > $o] :
% 13.71/7.68 ( ( finite_finite_nat @ A4 )
% 13.71/7.68 => ( ! [X3: nat] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: nat] :
% 13.71/7.68 ( ( member_nat @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: nat] :
% 13.71/7.68 ( ( member_nat @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bot_set_nat ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1099_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_int,R2: int > int > $o] :
% 13.71/7.68 ( ( finite_finite_int @ A4 )
% 13.71/7.68 => ( ! [X3: int] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: int,Y3: int,Z3: int] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: int] :
% 13.71/7.68 ( ( member_int @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: int] :
% 13.71/7.68 ( ( member_int @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bot_set_int ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1100_finite__transitivity__chain,axiom,
% 13.71/7.68 ! [A4: set_o,R2: $o > $o > $o] :
% 13.71/7.68 ( ( finite_finite_o @ A4 )
% 13.71/7.68 => ( ! [X3: $o] :
% 13.71/7.68 ~ ( R2 @ X3 @ X3 )
% 13.71/7.68 => ( ! [X3: $o,Y3: $o,Z3: $o] :
% 13.71/7.68 ( ( R2 @ X3 @ Y3 )
% 13.71/7.68 => ( ( R2 @ Y3 @ Z3 )
% 13.71/7.68 => ( R2 @ X3 @ Z3 ) ) )
% 13.71/7.68 => ( ! [X3: $o] :
% 13.71/7.68 ( ( member_o @ X3 @ A4 )
% 13.71/7.68 => ? [Y5: $o] :
% 13.71/7.68 ( ( member_o @ Y5 @ A4 )
% 13.71/7.68 & ( R2 @ X3 @ Y5 ) ) )
% 13.71/7.68 => ( A4 = bot_bot_set_o ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1101_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.71/7.68 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bo8194388402131092736T_VEBT )
% 13.71/7.68 => ( ( member_VEBT_VEBT @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ ( lattic6139528642216935859BT_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1102_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_real,Y: real,F: real > rat] :
% 13.71/7.68 ( ( finite_finite_real @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_real )
% 13.71/7.68 => ( ( member_real @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ ( lattic4420706379359479199al_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1103_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_complex,Y: complex,F: complex > rat] :
% 13.71/7.68 ( ( finite3207457112153483333omplex @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_complex )
% 13.71/7.68 => ( ( member_complex @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ ( lattic4729654577720512673ex_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1104_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_Code_integer,Y: code_integer,F: code_integer > rat] :
% 13.71/7.68 ( ( finite6017078050557962740nteger @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.71/7.68 => ( ( member_Code_integer @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ ( lattic5439806495466278992er_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1105_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_nat,Y: nat,F: nat > rat] :
% 13.71/7.68 ( ( finite_finite_nat @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_nat )
% 13.71/7.68 => ( ( member_nat @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ ( lattic6811802900495863747at_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1106_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_int,Y: int,F: int > rat] :
% 13.71/7.68 ( ( finite_finite_int @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_int )
% 13.71/7.68 => ( ( member_int @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ ( lattic7811156612396918303nt_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1107_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_o,Y: $o,F: $o > rat] :
% 13.71/7.68 ( ( finite_finite_o @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_o )
% 13.71/7.68 => ( ( member_o @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_rat @ ( F @ ( lattic2140725968369957399_o_rat @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1108_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_VEBT_VEBT,Y: vEBT_VEBT,F: vEBT_VEBT > num] :
% 13.71/7.68 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bo8194388402131092736T_VEBT )
% 13.71/7.68 => ( ( member_VEBT_VEBT @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_num @ ( F @ ( lattic3331990488459210229BT_num @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1109_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_real,Y: real,F: real > num] :
% 13.71/7.68 ( ( finite_finite_real @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_real )
% 13.71/7.68 => ( ( member_real @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_num @ ( F @ ( lattic1613168225601753569al_num @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1110_arg__min__least,axiom,
% 13.71/7.68 ! [S3: set_complex,Y: complex,F: complex > num] :
% 13.71/7.68 ( ( finite3207457112153483333omplex @ S3 )
% 13.71/7.68 => ( ( S3 != bot_bot_set_complex )
% 13.71/7.68 => ( ( member_complex @ Y @ S3 )
% 13.71/7.68 => ( ord_less_eq_num @ ( F @ ( lattic1922116423962787043ex_num @ F @ S3 ) ) @ ( F @ Y ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1111_minNull__delete__time__bound_H,axiom,
% 13.71/7.68 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.68 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.68 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 13.71/7.68 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) @ one_one_nat ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1112_vebt__member__code_I1_J,axiom,
% 13.71/7.68 ! [A: $o,B: $o,X: nat] :
% 13.71/7.68 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.71/7.68 = ( ( ( X = zero_zero_nat )
% 13.71/7.68 => A )
% 13.71/7.68 & ( ( X != zero_zero_nat )
% 13.71/7.68 => ( ( ( X = one_one_nat )
% 13.71/7.68 => B )
% 13.71/7.68 & ( X = one_one_nat ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1113_vebt__delete__code_I1_J,axiom,
% 13.71/7.68 ! [X: nat,A: $o,B: $o] :
% 13.71/7.68 ( ( ( X = zero_zero_nat )
% 13.71/7.68 => ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.71/7.68 = ( vEBT_Leaf @ $false @ B ) ) )
% 13.71/7.68 & ( ( X != zero_zero_nat )
% 13.71/7.68 => ( ( ( X = one_one_nat )
% 13.71/7.68 => ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.71/7.68 = ( vEBT_Leaf @ A @ $false ) ) )
% 13.71/7.68 & ( ( X != one_one_nat )
% 13.71/7.68 => ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.71/7.68 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1114_not__one__less__zero,axiom,
% 13.71/7.68 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1115_not__one__less__zero,axiom,
% 13.71/7.68 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1116_not__one__less__zero,axiom,
% 13.71/7.68 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1117_not__one__less__zero,axiom,
% 13.71/7.68 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1118_zero__less__one,axiom,
% 13.71/7.68 ord_less_real @ zero_zero_real @ one_one_real ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1119_zero__less__one,axiom,
% 13.71/7.68 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1120_zero__less__one,axiom,
% 13.71/7.68 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1121_zero__less__one,axiom,
% 13.71/7.68 ord_less_int @ zero_zero_int @ one_one_int ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1122_less__numeral__extra_I1_J,axiom,
% 13.71/7.68 ord_less_real @ zero_zero_real @ one_one_real ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1123_less__numeral__extra_I1_J,axiom,
% 13.71/7.68 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1124_less__numeral__extra_I1_J,axiom,
% 13.71/7.68 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1125_less__numeral__extra_I1_J,axiom,
% 13.71/7.68 ord_less_int @ zero_zero_int @ one_one_int ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1126_zero__less__one__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1127_zero__less__one__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1128_zero__less__one__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1129_zero__less__one__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1130_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1131_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1132_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1133_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 13.71/7.68 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1134_not__one__le__zero,axiom,
% 13.71/7.68 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1135_not__one__le__zero,axiom,
% 13.71/7.68 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1136_not__one__le__zero,axiom,
% 13.71/7.68 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1137_not__one__le__zero,axiom,
% 13.71/7.68 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1138_bot__empty__eq,axiom,
% 13.71/7.68 ( bot_bot_VEBT_VEBT_o
% 13.71/7.68 = ( ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1139_bot__empty__eq,axiom,
% 13.71/7.68 ( bot_bot_real_o
% 13.71/7.68 = ( ^ [X4: real] : ( member_real @ X4 @ bot_bot_set_real ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1140_bot__empty__eq,axiom,
% 13.71/7.68 ( bot_bot_set_nat_o
% 13.71/7.68 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1141_bot__empty__eq,axiom,
% 13.71/7.68 ( bot_bot_nat_o
% 13.71/7.68 = ( ^ [X4: nat] : ( member_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1142_bot__empty__eq,axiom,
% 13.71/7.68 ( bot_bot_int_o
% 13.71/7.68 = ( ^ [X4: int] : ( member_int @ X4 @ bot_bot_set_int ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1143_bot__empty__eq,axiom,
% 13.71/7.68 ( bot_bot_o_o
% 13.71/7.68 = ( ^ [X4: $o] : ( member_o @ X4 @ bot_bot_set_o ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1144_Collect__empty__eq__bot,axiom,
% 13.71/7.68 ! [P2: complex > $o] :
% 13.71/7.68 ( ( ( collect_complex @ P2 )
% 13.71/7.68 = bot_bot_set_complex )
% 13.71/7.68 = ( P2 = bot_bot_complex_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1145_Collect__empty__eq__bot,axiom,
% 13.71/7.68 ! [P2: list_nat > $o] :
% 13.71/7.68 ( ( ( collect_list_nat @ P2 )
% 13.71/7.68 = bot_bot_set_list_nat )
% 13.71/7.68 = ( P2 = bot_bot_list_nat_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1146_Collect__empty__eq__bot,axiom,
% 13.71/7.68 ! [P2: set_nat > $o] :
% 13.71/7.68 ( ( ( collect_set_nat @ P2 )
% 13.71/7.68 = bot_bot_set_set_nat )
% 13.71/7.68 = ( P2 = bot_bot_set_nat_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1147_Collect__empty__eq__bot,axiom,
% 13.71/7.68 ! [P2: nat > $o] :
% 13.71/7.68 ( ( ( collect_nat @ P2 )
% 13.71/7.68 = bot_bot_set_nat )
% 13.71/7.68 = ( P2 = bot_bot_nat_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1148_Collect__empty__eq__bot,axiom,
% 13.71/7.68 ! [P2: int > $o] :
% 13.71/7.68 ( ( ( collect_int @ P2 )
% 13.71/7.68 = bot_bot_set_int )
% 13.71/7.68 = ( P2 = bot_bot_int_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1149_Collect__empty__eq__bot,axiom,
% 13.71/7.68 ! [P2: $o > $o] :
% 13.71/7.68 ( ( ( collect_o @ P2 )
% 13.71/7.68 = bot_bot_set_o )
% 13.71/7.68 = ( P2 = bot_bot_o_o ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1150_assn__basic__inequalities_I3_J,axiom,
% 13.71/7.68 bot_bot_assn != one_one_assn ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1151_linorder__neqE__linordered__idom,axiom,
% 13.71/7.68 ! [X: real,Y: real] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_real @ X @ Y )
% 13.71/7.68 => ( ord_less_real @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1152_linorder__neqE__linordered__idom,axiom,
% 13.71/7.68 ! [X: rat,Y: rat] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_rat @ X @ Y )
% 13.71/7.68 => ( ord_less_rat @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1153_linorder__neqE__linordered__idom,axiom,
% 13.71/7.68 ! [X: int,Y: int] :
% 13.71/7.68 ( ( X != Y )
% 13.71/7.68 => ( ~ ( ord_less_int @ X @ Y )
% 13.71/7.68 => ( ord_less_int @ Y @ X ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1154_subrelI,axiom,
% 13.71/7.68 ! [R: set_Pr1773385645901665561uint32,S: set_Pr1773385645901665561uint32] :
% 13.71/7.68 ( ! [X3: uint32,Y3: uint32] :
% 13.71/7.68 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ R )
% 13.71/7.68 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ S ) )
% 13.71/7.68 => ( ord_le6429528607962791097uint32 @ R @ S ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1155_subrelI,axiom,
% 13.71/7.68 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 13.71/7.68 ( ! [X3: nat,Y3: nat] :
% 13.71/7.68 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 13.71/7.68 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S ) )
% 13.71/7.68 => ( ord_le3146513528884898305at_nat @ R @ S ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1156_subrelI,axiom,
% 13.71/7.68 ! [R: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 13.71/7.68 ( ! [X3: int,Y3: int] :
% 13.71/7.68 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R )
% 13.71/7.68 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ S ) )
% 13.71/7.68 => ( ord_le2843351958646193337nt_int @ R @ S ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1157_subrelI,axiom,
% 13.71/7.68 ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 13.71/7.68 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 13.71/7.68 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 13.71/7.68 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 13.71/7.68 => ( ord_le5966269811547037844et_nat @ R @ S ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1158_subrelI,axiom,
% 13.71/7.68 ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 13.71/7.68 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 13.71/7.68 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 13.71/7.68 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 13.71/7.68 => ( ord_le4763372923235995152et_nat @ R @ S ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1159_mod__emp__simp,axiom,
% 13.71/7.68 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1160_le__numeral__extra_I3_J,axiom,
% 13.71/7.68 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1161_le__numeral__extra_I3_J,axiom,
% 13.71/7.68 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1162_le__numeral__extra_I3_J,axiom,
% 13.71/7.68 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1163_le__numeral__extra_I3_J,axiom,
% 13.71/7.68 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1164_less__numeral__extra_I3_J,axiom,
% 13.71/7.68 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1165_less__numeral__extra_I3_J,axiom,
% 13.71/7.68 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1166_less__numeral__extra_I3_J,axiom,
% 13.71/7.68 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1167_less__numeral__extra_I3_J,axiom,
% 13.71/7.68 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1168_zero__neq__one,axiom,
% 13.71/7.68 zero_zero_uint32 != one_one_uint32 ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1169_zero__neq__one,axiom,
% 13.71/7.68 zero_zero_real != one_one_real ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1170_zero__neq__one,axiom,
% 13.71/7.68 zero_zero_rat != one_one_rat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1171_zero__neq__one,axiom,
% 13.71/7.68 zero_zero_nat != one_one_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1172_zero__neq__one,axiom,
% 13.71/7.68 zero_zero_int != one_one_int ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1173_le__numeral__extra_I4_J,axiom,
% 13.71/7.68 ord_less_eq_real @ one_one_real @ one_one_real ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1174_le__numeral__extra_I4_J,axiom,
% 13.71/7.68 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1175_le__numeral__extra_I4_J,axiom,
% 13.71/7.68 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1176_le__numeral__extra_I4_J,axiom,
% 13.71/7.68 ord_less_eq_int @ one_one_int @ one_one_int ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1177_less__numeral__extra_I4_J,axiom,
% 13.71/7.68 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1178_less__numeral__extra_I4_J,axiom,
% 13.71/7.68 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1179_less__numeral__extra_I4_J,axiom,
% 13.71/7.68 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1180_less__numeral__extra_I4_J,axiom,
% 13.71/7.68 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1181_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I2_J,axiom,
% 13.71/7.68 ! [A: $o,B: $o] :
% 13.71/7.68 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 13.71/7.68 = one_one_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1182_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I1_J,axiom,
% 13.71/7.68 ! [A: $o,B: $o] :
% 13.71/7.68 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 13.71/7.68 = one_one_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1183_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I3_J,axiom,
% 13.71/7.68 ! [A: $o,B: $o,N: nat] :
% 13.71/7.68 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 13.71/7.68 = one_one_nat ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1184_nat__descend__induct,axiom,
% 13.71/7.68 ! [N: nat,P2: nat > $o,M: nat] :
% 13.71/7.68 ( ! [K2: nat] :
% 13.71/7.68 ( ( ord_less_nat @ N @ K2 )
% 13.71/7.68 => ( P2 @ K2 ) )
% 13.71/7.68 => ( ! [K2: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ K2 @ N )
% 13.71/7.68 => ( ! [I4: nat] :
% 13.71/7.68 ( ( ord_less_nat @ K2 @ I4 )
% 13.71/7.68 => ( P2 @ I4 ) )
% 13.71/7.68 => ( P2 @ K2 ) ) )
% 13.71/7.68 => ( P2 @ M ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1185_exists__least__lemma,axiom,
% 13.71/7.68 ! [P2: nat > $o] :
% 13.71/7.68 ( ~ ( P2 @ zero_zero_nat )
% 13.71/7.68 => ( ? [X_12: nat] : ( P2 @ X_12 )
% 13.71/7.68 => ? [N2: nat] :
% 13.71/7.68 ( ~ ( P2 @ N2 )
% 13.71/7.68 & ( P2 @ ( suc @ N2 ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1186_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Ocases,axiom,
% 13.71/7.68 ! [X: nat] :
% 13.71/7.68 ( ( X != zero_zero_nat )
% 13.71/7.68 => ( ( X
% 13.71/7.68 != ( suc @ zero_zero_nat ) )
% 13.71/7.68 => ~ ! [Va: nat] :
% 13.71/7.68 ( X
% 13.71/7.68 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1187_list__decode_Ocases,axiom,
% 13.71/7.68 ! [X: nat] :
% 13.71/7.68 ( ( X != zero_zero_nat )
% 13.71/7.68 => ~ ! [N2: nat] :
% 13.71/7.68 ( X
% 13.71/7.68 != ( suc @ N2 ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1188_mod__h__bot__iff_I4_J,axiom,
% 13.71/7.68 ! [Q3: array_VEBT_VEBTi,Y: list_VEBT_VEBTi,H2: heap_e7401611519738050253t_unit] :
% 13.71/7.68 ~ ( rep_assn @ ( snga_assn_VEBT_VEBTi @ Q3 @ Y ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1189_complete__interval,axiom,
% 13.71/7.68 ! [A: real,B: real,P2: real > $o] :
% 13.71/7.68 ( ( ord_less_real @ A @ B )
% 13.71/7.68 => ( ( P2 @ A )
% 13.71/7.68 => ( ~ ( P2 @ B )
% 13.71/7.68 => ? [C: real] :
% 13.71/7.68 ( ( ord_less_eq_real @ A @ C )
% 13.71/7.68 & ( ord_less_eq_real @ C @ B )
% 13.71/7.68 & ! [X5: real] :
% 13.71/7.68 ( ( ( ord_less_eq_real @ A @ X5 )
% 13.71/7.68 & ( ord_less_real @ X5 @ C ) )
% 13.71/7.68 => ( P2 @ X5 ) )
% 13.71/7.68 & ! [D3: real] :
% 13.71/7.68 ( ! [X3: real] :
% 13.71/7.68 ( ( ( ord_less_eq_real @ A @ X3 )
% 13.71/7.68 & ( ord_less_real @ X3 @ D3 ) )
% 13.71/7.68 => ( P2 @ X3 ) )
% 13.71/7.68 => ( ord_less_eq_real @ D3 @ C ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1190_complete__interval,axiom,
% 13.71/7.68 ! [A: nat,B: nat,P2: nat > $o] :
% 13.71/7.68 ( ( ord_less_nat @ A @ B )
% 13.71/7.68 => ( ( P2 @ A )
% 13.71/7.68 => ( ~ ( P2 @ B )
% 13.71/7.68 => ? [C: nat] :
% 13.71/7.68 ( ( ord_less_eq_nat @ A @ C )
% 13.71/7.68 & ( ord_less_eq_nat @ C @ B )
% 13.71/7.68 & ! [X5: nat] :
% 13.71/7.68 ( ( ( ord_less_eq_nat @ A @ X5 )
% 13.71/7.68 & ( ord_less_nat @ X5 @ C ) )
% 13.71/7.68 => ( P2 @ X5 ) )
% 13.71/7.68 & ! [D3: nat] :
% 13.71/7.68 ( ! [X3: nat] :
% 13.71/7.68 ( ( ( ord_less_eq_nat @ A @ X3 )
% 13.71/7.68 & ( ord_less_nat @ X3 @ D3 ) )
% 13.71/7.68 => ( P2 @ X3 ) )
% 13.71/7.68 => ( ord_less_eq_nat @ D3 @ C ) ) ) ) ) ) ).
% 13.71/7.68
% 13.71/7.68 thf(fact_1191_complete__interval,axiom,
% 13.71/7.68 ! [A: int,B: int,P2: int > $o] :
% 13.71/7.68 ( ( ord_less_int @ A @ B )
% 13.71/7.68 => ( ( P2 @ A )
% 13.71/7.68 => ( ~ ( P2 @ B )
% 13.71/7.68 => ? [C: int] :
% 13.71/7.68 ( ( ord_less_eq_int @ A @ C )
% 13.71/7.68 & ( ord_less_eq_int @ C @ B )
% 13.71/7.68 & ! [X5: int] :
% 13.71/7.68 ( ( ( ord_less_eq_int @ A @ X5 )
% 13.71/7.68 & ( ord_less_int @ X5 @ C ) )
% 13.71/7.68 => ( P2 @ X5 ) )
% 13.71/7.68 & ! [D3: int] :
% 13.71/7.68 ( ! [X3: int] :
% 13.71/7.68 ( ( ( ord_less_eq_int @ A @ X3 )
% 13.71/7.68 & ( ord_less_int @ X3 @ D3 ) )
% 13.71/7.68 => ( P2 @ X3 ) )
% 13.71/7.69 => ( ord_less_eq_int @ D3 @ C ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1192_verit__comp__simplify1_I3_J,axiom,
% 13.71/7.69 ! [B2: real,A2: real] :
% 13.71/7.69 ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 13.71/7.69 = ( ord_less_real @ A2 @ B2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1193_verit__comp__simplify1_I3_J,axiom,
% 13.71/7.69 ! [B2: rat,A2: rat] :
% 13.71/7.69 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 13.71/7.69 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1194_verit__comp__simplify1_I3_J,axiom,
% 13.71/7.69 ! [B2: num,A2: num] :
% 13.71/7.69 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 13.71/7.69 = ( ord_less_num @ A2 @ B2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1195_verit__comp__simplify1_I3_J,axiom,
% 13.71/7.69 ! [B2: nat,A2: nat] :
% 13.71/7.69 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 13.71/7.69 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1196_verit__comp__simplify1_I3_J,axiom,
% 13.71/7.69 ! [B2: int,A2: int] :
% 13.71/7.69 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 13.71/7.69 = ( ord_less_int @ A2 @ B2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1197_verit__comp__simplify1_I2_J,axiom,
% 13.71/7.69 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1198_verit__comp__simplify1_I2_J,axiom,
% 13.71/7.69 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1199_verit__comp__simplify1_I2_J,axiom,
% 13.71/7.69 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1200_verit__comp__simplify1_I2_J,axiom,
% 13.71/7.69 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1201_verit__comp__simplify1_I2_J,axiom,
% 13.71/7.69 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1202_verit__la__disequality,axiom,
% 13.71/7.69 ! [A: rat,B: rat] :
% 13.71/7.69 ( ( A = B )
% 13.71/7.69 | ~ ( ord_less_eq_rat @ A @ B )
% 13.71/7.69 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1203_verit__la__disequality,axiom,
% 13.71/7.69 ! [A: num,B: num] :
% 13.71/7.69 ( ( A = B )
% 13.71/7.69 | ~ ( ord_less_eq_num @ A @ B )
% 13.71/7.69 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1204_verit__la__disequality,axiom,
% 13.71/7.69 ! [A: nat,B: nat] :
% 13.71/7.69 ( ( A = B )
% 13.71/7.69 | ~ ( ord_less_eq_nat @ A @ B )
% 13.71/7.69 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1205_verit__la__disequality,axiom,
% 13.71/7.69 ! [A: int,B: int] :
% 13.71/7.69 ( ( A = B )
% 13.71/7.69 | ~ ( ord_less_eq_int @ A @ B )
% 13.71/7.69 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1206_verit__comp__simplify1_I1_J,axiom,
% 13.71/7.69 ! [A: real] :
% 13.71/7.69 ~ ( ord_less_real @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1207_verit__comp__simplify1_I1_J,axiom,
% 13.71/7.69 ! [A: rat] :
% 13.71/7.69 ~ ( ord_less_rat @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1208_verit__comp__simplify1_I1_J,axiom,
% 13.71/7.69 ! [A: num] :
% 13.71/7.69 ~ ( ord_less_num @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1209_verit__comp__simplify1_I1_J,axiom,
% 13.71/7.69 ! [A: nat] :
% 13.71/7.69 ~ ( ord_less_nat @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1210_verit__comp__simplify1_I1_J,axiom,
% 13.71/7.69 ! [A: int] :
% 13.71/7.69 ~ ( ord_less_int @ A @ A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1211_ex__gt__or__lt,axiom,
% 13.71/7.69 ! [A: real] :
% 13.71/7.69 ? [B3: real] :
% 13.71/7.69 ( ( ord_less_real @ A @ B3 )
% 13.71/7.69 | ( ord_less_real @ B3 @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1212_minf_I8_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1213_minf_I8_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1214_minf_I8_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1215_minf_I8_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1216_minf_I8_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1217_minf_I6_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1218_minf_I6_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1219_minf_I6_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1220_minf_I6_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1221_minf_I6_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1222_pinf_I8_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1223_pinf_I8_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1224_pinf_I8_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1225_pinf_I8_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1226_pinf_I8_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1227_pinf_I6_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1228_pinf_I6_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1229_pinf_I6_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1230_pinf_I6_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1231_pinf_I6_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1232_field__lbound__gt__zero,axiom,
% 13.71/7.69 ! [D1: real,D22: real] :
% 13.71/7.69 ( ( ord_less_real @ zero_zero_real @ D1 )
% 13.71/7.69 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 13.71/7.69 => ? [E: real] :
% 13.71/7.69 ( ( ord_less_real @ zero_zero_real @ E )
% 13.71/7.69 & ( ord_less_real @ E @ D1 )
% 13.71/7.69 & ( ord_less_real @ E @ D22 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1233_field__lbound__gt__zero,axiom,
% 13.71/7.69 ! [D1: rat,D22: rat] :
% 13.71/7.69 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 13.71/7.69 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 13.71/7.69 => ? [E: rat] :
% 13.71/7.69 ( ( ord_less_rat @ zero_zero_rat @ E )
% 13.71/7.69 & ( ord_less_rat @ E @ D1 )
% 13.71/7.69 & ( ord_less_rat @ E @ D22 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1234_dbl__inc__simps_I2_J,axiom,
% 13.71/7.69 ( ( neg_nu4269007558841261821uint32 @ zero_zero_uint32 )
% 13.71/7.69 = one_one_uint32 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1235_dbl__inc__simps_I2_J,axiom,
% 13.71/7.69 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 13.71/7.69 = one_one_real ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1236_dbl__inc__simps_I2_J,axiom,
% 13.71/7.69 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 13.71/7.69 = one_one_rat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1237_dbl__inc__simps_I2_J,axiom,
% 13.71/7.69 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 13.71/7.69 = one_one_int ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1238_VEBT_Osize__gen_I2_J,axiom,
% 13.71/7.69 ! [X21: $o,X22: $o] :
% 13.71/7.69 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 13.71/7.69 = zero_zero_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1239_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J,axiom,
% 13.71/7.69 ! [A: $o,B: $o] :
% 13.71/7.69 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1240_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I6_J,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.71/7.69 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1241_frac__eq,axiom,
% 13.71/7.69 ! [X: real] :
% 13.71/7.69 ( ( ( archim2898591450579166408c_real @ X )
% 13.71/7.69 = X )
% 13.71/7.69 = ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.71/7.69 & ( ord_less_real @ X @ one_one_real ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1242_frac__eq,axiom,
% 13.71/7.69 ! [X: rat] :
% 13.71/7.69 ( ( ( archimedean_frac_rat @ X )
% 13.71/7.69 = X )
% 13.71/7.69 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 13.71/7.69 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1243_Suc__diff__1,axiom,
% 13.71/7.69 ! [N: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.69 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.71/7.69 = N ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1244_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 13.71/7.69 ! [A: rat] :
% 13.71/7.69 ( ( minus_minus_rat @ A @ A )
% 13.71/7.69 = zero_zero_rat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1245_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 13.71/7.69 ! [A: uint32] :
% 13.71/7.69 ( ( minus_minus_uint32 @ A @ A )
% 13.71/7.69 = zero_zero_uint32 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1246_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 13.71/7.69 ! [A: real] :
% 13.71/7.69 ( ( minus_minus_real @ A @ A )
% 13.71/7.69 = zero_zero_real ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1247_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 13.71/7.69 ! [A: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ A @ A )
% 13.71/7.69 = zero_zero_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1248_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 13.71/7.69 ! [A: int] :
% 13.71/7.69 ( ( minus_minus_int @ A @ A )
% 13.71/7.69 = zero_zero_int ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1249_diff__zero,axiom,
% 13.71/7.69 ! [A: rat] :
% 13.71/7.69 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1250_diff__zero,axiom,
% 13.71/7.69 ! [A: uint32] :
% 13.71/7.69 ( ( minus_minus_uint32 @ A @ zero_zero_uint32 )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1251_diff__zero,axiom,
% 13.71/7.69 ! [A: real] :
% 13.71/7.69 ( ( minus_minus_real @ A @ zero_zero_real )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1252_diff__zero,axiom,
% 13.71/7.69 ! [A: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1253_diff__zero,axiom,
% 13.71/7.69 ! [A: int] :
% 13.71/7.69 ( ( minus_minus_int @ A @ zero_zero_int )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1254_zero__diff,axiom,
% 13.71/7.69 ! [A: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 13.71/7.69 = zero_zero_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1255_diff__0__right,axiom,
% 13.71/7.69 ! [A: rat] :
% 13.71/7.69 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1256_diff__0__right,axiom,
% 13.71/7.69 ! [A: uint32] :
% 13.71/7.69 ( ( minus_minus_uint32 @ A @ zero_zero_uint32 )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1257_diff__0__right,axiom,
% 13.71/7.69 ! [A: real] :
% 13.71/7.69 ( ( minus_minus_real @ A @ zero_zero_real )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1258_diff__0__right,axiom,
% 13.71/7.69 ! [A: int] :
% 13.71/7.69 ( ( minus_minus_int @ A @ zero_zero_int )
% 13.71/7.69 = A ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1259_diff__self,axiom,
% 13.71/7.69 ! [A: rat] :
% 13.71/7.69 ( ( minus_minus_rat @ A @ A )
% 13.71/7.69 = zero_zero_rat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1260_diff__self,axiom,
% 13.71/7.69 ! [A: uint32] :
% 13.71/7.69 ( ( minus_minus_uint32 @ A @ A )
% 13.71/7.69 = zero_zero_uint32 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1261_diff__self,axiom,
% 13.71/7.69 ! [A: real] :
% 13.71/7.69 ( ( minus_minus_real @ A @ A )
% 13.71/7.69 = zero_zero_real ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1262_diff__self,axiom,
% 13.71/7.69 ! [A: int] :
% 13.71/7.69 ( ( minus_minus_int @ A @ A )
% 13.71/7.69 = zero_zero_int ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1263_Suc__diff__diff,axiom,
% 13.71/7.69 ! [M: nat,N: nat,K: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 13.71/7.69 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1264_diff__Suc__Suc,axiom,
% 13.71/7.69 ! [M: nat,N: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 13.71/7.69 = ( minus_minus_nat @ M @ N ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1265_diff__self__eq__0,axiom,
% 13.71/7.69 ! [M: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ M @ M )
% 13.71/7.69 = zero_zero_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1266_diff__0__eq__0,axiom,
% 13.71/7.69 ! [N: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 13.71/7.69 = zero_zero_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1267_diff__diff__cancel,axiom,
% 13.71/7.69 ! [I: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ I @ N )
% 13.71/7.69 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 13.71/7.69 = I ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1268_zero__comp__diff__simps_I1_J,axiom,
% 13.71/7.69 ! [A: real,B: real] :
% 13.71/7.69 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 13.71/7.69 = ( ord_less_eq_real @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1269_zero__comp__diff__simps_I1_J,axiom,
% 13.71/7.69 ! [A: rat,B: rat] :
% 13.71/7.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 13.71/7.69 = ( ord_less_eq_rat @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1270_zero__comp__diff__simps_I1_J,axiom,
% 13.71/7.69 ! [A: int,B: int] :
% 13.71/7.69 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 13.71/7.69 = ( ord_less_eq_int @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1271_diff__ge__0__iff__ge,axiom,
% 13.71/7.69 ! [A: real,B: real] :
% 13.71/7.69 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 13.71/7.69 = ( ord_less_eq_real @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1272_diff__ge__0__iff__ge,axiom,
% 13.71/7.69 ! [A: rat,B: rat] :
% 13.71/7.69 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 13.71/7.69 = ( ord_less_eq_rat @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1273_diff__ge__0__iff__ge,axiom,
% 13.71/7.69 ! [A: int,B: int] :
% 13.71/7.69 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 13.71/7.69 = ( ord_less_eq_int @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1274_zero__comp__diff__simps_I2_J,axiom,
% 13.71/7.69 ! [A: real,B: real] :
% 13.71/7.69 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 13.71/7.69 = ( ord_less_real @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1275_zero__comp__diff__simps_I2_J,axiom,
% 13.71/7.69 ! [A: rat,B: rat] :
% 13.71/7.69 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 13.71/7.69 = ( ord_less_rat @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1276_zero__comp__diff__simps_I2_J,axiom,
% 13.71/7.69 ! [A: int,B: int] :
% 13.71/7.69 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 13.71/7.69 = ( ord_less_int @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1277_diff__gt__0__iff__gt,axiom,
% 13.71/7.69 ! [A: real,B: real] :
% 13.71/7.69 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 13.71/7.69 = ( ord_less_real @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1278_diff__gt__0__iff__gt,axiom,
% 13.71/7.69 ! [A: rat,B: rat] :
% 13.71/7.69 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 13.71/7.69 = ( ord_less_rat @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1279_diff__gt__0__iff__gt,axiom,
% 13.71/7.69 ! [A: int,B: int] :
% 13.71/7.69 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 13.71/7.69 = ( ord_less_int @ B @ A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1280_diff__numeral__special_I9_J,axiom,
% 13.71/7.69 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 13.71/7.69 = zero_zero_rat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1281_diff__numeral__special_I9_J,axiom,
% 13.71/7.69 ( ( minus_minus_uint32 @ one_one_uint32 @ one_one_uint32 )
% 13.71/7.69 = zero_zero_uint32 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1282_diff__numeral__special_I9_J,axiom,
% 13.71/7.69 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 13.71/7.69 = zero_zero_real ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1283_diff__numeral__special_I9_J,axiom,
% 13.71/7.69 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 13.71/7.69 = zero_zero_int ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1284_zero__less__diff,axiom,
% 13.71/7.69 ! [N: nat,M: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 13.71/7.69 = ( ord_less_nat @ M @ N ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1285_diff__Suc__1,axiom,
% 13.71/7.69 ! [N: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 13.71/7.69 = N ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1286_diff__is__0__eq_H,axiom,
% 13.71/7.69 ! [M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.69 => ( ( minus_minus_nat @ M @ N )
% 13.71/7.69 = zero_zero_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1287_diff__is__0__eq,axiom,
% 13.71/7.69 ! [M: nat,N: nat] :
% 13.71/7.69 ( ( ( minus_minus_nat @ M @ N )
% 13.71/7.69 = zero_zero_nat )
% 13.71/7.69 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1288_Suc__pred,axiom,
% 13.71/7.69 ! [N: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.69 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 13.71/7.69 = N ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1289_Suc__diff,axiom,
% 13.71/7.69 ! [M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.69 => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 13.71/7.69 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 13.71/7.69 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1290_diff__eq__diff__eq,axiom,
% 13.71/7.69 ! [A: uint32,B: uint32,C2: uint32,D: uint32] :
% 13.71/7.69 ( ( ( minus_minus_uint32 @ A @ B )
% 13.71/7.69 = ( minus_minus_uint32 @ C2 @ D ) )
% 13.71/7.69 => ( ( A = B )
% 13.71/7.69 = ( C2 = D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1291_diff__eq__diff__eq,axiom,
% 13.71/7.69 ! [A: real,B: real,C2: real,D: real] :
% 13.71/7.69 ( ( ( minus_minus_real @ A @ B )
% 13.71/7.69 = ( minus_minus_real @ C2 @ D ) )
% 13.71/7.69 => ( ( A = B )
% 13.71/7.69 = ( C2 = D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1292_diff__eq__diff__eq,axiom,
% 13.71/7.69 ! [A: int,B: int,C2: int,D: int] :
% 13.71/7.69 ( ( ( minus_minus_int @ A @ B )
% 13.71/7.69 = ( minus_minus_int @ C2 @ D ) )
% 13.71/7.69 => ( ( A = B )
% 13.71/7.69 = ( C2 = D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1293_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 13.71/7.69 ! [A: uint32,C2: uint32,B: uint32] :
% 13.71/7.69 ( ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ C2 ) @ B )
% 13.71/7.69 = ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ C2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1294_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 13.71/7.69 ! [A: real,C2: real,B: real] :
% 13.71/7.69 ( ( minus_minus_real @ ( minus_minus_real @ A @ C2 ) @ B )
% 13.71/7.69 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1295_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 13.71/7.69 ! [A: nat,C2: nat,B: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B )
% 13.71/7.69 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1296_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 13.71/7.69 ! [A: int,C2: int,B: int] :
% 13.71/7.69 ( ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B )
% 13.71/7.69 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1297_diff__commute,axiom,
% 13.71/7.69 ! [I: nat,J: nat,K: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 13.71/7.69 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1298_le__some__optE,axiom,
% 13.71/7.69 ! [M: set_int,X: option_set_int] :
% 13.71/7.69 ( ( ord_le353528952715127954et_int @ ( some_set_int @ M ) @ X )
% 13.71/7.69 => ~ ! [M8: set_int] :
% 13.71/7.69 ( ( X
% 13.71/7.69 = ( some_set_int @ M8 ) )
% 13.71/7.69 => ~ ( ord_less_eq_set_int @ M @ M8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1299_le__some__optE,axiom,
% 13.71/7.69 ! [M: rat,X: option_rat] :
% 13.71/7.69 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M ) @ X )
% 13.71/7.69 => ~ ! [M8: rat] :
% 13.71/7.69 ( ( X
% 13.71/7.69 = ( some_rat @ M8 ) )
% 13.71/7.69 => ~ ( ord_less_eq_rat @ M @ M8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1300_le__some__optE,axiom,
% 13.71/7.69 ! [M: num,X: option_num] :
% 13.71/7.69 ( ( ord_le6622620407824499402on_num @ ( some_num @ M ) @ X )
% 13.71/7.69 => ~ ! [M8: num] :
% 13.71/7.69 ( ( X
% 13.71/7.69 = ( some_num @ M8 ) )
% 13.71/7.69 => ~ ( ord_less_eq_num @ M @ M8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1301_le__some__optE,axiom,
% 13.71/7.69 ! [M: nat,X: option_nat] :
% 13.71/7.69 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M ) @ X )
% 13.71/7.69 => ~ ! [M8: nat] :
% 13.71/7.69 ( ( X
% 13.71/7.69 = ( some_nat @ M8 ) )
% 13.71/7.69 => ~ ( ord_less_eq_nat @ M @ M8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1302_le__some__optE,axiom,
% 13.71/7.69 ! [M: int,X: option_int] :
% 13.71/7.69 ( ( ord_le1736525451366464988on_int @ ( some_int @ M ) @ X )
% 13.71/7.69 => ~ ! [M8: int] :
% 13.71/7.69 ( ( X
% 13.71/7.69 = ( some_int @ M8 ) )
% 13.71/7.69 => ~ ( ord_less_eq_int @ M @ M8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1303_eq__iff__diff__eq__0,axiom,
% 13.71/7.69 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 13.71/7.69 = ( ^ [A7: rat,B7: rat] :
% 13.71/7.69 ( ( minus_minus_rat @ A7 @ B7 )
% 13.71/7.69 = zero_zero_rat ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1304_eq__iff__diff__eq__0,axiom,
% 13.71/7.69 ( ( ^ [Y6: uint32,Z4: uint32] : ( Y6 = Z4 ) )
% 13.71/7.69 = ( ^ [A7: uint32,B7: uint32] :
% 13.71/7.69 ( ( minus_minus_uint32 @ A7 @ B7 )
% 13.71/7.69 = zero_zero_uint32 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1305_eq__iff__diff__eq__0,axiom,
% 13.71/7.69 ( ( ^ [Y6: real,Z4: real] : ( Y6 = Z4 ) )
% 13.71/7.69 = ( ^ [A7: real,B7: real] :
% 13.71/7.69 ( ( minus_minus_real @ A7 @ B7 )
% 13.71/7.69 = zero_zero_real ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1306_eq__iff__diff__eq__0,axiom,
% 13.71/7.69 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.71/7.69 = ( ^ [A7: int,B7: int] :
% 13.71/7.69 ( ( minus_minus_int @ A7 @ B7 )
% 13.71/7.69 = zero_zero_int ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1307_diff__mono,axiom,
% 13.71/7.69 ! [A: real,B: real,D: real,C2: real] :
% 13.71/7.69 ( ( ord_less_eq_real @ A @ B )
% 13.71/7.69 => ( ( ord_less_eq_real @ D @ C2 )
% 13.71/7.69 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1308_diff__mono,axiom,
% 13.71/7.69 ! [A: rat,B: rat,D: rat,C2: rat] :
% 13.71/7.69 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.69 => ( ( ord_less_eq_rat @ D @ C2 )
% 13.71/7.69 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1309_diff__mono,axiom,
% 13.71/7.69 ! [A: int,B: int,D: int,C2: int] :
% 13.71/7.69 ( ( ord_less_eq_int @ A @ B )
% 13.71/7.69 => ( ( ord_less_eq_int @ D @ C2 )
% 13.71/7.69 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1310_diff__left__mono,axiom,
% 13.71/7.69 ! [B: real,A: real,C2: real] :
% 13.71/7.69 ( ( ord_less_eq_real @ B @ A )
% 13.71/7.69 => ( ord_less_eq_real @ ( minus_minus_real @ C2 @ A ) @ ( minus_minus_real @ C2 @ B ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1311_diff__left__mono,axiom,
% 13.71/7.69 ! [B: rat,A: rat,C2: rat] :
% 13.71/7.69 ( ( ord_less_eq_rat @ B @ A )
% 13.71/7.69 => ( ord_less_eq_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1312_diff__left__mono,axiom,
% 13.71/7.69 ! [B: int,A: int,C2: int] :
% 13.71/7.69 ( ( ord_less_eq_int @ B @ A )
% 13.71/7.69 => ( ord_less_eq_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1313_diff__right__mono,axiom,
% 13.71/7.69 ! [A: real,B: real,C2: real] :
% 13.71/7.69 ( ( ord_less_eq_real @ A @ B )
% 13.71/7.69 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ C2 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1314_diff__right__mono,axiom,
% 13.71/7.69 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.69 ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.69 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1315_diff__right__mono,axiom,
% 13.71/7.69 ! [A: int,B: int,C2: int] :
% 13.71/7.69 ( ( ord_less_eq_int @ A @ B )
% 13.71/7.69 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1316_diff__eq__diff__less__eq,axiom,
% 13.71/7.69 ! [A: real,B: real,C2: real,D: real] :
% 13.71/7.69 ( ( ( minus_minus_real @ A @ B )
% 13.71/7.69 = ( minus_minus_real @ C2 @ D ) )
% 13.71/7.69 => ( ( ord_less_eq_real @ A @ B )
% 13.71/7.69 = ( ord_less_eq_real @ C2 @ D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1317_diff__eq__diff__less__eq,axiom,
% 13.71/7.69 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.71/7.69 ( ( ( minus_minus_rat @ A @ B )
% 13.71/7.69 = ( minus_minus_rat @ C2 @ D ) )
% 13.71/7.69 => ( ( ord_less_eq_rat @ A @ B )
% 13.71/7.69 = ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1318_diff__eq__diff__less__eq,axiom,
% 13.71/7.69 ! [A: int,B: int,C2: int,D: int] :
% 13.71/7.69 ( ( ( minus_minus_int @ A @ B )
% 13.71/7.69 = ( minus_minus_int @ C2 @ D ) )
% 13.71/7.69 => ( ( ord_less_eq_int @ A @ B )
% 13.71/7.69 = ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1319_diff__strict__right__mono,axiom,
% 13.71/7.69 ! [A: real,B: real,C2: real] :
% 13.71/7.69 ( ( ord_less_real @ A @ B )
% 13.71/7.69 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ C2 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1320_diff__strict__right__mono,axiom,
% 13.71/7.69 ! [A: rat,B: rat,C2: rat] :
% 13.71/7.69 ( ( ord_less_rat @ A @ B )
% 13.71/7.69 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1321_diff__strict__right__mono,axiom,
% 13.71/7.69 ! [A: int,B: int,C2: int] :
% 13.71/7.69 ( ( ord_less_int @ A @ B )
% 13.71/7.69 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1322_diff__strict__left__mono,axiom,
% 13.71/7.69 ! [B: real,A: real,C2: real] :
% 13.71/7.69 ( ( ord_less_real @ B @ A )
% 13.71/7.69 => ( ord_less_real @ ( minus_minus_real @ C2 @ A ) @ ( minus_minus_real @ C2 @ B ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1323_diff__strict__left__mono,axiom,
% 13.71/7.69 ! [B: rat,A: rat,C2: rat] :
% 13.71/7.69 ( ( ord_less_rat @ B @ A )
% 13.71/7.69 => ( ord_less_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1324_diff__strict__left__mono,axiom,
% 13.71/7.69 ! [B: int,A: int,C2: int] :
% 13.71/7.69 ( ( ord_less_int @ B @ A )
% 13.71/7.69 => ( ord_less_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1325_diff__eq__diff__less,axiom,
% 13.71/7.69 ! [A: real,B: real,C2: real,D: real] :
% 13.71/7.69 ( ( ( minus_minus_real @ A @ B )
% 13.71/7.69 = ( minus_minus_real @ C2 @ D ) )
% 13.71/7.69 => ( ( ord_less_real @ A @ B )
% 13.71/7.69 = ( ord_less_real @ C2 @ D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1326_diff__eq__diff__less,axiom,
% 13.71/7.69 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.71/7.69 ( ( ( minus_minus_rat @ A @ B )
% 13.71/7.69 = ( minus_minus_rat @ C2 @ D ) )
% 13.71/7.69 => ( ( ord_less_rat @ A @ B )
% 13.71/7.69 = ( ord_less_rat @ C2 @ D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1327_diff__eq__diff__less,axiom,
% 13.71/7.69 ! [A: int,B: int,C2: int,D: int] :
% 13.71/7.69 ( ( ( minus_minus_int @ A @ B )
% 13.71/7.69 = ( minus_minus_int @ C2 @ D ) )
% 13.71/7.69 => ( ( ord_less_int @ A @ B )
% 13.71/7.69 = ( ord_less_int @ C2 @ D ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1328_diff__strict__mono,axiom,
% 13.71/7.69 ! [A: real,B: real,D: real,C2: real] :
% 13.71/7.69 ( ( ord_less_real @ A @ B )
% 13.71/7.69 => ( ( ord_less_real @ D @ C2 )
% 13.71/7.69 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1329_diff__strict__mono,axiom,
% 13.71/7.69 ! [A: rat,B: rat,D: rat,C2: rat] :
% 13.71/7.69 ( ( ord_less_rat @ A @ B )
% 13.71/7.69 => ( ( ord_less_rat @ D @ C2 )
% 13.71/7.69 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1330_diff__strict__mono,axiom,
% 13.71/7.69 ! [A: int,B: int,D: int,C2: int] :
% 13.71/7.69 ( ( ord_less_int @ A @ B )
% 13.71/7.69 => ( ( ord_less_int @ D @ C2 )
% 13.71/7.69 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1331_zero__induct__lemma,axiom,
% 13.71/7.69 ! [P2: nat > $o,K: nat,I: nat] :
% 13.71/7.69 ( ( P2 @ K )
% 13.71/7.69 => ( ! [N2: nat] :
% 13.71/7.69 ( ( P2 @ ( suc @ N2 ) )
% 13.71/7.69 => ( P2 @ N2 ) )
% 13.71/7.69 => ( P2 @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1332_diffs0__imp__equal,axiom,
% 13.71/7.69 ! [M: nat,N: nat] :
% 13.71/7.69 ( ( ( minus_minus_nat @ M @ N )
% 13.71/7.69 = zero_zero_nat )
% 13.71/7.69 => ( ( ( minus_minus_nat @ N @ M )
% 13.71/7.69 = zero_zero_nat )
% 13.71/7.69 => ( M = N ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1333_minus__nat_Odiff__0,axiom,
% 13.71/7.69 ! [M: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 13.71/7.69 = M ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1334_less__imp__diff__less,axiom,
% 13.71/7.69 ! [J: nat,K: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_nat @ J @ K )
% 13.71/7.69 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1335_diff__less__mono2,axiom,
% 13.71/7.69 ! [M: nat,N: nat,L: nat] :
% 13.71/7.69 ( ( ord_less_nat @ M @ N )
% 13.71/7.69 => ( ( ord_less_nat @ M @ L )
% 13.71/7.69 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1336_eq__diff__iff,axiom,
% 13.71/7.69 ! [K: nat,M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ K @ M )
% 13.71/7.69 => ( ( ord_less_eq_nat @ K @ N )
% 13.71/7.69 => ( ( ( minus_minus_nat @ M @ K )
% 13.71/7.69 = ( minus_minus_nat @ N @ K ) )
% 13.71/7.69 = ( M = N ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1337_le__diff__iff,axiom,
% 13.71/7.69 ! [K: nat,M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ K @ M )
% 13.71/7.69 => ( ( ord_less_eq_nat @ K @ N )
% 13.71/7.69 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 13.71/7.69 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1338_Nat_Odiff__diff__eq,axiom,
% 13.71/7.69 ! [K: nat,M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ K @ M )
% 13.71/7.69 => ( ( ord_less_eq_nat @ K @ N )
% 13.71/7.69 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 13.71/7.69 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1339_diff__le__mono,axiom,
% 13.71/7.69 ! [M: nat,N: nat,L: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.69 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1340_diff__le__self,axiom,
% 13.71/7.69 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1341_le__diff__iff_H,axiom,
% 13.71/7.69 ! [A: nat,C2: nat,B: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ A @ C2 )
% 13.71/7.69 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.71/7.69 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C2 @ A ) @ ( minus_minus_nat @ C2 @ B ) )
% 13.71/7.69 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1342_diff__le__mono2,axiom,
% 13.71/7.69 ! [M: nat,N: nat,L: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.69 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1343_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.71/7.69 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1344_le__iff__diff__le__0,axiom,
% 13.71/7.69 ( ord_less_eq_real
% 13.71/7.69 = ( ^ [A7: real,B7: real] : ( ord_less_eq_real @ ( minus_minus_real @ A7 @ B7 ) @ zero_zero_real ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1345_le__iff__diff__le__0,axiom,
% 13.71/7.69 ( ord_less_eq_rat
% 13.71/7.69 = ( ^ [A7: rat,B7: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A7 @ B7 ) @ zero_zero_rat ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1346_le__iff__diff__le__0,axiom,
% 13.71/7.69 ( ord_less_eq_int
% 13.71/7.69 = ( ^ [A7: int,B7: int] : ( ord_less_eq_int @ ( minus_minus_int @ A7 @ B7 ) @ zero_zero_int ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1347_less__iff__diff__less__0,axiom,
% 13.71/7.69 ( ord_less_real
% 13.71/7.69 = ( ^ [A7: real,B7: real] : ( ord_less_real @ ( minus_minus_real @ A7 @ B7 ) @ zero_zero_real ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1348_less__iff__diff__less__0,axiom,
% 13.71/7.69 ( ord_less_rat
% 13.71/7.69 = ( ^ [A7: rat,B7: rat] : ( ord_less_rat @ ( minus_minus_rat @ A7 @ B7 ) @ zero_zero_rat ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1349_less__iff__diff__less__0,axiom,
% 13.71/7.69 ( ord_less_int
% 13.71/7.69 = ( ^ [A7: int,B7: int] : ( ord_less_int @ ( minus_minus_int @ A7 @ B7 ) @ zero_zero_int ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1350_Suc__to__right,axiom,
% 13.71/7.69 ! [N: nat,M: nat] :
% 13.71/7.69 ( ( ( suc @ N )
% 13.71/7.69 = M )
% 13.71/7.69 => ( N
% 13.71/7.69 = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1351_diff__less__Suc,axiom,
% 13.71/7.69 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1352_Suc__diff__Suc,axiom,
% 13.71/7.69 ! [N: nat,M: nat] :
% 13.71/7.69 ( ( ord_less_nat @ N @ M )
% 13.71/7.69 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 13.71/7.69 = ( minus_minus_nat @ M @ N ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1353_diff__less,axiom,
% 13.71/7.69 ! [N: nat,M: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.69 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.71/7.69 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1354_Suc__diff__le,axiom,
% 13.71/7.69 ! [N: nat,M: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ N @ M )
% 13.71/7.69 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 13.71/7.69 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1355_diff__Suc__eq__diff__pred,axiom,
% 13.71/7.69 ! [M: nat,N: nat] :
% 13.71/7.69 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 13.71/7.69 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1356_less__diff__iff,axiom,
% 13.71/7.69 ! [K: nat,M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ K @ M )
% 13.71/7.69 => ( ( ord_less_eq_nat @ K @ N )
% 13.71/7.69 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 13.71/7.69 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1357_diff__less__mono,axiom,
% 13.71/7.69 ! [A: nat,B: nat,C2: nat] :
% 13.71/7.69 ( ( ord_less_nat @ A @ B )
% 13.71/7.69 => ( ( ord_less_eq_nat @ C2 @ A )
% 13.71/7.69 => ( ord_less_nat @ ( minus_minus_nat @ A @ C2 ) @ ( minus_minus_nat @ B @ C2 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1358_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.71/7.69 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ TreeList @ Summary ) @ X )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1359_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 13.71/7.69 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 13.71/7.69 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1360_frac__ge__0,axiom,
% 13.71/7.69 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1361_frac__ge__0,axiom,
% 13.71/7.69 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1362_frac__lt__1,axiom,
% 13.71/7.69 ! [X: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X ) @ one_one_real ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1363_frac__lt__1,axiom,
% 13.71/7.69 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1364_diff__Suc__less,axiom,
% 13.71/7.69 ! [N: nat,I: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.69 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1365_pinf_I1_J,axiom,
% 13.71/7.69 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 13.71/7.69 ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1366_pinf_I1_J,axiom,
% 13.71/7.69 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 13.71/7.69 ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1367_pinf_I1_J,axiom,
% 13.71/7.69 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 13.71/7.69 ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1368_pinf_I1_J,axiom,
% 13.71/7.69 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 13.71/7.69 ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1369_pinf_I1_J,axiom,
% 13.71/7.69 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 13.71/7.69 ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1370_pinf_I2_J,axiom,
% 13.71/7.69 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 13.71/7.69 ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1371_pinf_I2_J,axiom,
% 13.71/7.69 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 13.71/7.69 ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1372_pinf_I2_J,axiom,
% 13.71/7.69 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 13.71/7.69 ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1373_pinf_I2_J,axiom,
% 13.71/7.69 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 13.71/7.69 ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1374_pinf_I2_J,axiom,
% 13.71/7.69 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 13.71/7.69 ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ Z5 @ X3 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ Z5 @ X3 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1375_pinf_I3_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1376_pinf_I3_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1377_pinf_I3_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1378_pinf_I3_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1379_pinf_I3_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1380_pinf_I4_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1381_pinf_I4_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1382_pinf_I4_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1383_pinf_I4_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1384_pinf_I4_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1385_pinf_I5_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_real @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1386_pinf_I5_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_rat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1387_pinf_I5_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_num @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1388_pinf_I5_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_nat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1389_pinf_I5_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ~ ( ord_less_int @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1390_pinf_I7_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_real @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1391_pinf_I7_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_rat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1392_pinf_I7_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_num @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1393_pinf_I7_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_nat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1394_pinf_I7_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ Z3 @ X5 )
% 13.71/7.69 => ( ord_less_int @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1395_minf_I1_J,axiom,
% 13.71/7.69 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 13.71/7.69 ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1396_minf_I1_J,axiom,
% 13.71/7.69 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 13.71/7.69 ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1397_minf_I1_J,axiom,
% 13.71/7.69 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 13.71/7.69 ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1398_minf_I1_J,axiom,
% 13.71/7.69 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 13.71/7.69 ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1399_minf_I1_J,axiom,
% 13.71/7.69 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 13.71/7.69 ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 & ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 & ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1400_minf_I2_J,axiom,
% 13.71/7.69 ! [P2: real > $o,P6: real > $o,Q2: real > $o,Q4: real > $o] :
% 13.71/7.69 ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: real] :
% 13.71/7.69 ! [X3: real] :
% 13.71/7.69 ( ( ord_less_real @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1401_minf_I2_J,axiom,
% 13.71/7.69 ! [P2: rat > $o,P6: rat > $o,Q2: rat > $o,Q4: rat > $o] :
% 13.71/7.69 ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: rat] :
% 13.71/7.69 ! [X3: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1402_minf_I2_J,axiom,
% 13.71/7.69 ! [P2: num > $o,P6: num > $o,Q2: num > $o,Q4: num > $o] :
% 13.71/7.69 ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: num] :
% 13.71/7.69 ! [X3: num] :
% 13.71/7.69 ( ( ord_less_num @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1403_minf_I2_J,axiom,
% 13.71/7.69 ! [P2: nat > $o,P6: nat > $o,Q2: nat > $o,Q4: nat > $o] :
% 13.71/7.69 ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: nat] :
% 13.71/7.69 ! [X3: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1404_minf_I2_J,axiom,
% 13.71/7.69 ! [P2: int > $o,P6: int > $o,Q2: int > $o,Q4: int > $o] :
% 13.71/7.69 ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ X3 @ Z5 )
% 13.71/7.69 => ( ( P2 @ X3 )
% 13.71/7.69 = ( P6 @ X3 ) ) )
% 13.71/7.69 => ( ? [Z5: int] :
% 13.71/7.69 ! [X3: int] :
% 13.71/7.69 ( ( ord_less_int @ X3 @ Z5 )
% 13.71/7.69 => ( ( Q2 @ X3 )
% 13.71/7.69 = ( Q4 @ X3 ) ) )
% 13.71/7.69 => ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ( ( ( P2 @ X5 )
% 13.71/7.69 | ( Q2 @ X5 ) )
% 13.71/7.69 = ( ( P6 @ X5 )
% 13.71/7.69 | ( Q4 @ X5 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1405_minf_I3_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1406_minf_I3_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1407_minf_I3_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1408_minf_I3_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1409_minf_I3_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1410_minf_I4_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1411_minf_I4_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1412_minf_I4_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1413_minf_I4_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1414_minf_I4_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ( X5 != T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1415_minf_I5_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_real @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1416_minf_I5_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_rat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1417_minf_I5_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_num @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1418_minf_I5_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_nat @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1419_minf_I5_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ( ord_less_int @ X5 @ T ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1420_minf_I7_J,axiom,
% 13.71/7.69 ! [T: real] :
% 13.71/7.69 ? [Z3: real] :
% 13.71/7.69 ! [X5: real] :
% 13.71/7.69 ( ( ord_less_real @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_real @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1421_minf_I7_J,axiom,
% 13.71/7.69 ! [T: rat] :
% 13.71/7.69 ? [Z3: rat] :
% 13.71/7.69 ! [X5: rat] :
% 13.71/7.69 ( ( ord_less_rat @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_rat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1422_minf_I7_J,axiom,
% 13.71/7.69 ! [T: num] :
% 13.71/7.69 ? [Z3: num] :
% 13.71/7.69 ! [X5: num] :
% 13.71/7.69 ( ( ord_less_num @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_num @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1423_minf_I7_J,axiom,
% 13.71/7.69 ! [T: nat] :
% 13.71/7.69 ? [Z3: nat] :
% 13.71/7.69 ! [X5: nat] :
% 13.71/7.69 ( ( ord_less_nat @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_nat @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1424_minf_I7_J,axiom,
% 13.71/7.69 ! [T: int] :
% 13.71/7.69 ? [Z3: int] :
% 13.71/7.69 ! [X5: int] :
% 13.71/7.69 ( ( ord_less_int @ X5 @ Z3 )
% 13.71/7.69 => ~ ( ord_less_int @ T @ X5 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1425_vebt__delete_Osimps_I5_J,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 13.71/7.69 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 13.71/7.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1426_vebt__member_Osimps_I3_J,axiom,
% 13.71/7.69 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 13.71/7.69 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1427_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT] :
% 13.71/7.69 ( ~ ( vEBT_VEBT_minNull @ X )
% 13.71/7.69 => ( ! [Uv: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Leaf @ $true @ Uv ) )
% 13.71/7.69 => ( ! [Uu: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Leaf @ Uu @ $true ) )
% 13.71/7.69 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1428_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 13.71/7.69 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X )
% 13.71/7.69 = ( ( X = Mi )
% 13.71/7.69 | ( X = Ma ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1429_nz__le__conv__less,axiom,
% 13.71/7.69 ! [K: nat,M: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.71/7.69 => ( ( ord_less_eq_nat @ K @ M )
% 13.71/7.69 => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1430_Suc__pred_H,axiom,
% 13.71/7.69 ! [N: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.69 => ( N
% 13.71/7.69 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1431_Suc__diff__eq__diff__pred,axiom,
% 13.71/7.69 ! [N: nat,M: nat] :
% 13.71/7.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.71/7.69 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 13.71/7.69 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1432_Suc__n__minus__m__eq,axiom,
% 13.71/7.69 ! [M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_eq_nat @ M @ N )
% 13.71/7.69 => ( ( ord_less_nat @ one_one_nat @ M )
% 13.71/7.69 => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 13.71/7.69 = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1433_vebt__delete_Osimps_I6_J,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 13.71/7.69 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 13.71/7.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1434_vebt__member_Osimps_I4_J,axiom,
% 13.71/7.69 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 13.71/7.69 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1435_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I5_J,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.71/7.69 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TreeList @ Summary ) @ X )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1436_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J,axiom,
% 13.71/7.69 ! [A: $o,B: $o,N: nat] :
% 13.71/7.69 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1437_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J,axiom,
% 13.71/7.69 ! [A: $o,B: $o] :
% 13.71/7.69 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1438_less__option__Some,axiom,
% 13.71/7.69 ! [X: real,Y: real] :
% 13.71/7.69 ( ( ord_less_option_real @ ( some_real @ X ) @ ( some_real @ Y ) )
% 13.71/7.69 = ( ord_less_real @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1439_less__option__Some,axiom,
% 13.71/7.69 ! [X: rat,Y: rat] :
% 13.71/7.69 ( ( ord_less_option_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 13.71/7.69 = ( ord_less_rat @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1440_less__option__Some,axiom,
% 13.71/7.69 ! [X: num,Y: num] :
% 13.71/7.69 ( ( ord_less_option_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 13.71/7.69 = ( ord_less_num @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1441_less__option__Some,axiom,
% 13.71/7.69 ! [X: nat,Y: nat] :
% 13.71/7.69 ( ( ord_less_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 13.71/7.69 = ( ord_less_nat @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1442_less__option__Some,axiom,
% 13.71/7.69 ! [X: int,Y: int] :
% 13.71/7.69 ( ( ord_less_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 13.71/7.69 = ( ord_less_int @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1443_less__eq__option__Some,axiom,
% 13.71/7.69 ! [X: set_int,Y: set_int] :
% 13.71/7.69 ( ( ord_le353528952715127954et_int @ ( some_set_int @ X ) @ ( some_set_int @ Y ) )
% 13.71/7.69 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1444_less__eq__option__Some,axiom,
% 13.71/7.69 ! [X: rat,Y: rat] :
% 13.71/7.69 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 13.71/7.69 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1445_less__eq__option__Some,axiom,
% 13.71/7.69 ! [X: num,Y: num] :
% 13.71/7.69 ( ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 13.71/7.69 = ( ord_less_eq_num @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1446_less__eq__option__Some,axiom,
% 13.71/7.69 ! [X: nat,Y: nat] :
% 13.71/7.69 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 13.71/7.69 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1447_less__eq__option__Some,axiom,
% 13.71/7.69 ! [X: int,Y: int] :
% 13.71/7.69 ( ( ord_le1736525451366464988on_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 13.71/7.69 = ( ord_less_eq_int @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1448_mi__eq__ma__no__ch,axiom,
% 13.71/7.69 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.71/7.69 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 13.71/7.69 => ( ( Mi = Ma )
% 13.71/7.69 => ( ! [X5: vEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.71/7.69 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 13.71/7.69 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1449_diff__shunt__var,axiom,
% 13.71/7.69 ! [X: assn,Y: assn] :
% 13.71/7.69 ( ( ( minus_minus_assn @ X @ Y )
% 13.71/7.69 = bot_bot_assn )
% 13.71/7.69 = ( ord_less_eq_assn @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1450_diff__shunt__var,axiom,
% 13.71/7.69 ! [X: set_o,Y: set_o] :
% 13.71/7.69 ( ( ( minus_minus_set_o @ X @ Y )
% 13.71/7.69 = bot_bot_set_o )
% 13.71/7.69 = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1451_diff__shunt__var,axiom,
% 13.71/7.69 ! [X: set_nat,Y: set_nat] :
% 13.71/7.69 ( ( ( minus_minus_set_nat @ X @ Y )
% 13.71/7.69 = bot_bot_set_nat )
% 13.71/7.69 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1452_diff__shunt__var,axiom,
% 13.71/7.69 ! [X: set_int,Y: set_int] :
% 13.71/7.69 ( ( ( minus_minus_set_int @ X @ Y )
% 13.71/7.69 = bot_bot_set_int )
% 13.71/7.69 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1453_prod__decode__aux_Osimps,axiom,
% 13.71/7.69 ( nat_prod_decode_aux
% 13.71/7.69 = ( ^ [K3: nat,M5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M5 @ K3 ) @ ( product_Pair_nat_nat @ M5 @ ( minus_minus_nat @ K3 @ M5 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M5 @ ( suc @ K3 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1454_prod__decode__aux_Oelims,axiom,
% 13.71/7.69 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 13.71/7.69 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 13.71/7.69 = Y )
% 13.71/7.69 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 13.71/7.69 => ( Y
% 13.71/7.69 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 13.71/7.69 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 13.71/7.69 => ( Y
% 13.71/7.69 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1455_VEBT__internal_Omembermima_Ocases,axiom,
% 13.71/7.69 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.69 ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 13.71/7.69 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz2: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz2 ) )
% 13.71/7.69 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X3 ) )
% 13.71/7.69 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ X3 ) )
% 13.71/7.69 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X3 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1456_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Ocases,axiom,
% 13.71/7.69 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.69 ( ! [A3: $o,B3: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) )
% 13.71/7.69 => ( ! [A3: $o,B3: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 13.71/7.69 => ( ! [A3: $o,B3: $o,N2: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) )
% 13.71/7.69 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Uu ) )
% 13.71/7.69 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ X3 ) )
% 13.71/7.69 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 13.71/7.69 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1457_diff__diff__less,axiom,
% 13.71/7.69 ! [I: nat,M: nat,N: nat] :
% 13.71/7.69 ( ( ord_less_nat @ I @ ( minus_minus_nat @ M @ ( minus_minus_nat @ M @ N ) ) )
% 13.71/7.69 = ( ( ord_less_nat @ I @ M )
% 13.71/7.69 & ( ord_less_nat @ I @ N ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1458_Diff__empty,axiom,
% 13.71/7.69 ! [A4: set_int] :
% 13.71/7.69 ( ( minus_minus_set_int @ A4 @ bot_bot_set_int )
% 13.71/7.69 = A4 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1459_Diff__empty,axiom,
% 13.71/7.69 ! [A4: set_o] :
% 13.71/7.69 ( ( minus_minus_set_o @ A4 @ bot_bot_set_o )
% 13.71/7.69 = A4 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1460_Diff__empty,axiom,
% 13.71/7.69 ! [A4: set_nat] :
% 13.71/7.69 ( ( minus_minus_set_nat @ A4 @ bot_bot_set_nat )
% 13.71/7.69 = A4 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1461_empty__Diff,axiom,
% 13.71/7.69 ! [A4: set_int] :
% 13.71/7.69 ( ( minus_minus_set_int @ bot_bot_set_int @ A4 )
% 13.71/7.69 = bot_bot_set_int ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1462_empty__Diff,axiom,
% 13.71/7.69 ! [A4: set_o] :
% 13.71/7.69 ( ( minus_minus_set_o @ bot_bot_set_o @ A4 )
% 13.71/7.69 = bot_bot_set_o ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1463_empty__Diff,axiom,
% 13.71/7.69 ! [A4: set_nat] :
% 13.71/7.69 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A4 )
% 13.71/7.69 = bot_bot_set_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1464_Diff__cancel,axiom,
% 13.71/7.69 ! [A4: set_int] :
% 13.71/7.69 ( ( minus_minus_set_int @ A4 @ A4 )
% 13.71/7.69 = bot_bot_set_int ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1465_Diff__cancel,axiom,
% 13.71/7.69 ! [A4: set_o] :
% 13.71/7.69 ( ( minus_minus_set_o @ A4 @ A4 )
% 13.71/7.69 = bot_bot_set_o ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1466_Diff__cancel,axiom,
% 13.71/7.69 ! [A4: set_nat] :
% 13.71/7.69 ( ( minus_minus_set_nat @ A4 @ A4 )
% 13.71/7.69 = bot_bot_set_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1467_finite__Diff,axiom,
% 13.71/7.69 ! [A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( finite_finite_int @ A4 )
% 13.71/7.69 => ( finite_finite_int @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1468_finite__Diff,axiom,
% 13.71/7.69 ! [A4: set_complex,B4: set_complex] :
% 13.71/7.69 ( ( finite3207457112153483333omplex @ A4 )
% 13.71/7.69 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1469_finite__Diff,axiom,
% 13.71/7.69 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.71/7.69 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.69 => ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1470_finite__Diff,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( finite_finite_nat @ A4 )
% 13.71/7.69 => ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1471_finite__Diff2,axiom,
% 13.71/7.69 ! [B4: set_int,A4: set_int] :
% 13.71/7.69 ( ( finite_finite_int @ B4 )
% 13.71/7.69 => ( ( finite_finite_int @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.71/7.69 = ( finite_finite_int @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1472_finite__Diff2,axiom,
% 13.71/7.69 ! [B4: set_complex,A4: set_complex] :
% 13.71/7.69 ( ( finite3207457112153483333omplex @ B4 )
% 13.71/7.69 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 13.71/7.69 = ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1473_finite__Diff2,axiom,
% 13.71/7.69 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.71/7.69 ( ( finite6017078050557962740nteger @ B4 )
% 13.71/7.69 => ( ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 13.71/7.69 = ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1474_finite__Diff2,axiom,
% 13.71/7.69 ! [B4: set_nat,A4: set_nat] :
% 13.71/7.69 ( ( finite_finite_nat @ B4 )
% 13.71/7.69 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.71/7.69 = ( finite_finite_nat @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1475_Diff__eq__empty__iff,axiom,
% 13.71/7.69 ! [A4: set_o,B4: set_o] :
% 13.71/7.69 ( ( ( minus_minus_set_o @ A4 @ B4 )
% 13.71/7.69 = bot_bot_set_o )
% 13.71/7.69 = ( ord_less_eq_set_o @ A4 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1476_Diff__eq__empty__iff,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( ( minus_minus_set_nat @ A4 @ B4 )
% 13.71/7.69 = bot_bot_set_nat )
% 13.71/7.69 = ( ord_less_eq_set_nat @ A4 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1477_Diff__eq__empty__iff,axiom,
% 13.71/7.69 ! [A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( ( minus_minus_set_int @ A4 @ B4 )
% 13.71/7.69 = bot_bot_set_int )
% 13.71/7.69 = ( ord_less_eq_set_int @ A4 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1478_lesseq__shift,axiom,
% 13.71/7.69 ( ord_less_eq_nat
% 13.71/7.69 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1479_less__eq__option__None__code,axiom,
% 13.71/7.69 ! [X: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1480_less__option__None,axiom,
% 13.71/7.69 ! [X: option_nat] :
% 13.71/7.69 ~ ( ord_less_option_nat @ X @ none_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1481_not__Some__eq2,axiom,
% 13.71/7.69 ! [V2: option3972171592325465343uint32] :
% 13.71/7.69 ( ( ! [X4: uint32,Y4: uint32] :
% 13.71/7.69 ( V2
% 13.71/7.69 != ( some_P6695178580830101022uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) ) ) )
% 13.71/7.69 = ( V2 = none_P7441528354948028570uint32 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1482_not__Some__eq2,axiom,
% 13.71/7.69 ! [V2: option4624381673175914239nt_int] :
% 13.71/7.69 ( ( ! [X4: int,Y4: int] :
% 13.71/7.69 ( V2
% 13.71/7.69 != ( some_P4184893108420464158nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) ) ) )
% 13.71/7.69 = ( V2 = none_P2377608414092835994nt_int ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1483_not__Some__eq2,axiom,
% 13.71/7.69 ! [V2: option5190343406534369742et_nat] :
% 13.71/7.69 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] :
% 13.71/7.69 ( V2
% 13.71/7.69 != ( some_P750831030444334937et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) ) ) )
% 13.71/7.69 = ( V2 = none_P4972525538344268765et_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1484_not__Some__eq2,axiom,
% 13.71/7.69 ! [V2: option2860828798490689354et_nat] :
% 13.71/7.69 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] :
% 13.71/7.69 ( V2
% 13.71/7.69 != ( some_P1630309045189364437et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) ) ) )
% 13.71/7.69 = ( V2 = none_P199884684680593241et_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1485_not__Some__eq2,axiom,
% 13.71/7.69 ! [V2: option4927543243414619207at_nat] :
% 13.71/7.69 ( ( ! [X4: nat,Y4: nat] :
% 13.71/7.69 ( V2
% 13.71/7.69 != ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) ) )
% 13.71/7.69 = ( V2 = none_P5556105721700978146at_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1486_less__eq__option__Some__None,axiom,
% 13.71/7.69 ! [X: nat] :
% 13.71/7.69 ~ ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ none_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1487_less__option__None__Some__code,axiom,
% 13.71/7.69 ! [X: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1488_less__eq__option__None,axiom,
% 13.71/7.69 ! [X: option_nat] : ( ord_le5914376470875661696on_nat @ none_nat @ X ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1489_less__eq__option__None__is__None,axiom,
% 13.71/7.69 ! [X: option_nat] :
% 13.71/7.69 ( ( ord_le5914376470875661696on_nat @ X @ none_nat )
% 13.71/7.69 => ( X = none_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1490_less__option__None__Some,axiom,
% 13.71/7.69 ! [X: nat] : ( ord_less_option_nat @ none_nat @ ( some_nat @ X ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1491_less__option__None__is__Some,axiom,
% 13.71/7.69 ! [X: option_nat] :
% 13.71/7.69 ( ( ord_less_option_nat @ none_nat @ X )
% 13.71/7.69 => ? [Z3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 = ( some_nat @ Z3 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1492_Diff__infinite__finite,axiom,
% 13.71/7.69 ! [T3: set_int,S3: set_int] :
% 13.71/7.69 ( ( finite_finite_int @ T3 )
% 13.71/7.69 => ( ~ ( finite_finite_int @ S3 )
% 13.71/7.69 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S3 @ T3 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1493_Diff__infinite__finite,axiom,
% 13.71/7.69 ! [T3: set_complex,S3: set_complex] :
% 13.71/7.69 ( ( finite3207457112153483333omplex @ T3 )
% 13.71/7.69 => ( ~ ( finite3207457112153483333omplex @ S3 )
% 13.71/7.69 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S3 @ T3 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1494_Diff__infinite__finite,axiom,
% 13.71/7.69 ! [T3: set_Code_integer,S3: set_Code_integer] :
% 13.71/7.69 ( ( finite6017078050557962740nteger @ T3 )
% 13.71/7.69 => ( ~ ( finite6017078050557962740nteger @ S3 )
% 13.71/7.69 => ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ S3 @ T3 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1495_Diff__infinite__finite,axiom,
% 13.71/7.69 ! [T3: set_nat,S3: set_nat] :
% 13.71/7.69 ( ( finite_finite_nat @ T3 )
% 13.71/7.69 => ( ~ ( finite_finite_nat @ S3 )
% 13.71/7.69 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S3 @ T3 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1496_Diff__mono,axiom,
% 13.71/7.69 ! [A4: set_nat,C3: set_nat,D4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( ord_less_eq_set_nat @ A4 @ C3 )
% 13.71/7.69 => ( ( ord_less_eq_set_nat @ D4 @ B4 )
% 13.71/7.69 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ ( minus_minus_set_nat @ C3 @ D4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1497_Diff__mono,axiom,
% 13.71/7.69 ! [A4: set_int,C3: set_int,D4: set_int,B4: set_int] :
% 13.71/7.69 ( ( ord_less_eq_set_int @ A4 @ C3 )
% 13.71/7.69 => ( ( ord_less_eq_set_int @ D4 @ B4 )
% 13.71/7.69 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B4 ) @ ( minus_minus_set_int @ C3 @ D4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1498_Diff__subset,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ A4 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1499_Diff__subset,axiom,
% 13.71/7.69 ! [A4: set_int,B4: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ B4 ) @ A4 ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1500_double__diff,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat,C3: set_nat] :
% 13.71/7.69 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.71/7.69 => ( ( ord_less_eq_set_nat @ B4 @ C3 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C3 @ A4 ) )
% 13.71/7.69 = A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1501_double__diff,axiom,
% 13.71/7.69 ! [A4: set_int,B4: set_int,C3: set_int] :
% 13.71/7.69 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.69 => ( ( ord_less_eq_set_int @ B4 @ C3 )
% 13.71/7.69 => ( ( minus_minus_set_int @ B4 @ ( minus_minus_set_int @ C3 @ A4 ) )
% 13.71/7.69 = A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1502_psubset__imp__ex__mem,axiom,
% 13.71/7.69 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( ord_le3480810397992357184T_VEBT @ A4 @ B4 )
% 13.71/7.69 => ? [B3: vEBT_VEBT] : ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1503_psubset__imp__ex__mem,axiom,
% 13.71/7.69 ! [A4: set_real,B4: set_real] :
% 13.71/7.69 ( ( ord_less_set_real @ A4 @ B4 )
% 13.71/7.69 => ? [B3: real] : ( member_real @ B3 @ ( minus_minus_set_real @ B4 @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1504_psubset__imp__ex__mem,axiom,
% 13.71/7.69 ! [A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( ord_less_set_int @ A4 @ B4 )
% 13.71/7.69 => ? [B3: int] : ( member_int @ B3 @ ( minus_minus_set_int @ B4 @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1505_psubset__imp__ex__mem,axiom,
% 13.71/7.69 ! [A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ( ord_less_set_set_nat @ A4 @ B4 )
% 13.71/7.69 => ? [B3: set_nat] : ( member_set_nat @ B3 @ ( minus_2163939370556025621et_nat @ B4 @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1506_psubset__imp__ex__mem,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( ord_less_set_nat @ A4 @ B4 )
% 13.71/7.69 => ? [B3: nat] : ( member_nat @ B3 @ ( minus_minus_set_nat @ B4 @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1507_subset__minus__empty,axiom,
% 13.71/7.69 ! [A4: set_o,B4: set_o] :
% 13.71/7.69 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_o @ A4 @ B4 )
% 13.71/7.69 = bot_bot_set_o ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1508_subset__minus__empty,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ A4 @ B4 )
% 13.71/7.69 = bot_bot_set_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1509_subset__minus__empty,axiom,
% 13.71/7.69 ! [A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_int @ A4 @ B4 )
% 13.71/7.69 = bot_bot_set_int ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1510_vebt__delete_Osimps_I4_J,axiom,
% 13.71/7.69 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 13.71/7.69 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu2 )
% 13.71/7.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1511_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 13.71/7.69 ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1512_vebt__member_Osimps_I2_J,axiom,
% 13.71/7.69 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X: nat] :
% 13.71/7.69 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1513_vebt__member__code_I2_J,axiom,
% 13.71/7.69 ! [T: nat,R: list_VEBT_VEBT,E2: vEBT_VEBT,X: nat] :
% 13.71/7.69 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ T @ R @ E2 ) @ X ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1514_bijective__def,axiom,
% 13.71/7.69 ( biject2923219584331114343uint32
% 13.71/7.69 = ( ^ [R3: set_Pr1773385645901665561uint32] :
% 13.71/7.69 ( ! [X4: uint32,Y4: uint32,Z2: uint32] :
% 13.71/7.69 ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R3 )
% 13.71/7.69 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( Y4 = Z2 ) )
% 13.71/7.69 & ! [X4: uint32,Y4: uint32,Z2: uint32] :
% 13.71/7.69 ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Z2 ) @ R3 )
% 13.71/7.69 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( X4 = Y4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1515_bijective__def,axiom,
% 13.71/7.69 ( bijective_nat_nat
% 13.71/7.69 = ( ^ [R3: set_Pr1261947904930325089at_nat] :
% 13.71/7.69 ( ! [X4: nat,Y4: nat,Z2: nat] :
% 13.71/7.69 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R3 )
% 13.71/7.69 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( Y4 = Z2 ) )
% 13.71/7.69 & ! [X4: nat,Y4: nat,Z2: nat] :
% 13.71/7.69 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Z2 ) @ R3 )
% 13.71/7.69 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( X4 = Y4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1516_bijective__def,axiom,
% 13.71/7.69 ( bijective_int_int
% 13.71/7.69 = ( ^ [R3: set_Pr958786334691620121nt_int] :
% 13.71/7.69 ( ! [X4: int,Y4: int,Z2: int] :
% 13.71/7.69 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R3 )
% 13.71/7.69 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( Y4 = Z2 ) )
% 13.71/7.69 & ! [X4: int,Y4: int,Z2: int] :
% 13.71/7.69 ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Z2 ) @ R3 )
% 13.71/7.69 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( X4 = Y4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1517_bijective__def,axiom,
% 13.71/7.69 ( biject2615096655818420098et_nat
% 13.71/7.69 = ( ^ [R3: set_Pr3286484037609594932et_nat] :
% 13.71/7.69 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat,Z2: produc3658429121746597890et_nat] :
% 13.71/7.69 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R3 )
% 13.71/7.69 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( Y4 = Z2 ) )
% 13.71/7.69 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z2: produc3658429121746597890et_nat] :
% 13.71/7.69 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z2 ) @ R3 )
% 13.71/7.69 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( X4 = Y4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1518_bijective__def,axiom,
% 13.71/7.69 ( biject1468766312547416318et_nat
% 13.71/7.69 = ( ^ [R3: set_Pr8536935166611901872et_nat] :
% 13.71/7.69 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat,Z2: produc3925858234332021118et_nat] :
% 13.71/7.69 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R3 )
% 13.71/7.69 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( Y4 = Z2 ) )
% 13.71/7.69 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z2: produc3925858234332021118et_nat] :
% 13.71/7.69 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z2 ) @ R3 )
% 13.71/7.69 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y4 @ Z2 ) @ R3 ) )
% 13.71/7.69 => ( X4 = Y4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1519_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT] :
% 13.71/7.69 ( ( vEBT_VEBT_minNull @ X )
% 13.71/7.69 => ( ( X
% 13.71/7.69 != ( vEBT_Leaf @ $false @ $false ) )
% 13.71/7.69 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1520_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 13.71/7.69 ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz: nat] :
% 13.71/7.69 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1521_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J,axiom,
% 13.71/7.69 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 13.71/7.69 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu2 )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1522_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I4_J,axiom,
% 13.71/7.69 ! [Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu2: nat] :
% 13.71/7.69 ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Uu2 )
% 13.71/7.69 = one_one_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1523_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,Y: $o] :
% 13.71/7.69 ( ( ( vEBT_VEBT_minNull @ X )
% 13.71/7.69 = Y )
% 13.71/7.69 => ( ( ( X
% 13.71/7.69 = ( vEBT_Leaf @ $false @ $false ) )
% 13.71/7.69 => ~ Y )
% 13.71/7.69 => ( ( ? [Uv: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 = ( vEBT_Leaf @ $true @ Uv ) )
% 13.71/7.69 => Y )
% 13.71/7.69 => ( ( ? [Uu: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 = ( vEBT_Leaf @ Uu @ $true ) )
% 13.71/7.69 => Y )
% 13.71/7.69 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 13.71/7.69 => ~ Y )
% 13.71/7.69 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 13.71/7.69 => Y ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1524_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases,axiom,
% 13.71/7.69 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.69 ( ! [Uu: $o,Uv: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) )
% 13.71/7.69 => ( ! [A3: $o,Uw: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 13.71/7.69 => ( ! [A3: $o,B3: $o,Va: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) )
% 13.71/7.69 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Vb2 ) )
% 13.71/7.69 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf ) )
% 13.71/7.69 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 13.71/7.69 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1525_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases,axiom,
% 13.71/7.69 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.69 ( ! [Uu: $o,B3: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) )
% 13.71/7.69 => ( ! [Uv: $o,Uw: $o,N2: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) )
% 13.71/7.69 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Va3 ) )
% 13.71/7.69 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve ) )
% 13.71/7.69 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 13.71/7.69 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1526_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases,axiom,
% 13.71/7.69 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.69 ( ! [A3: $o,B3: $o,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 13.71/7.69 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ X3 ) )
% 13.71/7.69 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ X3 ) )
% 13.71/7.69 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ X3 ) )
% 13.71/7.69 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1527_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 13.71/7.69 ! [X: produc9072475918466114483BT_nat] :
% 13.71/7.69 ( ! [A3: $o,B3: $o,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 13.71/7.69 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X3 ) )
% 13.71/7.69 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ X3 ) )
% 13.71/7.69 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 13.71/7.69 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1528_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT] :
% 13.71/7.69 ( ! [A3: $o,B3: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Leaf @ A3 @ B3 ) )
% 13.71/7.69 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.71/7.69 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1529_List_Ofinite__set,axiom,
% 13.71/7.69 ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1530_List_Ofinite__set,axiom,
% 13.71/7.69 ! [Xs: list_real] : ( finite_finite_real @ ( set_real2 @ Xs ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1531_List_Ofinite__set,axiom,
% 13.71/7.69 ! [Xs: list_o] : ( finite_finite_o @ ( set_o2 @ Xs ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1532_List_Ofinite__set,axiom,
% 13.71/7.69 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1533_List_Ofinite__set,axiom,
% 13.71/7.69 ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1534_List_Ofinite__set,axiom,
% 13.71/7.69 ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1535_List_Ofinite__set,axiom,
% 13.71/7.69 ! [Xs: list_Code_integer] : ( finite6017078050557962740nteger @ ( set_Code_integer2 @ Xs ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1536_delete__correct,axiom,
% 13.71/7.69 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.69 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.69 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 13.71/7.69 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1537_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT] :
% 13.71/7.69 ( ( X
% 13.71/7.69 != ( vEBT_Leaf @ $false @ $false ) )
% 13.71/7.69 => ( ! [Uv: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Leaf @ $true @ Uv ) )
% 13.71/7.69 => ( ! [Uu: $o] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Leaf @ Uu @ $true ) )
% 13.71/7.69 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 13.71/7.69 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.71/7.69 ( X
% 13.71/7.69 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1538_insertCI,axiom,
% 13.71/7.69 ! [A: $o,B4: set_o,B: $o] :
% 13.71/7.69 ( ( ~ ( member_o @ A @ B4 )
% 13.71/7.69 => ( A = B ) )
% 13.71/7.69 => ( member_o @ A @ ( insert_o @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1539_insertCI,axiom,
% 13.71/7.69 ! [A: nat,B4: set_nat,B: nat] :
% 13.71/7.69 ( ( ~ ( member_nat @ A @ B4 )
% 13.71/7.69 => ( A = B ) )
% 13.71/7.69 => ( member_nat @ A @ ( insert_nat @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1540_insertCI,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,B4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 13.71/7.69 ( ( ~ ( member_VEBT_VEBT @ A @ B4 )
% 13.71/7.69 => ( A = B ) )
% 13.71/7.69 => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1541_insertCI,axiom,
% 13.71/7.69 ! [A: real,B4: set_real,B: real] :
% 13.71/7.69 ( ( ~ ( member_real @ A @ B4 )
% 13.71/7.69 => ( A = B ) )
% 13.71/7.69 => ( member_real @ A @ ( insert_real @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1542_insertCI,axiom,
% 13.71/7.69 ! [A: int,B4: set_int,B: int] :
% 13.71/7.69 ( ( ~ ( member_int @ A @ B4 )
% 13.71/7.69 => ( A = B ) )
% 13.71/7.69 => ( member_int @ A @ ( insert_int @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1543_insertCI,axiom,
% 13.71/7.69 ! [A: set_nat,B4: set_set_nat,B: set_nat] :
% 13.71/7.69 ( ( ~ ( member_set_nat @ A @ B4 )
% 13.71/7.69 => ( A = B ) )
% 13.71/7.69 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1544_insert__iff,axiom,
% 13.71/7.69 ! [A: $o,B: $o,A4: set_o] :
% 13.71/7.69 ( ( member_o @ A @ ( insert_o @ B @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 | ( member_o @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1545_insert__iff,axiom,
% 13.71/7.69 ! [A: nat,B: nat,A4: set_nat] :
% 13.71/7.69 ( ( member_nat @ A @ ( insert_nat @ B @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 | ( member_nat @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1546_insert__iff,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,B: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 | ( member_VEBT_VEBT @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1547_insert__iff,axiom,
% 13.71/7.69 ! [A: real,B: real,A4: set_real] :
% 13.71/7.69 ( ( member_real @ A @ ( insert_real @ B @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 | ( member_real @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1548_insert__iff,axiom,
% 13.71/7.69 ! [A: int,B: int,A4: set_int] :
% 13.71/7.69 ( ( member_int @ A @ ( insert_int @ B @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 | ( member_int @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1549_insert__iff,axiom,
% 13.71/7.69 ! [A: set_nat,B: set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 | ( member_set_nat @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1550_insert__absorb2,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat] :
% 13.71/7.69 ( ( insert_nat @ X @ ( insert_nat @ X @ A4 ) )
% 13.71/7.69 = ( insert_nat @ X @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1551_insert__absorb2,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( insert_VEBT_VEBT @ X @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.71/7.69 = ( insert_VEBT_VEBT @ X @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1552_insert__absorb2,axiom,
% 13.71/7.69 ! [X: int,A4: set_int] :
% 13.71/7.69 ( ( insert_int @ X @ ( insert_int @ X @ A4 ) )
% 13.71/7.69 = ( insert_int @ X @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1553_insert__absorb2,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o] :
% 13.71/7.69 ( ( insert_o @ X @ ( insert_o @ X @ A4 ) )
% 13.71/7.69 = ( insert_o @ X @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1554_DiffI,axiom,
% 13.71/7.69 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ C2 @ A4 )
% 13.71/7.69 => ( ~ ( member_VEBT_VEBT @ C2 @ B4 )
% 13.71/7.69 => ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1555_DiffI,axiom,
% 13.71/7.69 ! [C2: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ( member_real @ C2 @ A4 )
% 13.71/7.69 => ( ~ ( member_real @ C2 @ B4 )
% 13.71/7.69 => ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1556_DiffI,axiom,
% 13.71/7.69 ! [C2: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( member_int @ C2 @ A4 )
% 13.71/7.69 => ( ~ ( member_int @ C2 @ B4 )
% 13.71/7.69 => ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1557_DiffI,axiom,
% 13.71/7.69 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ C2 @ A4 )
% 13.71/7.69 => ( ~ ( member_set_nat @ C2 @ B4 )
% 13.71/7.69 => ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1558_DiffI,axiom,
% 13.71/7.69 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( member_nat @ C2 @ A4 )
% 13.71/7.69 => ( ~ ( member_nat @ C2 @ B4 )
% 13.71/7.69 => ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1559_Diff__iff,axiom,
% 13.71/7.69 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 13.71/7.69 = ( ( member_VEBT_VEBT @ C2 @ A4 )
% 13.71/7.69 & ~ ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1560_Diff__iff,axiom,
% 13.71/7.69 ! [C2: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 13.71/7.69 = ( ( member_real @ C2 @ A4 )
% 13.71/7.69 & ~ ( member_real @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1561_Diff__iff,axiom,
% 13.71/7.69 ! [C2: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.71/7.69 = ( ( member_int @ C2 @ A4 )
% 13.71/7.69 & ~ ( member_int @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1562_Diff__iff,axiom,
% 13.71/7.69 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 13.71/7.69 = ( ( member_set_nat @ C2 @ A4 )
% 13.71/7.69 & ~ ( member_set_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1563_Diff__iff,axiom,
% 13.71/7.69 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.71/7.69 = ( ( member_nat @ C2 @ A4 )
% 13.71/7.69 & ~ ( member_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1564_Diff__idemp,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_nat @ A4 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1565_set__vebt__delete,axiom,
% 13.71/7.69 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.69 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.69 => ( ( vEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 13.71/7.69 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1566_delete__correct_H,axiom,
% 13.71/7.69 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.71/7.69 ( ( vEBT_invar_vebt @ T @ N )
% 13.71/7.69 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 13.71/7.69 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1567_singletonI,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1568_singletonI,axiom,
% 13.71/7.69 ! [A: real] : ( member_real @ A @ ( insert_real @ A @ bot_bot_set_real ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1569_singletonI,axiom,
% 13.71/7.69 ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1570_singletonI,axiom,
% 13.71/7.69 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1571_singletonI,axiom,
% 13.71/7.69 ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1572_singletonI,axiom,
% 13.71/7.69 ! [A: $o] : ( member_o @ A @ ( insert_o @ A @ bot_bot_set_o ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1573_finite__insert,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( finite5795047828879050333T_VEBT @ ( insert_VEBT_VEBT @ A @ A4 ) )
% 13.71/7.69 = ( finite5795047828879050333T_VEBT @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1574_finite__insert,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o] :
% 13.71/7.69 ( ( finite_finite_o @ ( insert_o @ A @ A4 ) )
% 13.71/7.69 = ( finite_finite_o @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1575_finite__insert,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat] :
% 13.71/7.69 ( ( finite_finite_nat @ ( insert_nat @ A @ A4 ) )
% 13.71/7.69 = ( finite_finite_nat @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1576_finite__insert,axiom,
% 13.71/7.69 ! [A: int,A4: set_int] :
% 13.71/7.69 ( ( finite_finite_int @ ( insert_int @ A @ A4 ) )
% 13.71/7.69 = ( finite_finite_int @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1577_finite__insert,axiom,
% 13.71/7.69 ! [A: complex,A4: set_complex] :
% 13.71/7.69 ( ( finite3207457112153483333omplex @ ( insert_complex @ A @ A4 ) )
% 13.71/7.69 = ( finite3207457112153483333omplex @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1578_finite__insert,axiom,
% 13.71/7.69 ! [A: code_integer,A4: set_Code_integer] :
% 13.71/7.69 ( ( finite6017078050557962740nteger @ ( insert_Code_integer @ A @ A4 ) )
% 13.71/7.69 = ( finite6017078050557962740nteger @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1579_insert__subset,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o,B4: set_o] :
% 13.71/7.69 ( ( ord_less_eq_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( ( member_o @ X @ B4 )
% 13.71/7.69 & ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1580_insert__subset,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( ( member_nat @ X @ B4 )
% 13.71/7.69 & ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1581_insert__subset,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( ( member_VEBT_VEBT @ X @ B4 )
% 13.71/7.69 & ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1582_insert__subset,axiom,
% 13.71/7.69 ! [X: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ( ord_less_eq_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( ( member_real @ X @ B4 )
% 13.71/7.69 & ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1583_insert__subset,axiom,
% 13.71/7.69 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( ( member_set_nat @ X @ B4 )
% 13.71/7.69 & ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1584_insert__subset,axiom,
% 13.71/7.69 ! [X: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( ( member_int @ X @ B4 )
% 13.71/7.69 & ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1585_Diff__insert0,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o,B4: set_o] :
% 13.71/7.69 ( ~ ( member_o @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_o @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1586_Diff__insert0,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.71/7.69 => ( ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 13.71/7.69 = ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1587_Diff__insert0,axiom,
% 13.71/7.69 ! [X: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ~ ( member_real @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_real @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1588_Diff__insert0,axiom,
% 13.71/7.69 ! [X: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ~ ( member_int @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1589_Diff__insert0,axiom,
% 13.71/7.69 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ~ ( member_set_nat @ X @ A4 )
% 13.71/7.69 => ( ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 13.71/7.69 = ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1590_Diff__insert0,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ~ ( member_nat @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1591_insert__Diff1,axiom,
% 13.71/7.69 ! [X: $o,B4: set_o,A4: set_o] :
% 13.71/7.69 ( ( member_o @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_o @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1592_insert__Diff1,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,B4: set_VEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ X @ B4 )
% 13.71/7.69 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1593_insert__Diff1,axiom,
% 13.71/7.69 ! [X: real,B4: set_real,A4: set_real] :
% 13.71/7.69 ( ( member_real @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_real @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1594_insert__Diff1,axiom,
% 13.71/7.69 ! [X: int,B4: set_int,A4: set_int] :
% 13.71/7.69 ( ( member_int @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1595_insert__Diff1,axiom,
% 13.71/7.69 ! [X: set_nat,B4: set_set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ X @ B4 )
% 13.71/7.69 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1596_insert__Diff1,axiom,
% 13.71/7.69 ! [X: nat,B4: set_nat,A4: set_nat] :
% 13.71/7.69 ( ( member_nat @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1597_singleton__insert__inj__eq_H,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 13.71/7.69 ( ( ( insert_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 = ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1598_singleton__insert__inj__eq_H,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat,B: nat] :
% 13.71/7.69 ( ( ( insert_nat @ A @ A4 )
% 13.71/7.69 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1599_singleton__insert__inj__eq_H,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o,B: $o] :
% 13.71/7.69 ( ( ( insert_o @ A @ A4 )
% 13.71/7.69 = ( insert_o @ B @ bot_bot_set_o ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1600_singleton__insert__inj__eq_H,axiom,
% 13.71/7.69 ! [A: int,A4: set_int,B: int] :
% 13.71/7.69 ( ( ( insert_int @ A @ A4 )
% 13.71/7.69 = ( insert_int @ B @ bot_bot_set_int ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1601_singleton__insert__inj__eq,axiom,
% 13.71/7.69 ! [B: vEBT_VEBT,A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT )
% 13.71/7.69 = ( insert_VEBT_VEBT @ A @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1602_singleton__insert__inj__eq,axiom,
% 13.71/7.69 ! [B: nat,A: nat,A4: set_nat] :
% 13.71/7.69 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 13.71/7.69 = ( insert_nat @ A @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1603_singleton__insert__inj__eq,axiom,
% 13.71/7.69 ! [B: $o,A: $o,A4: set_o] :
% 13.71/7.69 ( ( ( insert_o @ B @ bot_bot_set_o )
% 13.71/7.69 = ( insert_o @ A @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1604_singleton__insert__inj__eq,axiom,
% 13.71/7.69 ! [B: int,A: int,A4: set_int] :
% 13.71/7.69 ( ( ( insert_int @ B @ bot_bot_set_int )
% 13.71/7.69 = ( insert_int @ A @ A4 ) )
% 13.71/7.69 = ( ( A = B )
% 13.71/7.69 & ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1605_insert__Diff__single,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.71/7.69 = ( insert_VEBT_VEBT @ A @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1606_insert__Diff__single,axiom,
% 13.71/7.69 ! [A: int,A4: set_int] :
% 13.71/7.69 ( ( insert_int @ A @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.71/7.69 = ( insert_int @ A @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1607_insert__Diff__single,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o] :
% 13.71/7.69 ( ( insert_o @ A @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.71/7.69 = ( insert_o @ A @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1608_insert__Diff__single,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat] :
% 13.71/7.69 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 13.71/7.69 = ( insert_nat @ A @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1609_finite__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) ) )
% 13.71/7.69 = ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1610_finite__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_o,A: $o,B4: set_o] :
% 13.71/7.69 ( ( finite_finite_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) ) )
% 13.71/7.69 = ( finite_finite_o @ ( minus_minus_set_o @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1611_finite__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_int,A: int,B4: set_int] :
% 13.71/7.69 ( ( finite_finite_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) ) )
% 13.71/7.69 = ( finite_finite_int @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1612_finite__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_complex,A: complex,B4: set_complex] :
% 13.71/7.69 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ B4 ) ) )
% 13.71/7.69 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1613_finite__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_Code_integer,A: code_integer,B4: set_Code_integer] :
% 13.71/7.69 ( ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ B4 ) ) )
% 13.71/7.69 = ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1614_finite__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_nat,A: nat,B4: set_nat] :
% 13.71/7.69 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) ) )
% 13.71/7.69 = ( finite_finite_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1615_DiffE,axiom,
% 13.71/7.69 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( ( member_VEBT_VEBT @ C2 @ A4 )
% 13.71/7.69 => ( member_VEBT_VEBT @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1616_DiffE,axiom,
% 13.71/7.69 ! [C2: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( ( member_real @ C2 @ A4 )
% 13.71/7.69 => ( member_real @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1617_DiffE,axiom,
% 13.71/7.69 ! [C2: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( ( member_int @ C2 @ A4 )
% 13.71/7.69 => ( member_int @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1618_DiffE,axiom,
% 13.71/7.69 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( ( member_set_nat @ C2 @ A4 )
% 13.71/7.69 => ( member_set_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1619_DiffE,axiom,
% 13.71/7.69 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( ( member_nat @ C2 @ A4 )
% 13.71/7.69 => ( member_nat @ C2 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1620_DiffD1,axiom,
% 13.71/7.69 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 13.71/7.69 => ( member_VEBT_VEBT @ C2 @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1621_DiffD1,axiom,
% 13.71/7.69 ! [C2: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 13.71/7.69 => ( member_real @ C2 @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1622_DiffD1,axiom,
% 13.71/7.69 ! [C2: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.71/7.69 => ( member_int @ C2 @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1623_DiffD1,axiom,
% 13.71/7.69 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 13.71/7.69 => ( member_set_nat @ C2 @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1624_DiffD1,axiom,
% 13.71/7.69 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.71/7.69 => ( member_nat @ C2 @ A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1625_DiffD2,axiom,
% 13.71/7.69 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ C2 @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( member_VEBT_VEBT @ C2 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1626_DiffD2,axiom,
% 13.71/7.69 ! [C2: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ( member_real @ C2 @ ( minus_minus_set_real @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( member_real @ C2 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1627_DiffD2,axiom,
% 13.71/7.69 ! [C2: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ( member_int @ C2 @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( member_int @ C2 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1628_DiffD2,axiom,
% 13.71/7.69 ! [C2: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ C2 @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( member_set_nat @ C2 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1629_DiffD2,axiom,
% 13.71/7.69 ! [C2: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ( member_nat @ C2 @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.71/7.69 => ~ ( member_nat @ C2 @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1630_insert__Diff__if,axiom,
% 13.71/7.69 ! [X: $o,B4: set_o,A4: set_o] :
% 13.71/7.69 ( ( ( member_o @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_o @ A4 @ B4 ) ) )
% 13.71/7.69 & ( ~ ( member_o @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( insert_o @ X @ ( minus_minus_set_o @ A4 @ B4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1631_insert__Diff__if,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,B4: set_VEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( ( member_VEBT_VEBT @ X @ B4 )
% 13.71/7.69 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) )
% 13.71/7.69 & ( ~ ( member_VEBT_VEBT @ X @ B4 )
% 13.71/7.69 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1632_insert__Diff__if,axiom,
% 13.71/7.69 ! [X: real,B4: set_real,A4: set_real] :
% 13.71/7.69 ( ( ( member_real @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_real @ A4 @ B4 ) ) )
% 13.71/7.69 & ( ~ ( member_real @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( insert_real @ X @ ( minus_minus_set_real @ A4 @ B4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1633_insert__Diff__if,axiom,
% 13.71/7.69 ! [X: int,B4: set_int,A4: set_int] :
% 13.71/7.69 ( ( ( member_int @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_int @ A4 @ B4 ) ) )
% 13.71/7.69 & ( ~ ( member_int @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( insert_int @ X @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1634_insert__Diff__if,axiom,
% 13.71/7.69 ! [X: set_nat,B4: set_set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( ( member_set_nat @ X @ B4 )
% 13.71/7.69 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) )
% 13.71/7.69 & ( ~ ( member_set_nat @ X @ B4 )
% 13.71/7.69 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1635_insert__Diff__if,axiom,
% 13.71/7.69 ! [X: nat,B4: set_nat,A4: set_nat] :
% 13.71/7.69 ( ( ( member_nat @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( minus_minus_set_nat @ A4 @ B4 ) ) )
% 13.71/7.69 & ( ~ ( member_nat @ X @ B4 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ B4 )
% 13.71/7.69 = ( insert_nat @ X @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1636_insertE,axiom,
% 13.71/7.69 ! [A: $o,B: $o,A4: set_o] :
% 13.71/7.69 ( ( member_o @ A @ ( insert_o @ B @ A4 ) )
% 13.71/7.69 => ( ( A = ~ B )
% 13.71/7.69 => ( member_o @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1637_insertE,axiom,
% 13.71/7.69 ! [A: nat,B: nat,A4: set_nat] :
% 13.71/7.69 ( ( member_nat @ A @ ( insert_nat @ B @ A4 ) )
% 13.71/7.69 => ( ( A != B )
% 13.71/7.69 => ( member_nat @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1638_insertE,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,B: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ A4 ) )
% 13.71/7.69 => ( ( A != B )
% 13.71/7.69 => ( member_VEBT_VEBT @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1639_insertE,axiom,
% 13.71/7.69 ! [A: real,B: real,A4: set_real] :
% 13.71/7.69 ( ( member_real @ A @ ( insert_real @ B @ A4 ) )
% 13.71/7.69 => ( ( A != B )
% 13.71/7.69 => ( member_real @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1640_insertE,axiom,
% 13.71/7.69 ! [A: int,B: int,A4: set_int] :
% 13.71/7.69 ( ( member_int @ A @ ( insert_int @ B @ A4 ) )
% 13.71/7.69 => ( ( A != B )
% 13.71/7.69 => ( member_int @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1641_insertE,axiom,
% 13.71/7.69 ! [A: set_nat,B: set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ A @ ( insert_set_nat @ B @ A4 ) )
% 13.71/7.69 => ( ( A != B )
% 13.71/7.69 => ( member_set_nat @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1642_insertI1,axiom,
% 13.71/7.69 ! [A: $o,B4: set_o] : ( member_o @ A @ ( insert_o @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1643_insertI1,axiom,
% 13.71/7.69 ! [A: nat,B4: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1644_insertI1,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,B4: set_VEBT_VEBT] : ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1645_insertI1,axiom,
% 13.71/7.69 ! [A: real,B4: set_real] : ( member_real @ A @ ( insert_real @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1646_insertI1,axiom,
% 13.71/7.69 ! [A: int,B4: set_int] : ( member_int @ A @ ( insert_int @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1647_insertI1,axiom,
% 13.71/7.69 ! [A: set_nat,B4: set_set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1648_insertI2,axiom,
% 13.71/7.69 ! [A: $o,B4: set_o,B: $o] :
% 13.71/7.69 ( ( member_o @ A @ B4 )
% 13.71/7.69 => ( member_o @ A @ ( insert_o @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1649_insertI2,axiom,
% 13.71/7.69 ! [A: nat,B4: set_nat,B: nat] :
% 13.71/7.69 ( ( member_nat @ A @ B4 )
% 13.71/7.69 => ( member_nat @ A @ ( insert_nat @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1650_insertI2,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,B4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ A @ B4 )
% 13.71/7.69 => ( member_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1651_insertI2,axiom,
% 13.71/7.69 ! [A: real,B4: set_real,B: real] :
% 13.71/7.69 ( ( member_real @ A @ B4 )
% 13.71/7.69 => ( member_real @ A @ ( insert_real @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1652_insertI2,axiom,
% 13.71/7.69 ! [A: int,B4: set_int,B: int] :
% 13.71/7.69 ( ( member_int @ A @ B4 )
% 13.71/7.69 => ( member_int @ A @ ( insert_int @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1653_insertI2,axiom,
% 13.71/7.69 ! [A: set_nat,B4: set_set_nat,B: set_nat] :
% 13.71/7.69 ( ( member_set_nat @ A @ B4 )
% 13.71/7.69 => ( member_set_nat @ A @ ( insert_set_nat @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1654_Set_Oset__insert,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o] :
% 13.71/7.69 ( ( member_o @ X @ A4 )
% 13.71/7.69 => ~ ! [B8: set_o] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_o @ X @ B8 ) )
% 13.71/7.69 => ( member_o @ X @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1655_Set_Oset__insert,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat] :
% 13.71/7.69 ( ( member_nat @ X @ A4 )
% 13.71/7.69 => ~ ! [B8: set_nat] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_nat @ X @ B8 ) )
% 13.71/7.69 => ( member_nat @ X @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1656_Set_Oset__insert,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.71/7.69 => ~ ! [B8: set_VEBT_VEBT] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_VEBT_VEBT @ X @ B8 ) )
% 13.71/7.69 => ( member_VEBT_VEBT @ X @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1657_Set_Oset__insert,axiom,
% 13.71/7.69 ! [X: real,A4: set_real] :
% 13.71/7.69 ( ( member_real @ X @ A4 )
% 13.71/7.69 => ~ ! [B8: set_real] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_real @ X @ B8 ) )
% 13.71/7.69 => ( member_real @ X @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1658_Set_Oset__insert,axiom,
% 13.71/7.69 ! [X: int,A4: set_int] :
% 13.71/7.69 ( ( member_int @ X @ A4 )
% 13.71/7.69 => ~ ! [B8: set_int] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_int @ X @ B8 ) )
% 13.71/7.69 => ( member_int @ X @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1659_Set_Oset__insert,axiom,
% 13.71/7.69 ! [X: set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ X @ A4 )
% 13.71/7.69 => ~ ! [B8: set_set_nat] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_set_nat @ X @ B8 ) )
% 13.71/7.69 => ( member_set_nat @ X @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1660_insert__ident,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o,B4: set_o] :
% 13.71/7.69 ( ~ ( member_o @ X @ A4 )
% 13.71/7.69 => ( ~ ( member_o @ X @ B4 )
% 13.71/7.69 => ( ( ( insert_o @ X @ A4 )
% 13.71/7.69 = ( insert_o @ X @ B4 ) )
% 13.71/7.69 = ( A4 = B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1661_insert__ident,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ~ ( member_nat @ X @ A4 )
% 13.71/7.69 => ( ~ ( member_nat @ X @ B4 )
% 13.71/7.69 => ( ( ( insert_nat @ X @ A4 )
% 13.71/7.69 = ( insert_nat @ X @ B4 ) )
% 13.71/7.69 = ( A4 = B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1662_insert__ident,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.71/7.69 => ( ~ ( member_VEBT_VEBT @ X @ B4 )
% 13.71/7.69 => ( ( ( insert_VEBT_VEBT @ X @ A4 )
% 13.71/7.69 = ( insert_VEBT_VEBT @ X @ B4 ) )
% 13.71/7.69 = ( A4 = B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1663_insert__ident,axiom,
% 13.71/7.69 ! [X: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ~ ( member_real @ X @ A4 )
% 13.71/7.69 => ( ~ ( member_real @ X @ B4 )
% 13.71/7.69 => ( ( ( insert_real @ X @ A4 )
% 13.71/7.69 = ( insert_real @ X @ B4 ) )
% 13.71/7.69 = ( A4 = B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1664_insert__ident,axiom,
% 13.71/7.69 ! [X: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ~ ( member_int @ X @ A4 )
% 13.71/7.69 => ( ~ ( member_int @ X @ B4 )
% 13.71/7.69 => ( ( ( insert_int @ X @ A4 )
% 13.71/7.69 = ( insert_int @ X @ B4 ) )
% 13.71/7.69 = ( A4 = B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1665_insert__ident,axiom,
% 13.71/7.69 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ~ ( member_set_nat @ X @ A4 )
% 13.71/7.69 => ( ~ ( member_set_nat @ X @ B4 )
% 13.71/7.69 => ( ( ( insert_set_nat @ X @ A4 )
% 13.71/7.69 = ( insert_set_nat @ X @ B4 ) )
% 13.71/7.69 = ( A4 = B4 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1666_insert__absorb,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o] :
% 13.71/7.69 ( ( member_o @ A @ A4 )
% 13.71/7.69 => ( ( insert_o @ A @ A4 )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1667_insert__absorb,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat] :
% 13.71/7.69 ( ( member_nat @ A @ A4 )
% 13.71/7.69 => ( ( insert_nat @ A @ A4 )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1668_insert__absorb,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 => ( ( insert_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1669_insert__absorb,axiom,
% 13.71/7.69 ! [A: real,A4: set_real] :
% 13.71/7.69 ( ( member_real @ A @ A4 )
% 13.71/7.69 => ( ( insert_real @ A @ A4 )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1670_insert__absorb,axiom,
% 13.71/7.69 ! [A: int,A4: set_int] :
% 13.71/7.69 ( ( member_int @ A @ A4 )
% 13.71/7.69 => ( ( insert_int @ A @ A4 )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1671_insert__absorb,axiom,
% 13.71/7.69 ! [A: set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ A @ A4 )
% 13.71/7.69 => ( ( insert_set_nat @ A @ A4 )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1672_insert__eq__iff,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o,B: $o,B4: set_o] :
% 13.71/7.69 ( ~ ( member_o @ A @ A4 )
% 13.71/7.69 => ( ~ ( member_o @ B @ B4 )
% 13.71/7.69 => ( ( ( insert_o @ A @ A4 )
% 13.71/7.69 = ( insert_o @ B @ B4 ) )
% 13.71/7.69 = ( ( ( A = B )
% 13.71/7.69 => ( A4 = B4 ) )
% 13.71/7.69 & ( ( A = ~ B )
% 13.71/7.69 => ? [C4: set_o] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_o @ B @ C4 ) )
% 13.71/7.69 & ~ ( member_o @ B @ C4 )
% 13.71/7.69 & ( B4
% 13.71/7.69 = ( insert_o @ A @ C4 ) )
% 13.71/7.69 & ~ ( member_o @ A @ C4 ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1673_insert__eq__iff,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat,B: nat,B4: set_nat] :
% 13.71/7.69 ( ~ ( member_nat @ A @ A4 )
% 13.71/7.69 => ( ~ ( member_nat @ B @ B4 )
% 13.71/7.69 => ( ( ( insert_nat @ A @ A4 )
% 13.71/7.69 = ( insert_nat @ B @ B4 ) )
% 13.71/7.69 = ( ( ( A = B )
% 13.71/7.69 => ( A4 = B4 ) )
% 13.71/7.69 & ( ( A != B )
% 13.71/7.69 => ? [C4: set_nat] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_nat @ B @ C4 ) )
% 13.71/7.69 & ~ ( member_nat @ B @ C4 )
% 13.71/7.69 & ( B4
% 13.71/7.69 = ( insert_nat @ A @ C4 ) )
% 13.71/7.69 & ~ ( member_nat @ A @ C4 ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1674_insert__eq__iff,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 => ( ~ ( member_VEBT_VEBT @ B @ B4 )
% 13.71/7.69 => ( ( ( insert_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 = ( insert_VEBT_VEBT @ B @ B4 ) )
% 13.71/7.69 = ( ( ( A = B )
% 13.71/7.69 => ( A4 = B4 ) )
% 13.71/7.69 & ( ( A != B )
% 13.71/7.69 => ? [C4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_VEBT_VEBT @ B @ C4 ) )
% 13.71/7.69 & ~ ( member_VEBT_VEBT @ B @ C4 )
% 13.71/7.69 & ( B4
% 13.71/7.69 = ( insert_VEBT_VEBT @ A @ C4 ) )
% 13.71/7.69 & ~ ( member_VEBT_VEBT @ A @ C4 ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1675_insert__eq__iff,axiom,
% 13.71/7.69 ! [A: real,A4: set_real,B: real,B4: set_real] :
% 13.71/7.69 ( ~ ( member_real @ A @ A4 )
% 13.71/7.69 => ( ~ ( member_real @ B @ B4 )
% 13.71/7.69 => ( ( ( insert_real @ A @ A4 )
% 13.71/7.69 = ( insert_real @ B @ B4 ) )
% 13.71/7.69 = ( ( ( A = B )
% 13.71/7.69 => ( A4 = B4 ) )
% 13.71/7.69 & ( ( A != B )
% 13.71/7.69 => ? [C4: set_real] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_real @ B @ C4 ) )
% 13.71/7.69 & ~ ( member_real @ B @ C4 )
% 13.71/7.69 & ( B4
% 13.71/7.69 = ( insert_real @ A @ C4 ) )
% 13.71/7.69 & ~ ( member_real @ A @ C4 ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1676_insert__eq__iff,axiom,
% 13.71/7.69 ! [A: int,A4: set_int,B: int,B4: set_int] :
% 13.71/7.69 ( ~ ( member_int @ A @ A4 )
% 13.71/7.69 => ( ~ ( member_int @ B @ B4 )
% 13.71/7.69 => ( ( ( insert_int @ A @ A4 )
% 13.71/7.69 = ( insert_int @ B @ B4 ) )
% 13.71/7.69 = ( ( ( A = B )
% 13.71/7.69 => ( A4 = B4 ) )
% 13.71/7.69 & ( ( A != B )
% 13.71/7.69 => ? [C4: set_int] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_int @ B @ C4 ) )
% 13.71/7.69 & ~ ( member_int @ B @ C4 )
% 13.71/7.69 & ( B4
% 13.71/7.69 = ( insert_int @ A @ C4 ) )
% 13.71/7.69 & ~ ( member_int @ A @ C4 ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1677_insert__eq__iff,axiom,
% 13.71/7.69 ! [A: set_nat,A4: set_set_nat,B: set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ~ ( member_set_nat @ A @ A4 )
% 13.71/7.69 => ( ~ ( member_set_nat @ B @ B4 )
% 13.71/7.69 => ( ( ( insert_set_nat @ A @ A4 )
% 13.71/7.69 = ( insert_set_nat @ B @ B4 ) )
% 13.71/7.69 = ( ( ( A = B )
% 13.71/7.69 => ( A4 = B4 ) )
% 13.71/7.69 & ( ( A != B )
% 13.71/7.69 => ? [C4: set_set_nat] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_set_nat @ B @ C4 ) )
% 13.71/7.69 & ~ ( member_set_nat @ B @ C4 )
% 13.71/7.69 & ( B4
% 13.71/7.69 = ( insert_set_nat @ A @ C4 ) )
% 13.71/7.69 & ~ ( member_set_nat @ A @ C4 ) ) ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1678_insert__commute,axiom,
% 13.71/7.69 ! [X: nat,Y: nat,A4: set_nat] :
% 13.71/7.69 ( ( insert_nat @ X @ ( insert_nat @ Y @ A4 ) )
% 13.71/7.69 = ( insert_nat @ Y @ ( insert_nat @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1679_insert__commute,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,Y: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( insert_VEBT_VEBT @ X @ ( insert_VEBT_VEBT @ Y @ A4 ) )
% 13.71/7.69 = ( insert_VEBT_VEBT @ Y @ ( insert_VEBT_VEBT @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1680_insert__commute,axiom,
% 13.71/7.69 ! [X: int,Y: int,A4: set_int] :
% 13.71/7.69 ( ( insert_int @ X @ ( insert_int @ Y @ A4 ) )
% 13.71/7.69 = ( insert_int @ Y @ ( insert_int @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1681_insert__commute,axiom,
% 13.71/7.69 ! [X: $o,Y: $o,A4: set_o] :
% 13.71/7.69 ( ( insert_o @ X @ ( insert_o @ Y @ A4 ) )
% 13.71/7.69 = ( insert_o @ Y @ ( insert_o @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1682_mk__disjoint__insert,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o] :
% 13.71/7.69 ( ( member_o @ A @ A4 )
% 13.71/7.69 => ? [B8: set_o] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_o @ A @ B8 ) )
% 13.71/7.69 & ~ ( member_o @ A @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1683_mk__disjoint__insert,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat] :
% 13.71/7.69 ( ( member_nat @ A @ A4 )
% 13.71/7.69 => ? [B8: set_nat] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_nat @ A @ B8 ) )
% 13.71/7.69 & ~ ( member_nat @ A @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1684_mk__disjoint__insert,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 => ? [B8: set_VEBT_VEBT] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_VEBT_VEBT @ A @ B8 ) )
% 13.71/7.69 & ~ ( member_VEBT_VEBT @ A @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1685_mk__disjoint__insert,axiom,
% 13.71/7.69 ! [A: real,A4: set_real] :
% 13.71/7.69 ( ( member_real @ A @ A4 )
% 13.71/7.69 => ? [B8: set_real] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_real @ A @ B8 ) )
% 13.71/7.69 & ~ ( member_real @ A @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1686_mk__disjoint__insert,axiom,
% 13.71/7.69 ! [A: int,A4: set_int] :
% 13.71/7.69 ( ( member_int @ A @ A4 )
% 13.71/7.69 => ? [B8: set_int] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_int @ A @ B8 ) )
% 13.71/7.69 & ~ ( member_int @ A @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1687_mk__disjoint__insert,axiom,
% 13.71/7.69 ! [A: set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ A @ A4 )
% 13.71/7.69 => ? [B8: set_set_nat] :
% 13.71/7.69 ( ( A4
% 13.71/7.69 = ( insert_set_nat @ A @ B8 ) )
% 13.71/7.69 & ~ ( member_set_nat @ A @ B8 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1688_singleton__inject,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,B: vEBT_VEBT] :
% 13.71/7.69 ( ( ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT )
% 13.71/7.69 = ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 => ( A = B ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1689_singleton__inject,axiom,
% 13.71/7.69 ! [A: nat,B: nat] :
% 13.71/7.69 ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 13.71/7.69 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 13.71/7.69 => ( A = B ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1690_singleton__inject,axiom,
% 13.71/7.69 ! [A: int,B: int] :
% 13.71/7.69 ( ( ( insert_int @ A @ bot_bot_set_int )
% 13.71/7.69 = ( insert_int @ B @ bot_bot_set_int ) )
% 13.71/7.69 => ( A = B ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1691_singleton__inject,axiom,
% 13.71/7.69 ! [A: $o,B: $o] :
% 13.71/7.69 ( ( ( insert_o @ A @ bot_bot_set_o )
% 13.71/7.69 = ( insert_o @ B @ bot_bot_set_o ) )
% 13.71/7.69 => ( A = B ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1692_insert__not__empty,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( insert_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 != bot_bo8194388402131092736T_VEBT ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1693_insert__not__empty,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat] :
% 13.71/7.69 ( ( insert_nat @ A @ A4 )
% 13.71/7.69 != bot_bot_set_nat ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1694_insert__not__empty,axiom,
% 13.71/7.69 ! [A: int,A4: set_int] :
% 13.71/7.69 ( ( insert_int @ A @ A4 )
% 13.71/7.69 != bot_bot_set_int ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1695_insert__not__empty,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o] :
% 13.71/7.69 ( ( insert_o @ A @ A4 )
% 13.71/7.69 != bot_bot_set_o ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1696_doubleton__eq__iff,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,B: vEBT_VEBT,C2: vEBT_VEBT,D: vEBT_VEBT] :
% 13.71/7.69 ( ( ( insert_VEBT_VEBT @ A @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 = ( insert_VEBT_VEBT @ C2 @ ( insert_VEBT_VEBT @ D @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.71/7.69 = ( ( ( A = C2 )
% 13.71/7.69 & ( B = D ) )
% 13.71/7.69 | ( ( A = D )
% 13.71/7.69 & ( B = C2 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1697_doubleton__eq__iff,axiom,
% 13.71/7.69 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.71/7.69 ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 13.71/7.69 = ( insert_nat @ C2 @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 13.71/7.69 = ( ( ( A = C2 )
% 13.71/7.69 & ( B = D ) )
% 13.71/7.69 | ( ( A = D )
% 13.71/7.69 & ( B = C2 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1698_doubleton__eq__iff,axiom,
% 13.71/7.69 ! [A: int,B: int,C2: int,D: int] :
% 13.71/7.69 ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 13.71/7.69 = ( insert_int @ C2 @ ( insert_int @ D @ bot_bot_set_int ) ) )
% 13.71/7.69 = ( ( ( A = C2 )
% 13.71/7.69 & ( B = D ) )
% 13.71/7.69 | ( ( A = D )
% 13.71/7.69 & ( B = C2 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1699_doubleton__eq__iff,axiom,
% 13.71/7.69 ! [A: $o,B: $o,C2: $o,D: $o] :
% 13.71/7.69 ( ( ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) )
% 13.71/7.69 = ( insert_o @ C2 @ ( insert_o @ D @ bot_bot_set_o ) ) )
% 13.71/7.69 = ( ( ( A = C2 )
% 13.71/7.69 & ( B = D ) )
% 13.71/7.69 | ( ( A = D )
% 13.71/7.69 & ( B = C2 ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1700_singleton__iff,axiom,
% 13.71/7.69 ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 = ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1701_singleton__iff,axiom,
% 13.71/7.69 ! [B: real,A: real] :
% 13.71/7.69 ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 13.71/7.69 = ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1702_singleton__iff,axiom,
% 13.71/7.69 ! [B: set_nat,A: set_nat] :
% 13.71/7.69 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 13.71/7.69 = ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1703_singleton__iff,axiom,
% 13.71/7.69 ! [B: nat,A: nat] :
% 13.71/7.69 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 13.71/7.69 = ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1704_singleton__iff,axiom,
% 13.71/7.69 ! [B: int,A: int] :
% 13.71/7.69 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 13.71/7.69 = ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1705_singleton__iff,axiom,
% 13.71/7.69 ! [B: $o,A: $o] :
% 13.71/7.69 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 13.71/7.69 = ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1706_singletonD,axiom,
% 13.71/7.69 ! [B: vEBT_VEBT,A: vEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ B @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 => ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1707_singletonD,axiom,
% 13.71/7.69 ! [B: real,A: real] :
% 13.71/7.69 ( ( member_real @ B @ ( insert_real @ A @ bot_bot_set_real ) )
% 13.71/7.69 => ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1708_singletonD,axiom,
% 13.71/7.69 ! [B: set_nat,A: set_nat] :
% 13.71/7.69 ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 13.71/7.69 => ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1709_singletonD,axiom,
% 13.71/7.69 ! [B: nat,A: nat] :
% 13.71/7.69 ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 13.71/7.69 => ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1710_singletonD,axiom,
% 13.71/7.69 ! [B: int,A: int] :
% 13.71/7.69 ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 13.71/7.69 => ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1711_singletonD,axiom,
% 13.71/7.69 ! [B: $o,A: $o] :
% 13.71/7.69 ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 13.71/7.69 => ( B = A ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1712_insert__minus__eq,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,Y: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( X != Y )
% 13.71/7.69 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ ( insert_VEBT_VEBT @ Y @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ Y @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1713_insert__minus__eq,axiom,
% 13.71/7.69 ! [X: int,Y: int,A4: set_int] :
% 13.71/7.69 ( ( X != Y )
% 13.71/7.69 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 13.71/7.69 = ( insert_int @ X @ ( minus_minus_set_int @ A4 @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1714_insert__minus__eq,axiom,
% 13.71/7.69 ! [X: $o,Y: $o,A4: set_o] :
% 13.71/7.69 ( ( X != Y )
% 13.71/7.69 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 13.71/7.69 = ( insert_o @ X @ ( minus_minus_set_o @ A4 @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1715_insert__minus__eq,axiom,
% 13.71/7.69 ! [X: nat,Y: nat,A4: set_nat] :
% 13.71/7.69 ( ( X != Y )
% 13.71/7.69 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 13.71/7.69 = ( insert_nat @ X @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1716_set__minus__singleton__eq,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,X6: set_VEBT_VEBT] :
% 13.71/7.69 ( ~ ( member_VEBT_VEBT @ X @ X6 )
% 13.71/7.69 => ( ( minus_5127226145743854075T_VEBT @ X6 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 = X6 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1717_set__minus__singleton__eq,axiom,
% 13.71/7.69 ! [X: real,X6: set_real] :
% 13.71/7.69 ( ~ ( member_real @ X @ X6 )
% 13.71/7.69 => ( ( minus_minus_set_real @ X6 @ ( insert_real @ X @ bot_bot_set_real ) )
% 13.71/7.69 = X6 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1718_set__minus__singleton__eq,axiom,
% 13.71/7.69 ! [X: set_nat,X6: set_set_nat] :
% 13.71/7.69 ( ~ ( member_set_nat @ X @ X6 )
% 13.71/7.69 => ( ( minus_2163939370556025621et_nat @ X6 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 13.71/7.69 = X6 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1719_set__minus__singleton__eq,axiom,
% 13.71/7.69 ! [X: int,X6: set_int] :
% 13.71/7.69 ( ~ ( member_int @ X @ X6 )
% 13.71/7.69 => ( ( minus_minus_set_int @ X6 @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.71/7.69 = X6 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1720_set__minus__singleton__eq,axiom,
% 13.71/7.69 ! [X: $o,X6: set_o] :
% 13.71/7.69 ( ~ ( member_o @ X @ X6 )
% 13.71/7.69 => ( ( minus_minus_set_o @ X6 @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.71/7.69 = X6 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1721_set__minus__singleton__eq,axiom,
% 13.71/7.69 ! [X: nat,X6: set_nat] :
% 13.71/7.69 ( ~ ( member_nat @ X @ X6 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ X6 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.71/7.69 = X6 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1722_Diff__insert__absorb,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.71/7.69 => ( ( minus_5127226145743854075T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1723_Diff__insert__absorb,axiom,
% 13.71/7.69 ! [X: real,A4: set_real] :
% 13.71/7.69 ( ~ ( member_real @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_real @ ( insert_real @ X @ A4 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1724_Diff__insert__absorb,axiom,
% 13.71/7.69 ! [X: set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ~ ( member_set_nat @ X @ A4 )
% 13.71/7.69 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A4 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1725_Diff__insert__absorb,axiom,
% 13.71/7.69 ! [X: int,A4: set_int] :
% 13.71/7.69 ( ~ ( member_int @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_int @ ( insert_int @ X @ A4 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1726_Diff__insert__absorb,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o] :
% 13.71/7.69 ( ~ ( member_o @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_o @ ( insert_o @ X @ A4 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1727_Diff__insert__absorb,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat] :
% 13.71/7.69 ( ~ ( member_nat @ X @ A4 )
% 13.71/7.69 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A4 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1728_Diff__insert2,axiom,
% 13.71/7.69 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 13.71/7.69 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1729_Diff__insert2,axiom,
% 13.71/7.69 ! [A4: set_int,A: int,B4: set_int] :
% 13.71/7.69 ( ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1730_Diff__insert2,axiom,
% 13.71/7.69 ! [A4: set_o,A: $o,B4: set_o] :
% 13.71/7.69 ( ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1731_Diff__insert2,axiom,
% 13.71/7.69 ! [A4: set_nat,A: nat,B4: set_nat] :
% 13.71/7.69 ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1732_insert__Diff,axiom,
% 13.71/7.69 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ A @ A4 )
% 13.71/7.69 => ( ( insert_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1733_insert__Diff,axiom,
% 13.71/7.69 ! [A: real,A4: set_real] :
% 13.71/7.69 ( ( member_real @ A @ A4 )
% 13.71/7.69 => ( ( insert_real @ A @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1734_insert__Diff,axiom,
% 13.71/7.69 ! [A: set_nat,A4: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ A @ A4 )
% 13.71/7.69 => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1735_insert__Diff,axiom,
% 13.71/7.69 ! [A: int,A4: set_int] :
% 13.71/7.69 ( ( member_int @ A @ A4 )
% 13.71/7.69 => ( ( insert_int @ A @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1736_insert__Diff,axiom,
% 13.71/7.69 ! [A: $o,A4: set_o] :
% 13.71/7.69 ( ( member_o @ A @ A4 )
% 13.71/7.69 => ( ( insert_o @ A @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1737_insert__Diff,axiom,
% 13.71/7.69 ! [A: nat,A4: set_nat] :
% 13.71/7.69 ( ( member_nat @ A @ A4 )
% 13.71/7.69 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 13.71/7.69 = A4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1738_Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 13.71/7.69 = ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1739_Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_int,A: int,B4: set_int] :
% 13.71/7.69 ( ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ B4 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1740_Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_o,A: $o,B4: set_o] :
% 13.71/7.69 ( ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ B4 ) @ ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1741_Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_nat,A: nat,B4: set_nat] :
% 13.71/7.69 ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) )
% 13.71/7.69 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ B4 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1742_finite_OinsertI,axiom,
% 13.71/7.69 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT] :
% 13.71/7.69 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.71/7.69 => ( finite5795047828879050333T_VEBT @ ( insert_VEBT_VEBT @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1743_finite_OinsertI,axiom,
% 13.71/7.69 ! [A4: set_o,A: $o] :
% 13.71/7.69 ( ( finite_finite_o @ A4 )
% 13.71/7.69 => ( finite_finite_o @ ( insert_o @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1744_finite_OinsertI,axiom,
% 13.71/7.69 ! [A4: set_nat,A: nat] :
% 13.71/7.69 ( ( finite_finite_nat @ A4 )
% 13.71/7.69 => ( finite_finite_nat @ ( insert_nat @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1745_finite_OinsertI,axiom,
% 13.71/7.69 ! [A4: set_int,A: int] :
% 13.71/7.69 ( ( finite_finite_int @ A4 )
% 13.71/7.69 => ( finite_finite_int @ ( insert_int @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1746_finite_OinsertI,axiom,
% 13.71/7.69 ! [A4: set_complex,A: complex] :
% 13.71/7.69 ( ( finite3207457112153483333omplex @ A4 )
% 13.71/7.69 => ( finite3207457112153483333omplex @ ( insert_complex @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1747_finite_OinsertI,axiom,
% 13.71/7.69 ! [A4: set_Code_integer,A: code_integer] :
% 13.71/7.69 ( ( finite6017078050557962740nteger @ A4 )
% 13.71/7.69 => ( finite6017078050557962740nteger @ ( insert_Code_integer @ A @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1748_subset__insertI2,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat,B: nat] :
% 13.71/7.69 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.71/7.69 => ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1749_subset__insertI2,axiom,
% 13.71/7.69 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 13.71/7.69 ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.71/7.69 => ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1750_subset__insertI2,axiom,
% 13.71/7.69 ! [A4: set_o,B4: set_o,B: $o] :
% 13.71/7.69 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 13.71/7.69 => ( ord_less_eq_set_o @ A4 @ ( insert_o @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1751_subset__insertI2,axiom,
% 13.71/7.69 ! [A4: set_int,B4: set_int,B: int] :
% 13.71/7.69 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.71/7.69 => ( ord_less_eq_set_int @ A4 @ ( insert_int @ B @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1752_subset__insertI,axiom,
% 13.71/7.69 ! [B4: set_nat,A: nat] : ( ord_less_eq_set_nat @ B4 @ ( insert_nat @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1753_subset__insertI,axiom,
% 13.71/7.69 ! [B4: set_VEBT_VEBT,A: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ B4 @ ( insert_VEBT_VEBT @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1754_subset__insertI,axiom,
% 13.71/7.69 ! [B4: set_o,A: $o] : ( ord_less_eq_set_o @ B4 @ ( insert_o @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1755_subset__insertI,axiom,
% 13.71/7.69 ! [B4: set_int,A: int] : ( ord_less_eq_set_int @ B4 @ ( insert_int @ A @ B4 ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1756_subset__insert,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o,B4: set_o] :
% 13.71/7.69 ( ~ ( member_o @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 13.71/7.69 = ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1757_subset__insert,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat,B4: set_nat] :
% 13.71/7.69 ( ~ ( member_nat @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 13.71/7.69 = ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1758_subset__insert,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.71/7.69 ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.71/7.69 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 13.71/7.69 = ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1759_subset__insert,axiom,
% 13.71/7.69 ! [X: real,A4: set_real,B4: set_real] :
% 13.71/7.69 ( ~ ( member_real @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 13.71/7.69 = ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1760_subset__insert,axiom,
% 13.71/7.69 ! [X: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.71/7.69 ( ~ ( member_set_nat @ X @ A4 )
% 13.71/7.69 => ( ( ord_le6893508408891458716et_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 13.71/7.69 = ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1761_subset__insert,axiom,
% 13.71/7.69 ! [X: int,A4: set_int,B4: set_int] :
% 13.71/7.69 ( ~ ( member_int @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 13.71/7.69 = ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1762_insert__mono,axiom,
% 13.71/7.69 ! [C3: set_nat,D4: set_nat,A: nat] :
% 13.71/7.69 ( ( ord_less_eq_set_nat @ C3 @ D4 )
% 13.71/7.69 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C3 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1763_insert__mono,axiom,
% 13.71/7.69 ! [C3: set_VEBT_VEBT,D4: set_VEBT_VEBT,A: vEBT_VEBT] :
% 13.71/7.69 ( ( ord_le4337996190870823476T_VEBT @ C3 @ D4 )
% 13.71/7.69 => ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ A @ C3 ) @ ( insert_VEBT_VEBT @ A @ D4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1764_insert__mono,axiom,
% 13.71/7.69 ! [C3: set_o,D4: set_o,A: $o] :
% 13.71/7.69 ( ( ord_less_eq_set_o @ C3 @ D4 )
% 13.71/7.69 => ( ord_less_eq_set_o @ ( insert_o @ A @ C3 ) @ ( insert_o @ A @ D4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1765_insert__mono,axiom,
% 13.71/7.69 ! [C3: set_int,D4: set_int,A: int] :
% 13.71/7.69 ( ( ord_less_eq_set_int @ C3 @ D4 )
% 13.71/7.69 => ( ord_less_eq_set_int @ ( insert_int @ A @ C3 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1766_insert__subsetI,axiom,
% 13.71/7.69 ! [X: $o,A4: set_o,X6: set_o] :
% 13.71/7.69 ( ( member_o @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_o @ X6 @ A4 )
% 13.71/7.69 => ( ord_less_eq_set_o @ ( insert_o @ X @ X6 ) @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1767_insert__subsetI,axiom,
% 13.71/7.69 ! [X: nat,A4: set_nat,X6: set_nat] :
% 13.71/7.69 ( ( member_nat @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_nat @ X6 @ A4 )
% 13.71/7.69 => ( ord_less_eq_set_nat @ ( insert_nat @ X @ X6 ) @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1768_insert__subsetI,axiom,
% 13.71/7.69 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,X6: set_VEBT_VEBT] :
% 13.71/7.69 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.71/7.69 => ( ( ord_le4337996190870823476T_VEBT @ X6 @ A4 )
% 13.71/7.69 => ( ord_le4337996190870823476T_VEBT @ ( insert_VEBT_VEBT @ X @ X6 ) @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1769_insert__subsetI,axiom,
% 13.71/7.69 ! [X: real,A4: set_real,X6: set_real] :
% 13.71/7.69 ( ( member_real @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_real @ X6 @ A4 )
% 13.71/7.69 => ( ord_less_eq_set_real @ ( insert_real @ X @ X6 ) @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1770_insert__subsetI,axiom,
% 13.71/7.69 ! [X: set_nat,A4: set_set_nat,X6: set_set_nat] :
% 13.71/7.69 ( ( member_set_nat @ X @ A4 )
% 13.71/7.69 => ( ( ord_le6893508408891458716et_nat @ X6 @ A4 )
% 13.71/7.69 => ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ X6 ) @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1771_insert__subsetI,axiom,
% 13.71/7.69 ! [X: int,A4: set_int,X6: set_int] :
% 13.71/7.69 ( ( member_int @ X @ A4 )
% 13.71/7.69 => ( ( ord_less_eq_set_int @ X6 @ A4 )
% 13.71/7.69 => ( ord_less_eq_set_int @ ( insert_int @ X @ X6 ) @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1772_subset__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_o,B4: set_o,X: $o,C3: set_o] :
% 13.71/7.69 ( ( ord_less_eq_set_o @ A4 @ ( minus_minus_set_o @ B4 @ ( insert_o @ X @ C3 ) ) )
% 13.71/7.69 = ( ( ord_less_eq_set_o @ A4 @ ( minus_minus_set_o @ B4 @ C3 ) )
% 13.71/7.69 & ~ ( member_o @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1773_subset__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,X: vEBT_VEBT,C3: set_VEBT_VEBT] :
% 13.71/7.69 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ B4 @ ( insert_VEBT_VEBT @ X @ C3 ) ) )
% 13.71/7.69 = ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( minus_5127226145743854075T_VEBT @ B4 @ C3 ) )
% 13.71/7.69 & ~ ( member_VEBT_VEBT @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1774_subset__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_real,B4: set_real,X: real,C3: set_real] :
% 13.71/7.69 ( ( ord_less_eq_set_real @ A4 @ ( minus_minus_set_real @ B4 @ ( insert_real @ X @ C3 ) ) )
% 13.71/7.69 = ( ( ord_less_eq_set_real @ A4 @ ( minus_minus_set_real @ B4 @ C3 ) )
% 13.71/7.69 & ~ ( member_real @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1775_subset__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_set_nat,B4: set_set_nat,X: set_nat,C3: set_set_nat] :
% 13.71/7.69 ( ( ord_le6893508408891458716et_nat @ A4 @ ( minus_2163939370556025621et_nat @ B4 @ ( insert_set_nat @ X @ C3 ) ) )
% 13.71/7.69 = ( ( ord_le6893508408891458716et_nat @ A4 @ ( minus_2163939370556025621et_nat @ B4 @ C3 ) )
% 13.71/7.69 & ~ ( member_set_nat @ X @ A4 ) ) ) ).
% 13.71/7.69
% 13.71/7.69 thf(fact_1776_subset__Diff__insert,axiom,
% 13.71/7.69 ! [A4: set_nat,B4: set_nat,X: nat,C3: set_nat] :
% 13.71/7.69 ( ( ord_less_eq_set_nat @ A4 @ ( minus_minus_set_nat @ B4 @ ( insert_nat @ X @ C3 ) ) )
% 13.71/7.70 = ( ( ord_less_eq_set_nat @ A4 @ ( minus_minus_set_nat @ B4 @ C3 ) )
% 13.71/7.70 & ~ ( member_nat @ X @ A4 ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1777_subset__Diff__insert,axiom,
% 13.71/7.70 ! [A4: set_int,B4: set_int,X: int,C3: set_int] :
% 13.71/7.70 ( ( ord_less_eq_set_int @ A4 @ ( minus_minus_set_int @ B4 @ ( insert_int @ X @ C3 ) ) )
% 13.71/7.70 = ( ( ord_less_eq_set_int @ A4 @ ( minus_minus_set_int @ B4 @ C3 ) )
% 13.71/7.70 & ~ ( member_int @ X @ A4 ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1778_finite_Ocases,axiom,
% 13.71/7.70 ! [A: set_VEBT_VEBT] :
% 13.71/7.70 ( ( finite5795047828879050333T_VEBT @ A )
% 13.71/7.70 => ( ( A != bot_bo8194388402131092736T_VEBT )
% 13.71/7.70 => ~ ! [A5: set_VEBT_VEBT] :
% 13.71/7.70 ( ? [A3: vEBT_VEBT] :
% 13.71/7.70 ( A
% 13.71/7.70 = ( insert_VEBT_VEBT @ A3 @ A5 ) )
% 13.71/7.70 => ~ ( finite5795047828879050333T_VEBT @ A5 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1779_finite_Ocases,axiom,
% 13.71/7.70 ! [A: set_complex] :
% 13.71/7.70 ( ( finite3207457112153483333omplex @ A )
% 13.71/7.70 => ( ( A != bot_bot_set_complex )
% 13.71/7.70 => ~ ! [A5: set_complex] :
% 13.71/7.70 ( ? [A3: complex] :
% 13.71/7.70 ( A
% 13.71/7.70 = ( insert_complex @ A3 @ A5 ) )
% 13.71/7.70 => ~ ( finite3207457112153483333omplex @ A5 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1780_finite_Ocases,axiom,
% 13.71/7.70 ! [A: set_Code_integer] :
% 13.71/7.70 ( ( finite6017078050557962740nteger @ A )
% 13.71/7.70 => ( ( A != bot_bo3990330152332043303nteger )
% 13.71/7.70 => ~ ! [A5: set_Code_integer] :
% 13.71/7.70 ( ? [A3: code_integer] :
% 13.71/7.70 ( A
% 13.71/7.70 = ( insert_Code_integer @ A3 @ A5 ) )
% 13.71/7.70 => ~ ( finite6017078050557962740nteger @ A5 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1781_finite_Ocases,axiom,
% 13.71/7.70 ! [A: set_nat] :
% 13.71/7.70 ( ( finite_finite_nat @ A )
% 13.71/7.70 => ( ( A != bot_bot_set_nat )
% 13.71/7.70 => ~ ! [A5: set_nat] :
% 13.71/7.70 ( ? [A3: nat] :
% 13.71/7.70 ( A
% 13.71/7.70 = ( insert_nat @ A3 @ A5 ) )
% 13.71/7.70 => ~ ( finite_finite_nat @ A5 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1782_finite_Ocases,axiom,
% 13.71/7.70 ! [A: set_int] :
% 13.71/7.70 ( ( finite_finite_int @ A )
% 13.71/7.70 => ( ( A != bot_bot_set_int )
% 13.71/7.70 => ~ ! [A5: set_int] :
% 13.71/7.70 ( ? [A3: int] :
% 13.71/7.70 ( A
% 13.71/7.70 = ( insert_int @ A3 @ A5 ) )
% 13.71/7.70 => ~ ( finite_finite_int @ A5 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1783_finite_Ocases,axiom,
% 13.71/7.70 ! [A: set_o] :
% 13.71/7.70 ( ( finite_finite_o @ A )
% 13.71/7.70 => ( ( A != bot_bot_set_o )
% 13.71/7.70 => ~ ! [A5: set_o] :
% 13.71/7.70 ( ? [A3: $o] :
% 13.71/7.70 ( A
% 13.71/7.70 = ( insert_o @ A3 @ A5 ) )
% 13.71/7.70 => ~ ( finite_finite_o @ A5 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1784_finite_Osimps,axiom,
% 13.71/7.70 ( finite5795047828879050333T_VEBT
% 13.71/7.70 = ( ^ [A7: set_VEBT_VEBT] :
% 13.71/7.70 ( ( A7 = bot_bo8194388402131092736T_VEBT )
% 13.71/7.70 | ? [A6: set_VEBT_VEBT,B7: vEBT_VEBT] :
% 13.71/7.70 ( ( A7
% 13.71/7.70 = ( insert_VEBT_VEBT @ B7 @ A6 ) )
% 13.71/7.70 & ( finite5795047828879050333T_VEBT @ A6 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1785_finite_Osimps,axiom,
% 13.71/7.70 ( finite3207457112153483333omplex
% 13.71/7.70 = ( ^ [A7: set_complex] :
% 13.71/7.70 ( ( A7 = bot_bot_set_complex )
% 13.71/7.70 | ? [A6: set_complex,B7: complex] :
% 13.71/7.70 ( ( A7
% 13.71/7.70 = ( insert_complex @ B7 @ A6 ) )
% 13.71/7.70 & ( finite3207457112153483333omplex @ A6 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1786_finite_Osimps,axiom,
% 13.71/7.70 ( finite6017078050557962740nteger
% 13.71/7.70 = ( ^ [A7: set_Code_integer] :
% 13.71/7.70 ( ( A7 = bot_bo3990330152332043303nteger )
% 13.71/7.70 | ? [A6: set_Code_integer,B7: code_integer] :
% 13.71/7.70 ( ( A7
% 13.71/7.70 = ( insert_Code_integer @ B7 @ A6 ) )
% 13.71/7.70 & ( finite6017078050557962740nteger @ A6 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1787_finite_Osimps,axiom,
% 13.71/7.70 ( finite_finite_nat
% 13.71/7.70 = ( ^ [A7: set_nat] :
% 13.71/7.70 ( ( A7 = bot_bot_set_nat )
% 13.71/7.70 | ? [A6: set_nat,B7: nat] :
% 13.71/7.70 ( ( A7
% 13.71/7.70 = ( insert_nat @ B7 @ A6 ) )
% 13.71/7.70 & ( finite_finite_nat @ A6 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1788_finite_Osimps,axiom,
% 13.71/7.70 ( finite_finite_int
% 13.71/7.70 = ( ^ [A7: set_int] :
% 13.71/7.70 ( ( A7 = bot_bot_set_int )
% 13.71/7.70 | ? [A6: set_int,B7: int] :
% 13.71/7.70 ( ( A7
% 13.71/7.70 = ( insert_int @ B7 @ A6 ) )
% 13.71/7.70 & ( finite_finite_int @ A6 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1789_finite_Osimps,axiom,
% 13.71/7.70 ( finite_finite_o
% 13.71/7.70 = ( ^ [A7: set_o] :
% 13.71/7.70 ( ( A7 = bot_bot_set_o )
% 13.71/7.70 | ? [A6: set_o,B7: $o] :
% 13.71/7.70 ( ( A7
% 13.71/7.70 = ( insert_o @ B7 @ A6 ) )
% 13.71/7.70 & ( finite_finite_o @ A6 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1790_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 13.71/7.70 ( ( finite5795047828879050333T_VEBT @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.71/7.70 => ( ! [X3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 13.71/7.70 ( ( finite5795047828879050333T_VEBT @ F3 )
% 13.71/7.70 => ( ~ ( member_VEBT_VEBT @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1791_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_real,P2: set_real > $o] :
% 13.71/7.70 ( ( finite_finite_real @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.71/7.70 => ( ! [X3: real,F3: set_real] :
% 13.71/7.70 ( ( finite_finite_real @ F3 )
% 13.71/7.70 => ( ~ ( member_real @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_real @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1792_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_set_nat,P2: set_set_nat > $o] :
% 13.71/7.70 ( ( finite1152437895449049373et_nat @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_set_nat )
% 13.71/7.70 => ( ! [X3: set_nat,F3: set_set_nat] :
% 13.71/7.70 ( ( finite1152437895449049373et_nat @ F3 )
% 13.71/7.70 => ( ~ ( member_set_nat @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_set_nat @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1793_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_complex,P2: set_complex > $o] :
% 13.71/7.70 ( ( finite3207457112153483333omplex @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.71/7.70 => ( ! [X3: complex,F3: set_complex] :
% 13.71/7.70 ( ( finite3207457112153483333omplex @ F3 )
% 13.71/7.70 => ( ~ ( member_complex @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_complex @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1794_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_Code_integer,P2: set_Code_integer > $o] :
% 13.71/7.70 ( ( finite6017078050557962740nteger @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.71/7.70 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 13.71/7.70 ( ( finite6017078050557962740nteger @ F3 )
% 13.71/7.70 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1795_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_nat,P2: set_nat > $o] :
% 13.71/7.70 ( ( finite_finite_nat @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.71/7.70 => ( ! [X3: nat,F3: set_nat] :
% 13.71/7.70 ( ( finite_finite_nat @ F3 )
% 13.71/7.70 => ( ~ ( member_nat @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_nat @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1796_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_int,P2: set_int > $o] :
% 13.71/7.70 ( ( finite_finite_int @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.71/7.70 => ( ! [X3: int,F3: set_int] :
% 13.71/7.70 ( ( finite_finite_int @ F3 )
% 13.71/7.70 => ( ~ ( member_int @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_int @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1797_finite__induct,axiom,
% 13.71/7.70 ! [F2: set_o,P2: set_o > $o] :
% 13.71/7.70 ( ( finite_finite_o @ F2 )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.71/7.70 => ( ! [X3: $o,F3: set_o] :
% 13.71/7.70 ( ( finite_finite_o @ F3 )
% 13.71/7.70 => ( ~ ( member_o @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_o @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1798_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 13.71/7.70 ( ( finite5795047828879050333T_VEBT @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bo8194388402131092736T_VEBT )
% 13.71/7.70 => ( ! [X3: vEBT_VEBT] : ( P2 @ ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) )
% 13.71/7.70 => ( ! [X3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 13.71/7.70 ( ( finite5795047828879050333T_VEBT @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bo8194388402131092736T_VEBT )
% 13.71/7.70 => ( ~ ( member_VEBT_VEBT @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1799_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_real,P2: set_real > $o] :
% 13.71/7.70 ( ( finite_finite_real @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bot_set_real )
% 13.71/7.70 => ( ! [X3: real] : ( P2 @ ( insert_real @ X3 @ bot_bot_set_real ) )
% 13.71/7.70 => ( ! [X3: real,F3: set_real] :
% 13.71/7.70 ( ( finite_finite_real @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bot_set_real )
% 13.71/7.70 => ( ~ ( member_real @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_real @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1800_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_set_nat,P2: set_set_nat > $o] :
% 13.71/7.70 ( ( finite1152437895449049373et_nat @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bot_set_set_nat )
% 13.71/7.70 => ( ! [X3: set_nat] : ( P2 @ ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) )
% 13.71/7.70 => ( ! [X3: set_nat,F3: set_set_nat] :
% 13.71/7.70 ( ( finite1152437895449049373et_nat @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bot_set_set_nat )
% 13.71/7.70 => ( ~ ( member_set_nat @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_set_nat @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1801_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_complex,P2: set_complex > $o] :
% 13.71/7.70 ( ( finite3207457112153483333omplex @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bot_set_complex )
% 13.71/7.70 => ( ! [X3: complex] : ( P2 @ ( insert_complex @ X3 @ bot_bot_set_complex ) )
% 13.71/7.70 => ( ! [X3: complex,F3: set_complex] :
% 13.71/7.70 ( ( finite3207457112153483333omplex @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bot_set_complex )
% 13.71/7.70 => ( ~ ( member_complex @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_complex @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1802_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_Code_integer,P2: set_Code_integer > $o] :
% 13.71/7.70 ( ( finite6017078050557962740nteger @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bo3990330152332043303nteger )
% 13.71/7.70 => ( ! [X3: code_integer] : ( P2 @ ( insert_Code_integer @ X3 @ bot_bo3990330152332043303nteger ) )
% 13.71/7.70 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 13.71/7.70 ( ( finite6017078050557962740nteger @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bo3990330152332043303nteger )
% 13.71/7.70 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1803_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_nat,P2: set_nat > $o] :
% 13.71/7.70 ( ( finite_finite_nat @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bot_set_nat )
% 13.71/7.70 => ( ! [X3: nat] : ( P2 @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 13.71/7.70 => ( ! [X3: nat,F3: set_nat] :
% 13.71/7.70 ( ( finite_finite_nat @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bot_set_nat )
% 13.71/7.70 => ( ~ ( member_nat @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_nat @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1804_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_int,P2: set_int > $o] :
% 13.71/7.70 ( ( finite_finite_int @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bot_set_int )
% 13.71/7.70 => ( ! [X3: int] : ( P2 @ ( insert_int @ X3 @ bot_bot_set_int ) )
% 13.71/7.70 => ( ! [X3: int,F3: set_int] :
% 13.71/7.70 ( ( finite_finite_int @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bot_set_int )
% 13.71/7.70 => ( ~ ( member_int @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_int @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1805_finite__ne__induct,axiom,
% 13.71/7.70 ! [F2: set_o,P2: set_o > $o] :
% 13.71/7.70 ( ( finite_finite_o @ F2 )
% 13.71/7.70 => ( ( F2 != bot_bot_set_o )
% 13.71/7.70 => ( ! [X3: $o] : ( P2 @ ( insert_o @ X3 @ bot_bot_set_o ) )
% 13.71/7.70 => ( ! [X3: $o,F3: set_o] :
% 13.71/7.70 ( ( finite_finite_o @ F3 )
% 13.71/7.70 => ( ( F3 != bot_bot_set_o )
% 13.71/7.70 => ( ~ ( member_o @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_o @ X3 @ F3 ) ) ) ) ) )
% 13.71/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1806_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_VEBT_VEBT > $o,A4: set_VEBT_VEBT] :
% 13.71/7.70 ( ! [A5: set_VEBT_VEBT] :
% 13.71/7.70 ( ~ ( finite5795047828879050333T_VEBT @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.71/7.70 => ( ! [X3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 13.71/7.70 ( ( finite5795047828879050333T_VEBT @ F3 )
% 13.71/7.70 => ( ~ ( member_VEBT_VEBT @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1807_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_real > $o,A4: set_real] :
% 13.71/7.70 ( ! [A5: set_real] :
% 13.71/7.70 ( ~ ( finite_finite_real @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.71/7.70 => ( ! [X3: real,F3: set_real] :
% 13.71/7.70 ( ( finite_finite_real @ F3 )
% 13.71/7.70 => ( ~ ( member_real @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_real @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1808_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_set_nat > $o,A4: set_set_nat] :
% 13.71/7.70 ( ! [A5: set_set_nat] :
% 13.71/7.70 ( ~ ( finite1152437895449049373et_nat @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_set_nat )
% 13.71/7.70 => ( ! [X3: set_nat,F3: set_set_nat] :
% 13.71/7.70 ( ( finite1152437895449049373et_nat @ F3 )
% 13.71/7.70 => ( ~ ( member_set_nat @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_set_nat @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1809_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_complex > $o,A4: set_complex] :
% 13.71/7.70 ( ! [A5: set_complex] :
% 13.71/7.70 ( ~ ( finite3207457112153483333omplex @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.71/7.70 => ( ! [X3: complex,F3: set_complex] :
% 13.71/7.70 ( ( finite3207457112153483333omplex @ F3 )
% 13.71/7.70 => ( ~ ( member_complex @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_complex @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1810_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_Code_integer > $o,A4: set_Code_integer] :
% 13.71/7.70 ( ! [A5: set_Code_integer] :
% 13.71/7.70 ( ~ ( finite6017078050557962740nteger @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.71/7.70 => ( ! [X3: code_integer,F3: set_Code_integer] :
% 13.71/7.70 ( ( finite6017078050557962740nteger @ F3 )
% 13.71/7.70 => ( ~ ( member_Code_integer @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_Code_integer @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1811_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_nat > $o,A4: set_nat] :
% 13.71/7.70 ( ! [A5: set_nat] :
% 13.71/7.70 ( ~ ( finite_finite_nat @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.71/7.70 => ( ! [X3: nat,F3: set_nat] :
% 13.71/7.70 ( ( finite_finite_nat @ F3 )
% 13.71/7.70 => ( ~ ( member_nat @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_nat @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1812_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_int > $o,A4: set_int] :
% 13.71/7.70 ( ! [A5: set_int] :
% 13.71/7.70 ( ~ ( finite_finite_int @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.71/7.70 => ( ! [X3: int,F3: set_int] :
% 13.71/7.70 ( ( finite_finite_int @ F3 )
% 13.71/7.70 => ( ~ ( member_int @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_int @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1813_infinite__finite__induct,axiom,
% 13.71/7.70 ! [P2: set_o > $o,A4: set_o] :
% 13.71/7.70 ( ! [A5: set_o] :
% 13.71/7.70 ( ~ ( finite_finite_o @ A5 )
% 13.71/7.70 => ( P2 @ A5 ) )
% 13.71/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.71/7.70 => ( ! [X3: $o,F3: set_o] :
% 13.71/7.70 ( ( finite_finite_o @ F3 )
% 13.71/7.70 => ( ~ ( member_o @ X3 @ F3 )
% 13.71/7.70 => ( ( P2 @ F3 )
% 13.71/7.70 => ( P2 @ ( insert_o @ X3 @ F3 ) ) ) ) )
% 13.71/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1814_infinite__remove,axiom,
% 13.71/7.70 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT] :
% 13.71/7.70 ( ~ ( finite5795047828879050333T_VEBT @ S3 )
% 13.71/7.70 => ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1815_infinite__remove,axiom,
% 13.71/7.70 ! [S3: set_complex,A: complex] :
% 13.71/7.70 ( ~ ( finite3207457112153483333omplex @ S3 )
% 13.71/7.70 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1816_infinite__remove,axiom,
% 13.71/7.70 ! [S3: set_Code_integer,A: code_integer] :
% 13.71/7.70 ( ~ ( finite6017078050557962740nteger @ S3 )
% 13.71/7.70 => ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1817_infinite__remove,axiom,
% 13.71/7.70 ! [S3: set_int,A: int] :
% 13.71/7.70 ( ~ ( finite_finite_int @ S3 )
% 13.71/7.70 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1818_infinite__remove,axiom,
% 13.71/7.70 ! [S3: set_o,A: $o] :
% 13.71/7.70 ( ~ ( finite_finite_o @ S3 )
% 13.71/7.70 => ~ ( finite_finite_o @ ( minus_minus_set_o @ S3 @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1819_infinite__remove,axiom,
% 13.71/7.70 ! [S3: set_nat,A: nat] :
% 13.71/7.70 ( ~ ( finite_finite_nat @ S3 )
% 13.71/7.70 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1820_infinite__coinduct,axiom,
% 13.71/7.70 ! [X6: set_VEBT_VEBT > $o,A4: set_VEBT_VEBT] :
% 13.71/7.70 ( ( X6 @ A4 )
% 13.71/7.70 => ( ! [A5: set_VEBT_VEBT] :
% 13.71/7.70 ( ( X6 @ A5 )
% 13.71/7.70 => ? [X5: vEBT_VEBT] :
% 13.71/7.70 ( ( member_VEBT_VEBT @ X5 @ A5 )
% 13.71/7.70 & ( ( X6 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.71/7.70 | ~ ( finite5795047828879050333T_VEBT @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 13.71/7.70 => ~ ( finite5795047828879050333T_VEBT @ A4 ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1821_infinite__coinduct,axiom,
% 13.71/7.70 ! [X6: set_complex > $o,A4: set_complex] :
% 13.71/7.70 ( ( X6 @ A4 )
% 13.71/7.70 => ( ! [A5: set_complex] :
% 13.71/7.70 ( ( X6 @ A5 )
% 13.71/7.70 => ? [X5: complex] :
% 13.71/7.70 ( ( member_complex @ X5 @ A5 )
% 13.71/7.70 & ( ( X6 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) )
% 13.71/7.70 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) ) ) )
% 13.71/7.70 => ~ ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 13.71/7.70
% 13.71/7.70 thf(fact_1822_infinite__coinduct,axiom,
% 13.71/7.70 ! [X6: set_Code_integer > $o,A4: set_Code_integer] :
% 13.71/7.70 ( ( X6 @ A4 )
% 13.71/7.70 => ( ! [A5: set_Code_integer] :
% 13.71/7.70 ( ( X6 @ A5 )
% 13.71/7.70 => ? [X5: code_integer] :
% 13.71/7.70 ( ( member_Code_integer @ X5 @ A5 )
% 13.77/7.70 & ( ( X6 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.70 | ~ ( finite6017078050557962740nteger @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 13.77/7.70 => ~ ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1823_infinite__coinduct,axiom,
% 13.77/7.70 ! [X6: set_int > $o,A4: set_int] :
% 13.77/7.70 ( ( X6 @ A4 )
% 13.77/7.70 => ( ! [A5: set_int] :
% 13.77/7.70 ( ( X6 @ A5 )
% 13.77/7.70 => ? [X5: int] :
% 13.77/7.70 ( ( member_int @ X5 @ A5 )
% 13.77/7.70 & ( ( X6 @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) )
% 13.77/7.70 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) ) ) )
% 13.77/7.70 => ~ ( finite_finite_int @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1824_infinite__coinduct,axiom,
% 13.77/7.70 ! [X6: set_o > $o,A4: set_o] :
% 13.77/7.70 ( ( X6 @ A4 )
% 13.77/7.70 => ( ! [A5: set_o] :
% 13.77/7.70 ( ( X6 @ A5 )
% 13.77/7.70 => ? [X5: $o] :
% 13.77/7.70 ( ( member_o @ X5 @ A5 )
% 13.77/7.70 & ( ( X6 @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) )
% 13.77/7.70 | ~ ( finite_finite_o @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) ) ) )
% 13.77/7.70 => ~ ( finite_finite_o @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1825_infinite__coinduct,axiom,
% 13.77/7.70 ! [X6: set_nat > $o,A4: set_nat] :
% 13.77/7.70 ( ( X6 @ A4 )
% 13.77/7.70 => ( ! [A5: set_nat] :
% 13.77/7.70 ( ( X6 @ A5 )
% 13.77/7.70 => ? [X5: nat] :
% 13.77/7.70 ( ( member_nat @ X5 @ A5 )
% 13.77/7.70 & ( ( X6 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
% 13.77/7.70 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ) )
% 13.77/7.70 => ~ ( finite_finite_nat @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1826_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: vEBT_VEBT,A5: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ A5 )
% 13.77/7.70 => ( ( member_VEBT_VEBT @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ A3 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1827_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_real,P2: set_real > $o] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: real,A5: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A5 )
% 13.77/7.70 => ( ( member_real @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_real @ A5 @ ( insert_real @ A3 @ bot_bot_set_real ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bot_set_real ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1828_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_set_nat,P2: set_set_nat > $o] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: set_nat,A5: set_set_nat] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ A5 )
% 13.77/7.70 => ( ( member_set_nat @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ A3 @ bot_bot_set_set_nat ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bot_set_set_nat ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1829_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_complex,P2: set_complex > $o] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: complex,A5: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ A5 )
% 13.77/7.70 => ( ( member_complex @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ A3 @ bot_bot_set_complex ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bot_set_complex ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1830_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: code_integer,A5: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A5 )
% 13.77/7.70 => ( ( member_Code_integer @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ A3 @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1831_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_int,P2: set_int > $o] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: int,A5: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A5 )
% 13.77/7.70 => ( ( member_int @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_int @ A5 @ ( insert_int @ A3 @ bot_bot_set_int ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1832_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_o,P2: set_o > $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: $o,A5: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A5 )
% 13.77/7.70 => ( ( member_o @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_o @ A5 @ ( insert_o @ A3 @ bot_bot_set_o ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1833_finite__empty__induct,axiom,
% 13.77/7.70 ! [A4: set_nat,P2: set_nat > $o] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( P2 @ A4 )
% 13.77/7.70 => ( ! [A3: nat,A5: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A5 )
% 13.77/7.70 => ( ( member_nat @ A3 @ A5 )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ A3 @ bot_bot_set_nat ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1834_subset__singleton__iff,axiom,
% 13.77/7.70 ! [X6: set_VEBT_VEBT,A: vEBT_VEBT] :
% 13.77/7.70 ( ( ord_le4337996190870823476T_VEBT @ X6 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) )
% 13.77/7.70 = ( ( X6 = bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 | ( X6
% 13.77/7.70 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1835_subset__singleton__iff,axiom,
% 13.77/7.70 ! [X6: set_nat,A: nat] :
% 13.77/7.70 ( ( ord_less_eq_set_nat @ X6 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 13.77/7.70 = ( ( X6 = bot_bot_set_nat )
% 13.77/7.70 | ( X6
% 13.77/7.70 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1836_subset__singleton__iff,axiom,
% 13.77/7.70 ! [X6: set_o,A: $o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ X6 @ ( insert_o @ A @ bot_bot_set_o ) )
% 13.77/7.70 = ( ( X6 = bot_bot_set_o )
% 13.77/7.70 | ( X6
% 13.77/7.70 = ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1837_subset__singleton__iff,axiom,
% 13.77/7.70 ! [X6: set_int,A: int] :
% 13.77/7.70 ( ( ord_less_eq_set_int @ X6 @ ( insert_int @ A @ bot_bot_set_int ) )
% 13.77/7.70 = ( ( X6 = bot_bot_set_int )
% 13.77/7.70 | ( X6
% 13.77/7.70 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1838_subset__singletonD,axiom,
% 13.77/7.70 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.70 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 13.77/7.70 => ( ( A4 = bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 | ( A4
% 13.77/7.70 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1839_subset__singletonD,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.70 => ( ( A4 = bot_bot_set_nat )
% 13.77/7.70 | ( A4
% 13.77/7.70 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1840_subset__singletonD,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.70 => ( ( A4 = bot_bot_set_o )
% 13.77/7.70 | ( A4
% 13.77/7.70 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1841_subset__singletonD,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.70 => ( ( A4 = bot_bot_set_int )
% 13.77/7.70 | ( A4
% 13.77/7.70 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1842_subset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.70 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.70 => ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.70 => ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1843_subset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_real,X: real,B4: set_real] :
% 13.77/7.70 ( ( ord_less_eq_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_real @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_real @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1844_subset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_set_nat,X: set_nat,B4: set_set_nat] :
% 13.77/7.70 ( ( ord_le6893508408891458716et_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_set_nat @ X @ A4 )
% 13.77/7.70 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_set_nat @ X @ A4 )
% 13.77/7.70 => ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1845_subset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o,B4: set_o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_o @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_o @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1846_subset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat,B4: set_nat] :
% 13.77/7.70 ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1847_subset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int,B4: set_int] :
% 13.77/7.70 ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_int @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_int @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1848_Diff__single__insert,axiom,
% 13.77/7.70 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.70 ( ( ord_le4337996190870823476T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 )
% 13.77/7.70 => ( ord_le4337996190870823476T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1849_Diff__single__insert,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o,B4: set_o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 )
% 13.77/7.70 => ( ord_less_eq_set_o @ A4 @ ( insert_o @ X @ B4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1850_Diff__single__insert,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat,B4: set_nat] :
% 13.77/7.70 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 )
% 13.77/7.70 => ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ X @ B4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1851_Diff__single__insert,axiom,
% 13.77/7.70 ! [A4: set_int,X: int,B4: set_int] :
% 13.77/7.70 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 )
% 13.77/7.70 => ( ord_less_eq_set_int @ A4 @ ( insert_int @ X @ B4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1852_remove__subset,axiom,
% 13.77/7.70 ! [X: vEBT_VEBT,S3: set_VEBT_VEBT] :
% 13.77/7.70 ( ( member_VEBT_VEBT @ X @ S3 )
% 13.77/7.70 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ S3 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1853_remove__subset,axiom,
% 13.77/7.70 ! [X: real,S3: set_real] :
% 13.77/7.70 ( ( member_real @ X @ S3 )
% 13.77/7.70 => ( ord_less_set_real @ ( minus_minus_set_real @ S3 @ ( insert_real @ X @ bot_bot_set_real ) ) @ S3 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1854_remove__subset,axiom,
% 13.77/7.70 ! [X: set_nat,S3: set_set_nat] :
% 13.77/7.70 ( ( member_set_nat @ X @ S3 )
% 13.77/7.70 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ S3 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ S3 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1855_remove__subset,axiom,
% 13.77/7.70 ! [X: int,S3: set_int] :
% 13.77/7.70 ( ( member_int @ X @ S3 )
% 13.77/7.70 => ( ord_less_set_int @ ( minus_minus_set_int @ S3 @ ( insert_int @ X @ bot_bot_set_int ) ) @ S3 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1856_remove__subset,axiom,
% 13.77/7.70 ! [X: $o,S3: set_o] :
% 13.77/7.70 ( ( member_o @ X @ S3 )
% 13.77/7.70 => ( ord_less_set_o @ ( minus_minus_set_o @ S3 @ ( insert_o @ X @ bot_bot_set_o ) ) @ S3 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1857_remove__subset,axiom,
% 13.77/7.70 ! [X: nat,S3: set_nat] :
% 13.77/7.70 ( ( member_nat @ X @ S3 )
% 13.77/7.70 => ( ord_less_set_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S3 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1858_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ! [X3: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ S5 )
% 13.77/7.70 => ( ! [Y5: vEBT_VEBT] :
% 13.77/7.70 ( ( member_VEBT_VEBT @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1859_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_real,P2: set_real > $o,F: real > rat] :
% 13.77/7.70 ( ( finite_finite_real @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ! [X3: real,S5: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ S5 )
% 13.77/7.70 => ( ! [Y5: real] :
% 13.77/7.70 ( ( member_real @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_real @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1860_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_complex,P2: set_complex > $o,F: complex > rat] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.77/7.70 => ( ! [X3: complex,S5: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ S5 )
% 13.77/7.70 => ( ! [Y5: complex] :
% 13.77/7.70 ( ( member_complex @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_complex @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1861_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_Code_integer,P2: set_Code_integer > $o,F: code_integer > rat] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [X3: code_integer,S5: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ S5 )
% 13.77/7.70 => ( ! [Y5: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_Code_integer @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1862_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_nat,P2: set_nat > $o,F: nat > rat] :
% 13.77/7.70 ( ( finite_finite_nat @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ! [X3: nat,S5: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ S5 )
% 13.77/7.70 => ( ! [Y5: nat] :
% 13.77/7.70 ( ( member_nat @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_nat @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1863_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_int,P2: set_int > $o,F: int > rat] :
% 13.77/7.70 ( ( finite_finite_int @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ! [X3: int,S5: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ S5 )
% 13.77/7.70 => ( ! [Y5: int] :
% 13.77/7.70 ( ( member_int @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_int @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1864_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_o,P2: set_o > $o,F: $o > rat] :
% 13.77/7.70 ( ( finite_finite_o @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ! [X3: $o,S5: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ S5 )
% 13.77/7.70 => ( ! [Y5: $o] :
% 13.77/7.70 ( ( member_o @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_o @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1865_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ! [X3: vEBT_VEBT,S5: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ S5 )
% 13.77/7.70 => ( ! [Y5: vEBT_VEBT] :
% 13.77/7.70 ( ( member_VEBT_VEBT @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_VEBT_VEBT @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1866_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_real,P2: set_real > $o,F: real > num] :
% 13.77/7.70 ( ( finite_finite_real @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ! [X3: real,S5: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ S5 )
% 13.77/7.70 => ( ! [Y5: real] :
% 13.77/7.70 ( ( member_real @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_real @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1867_finite__ranking__induct,axiom,
% 13.77/7.70 ! [S3: set_complex,P2: set_complex > $o,F: complex > num] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.77/7.70 => ( ! [X3: complex,S5: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ S5 )
% 13.77/7.70 => ( ! [Y5: complex] :
% 13.77/7.70 ( ( member_complex @ Y5 @ S5 )
% 13.77/7.70 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X3 ) ) )
% 13.77/7.70 => ( ( P2 @ S5 )
% 13.77/7.70 => ( P2 @ ( insert_complex @ X3 @ S5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1868_finite__linorder__max__induct,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [B3: code_integer,A5: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A5 )
% 13.77/7.70 => ( ! [X5: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X5 @ A5 )
% 13.77/7.70 => ( ord_le6747313008572928689nteger @ X5 @ B3 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_Code_integer @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1869_finite__linorder__max__induct,axiom,
% 13.77/7.70 ! [A4: set_o,P2: set_o > $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ! [B3: $o,A5: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A5 )
% 13.77/7.70 => ( ! [X5: $o] :
% 13.77/7.70 ( ( member_o @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_o @ X5 @ B3 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_o @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1870_finite__linorder__max__induct,axiom,
% 13.77/7.70 ! [A4: set_real,P2: set_real > $o] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ! [B3: real,A5: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A5 )
% 13.77/7.70 => ( ! [X5: real] :
% 13.77/7.70 ( ( member_real @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_real @ X5 @ B3 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_real @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1871_finite__linorder__max__induct,axiom,
% 13.77/7.70 ! [A4: set_rat,P2: set_rat > $o] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_rat )
% 13.77/7.70 => ( ! [B3: rat,A5: set_rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A5 )
% 13.77/7.70 => ( ! [X5: rat] :
% 13.77/7.70 ( ( member_rat @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_rat @ X5 @ B3 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_rat @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1872_finite__linorder__max__induct,axiom,
% 13.77/7.70 ! [A4: set_num,P2: set_num > $o] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_num )
% 13.77/7.70 => ( ! [B3: num,A5: set_num] :
% 13.77/7.70 ( ( finite_finite_num @ A5 )
% 13.77/7.70 => ( ! [X5: num] :
% 13.77/7.70 ( ( member_num @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_num @ X5 @ B3 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_num @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1873_finite__linorder__max__induct,axiom,
% 13.77/7.70 ! [A4: set_nat,P2: set_nat > $o] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ! [B3: nat,A5: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A5 )
% 13.77/7.70 => ( ! [X5: nat] :
% 13.77/7.70 ( ( member_nat @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_nat @ X5 @ B3 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_nat @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1874_finite__linorder__max__induct,axiom,
% 13.77/7.70 ! [A4: set_int,P2: set_int > $o] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ! [B3: int,A5: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A5 )
% 13.77/7.70 => ( ! [X5: int] :
% 13.77/7.70 ( ( member_int @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_int @ X5 @ B3 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_int @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1875_finite__linorder__min__induct,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [B3: code_integer,A5: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A5 )
% 13.77/7.70 => ( ! [X5: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X5 @ A5 )
% 13.77/7.70 => ( ord_le6747313008572928689nteger @ B3 @ X5 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_Code_integer @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1876_finite__linorder__min__induct,axiom,
% 13.77/7.70 ! [A4: set_o,P2: set_o > $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ! [B3: $o,A5: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A5 )
% 13.77/7.70 => ( ! [X5: $o] :
% 13.77/7.70 ( ( member_o @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_o @ B3 @ X5 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_o @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1877_finite__linorder__min__induct,axiom,
% 13.77/7.70 ! [A4: set_real,P2: set_real > $o] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ! [B3: real,A5: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A5 )
% 13.77/7.70 => ( ! [X5: real] :
% 13.77/7.70 ( ( member_real @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_real @ B3 @ X5 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_real @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1878_finite__linorder__min__induct,axiom,
% 13.77/7.70 ! [A4: set_rat,P2: set_rat > $o] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_rat )
% 13.77/7.70 => ( ! [B3: rat,A5: set_rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A5 )
% 13.77/7.70 => ( ! [X5: rat] :
% 13.77/7.70 ( ( member_rat @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_rat @ B3 @ X5 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_rat @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1879_finite__linorder__min__induct,axiom,
% 13.77/7.70 ! [A4: set_num,P2: set_num > $o] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_num )
% 13.77/7.70 => ( ! [B3: num,A5: set_num] :
% 13.77/7.70 ( ( finite_finite_num @ A5 )
% 13.77/7.70 => ( ! [X5: num] :
% 13.77/7.70 ( ( member_num @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_num @ B3 @ X5 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_num @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1880_finite__linorder__min__induct,axiom,
% 13.77/7.70 ! [A4: set_nat,P2: set_nat > $o] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ! [B3: nat,A5: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A5 )
% 13.77/7.70 => ( ! [X5: nat] :
% 13.77/7.70 ( ( member_nat @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_nat @ B3 @ X5 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_nat @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1881_finite__linorder__min__induct,axiom,
% 13.77/7.70 ! [A4: set_int,P2: set_int > $o] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ! [B3: int,A5: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A5 )
% 13.77/7.70 => ( ! [X5: int] :
% 13.77/7.70 ( ( member_int @ X5 @ A5 )
% 13.77/7.70 => ( ord_less_int @ B3 @ X5 ) )
% 13.77/7.70 => ( ( P2 @ A5 )
% 13.77/7.70 => ( P2 @ ( insert_int @ B3 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1882_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_VEBT_VEBT,A4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ F2 )
% 13.77/7.70 => ( ( ord_le4337996190870823476T_VEBT @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ! [A3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ F3 )
% 13.77/7.70 => ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_VEBT_VEBT @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_VEBT_VEBT @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1883_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_real,A4: set_real,P2: set_real > $o] :
% 13.77/7.70 ( ( finite_finite_real @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_real @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ! [A3: real,F3: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ F3 )
% 13.77/7.70 => ( ( member_real @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_real @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_real @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1884_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_set_nat,A4: set_set_nat,P2: set_set_nat > $o] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ F2 )
% 13.77/7.70 => ( ( ord_le6893508408891458716et_nat @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_set_nat )
% 13.77/7.70 => ( ! [A3: set_nat,F3: set_set_nat] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ F3 )
% 13.77/7.70 => ( ( member_set_nat @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_set_nat @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_set_nat @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1885_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_complex,A4: set_complex,P2: set_complex > $o] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ F2 )
% 13.77/7.70 => ( ( ord_le211207098394363844omplex @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.77/7.70 => ( ! [A3: complex,F3: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ F3 )
% 13.77/7.70 => ( ( member_complex @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_complex @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_complex @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1886_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_Code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ F2 )
% 13.77/7.70 => ( ( ord_le7084787975880047091nteger @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [A3: code_integer,F3: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ F3 )
% 13.77/7.70 => ( ( member_Code_integer @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_Code_integer @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_Code_integer @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1887_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_nat,A4: set_nat,P2: set_nat > $o] :
% 13.77/7.70 ( ( finite_finite_nat @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_nat @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ! [A3: nat,F3: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ F3 )
% 13.77/7.70 => ( ( member_nat @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_nat @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_nat @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1888_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_o,A4: set_o,P2: set_o > $o] :
% 13.77/7.70 ( ( finite_finite_o @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_o @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ! [A3: $o,F3: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ F3 )
% 13.77/7.70 => ( ( member_o @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_o @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_o @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1889_finite__subset__induct,axiom,
% 13.77/7.70 ! [F2: set_int,A4: set_int,P2: set_int > $o] :
% 13.77/7.70 ( ( finite_finite_int @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_int @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ! [A3: int,F3: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ F3 )
% 13.77/7.70 => ( ( member_int @ A3 @ A4 )
% 13.77/7.70 => ( ~ ( member_int @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_int @ A3 @ F3 ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1890_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_VEBT_VEBT,A4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ F2 )
% 13.77/7.70 => ( ( ord_le4337996190870823476T_VEBT @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ! [A3: vEBT_VEBT,F3: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ F3 )
% 13.77/7.70 => ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_le4337996190870823476T_VEBT @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_VEBT_VEBT @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_VEBT_VEBT @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1891_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_real,A4: set_real,P2: set_real > $o] :
% 13.77/7.70 ( ( finite_finite_real @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_real @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ! [A3: real,F3: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ F3 )
% 13.77/7.70 => ( ( member_real @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_less_eq_set_real @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_real @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_real @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1892_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_set_nat,A4: set_set_nat,P2: set_set_nat > $o] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ F2 )
% 13.77/7.70 => ( ( ord_le6893508408891458716et_nat @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_set_nat )
% 13.77/7.70 => ( ! [A3: set_nat,F3: set_set_nat] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ F3 )
% 13.77/7.70 => ( ( member_set_nat @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_le6893508408891458716et_nat @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_set_nat @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_set_nat @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1893_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_complex,A4: set_complex,P2: set_complex > $o] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ F2 )
% 13.77/7.70 => ( ( ord_le211207098394363844omplex @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.77/7.70 => ( ! [A3: complex,F3: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ F3 )
% 13.77/7.70 => ( ( member_complex @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_le211207098394363844omplex @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_complex @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_complex @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1894_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_Code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ F2 )
% 13.77/7.70 => ( ( ord_le7084787975880047091nteger @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [A3: code_integer,F3: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ F3 )
% 13.77/7.70 => ( ( member_Code_integer @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_le7084787975880047091nteger @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_Code_integer @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_Code_integer @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1895_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_nat,A4: set_nat,P2: set_nat > $o] :
% 13.77/7.70 ( ( finite_finite_nat @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_nat @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ! [A3: nat,F3: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ F3 )
% 13.77/7.70 => ( ( member_nat @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_less_eq_set_nat @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_nat @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_nat @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1896_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_o,A4: set_o,P2: set_o > $o] :
% 13.77/7.70 ( ( finite_finite_o @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_o @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ! [A3: $o,F3: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ F3 )
% 13.77/7.70 => ( ( member_o @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_less_eq_set_o @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_o @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_o @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1897_finite__subset__induct_H,axiom,
% 13.77/7.70 ! [F2: set_int,A4: set_int,P2: set_int > $o] :
% 13.77/7.70 ( ( finite_finite_int @ F2 )
% 13.77/7.70 => ( ( ord_less_eq_set_int @ F2 @ A4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ! [A3: int,F3: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ F3 )
% 13.77/7.70 => ( ( member_int @ A3 @ A4 )
% 13.77/7.70 => ( ( ord_less_eq_set_int @ F3 @ A4 )
% 13.77/7.70 => ( ~ ( member_int @ A3 @ F3 )
% 13.77/7.70 => ( ( P2 @ F3 )
% 13.77/7.70 => ( P2 @ ( insert_int @ A3 @ F3 ) ) ) ) ) ) )
% 13.77/7.70 => ( P2 @ F2 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1898_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_VEBT_VEBT > $o,B4: set_VEBT_VEBT] :
% 13.77/7.70 ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ( ~ ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ( ord_le4337996190870823476T_VEBT @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: vEBT_VEBT] :
% 13.77/7.70 ( ( member_VEBT_VEBT @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1899_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_real > $o,B4: set_real] :
% 13.77/7.70 ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ( ~ ( finite_finite_real @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_eq_set_real @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: real] :
% 13.77/7.70 ( ( member_real @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_real @ A5 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1900_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_set_nat > $o,B4: set_set_nat] :
% 13.77/7.70 ( ( P2 @ bot_bot_set_set_nat )
% 13.77/7.70 => ( ( ~ ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_set_nat] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_set_nat )
% 13.77/7.70 => ( ( ord_le6893508408891458716et_nat @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: set_nat] :
% 13.77/7.70 ( ( member_set_nat @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1901_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_complex > $o,B4: set_complex] :
% 13.77/7.70 ( ( P2 @ bot_bot_set_complex )
% 13.77/7.70 => ( ( ~ ( finite3207457112153483333omplex @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_complex )
% 13.77/7.70 => ( ( ord_le211207098394363844omplex @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: complex] :
% 13.77/7.70 ( ( member_complex @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1902_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_Code_integer > $o,B4: set_Code_integer] :
% 13.77/7.70 ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ~ ( finite6017078050557962740nteger @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le7084787975880047091nteger @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1903_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_o > $o,B4: set_o] :
% 13.77/7.70 ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ( ~ ( finite_finite_o @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_set_o @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: $o] :
% 13.77/7.70 ( ( member_o @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1904_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_nat > $o,B4: set_nat] :
% 13.77/7.70 ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ( ~ ( finite_finite_nat @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: nat] :
% 13.77/7.70 ( ( member_nat @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1905_remove__induct,axiom,
% 13.77/7.70 ! [P2: set_int > $o,B4: set_int] :
% 13.77/7.70 ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ( ~ ( finite_finite_int @ B4 )
% 13.77/7.70 => ( P2 @ B4 ) )
% 13.77/7.70 => ( ! [A5: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_set_int @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: int] :
% 13.77/7.70 ( ( member_int @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1906_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ! [A5: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ( ord_le4337996190870823476T_VEBT @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: vEBT_VEBT] :
% 13.77/7.70 ( ( member_VEBT_VEBT @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_5127226145743854075T_VEBT @ A5 @ ( insert_VEBT_VEBT @ X5 @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1907_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_real,P2: set_real > $o] :
% 13.77/7.70 ( ( finite_finite_real @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_real )
% 13.77/7.70 => ( ! [A5: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_eq_set_real @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: real] :
% 13.77/7.70 ( ( member_real @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_real @ A5 @ ( insert_real @ X5 @ bot_bot_set_real ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1908_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_set_nat,P2: set_set_nat > $o] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_set_nat )
% 13.77/7.70 => ( ! [A5: set_set_nat] :
% 13.77/7.70 ( ( finite1152437895449049373et_nat @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_set_nat )
% 13.77/7.70 => ( ( ord_le6893508408891458716et_nat @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: set_nat] :
% 13.77/7.70 ( ( member_set_nat @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_2163939370556025621et_nat @ A5 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1909_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_complex,P2: set_complex > $o] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.77/7.70 => ( ! [A5: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_complex )
% 13.77/7.70 => ( ( ord_le211207098394363844omplex @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: complex] :
% 13.77/7.70 ( ( member_complex @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_811609699411566653omplex @ A5 @ ( insert_complex @ X5 @ bot_bot_set_complex ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1910_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [A5: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le7084787975880047091nteger @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_2355218937544613996nteger @ A5 @ ( insert_Code_integer @ X5 @ bot_bo3990330152332043303nteger ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1911_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_o,P2: set_o > $o] :
% 13.77/7.70 ( ( finite_finite_o @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ! [A5: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_set_o @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: $o] :
% 13.77/7.70 ( ( member_o @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_o @ A5 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1912_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_nat,P2: set_nat > $o] :
% 13.77/7.70 ( ( finite_finite_nat @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ! [A5: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: nat] :
% 13.77/7.70 ( ( member_nat @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_nat @ A5 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1913_finite__remove__induct,axiom,
% 13.77/7.70 ! [B4: set_int,P2: set_int > $o] :
% 13.77/7.70 ( ( finite_finite_int @ B4 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ! [A5: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A5 )
% 13.77/7.70 => ( ( A5 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_set_int @ A5 @ B4 )
% 13.77/7.70 => ( ! [X5: int] :
% 13.77/7.70 ( ( member_int @ X5 @ A5 )
% 13.77/7.70 => ( P2 @ ( minus_minus_set_int @ A5 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 13.77/7.70 => ( P2 @ A5 ) ) ) ) )
% 13.77/7.70 => ( P2 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1914_finite__induct__select,axiom,
% 13.77/7.70 ! [S3: set_VEBT_VEBT,P2: set_VEBT_VEBT > $o] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bo8194388402131092736T_VEBT )
% 13.77/7.70 => ( ! [T4: set_VEBT_VEBT] :
% 13.77/7.70 ( ( ord_le3480810397992357184T_VEBT @ T4 @ S3 )
% 13.77/7.70 => ( ( P2 @ T4 )
% 13.77/7.70 => ? [X5: vEBT_VEBT] :
% 13.77/7.70 ( ( member_VEBT_VEBT @ X5 @ ( minus_5127226145743854075T_VEBT @ S3 @ T4 ) )
% 13.77/7.70 & ( P2 @ ( insert_VEBT_VEBT @ X5 @ T4 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1915_finite__induct__select,axiom,
% 13.77/7.70 ! [S3: set_complex,P2: set_complex > $o] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_complex )
% 13.77/7.70 => ( ! [T4: set_complex] :
% 13.77/7.70 ( ( ord_less_set_complex @ T4 @ S3 )
% 13.77/7.70 => ( ( P2 @ T4 )
% 13.77/7.70 => ? [X5: complex] :
% 13.77/7.70 ( ( member_complex @ X5 @ ( minus_811609699411566653omplex @ S3 @ T4 ) )
% 13.77/7.70 & ( P2 @ ( insert_complex @ X5 @ T4 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1916_finite__induct__select,axiom,
% 13.77/7.70 ! [S3: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [T4: set_Code_integer] :
% 13.77/7.70 ( ( ord_le1307284697595431911nteger @ T4 @ S3 )
% 13.77/7.70 => ( ( P2 @ T4 )
% 13.77/7.70 => ? [X5: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X5 @ ( minus_2355218937544613996nteger @ S3 @ T4 ) )
% 13.77/7.70 & ( P2 @ ( insert_Code_integer @ X5 @ T4 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1917_finite__induct__select,axiom,
% 13.77/7.70 ! [S3: set_int,P2: set_int > $o] :
% 13.77/7.70 ( ( finite_finite_int @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_int )
% 13.77/7.70 => ( ! [T4: set_int] :
% 13.77/7.70 ( ( ord_less_set_int @ T4 @ S3 )
% 13.77/7.70 => ( ( P2 @ T4 )
% 13.77/7.70 => ? [X5: int] :
% 13.77/7.70 ( ( member_int @ X5 @ ( minus_minus_set_int @ S3 @ T4 ) )
% 13.77/7.70 & ( P2 @ ( insert_int @ X5 @ T4 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1918_finite__induct__select,axiom,
% 13.77/7.70 ! [S3: set_o,P2: set_o > $o] :
% 13.77/7.70 ( ( finite_finite_o @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_o )
% 13.77/7.70 => ( ! [T4: set_o] :
% 13.77/7.70 ( ( ord_less_set_o @ T4 @ S3 )
% 13.77/7.70 => ( ( P2 @ T4 )
% 13.77/7.70 => ? [X5: $o] :
% 13.77/7.70 ( ( member_o @ X5 @ ( minus_minus_set_o @ S3 @ T4 ) )
% 13.77/7.70 & ( P2 @ ( insert_o @ X5 @ T4 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1919_finite__induct__select,axiom,
% 13.77/7.70 ! [S3: set_nat,P2: set_nat > $o] :
% 13.77/7.70 ( ( finite_finite_nat @ S3 )
% 13.77/7.70 => ( ( P2 @ bot_bot_set_nat )
% 13.77/7.70 => ( ! [T4: set_nat] :
% 13.77/7.70 ( ( ord_less_set_nat @ T4 @ S3 )
% 13.77/7.70 => ( ( P2 @ T4 )
% 13.77/7.70 => ? [X5: nat] :
% 13.77/7.70 ( ( member_nat @ X5 @ ( minus_minus_set_nat @ S3 @ T4 ) )
% 13.77/7.70 & ( P2 @ ( insert_nat @ X5 @ T4 ) ) ) ) )
% 13.77/7.70 => ( P2 @ S3 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1920_psubset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.70 ( ( ord_le3480810397992357184T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_VEBT_VEBT @ X @ B4 )
% 13.77/7.70 => ( ord_le3480810397992357184T_VEBT @ A4 @ B4 ) )
% 13.77/7.70 & ( ~ ( member_VEBT_VEBT @ X @ B4 )
% 13.77/7.70 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.70 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.70 => ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1921_psubset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_real,X: real,B4: set_real] :
% 13.77/7.70 ( ( ord_less_set_real @ A4 @ ( insert_real @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_real @ X @ B4 )
% 13.77/7.70 => ( ord_less_set_real @ A4 @ B4 ) )
% 13.77/7.70 & ( ~ ( member_real @ X @ B4 )
% 13.77/7.70 => ( ( ( member_real @ X @ A4 )
% 13.77/7.70 => ( ord_less_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_real @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1922_psubset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_set_nat,X: set_nat,B4: set_set_nat] :
% 13.77/7.70 ( ( ord_less_set_set_nat @ A4 @ ( insert_set_nat @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_set_nat @ X @ B4 )
% 13.77/7.70 => ( ord_less_set_set_nat @ A4 @ B4 ) )
% 13.77/7.70 & ( ~ ( member_set_nat @ X @ B4 )
% 13.77/7.70 => ( ( ( member_set_nat @ X @ A4 )
% 13.77/7.70 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_set_nat @ X @ A4 )
% 13.77/7.70 => ( ord_le6893508408891458716et_nat @ A4 @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1923_psubset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o,B4: set_o] :
% 13.77/7.70 ( ( ord_less_set_o @ A4 @ ( insert_o @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_o @ X @ B4 )
% 13.77/7.70 => ( ord_less_set_o @ A4 @ B4 ) )
% 13.77/7.70 & ( ~ ( member_o @ X @ B4 )
% 13.77/7.70 => ( ( ( member_o @ X @ A4 )
% 13.77/7.70 => ( ord_less_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_o @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_o @ A4 @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1924_psubset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat,B4: set_nat] :
% 13.77/7.70 ( ( ord_less_set_nat @ A4 @ ( insert_nat @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_nat @ X @ B4 )
% 13.77/7.70 => ( ord_less_set_nat @ A4 @ B4 ) )
% 13.77/7.70 & ( ~ ( member_nat @ X @ B4 )
% 13.77/7.70 => ( ( ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1925_psubset__insert__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int,B4: set_int] :
% 13.77/7.70 ( ( ord_less_set_int @ A4 @ ( insert_int @ X @ B4 ) )
% 13.77/7.70 = ( ( ( member_int @ X @ B4 )
% 13.77/7.70 => ( ord_less_set_int @ A4 @ B4 ) )
% 13.77/7.70 & ( ~ ( member_int @ X @ B4 )
% 13.77/7.70 => ( ( ( member_int @ X @ A4 )
% 13.77/7.70 => ( ord_less_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) )
% 13.77/7.70 & ( ~ ( member_int @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1926_finite__list,axiom,
% 13.77/7.70 ! [A4: set_VEBT_VEBT] :
% 13.77/7.70 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.70 => ? [Xs3: list_VEBT_VEBT] :
% 13.77/7.70 ( ( set_VEBT_VEBT2 @ Xs3 )
% 13.77/7.70 = A4 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1927_finite__list,axiom,
% 13.77/7.70 ! [A4: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ? [Xs3: list_real] :
% 13.77/7.70 ( ( set_real2 @ Xs3 )
% 13.77/7.70 = A4 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1928_finite__list,axiom,
% 13.77/7.70 ! [A4: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ? [Xs3: list_o] :
% 13.77/7.70 ( ( set_o2 @ Xs3 )
% 13.77/7.70 = A4 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1929_finite__list,axiom,
% 13.77/7.70 ! [A4: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ? [Xs3: list_nat] :
% 13.77/7.70 ( ( set_nat2 @ Xs3 )
% 13.77/7.70 = A4 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1930_finite__list,axiom,
% 13.77/7.70 ! [A4: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ? [Xs3: list_int] :
% 13.77/7.70 ( ( set_int2 @ Xs3 )
% 13.77/7.70 = A4 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1931_finite__list,axiom,
% 13.77/7.70 ! [A4: set_complex] :
% 13.77/7.70 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.70 => ? [Xs3: list_complex] :
% 13.77/7.70 ( ( set_complex2 @ Xs3 )
% 13.77/7.70 = A4 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1932_finite__list,axiom,
% 13.77/7.70 ! [A4: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ? [Xs3: list_Code_integer] :
% 13.77/7.70 ( ( set_Code_integer2 @ Xs3 )
% 13.77/7.70 = A4 ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1933_subset__code_I1_J,axiom,
% 13.77/7.70 ! [Xs: list_set_nat,B4: set_set_nat] :
% 13.77/7.70 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B4 )
% 13.77/7.70 = ( ! [X4: set_nat] :
% 13.77/7.70 ( ( member_set_nat @ X4 @ ( set_set_nat2 @ Xs ) )
% 13.77/7.70 => ( member_set_nat @ X4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1934_subset__code_I1_J,axiom,
% 13.77/7.70 ! [Xs: list_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.70 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B4 )
% 13.77/7.70 = ( ! [X4: vEBT_VEBT] :
% 13.77/7.70 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.70 => ( member_VEBT_VEBT @ X4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1935_subset__code_I1_J,axiom,
% 13.77/7.70 ! [Xs: list_nat,B4: set_nat] :
% 13.77/7.70 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B4 )
% 13.77/7.70 = ( ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 13.77/7.70 => ( member_nat @ X4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1936_subset__code_I1_J,axiom,
% 13.77/7.70 ! [Xs: list_real,B4: set_real] :
% 13.77/7.70 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B4 )
% 13.77/7.70 = ( ! [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 13.77/7.70 => ( member_real @ X4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1937_subset__code_I1_J,axiom,
% 13.77/7.70 ! [Xs: list_o,B4: set_o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ B4 )
% 13.77/7.70 = ( ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 13.77/7.70 => ( member_o @ X4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1938_subset__code_I1_J,axiom,
% 13.77/7.70 ! [Xs: list_int,B4: set_int] :
% 13.77/7.70 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B4 )
% 13.77/7.70 = ( ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 13.77/7.70 => ( member_int @ X4 @ B4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1939_geqmaxNone,axiom,
% 13.77/7.70 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 13.77/7.70 => ( ( ord_less_eq_nat @ Ma @ X )
% 13.77/7.70 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.70 = none_nat ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1940_pred__corr,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_pred @ T @ X )
% 13.77/7.70 = ( some_nat @ Px ) )
% 13.77/7.70 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1941_pred__correct,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_pred @ T @ X )
% 13.77/7.70 = ( some_nat @ Sx ) )
% 13.77/7.70 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1942_set__vebt__pred,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_pred @ T @ X )
% 13.77/7.70 = ( some_nat @ Px ) )
% 13.77/7.70 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1943_succ__corr,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_succ @ T @ X )
% 13.77/7.70 = ( some_nat @ Sx ) )
% 13.77/7.70 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1944_succ__correct,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_succ @ T @ X )
% 13.77/7.70 = ( some_nat @ Sx ) )
% 13.77/7.70 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1945_maxt__sound,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 13.77/7.70 => ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1946_maxt__corr,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ X ) )
% 13.77/7.70 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1947_set__vebt__maxt,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ X ) )
% 13.77/7.70 = ( vEBT_VEBT_max_in_set @ ( vEBT_set_vebt @ T ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1948_mint__sound,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 13.77/7.70 => ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = ( some_nat @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1949_maxbmo,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,X: nat] :
% 13.77/7.70 ( ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ X ) )
% 13.77/7.70 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1950_minNullmin,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT] :
% 13.77/7.70 ( ( vEBT_VEBT_minNull @ T )
% 13.77/7.70 => ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = none_nat ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1951_minminNull,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT] :
% 13.77/7.70 ( ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = none_nat )
% 13.77/7.70 => ( vEBT_VEBT_minNull @ T ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1952_vebt__minNull__mint,axiom,
% 13.77/7.70 ( vEBT_VEBT_minNull
% 13.77/7.70 = ( ^ [T2: vEBT_VEBT] :
% 13.77/7.70 ( ( vEBT_vebt_mint @ T2 )
% 13.77/7.70 = none_nat ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1953_mint__member,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = ( some_nat @ Maxi ) )
% 13.77/7.70 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1954_maxt__member,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ Maxi ) )
% 13.77/7.70 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1955_mint__corr__help,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = ( some_nat @ Mini ) )
% 13.77/7.70 => ( ( vEBT_vebt_member @ T @ X )
% 13.77/7.70 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1956_maxt__corr__help,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ Maxi ) )
% 13.77/7.70 => ( ( vEBT_vebt_member @ T @ X )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1957_set__vebt__mint_H,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = ( some_nat @ X ) )
% 13.77/7.70 = ( ( member_nat @ X @ ( vEBT_set_vebt @ T ) )
% 13.77/7.70 & ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ X4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1958_set__vebt__maxt_H,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ X ) )
% 13.77/7.70 = ( ( member_nat @ X @ ( vEBT_set_vebt @ T ) )
% 13.77/7.70 & ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.70 => ( ord_less_eq_nat @ X4 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1959_mint__corr__help__empty,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = none_nat )
% 13.77/7.70 => ( ( vEBT_VEBT_set_vebt @ T )
% 13.77/7.70 = bot_bot_set_nat ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1960_maxt__corr__help__empty,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = none_nat )
% 13.77/7.70 => ( ( vEBT_VEBT_set_vebt @ T )
% 13.77/7.70 = bot_bot_set_nat ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1961_set__vebt__mint,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = ( some_nat @ X ) )
% 13.77/7.70 = ( vEBT_VEBT_min_in_set @ ( vEBT_set_vebt @ T ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1962_mint__corr,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = ( some_nat @ X ) )
% 13.77/7.70 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1963_vebt__succ_Osimps_I2_J,axiom,
% 13.77/7.70 ! [Uv2: $o,Uw2: $o,N: nat] :
% 13.77/7.70 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1964_vebt__pred_Osimps_I1_J,axiom,
% 13.77/7.70 ! [Uu2: $o,Uv2: $o] :
% 13.77/7.70 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1965_vebt__succ_Osimps_I3_J,axiom,
% 13.77/7.70 ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 13.77/7.70 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz ) @ Va2 )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1966_vebt__pred_Osimps_I4_J,axiom,
% 13.77/7.70 ! [Uy2: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 13.77/7.70 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz @ Va2 ) @ Vb )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1967_vebt__succ_Osimps_I4_J,axiom,
% 13.77/7.70 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 13.77/7.70 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1968_vebt__pred_Osimps_I5_J,axiom,
% 13.77/7.70 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 13.77/7.70 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1969_vebt__succ_Osimps_I5_J,axiom,
% 13.77/7.70 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 13.77/7.70 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1970_vebt__pred_Osimps_I6_J,axiom,
% 13.77/7.70 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 13.77/7.70 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1971_vebt__succ_Osimps_I1_J,axiom,
% 13.77/7.70 ! [B: $o,Uu2: $o] :
% 13.77/7.70 ( ( B
% 13.77/7.70 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ B
% 13.77/7.70 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 13.77/7.70 = none_nat ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1972_vebt__succ__code_I1_J,axiom,
% 13.77/7.70 ! [B: $o,X: nat,A: $o] :
% 13.77/7.70 ( ( ( B
% 13.77/7.70 & ( X = zero_zero_nat ) )
% 13.77/7.70 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ ( B
% 13.77/7.70 & ( X = zero_zero_nat ) )
% 13.77/7.70 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = none_nat ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1973_vebt__pred_Osimps_I2_J,axiom,
% 13.77/7.70 ! [A: $o,Uw2: $o] :
% 13.77/7.70 ( ( A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.70 = none_nat ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1974_vebt__pred__code,axiom,
% 13.77/7.70 ! [X: nat,A: $o,B: $o] :
% 13.77/7.70 ( ( ( X = zero_zero_nat )
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = none_nat ) )
% 13.77/7.70 & ( ( X != zero_zero_nat )
% 13.77/7.70 => ( ( ( X = one_one_nat )
% 13.77/7.70 => ( ( A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = none_nat ) ) ) )
% 13.77/7.70 & ( ( X != one_one_nat )
% 13.77/7.70 => ( ( B
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ B
% 13.77/7.70 => ( ( A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.70 = none_nat ) ) ) ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1975_vebt__pred_Osimps_I3_J,axiom,
% 13.77/7.70 ! [B: $o,A: $o,Va2: nat] :
% 13.77/7.70 ( ( B
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ B
% 13.77/7.70 => ( ( A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A
% 13.77/7.70 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.70 = none_nat ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1976_vebt__maxt_Oelims,axiom,
% 13.77/7.70 ! [X: vEBT_VEBT,Y: option_nat] :
% 13.77/7.70 ( ( ( vEBT_vebt_maxt @ X )
% 13.77/7.70 = Y )
% 13.77/7.70 => ( ! [A3: $o,B3: $o] :
% 13.77/7.70 ( ( X
% 13.77/7.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.70 => ~ ( ( B3
% 13.77/7.70 => ( Y
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ B3
% 13.77/7.70 => ( ( A3
% 13.77/7.70 => ( Y
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A3
% 13.77/7.70 => ( Y = none_nat ) ) ) ) ) )
% 13.77/7.70 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.70 ( X
% 13.77/7.70 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.70 => ( Y != none_nat ) )
% 13.77/7.70 => ~ ! [Mi2: nat,Ma2: nat] :
% 13.77/7.70 ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.70 ( X
% 13.77/7.70 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.70 => ( Y
% 13.77/7.70 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1977_vebt__mint_Oelims,axiom,
% 13.77/7.70 ! [X: vEBT_VEBT,Y: option_nat] :
% 13.77/7.70 ( ( ( vEBT_vebt_mint @ X )
% 13.77/7.70 = Y )
% 13.77/7.70 => ( ! [A3: $o,B3: $o] :
% 13.77/7.70 ( ( X
% 13.77/7.70 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.70 => ~ ( ( A3
% 13.77/7.70 => ( Y
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A3
% 13.77/7.70 => ( ( B3
% 13.77/7.70 => ( Y
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ B3
% 13.77/7.70 => ( Y = none_nat ) ) ) ) ) )
% 13.77/7.70 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.70 ( X
% 13.77/7.70 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.70 => ( Y != none_nat ) )
% 13.77/7.70 => ~ ! [Mi2: nat] :
% 13.77/7.70 ( ? [Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.70 ( X
% 13.77/7.70 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.70 => ( Y
% 13.77/7.70 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1978_vebt__maxt_Osimps_I1_J,axiom,
% 13.77/7.70 ! [B: $o,A: $o] :
% 13.77/7.70 ( ( B
% 13.77/7.70 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ B
% 13.77/7.70 => ( ( A
% 13.77/7.70 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A
% 13.77/7.70 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.70 = none_nat ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1979_vebt__mint_Osimps_I1_J,axiom,
% 13.77/7.70 ! [A: $o,B: $o] :
% 13.77/7.70 ( ( A
% 13.77/7.70 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.70 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.70 & ( ~ A
% 13.77/7.70 => ( ( B
% 13.77/7.70 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.70 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.70 & ( ~ B
% 13.77/7.70 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.70 = none_nat ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1980_vebt__maxt_Osimps_I3_J,axiom,
% 13.77/7.70 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 13.77/7.70 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 13.77/7.70 = ( some_nat @ Ma ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1981_vebt__mint_Osimps_I3_J,axiom,
% 13.77/7.70 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 13.77/7.70 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 13.77/7.70 = ( some_nat @ Mi ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1982_set__vebt__mint_H_H,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( ( vEBT_set_vebt @ T )
% 13.77/7.70 = bot_bot_set_nat )
% 13.77/7.70 => ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = none_nat ) )
% 13.77/7.70 & ( ( ( vEBT_set_vebt @ T )
% 13.77/7.70 != bot_bot_set_nat )
% 13.77/7.70 => ( ( vEBT_vebt_mint @ T )
% 13.77/7.70 = ( some_nat @ ( lattic8721135487736765967in_nat @ ( vEBT_set_vebt @ T ) ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1983_set__vebt__maxt_H_H,axiom,
% 13.77/7.70 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.70 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.70 => ( ( ( ( vEBT_set_vebt @ T )
% 13.77/7.70 = bot_bot_set_nat )
% 13.77/7.70 => ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = none_nat ) )
% 13.77/7.70 & ( ( ( vEBT_set_vebt @ T )
% 13.77/7.70 != bot_bot_set_nat )
% 13.77/7.70 => ( ( vEBT_vebt_maxt @ T )
% 13.77/7.70 = ( some_nat @ ( lattic8265883725875713057ax_nat @ ( vEBT_set_vebt @ T ) ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1984_vebt__maxt_Osimps_I2_J,axiom,
% 13.77/7.70 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 13.77/7.70 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1985_vebt__mint_Osimps_I2_J,axiom,
% 13.77/7.70 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 13.77/7.70 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 13.77/7.70 = none_nat ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1986_Max__singleton,axiom,
% 13.77/7.70 ! [X: int] :
% 13.77/7.70 ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.70 = X ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1987_Max__singleton,axiom,
% 13.77/7.70 ! [X: $o] :
% 13.77/7.70 ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.70 = X ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1988_Max__singleton,axiom,
% 13.77/7.70 ! [X: nat] :
% 13.77/7.70 ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.70 = X ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1989_Min__singleton,axiom,
% 13.77/7.70 ! [X: int] :
% 13.77/7.70 ( ( lattic8718645017227715691in_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.70 = X ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1990_Min__singleton,axiom,
% 13.77/7.70 ! [X: $o] :
% 13.77/7.70 ( ( lattic1973801136483472281_Min_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.70 = X ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1991_Min__singleton,axiom,
% 13.77/7.70 ! [X: nat] :
% 13.77/7.70 ( ( lattic8721135487736765967in_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.70 = X ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1992_Max_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1993_Max_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1994_Max_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1995_Max_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1996_Max_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1997_Max_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1998_Max__less__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le6747313008572928689nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le6747313008572928689nteger @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_1999_Max__less__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_o @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2000_Max__less__iff,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_real @ ( lattic4275903605611617917x_real @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_real @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2001_Max__less__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_rat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2002_Max__less__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_num @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2003_Max__less__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_int @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2004_Max__less__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X )
% 13.77/7.70 = ( ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_nat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2005_Min_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) )
% 13.77/7.70 = ( ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2006_Min_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) )
% 13.77/7.70 = ( ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2007_Min_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) )
% 13.77/7.70 = ( ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2008_Min_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_eq_num @ X @ ( lattic5278467273892544601in_num @ A4 ) )
% 13.77/7.70 = ( ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2009_Min_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A4 ) )
% 13.77/7.70 = ( ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2010_Min_Obounded__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) )
% 13.77/7.70 = ( ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2011_Min__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le6747313008572928689nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) )
% 13.77/7.70 = ( ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le6747313008572928689nteger @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2012_Min__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) )
% 13.77/7.70 = ( ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_o @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2013_Min__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_real @ X @ ( lattic3629708407755379051n_real @ A4 ) )
% 13.77/7.70 = ( ! [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_real @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2014_Min__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) )
% 13.77/7.70 = ( ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_rat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2015_Min__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_num @ X @ ( lattic5278467273892544601in_num @ A4 ) )
% 13.77/7.70 = ( ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_num @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2016_Min__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_int @ X @ ( lattic8718645017227715691in_int @ A4 ) )
% 13.77/7.70 = ( ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_int @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2017_Min__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) )
% 13.77/7.70 = ( ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_nat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2018_Min_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_real,A: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( member_real @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ ( lattic3629708407755379051n_real @ A4 ) @ A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2019_Min_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,A: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( member_Code_integer @ A @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ A4 ) @ A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2020_Min_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_rat,A: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( member_rat @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2021_Min_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_num,A: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( member_num @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ A4 ) @ A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2022_Min_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_int,A: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( member_int @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ A4 ) @ A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2023_Min_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_nat,A: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( member_nat @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2024_Min__eqI,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ! [Y3: real] :
% 13.77/7.70 ( ( member_real @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ X @ Y3 ) )
% 13.77/7.70 => ( ( member_real @ X @ A4 )
% 13.77/7.70 => ( ( lattic3629708407755379051n_real @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2025_Min__eqI,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ! [Y3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ Y3 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X @ Y3 ) )
% 13.77/7.70 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.70 => ( ( lattic1063845414844153500nteger @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2026_Min__eqI,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ! [Y3: rat] :
% 13.77/7.70 ( ( member_rat @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X @ Y3 ) )
% 13.77/7.70 => ( ( member_rat @ X @ A4 )
% 13.77/7.70 => ( ( lattic8086005427650270231in_rat @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2027_Min__eqI,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ! [Y3: num] :
% 13.77/7.70 ( ( member_num @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X @ Y3 ) )
% 13.77/7.70 => ( ( member_num @ X @ A4 )
% 13.77/7.70 => ( ( lattic5278467273892544601in_num @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2028_Min__eqI,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ! [Y3: int] :
% 13.77/7.70 ( ( member_int @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X @ Y3 ) )
% 13.77/7.70 => ( ( member_int @ X @ A4 )
% 13.77/7.70 => ( ( lattic8718645017227715691in_int @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2029_Min__eqI,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ! [Y3: nat] :
% 13.77/7.70 ( ( member_nat @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ Y3 ) )
% 13.77/7.70 => ( ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ( lattic8721135487736765967in_nat @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2030_Min__le,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( member_real @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ ( lattic3629708407755379051n_real @ A4 ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2031_Min__le,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ A4 ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2032_Min__le,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( member_rat @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2033_Min__le,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( member_num @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ A4 ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2034_Min__le,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( member_int @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ A4 ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2035_Min__le,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ X ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2036_Min__in,axiom,
% 13.77/7.70 ! [A4: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( member_real @ ( lattic3629708407755379051n_real @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2037_Min__in,axiom,
% 13.77/7.70 ! [A4: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( member_Code_integer @ ( lattic1063845414844153500nteger @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2038_Min__in,axiom,
% 13.77/7.70 ! [A4: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( member_int @ ( lattic8718645017227715691in_int @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2039_Min__in,axiom,
% 13.77/7.70 ! [A4: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( member_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2040_Min__in,axiom,
% 13.77/7.70 ! [A4: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( member_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2041_Max_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_real,A: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( member_real @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ A @ ( lattic4275903605611617917x_real @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2042_Max_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,A: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( member_Code_integer @ A @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ A @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2043_Max_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_rat,A: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( member_rat @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ A @ ( lattic7630753665789217321ax_rat @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2044_Max_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_num,A: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( member_num @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ A @ ( lattic4823215512031491691ax_num @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2045_Max_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_int,A: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( member_int @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ A @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2046_Max_OcoboundedI,axiom,
% 13.77/7.70 ! [A4: set_nat,A: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( member_nat @ A @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ A @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2047_Max__eq__if,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.70 => ( ! [X3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X3 @ A4 )
% 13.77/7.70 => ? [Xa: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ Xa @ B4 )
% 13.77/7.70 & ( ord_le3102999989581377725nteger @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ! [X3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X3 @ B4 )
% 13.77/7.70 => ? [Xa: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ Xa @ A4 )
% 13.77/7.70 & ( ord_le3102999989581377725nteger @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ( lattic4901227151466704046nteger @ A4 )
% 13.77/7.70 = ( lattic4901227151466704046nteger @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2048_Max__eq__if,axiom,
% 13.77/7.70 ! [A4: set_rat,B4: set_rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( finite_finite_rat @ B4 )
% 13.77/7.70 => ( ! [X3: rat] :
% 13.77/7.70 ( ( member_rat @ X3 @ A4 )
% 13.77/7.70 => ? [Xa: rat] :
% 13.77/7.70 ( ( member_rat @ Xa @ B4 )
% 13.77/7.70 & ( ord_less_eq_rat @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ! [X3: rat] :
% 13.77/7.70 ( ( member_rat @ X3 @ B4 )
% 13.77/7.70 => ? [Xa: rat] :
% 13.77/7.70 ( ( member_rat @ Xa @ A4 )
% 13.77/7.70 & ( ord_less_eq_rat @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ( lattic7630753665789217321ax_rat @ A4 )
% 13.77/7.70 = ( lattic7630753665789217321ax_rat @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2049_Max__eq__if,axiom,
% 13.77/7.70 ! [A4: set_num,B4: set_num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( finite_finite_num @ B4 )
% 13.77/7.70 => ( ! [X3: num] :
% 13.77/7.70 ( ( member_num @ X3 @ A4 )
% 13.77/7.70 => ? [Xa: num] :
% 13.77/7.70 ( ( member_num @ Xa @ B4 )
% 13.77/7.70 & ( ord_less_eq_num @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ! [X3: num] :
% 13.77/7.70 ( ( member_num @ X3 @ B4 )
% 13.77/7.70 => ? [Xa: num] :
% 13.77/7.70 ( ( member_num @ Xa @ A4 )
% 13.77/7.70 & ( ord_less_eq_num @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ( lattic4823215512031491691ax_num @ A4 )
% 13.77/7.70 = ( lattic4823215512031491691ax_num @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2050_Max__eq__if,axiom,
% 13.77/7.70 ! [A4: set_int,B4: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( finite_finite_int @ B4 )
% 13.77/7.70 => ( ! [X3: int] :
% 13.77/7.70 ( ( member_int @ X3 @ A4 )
% 13.77/7.70 => ? [Xa: int] :
% 13.77/7.70 ( ( member_int @ Xa @ B4 )
% 13.77/7.70 & ( ord_less_eq_int @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ! [X3: int] :
% 13.77/7.70 ( ( member_int @ X3 @ B4 )
% 13.77/7.70 => ? [Xa: int] :
% 13.77/7.70 ( ( member_int @ Xa @ A4 )
% 13.77/7.70 & ( ord_less_eq_int @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ( lattic8263393255366662781ax_int @ A4 )
% 13.77/7.70 = ( lattic8263393255366662781ax_int @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2051_Max__eq__if,axiom,
% 13.77/7.70 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( finite_finite_nat @ B4 )
% 13.77/7.70 => ( ! [X3: nat] :
% 13.77/7.70 ( ( member_nat @ X3 @ A4 )
% 13.77/7.70 => ? [Xa: nat] :
% 13.77/7.70 ( ( member_nat @ Xa @ B4 )
% 13.77/7.70 & ( ord_less_eq_nat @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ! [X3: nat] :
% 13.77/7.70 ( ( member_nat @ X3 @ B4 )
% 13.77/7.70 => ? [Xa: nat] :
% 13.77/7.70 ( ( member_nat @ Xa @ A4 )
% 13.77/7.70 & ( ord_less_eq_nat @ X3 @ Xa ) ) )
% 13.77/7.70 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 13.77/7.70 = ( lattic8265883725875713057ax_nat @ B4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2052_Max__eqI,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ! [Y3: real] :
% 13.77/7.70 ( ( member_real @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ Y3 @ X ) )
% 13.77/7.70 => ( ( member_real @ X @ A4 )
% 13.77/7.70 => ( ( lattic4275903605611617917x_real @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2053_Max__eqI,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ! [Y3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ Y3 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ Y3 @ X ) )
% 13.77/7.70 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.70 => ( ( lattic4901227151466704046nteger @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2054_Max__eqI,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ! [Y3: rat] :
% 13.77/7.70 ( ( member_rat @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ Y3 @ X ) )
% 13.77/7.70 => ( ( member_rat @ X @ A4 )
% 13.77/7.70 => ( ( lattic7630753665789217321ax_rat @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2055_Max__eqI,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ! [Y3: num] :
% 13.77/7.70 ( ( member_num @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ Y3 @ X ) )
% 13.77/7.70 => ( ( member_num @ X @ A4 )
% 13.77/7.70 => ( ( lattic4823215512031491691ax_num @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2056_Max__eqI,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ! [Y3: int] :
% 13.77/7.70 ( ( member_int @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ Y3 @ X ) )
% 13.77/7.70 => ( ( member_int @ X @ A4 )
% 13.77/7.70 => ( ( lattic8263393255366662781ax_int @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2057_Max__eqI,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ! [Y3: nat] :
% 13.77/7.70 ( ( member_nat @ Y3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ Y3 @ X ) )
% 13.77/7.70 => ( ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 13.77/7.70 = X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2058_Max__ge,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( member_real @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ X @ ( lattic4275903605611617917x_real @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2059_Max__ge,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2060_Max__ge,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( member_rat @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X @ ( lattic7630753665789217321ax_rat @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2061_Max__ge,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( member_num @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X @ ( lattic4823215512031491691ax_num @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2062_Max__ge,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( member_int @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2063_Max__ge,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( member_nat @ X @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2064_Max__in,axiom,
% 13.77/7.70 ! [A4: set_real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( member_real @ ( lattic4275903605611617917x_real @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2065_Max__in,axiom,
% 13.77/7.70 ! [A4: set_Code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( member_Code_integer @ ( lattic4901227151466704046nteger @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2066_Max__in,axiom,
% 13.77/7.70 ! [A4: set_int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( member_int @ ( lattic8263393255366662781ax_int @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2067_Max__in,axiom,
% 13.77/7.70 ! [A4: set_o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( member_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2068_Max__in,axiom,
% 13.77/7.70 ! [A4: set_nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( member_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ A4 ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2069_Min__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_real,M: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ( lattic3629708407755379051n_real @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_real @ M @ A4 )
% 13.77/7.70 & ! [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2070_Min__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,M: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ( lattic1063845414844153500nteger @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_Code_integer @ M @ A4 )
% 13.77/7.70 & ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2071_Min__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_o,M: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ( lattic1973801136483472281_Min_o @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_o @ M @ A4 )
% 13.77/7.70 & ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2072_Min__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,M: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ( lattic8086005427650270231in_rat @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_rat @ M @ A4 )
% 13.77/7.70 & ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2073_Min__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_num,M: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ( lattic5278467273892544601in_num @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_num @ M @ A4 )
% 13.77/7.70 & ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2074_Min__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_int,M: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ( lattic8718645017227715691in_int @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_int @ M @ A4 )
% 13.77/7.70 & ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2075_Min__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,M: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ( lattic8721135487736765967in_nat @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_nat @ M @ A4 )
% 13.77/7.70 & ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2076_Min__le__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 & ( ord_le3102999989581377725nteger @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2077_Min__le__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_o @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2078_Min__le__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_rat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2079_Min__le__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_num @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2080_Min__le__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_int @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2081_Min__le__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_nat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2082_eq__Min__iff,axiom,
% 13.77/7.70 ! [A4: set_real,M: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic3629708407755379051n_real @ A4 ) )
% 13.77/7.70 = ( ( member_real @ M @ A4 )
% 13.77/7.70 & ! [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2083_eq__Min__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,M: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic1063845414844153500nteger @ A4 ) )
% 13.77/7.70 = ( ( member_Code_integer @ M @ A4 )
% 13.77/7.70 & ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2084_eq__Min__iff,axiom,
% 13.77/7.70 ! [A4: set_o,M: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic1973801136483472281_Min_o @ A4 ) )
% 13.77/7.70 = ( ( member_o @ M @ A4 )
% 13.77/7.70 & ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2085_eq__Min__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,M: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic8086005427650270231in_rat @ A4 ) )
% 13.77/7.70 = ( ( member_rat @ M @ A4 )
% 13.77/7.70 & ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2086_eq__Min__iff,axiom,
% 13.77/7.70 ! [A4: set_num,M: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic5278467273892544601in_num @ A4 ) )
% 13.77/7.70 = ( ( member_num @ M @ A4 )
% 13.77/7.70 & ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2087_eq__Min__iff,axiom,
% 13.77/7.70 ! [A4: set_int,M: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic8718645017227715691in_int @ A4 ) )
% 13.77/7.70 = ( ( member_int @ M @ A4 )
% 13.77/7.70 & ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2088_eq__Min__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,M: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic8721135487736765967in_nat @ A4 ) )
% 13.77/7.70 = ( ( member_nat @ M @ A4 )
% 13.77/7.70 & ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ M @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2089_Min_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_eq_real @ X @ ( lattic3629708407755379051n_real @ A4 ) )
% 13.77/7.70 => ! [A8: real] :
% 13.77/7.70 ( ( member_real @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ X @ A8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2090_Min_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) )
% 13.77/7.70 => ! [A8: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ A8 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X @ A8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2091_Min_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) )
% 13.77/7.70 => ! [A8: $o] :
% 13.77/7.70 ( ( member_o @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ X @ A8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2092_Min_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) )
% 13.77/7.70 => ! [A8: rat] :
% 13.77/7.70 ( ( member_rat @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X @ A8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2093_Min_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_eq_num @ X @ ( lattic5278467273892544601in_num @ A4 ) )
% 13.77/7.70 => ! [A8: num] :
% 13.77/7.70 ( ( member_num @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X @ A8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2094_Min_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A4 ) )
% 13.77/7.70 => ! [A8: int] :
% 13.77/7.70 ( ( member_int @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X @ A8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2095_Min_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) )
% 13.77/7.70 => ! [A8: nat] :
% 13.77/7.70 ( ( member_nat @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ A8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2096_Min_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ! [A3: real] :
% 13.77/7.70 ( ( member_real @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ X @ A3 ) )
% 13.77/7.70 => ( ord_less_eq_real @ X @ ( lattic3629708407755379051n_real @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2097_Min_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [A3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ A3 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X @ A3 ) )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X @ ( lattic1063845414844153500nteger @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2098_Min_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ! [A3: $o] :
% 13.77/7.70 ( ( member_o @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ X @ A3 ) )
% 13.77/7.70 => ( ord_less_eq_o @ X @ ( lattic1973801136483472281_Min_o @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2099_Min_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ! [A3: rat] :
% 13.77/7.70 ( ( member_rat @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X @ A3 ) )
% 13.77/7.70 => ( ord_less_eq_rat @ X @ ( lattic8086005427650270231in_rat @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2100_Min_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ! [A3: num] :
% 13.77/7.70 ( ( member_num @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X @ A3 ) )
% 13.77/7.70 => ( ord_less_eq_num @ X @ ( lattic5278467273892544601in_num @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2101_Min_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ! [A3: int] :
% 13.77/7.70 ( ( member_int @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X @ A3 ) )
% 13.77/7.70 => ( ord_less_eq_int @ X @ ( lattic8718645017227715691in_int @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2102_Min_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ! [A3: nat] :
% 13.77/7.70 ( ( member_nat @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ A3 ) )
% 13.77/7.70 => ( ord_less_eq_nat @ X @ ( lattic8721135487736765967in_nat @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2103_Min__less__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le6747313008572928689nteger @ ( lattic1063845414844153500nteger @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 & ( ord_le6747313008572928689nteger @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2104_Min__less__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_o @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2105_Min__less__iff,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_real @ ( lattic3629708407755379051n_real @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_real @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2106_Min__less__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_rat @ ( lattic8086005427650270231in_rat @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_rat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2107_Min__less__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_num @ ( lattic5278467273892544601in_num @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_num @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2108_Min__less__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_int @ ( lattic8718645017227715691in_int @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_int @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2109_Min__less__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ X )
% 13.77/7.70 = ( ? [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_nat @ X4 @ X ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2110_Min__insert2,axiom,
% 13.77/7.70 ! [A4: set_o,A: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ! [B3: $o] :
% 13.77/7.70 ( ( member_o @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ A @ B3 ) )
% 13.77/7.70 => ( ( lattic1973801136483472281_Min_o @ ( insert_o @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2111_Min__insert2,axiom,
% 13.77/7.70 ! [A4: set_real,A: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ! [B3: real] :
% 13.77/7.70 ( ( member_real @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ A @ B3 ) )
% 13.77/7.70 => ( ( lattic3629708407755379051n_real @ ( insert_real @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2112_Min__insert2,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,A: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ! [B3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ B3 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ A @ B3 ) )
% 13.77/7.70 => ( ( lattic1063845414844153500nteger @ ( insert_Code_integer @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2113_Min__insert2,axiom,
% 13.77/7.70 ! [A4: set_rat,A: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ! [B3: rat] :
% 13.77/7.70 ( ( member_rat @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ A @ B3 ) )
% 13.77/7.70 => ( ( lattic8086005427650270231in_rat @ ( insert_rat @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2114_Min__insert2,axiom,
% 13.77/7.70 ! [A4: set_num,A: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ! [B3: num] :
% 13.77/7.70 ( ( member_num @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ A @ B3 ) )
% 13.77/7.70 => ( ( lattic5278467273892544601in_num @ ( insert_num @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2115_Min__insert2,axiom,
% 13.77/7.70 ! [A4: set_int,A: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ! [B3: int] :
% 13.77/7.70 ( ( member_int @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ A @ B3 ) )
% 13.77/7.70 => ( ( lattic8718645017227715691in_int @ ( insert_int @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2116_Min__insert2,axiom,
% 13.77/7.70 ! [A4: set_nat,A: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ! [B3: nat] :
% 13.77/7.70 ( ( member_nat @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ A @ B3 ) )
% 13.77/7.70 => ( ( lattic8721135487736765967in_nat @ ( insert_nat @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2117_Max__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_real,M: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ( lattic4275903605611617917x_real @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_real @ M @ A4 )
% 13.77/7.70 & ! [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2118_Max__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,M: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ( lattic4901227151466704046nteger @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_Code_integer @ M @ A4 )
% 13.77/7.70 & ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2119_Max__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_o,M: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ( lattic1921953407002678535_Max_o @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_o @ M @ A4 )
% 13.77/7.70 & ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2120_Max__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,M: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ( lattic7630753665789217321ax_rat @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_rat @ M @ A4 )
% 13.77/7.70 & ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2121_Max__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_num,M: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ( lattic4823215512031491691ax_num @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_num @ M @ A4 )
% 13.77/7.70 & ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2122_Max__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_int,M: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ( lattic8263393255366662781ax_int @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_int @ M @ A4 )
% 13.77/7.70 & ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2123_Max__eq__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,M: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ( lattic8265883725875713057ax_nat @ A4 )
% 13.77/7.70 = M )
% 13.77/7.70 = ( ( member_nat @ M @ A4 )
% 13.77/7.70 & ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2124_Max__ge__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le3102999989581377725nteger @ X @ ( lattic4901227151466704046nteger @ A4 ) )
% 13.77/7.70 = ( ? [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 & ( ord_le3102999989581377725nteger @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2125_Max__ge__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) )
% 13.77/7.70 = ( ? [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_o @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2126_Max__ge__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_eq_rat @ X @ ( lattic7630753665789217321ax_rat @ A4 ) )
% 13.77/7.70 = ( ? [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_rat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2127_Max__ge__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_eq_num @ X @ ( lattic4823215512031491691ax_num @ A4 ) )
% 13.77/7.70 = ( ? [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_num @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2128_Max__ge__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) )
% 13.77/7.70 = ( ? [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_int @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2129_Max__ge__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 13.77/7.70 = ( ? [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_eq_nat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2130_eq__Max__iff,axiom,
% 13.77/7.70 ! [A4: set_real,M: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic4275903605611617917x_real @ A4 ) )
% 13.77/7.70 = ( ( member_real @ M @ A4 )
% 13.77/7.70 & ! [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2131_eq__Max__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,M: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic4901227151466704046nteger @ A4 ) )
% 13.77/7.70 = ( ( member_Code_integer @ M @ A4 )
% 13.77/7.70 & ! [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2132_eq__Max__iff,axiom,
% 13.77/7.70 ! [A4: set_o,M: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic1921953407002678535_Max_o @ A4 ) )
% 13.77/7.70 = ( ( member_o @ M @ A4 )
% 13.77/7.70 & ! [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2133_eq__Max__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,M: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic7630753665789217321ax_rat @ A4 ) )
% 13.77/7.70 = ( ( member_rat @ M @ A4 )
% 13.77/7.70 & ! [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2134_eq__Max__iff,axiom,
% 13.77/7.70 ! [A4: set_num,M: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic4823215512031491691ax_num @ A4 ) )
% 13.77/7.70 = ( ( member_num @ M @ A4 )
% 13.77/7.70 & ! [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2135_eq__Max__iff,axiom,
% 13.77/7.70 ! [A4: set_int,M: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic8263393255366662781ax_int @ A4 ) )
% 13.77/7.70 = ( ( member_int @ M @ A4 )
% 13.77/7.70 & ! [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2136_eq__Max__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,M: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( M
% 13.77/7.70 = ( lattic8265883725875713057ax_nat @ A4 ) )
% 13.77/7.70 = ( ( member_nat @ M @ A4 )
% 13.77/7.70 & ! [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ X4 @ M ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2137_Max_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_eq_real @ ( lattic4275903605611617917x_real @ A4 ) @ X )
% 13.77/7.70 => ! [A8: real] :
% 13.77/7.70 ( ( member_real @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ A8 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2138_Max_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X )
% 13.77/7.70 => ! [A8: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ A8 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ A8 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2139_Max_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X )
% 13.77/7.70 => ! [A8: $o] :
% 13.77/7.70 ( ( member_o @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ A8 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2140_Max_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X )
% 13.77/7.70 => ! [A8: rat] :
% 13.77/7.70 ( ( member_rat @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ A8 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2141_Max_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X )
% 13.77/7.70 => ! [A8: num] :
% 13.77/7.70 ( ( member_num @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ A8 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2142_Max_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X )
% 13.77/7.70 => ! [A8: int] :
% 13.77/7.70 ( ( member_int @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ A8 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2143_Max_OboundedE,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X )
% 13.77/7.70 => ! [A8: nat] :
% 13.77/7.70 ( ( member_nat @ A8 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ A8 @ X ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2144_Max_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ! [A3: real] :
% 13.77/7.70 ( ( member_real @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ A3 @ X ) )
% 13.77/7.70 => ( ord_less_eq_real @ ( lattic4275903605611617917x_real @ A4 ) @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2145_Max_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ! [A3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ A3 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ A3 @ X ) )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2146_Max_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ! [A3: $o] :
% 13.77/7.70 ( ( member_o @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ A3 @ X ) )
% 13.77/7.70 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2147_Max_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ! [A3: rat] :
% 13.77/7.70 ( ( member_rat @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ A3 @ X ) )
% 13.77/7.70 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2148_Max_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ! [A3: num] :
% 13.77/7.70 ( ( member_num @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ A3 @ X ) )
% 13.77/7.70 => ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2149_Max_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ! [A3: int] :
% 13.77/7.70 ( ( member_int @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ A3 @ X ) )
% 13.77/7.70 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2150_Max_OboundedI,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ! [A3: nat] :
% 13.77/7.70 ( ( member_nat @ A3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ A3 @ X ) )
% 13.77/7.70 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ X ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2151_Max__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( ord_le6747313008572928689nteger @ X @ ( lattic4901227151466704046nteger @ A4 ) )
% 13.77/7.70 = ( ? [X4: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.70 & ( ord_le6747313008572928689nteger @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2152_Max__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_o,X: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( ord_less_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) )
% 13.77/7.70 = ( ? [X4: $o] :
% 13.77/7.70 ( ( member_o @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_o @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2153_Max__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_real,X: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_real )
% 13.77/7.70 => ( ( ord_less_real @ X @ ( lattic4275903605611617917x_real @ A4 ) )
% 13.77/7.70 = ( ? [X4: real] :
% 13.77/7.70 ( ( member_real @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_real @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2154_Max__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_rat,X: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( ord_less_rat @ X @ ( lattic7630753665789217321ax_rat @ A4 ) )
% 13.77/7.70 = ( ? [X4: rat] :
% 13.77/7.70 ( ( member_rat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_rat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2155_Max__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_num,X: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( ord_less_num @ X @ ( lattic4823215512031491691ax_num @ A4 ) )
% 13.77/7.70 = ( ? [X4: num] :
% 13.77/7.70 ( ( member_num @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_num @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2156_Max__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_int,X: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( ord_less_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) )
% 13.77/7.70 = ( ? [X4: int] :
% 13.77/7.70 ( ( member_int @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_int @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2157_Max__gr__iff,axiom,
% 13.77/7.70 ! [A4: set_nat,X: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( ord_less_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 13.77/7.70 = ( ? [X4: nat] :
% 13.77/7.70 ( ( member_nat @ X4 @ A4 )
% 13.77/7.70 & ( ord_less_nat @ X @ X4 ) ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2158_Max__insert2,axiom,
% 13.77/7.70 ! [A4: set_o,A: $o] :
% 13.77/7.70 ( ( finite_finite_o @ A4 )
% 13.77/7.70 => ( ! [B3: $o] :
% 13.77/7.70 ( ( member_o @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_o @ B3 @ A ) )
% 13.77/7.70 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2159_Max__insert2,axiom,
% 13.77/7.70 ! [A4: set_real,A: real] :
% 13.77/7.70 ( ( finite_finite_real @ A4 )
% 13.77/7.70 => ( ! [B3: real] :
% 13.77/7.70 ( ( member_real @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_real @ B3 @ A ) )
% 13.77/7.70 => ( ( lattic4275903605611617917x_real @ ( insert_real @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2160_Max__insert2,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,A: code_integer] :
% 13.77/7.70 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.70 => ( ! [B3: code_integer] :
% 13.77/7.70 ( ( member_Code_integer @ B3 @ A4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ B3 @ A ) )
% 13.77/7.70 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2161_Max__insert2,axiom,
% 13.77/7.70 ! [A4: set_rat,A: rat] :
% 13.77/7.70 ( ( finite_finite_rat @ A4 )
% 13.77/7.70 => ( ! [B3: rat] :
% 13.77/7.70 ( ( member_rat @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_rat @ B3 @ A ) )
% 13.77/7.70 => ( ( lattic7630753665789217321ax_rat @ ( insert_rat @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2162_Max__insert2,axiom,
% 13.77/7.70 ! [A4: set_num,A: num] :
% 13.77/7.70 ( ( finite_finite_num @ A4 )
% 13.77/7.70 => ( ! [B3: num] :
% 13.77/7.70 ( ( member_num @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_num @ B3 @ A ) )
% 13.77/7.70 => ( ( lattic4823215512031491691ax_num @ ( insert_num @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2163_Max__insert2,axiom,
% 13.77/7.70 ! [A4: set_int,A: int] :
% 13.77/7.70 ( ( finite_finite_int @ A4 )
% 13.77/7.70 => ( ! [B3: int] :
% 13.77/7.70 ( ( member_int @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_int @ B3 @ A ) )
% 13.77/7.70 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2164_Max__insert2,axiom,
% 13.77/7.70 ! [A4: set_nat,A: nat] :
% 13.77/7.70 ( ( finite_finite_nat @ A4 )
% 13.77/7.70 => ( ! [B3: nat] :
% 13.77/7.70 ( ( member_nat @ B3 @ A4 )
% 13.77/7.70 => ( ord_less_eq_nat @ B3 @ A ) )
% 13.77/7.70 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ A @ A4 ) )
% 13.77/7.70 = A ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2165_Min__antimono,axiom,
% 13.77/7.70 ! [M7: set_Code_integer,N8: set_Code_integer] :
% 13.77/7.70 ( ( ord_le7084787975880047091nteger @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( finite6017078050557962740nteger @ N8 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ N8 ) @ ( lattic1063845414844153500nteger @ M7 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2166_Min__antimono,axiom,
% 13.77/7.70 ! [M7: set_o,N8: set_o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bot_set_o )
% 13.77/7.70 => ( ( finite_finite_o @ N8 )
% 13.77/7.70 => ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ N8 ) @ ( lattic1973801136483472281_Min_o @ M7 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2167_Min__antimono,axiom,
% 13.77/7.70 ! [M7: set_rat,N8: set_rat] :
% 13.77/7.70 ( ( ord_less_eq_set_rat @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bot_set_rat )
% 13.77/7.70 => ( ( finite_finite_rat @ N8 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ N8 ) @ ( lattic8086005427650270231in_rat @ M7 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2168_Min__antimono,axiom,
% 13.77/7.70 ! [M7: set_num,N8: set_num] :
% 13.77/7.70 ( ( ord_less_eq_set_num @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bot_set_num )
% 13.77/7.70 => ( ( finite_finite_num @ N8 )
% 13.77/7.70 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ N8 ) @ ( lattic5278467273892544601in_num @ M7 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2169_Min__antimono,axiom,
% 13.77/7.70 ! [M7: set_int,N8: set_int] :
% 13.77/7.70 ( ( ord_less_eq_set_int @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bot_set_int )
% 13.77/7.70 => ( ( finite_finite_int @ N8 )
% 13.77/7.70 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ N8 ) @ ( lattic8718645017227715691in_int @ M7 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2170_Min__antimono,axiom,
% 13.77/7.70 ! [M7: set_nat,N8: set_nat] :
% 13.77/7.70 ( ( ord_less_eq_set_nat @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bot_set_nat )
% 13.77/7.70 => ( ( finite_finite_nat @ N8 )
% 13.77/7.70 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ N8 ) @ ( lattic8721135487736765967in_nat @ M7 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2171_Min_Osubset__imp,axiom,
% 13.77/7.70 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.77/7.70 ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.70 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ ( lattic1063845414844153500nteger @ B4 ) @ ( lattic1063845414844153500nteger @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2172_Min_Osubset__imp,axiom,
% 13.77/7.70 ! [A4: set_o,B4: set_o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_o )
% 13.77/7.70 => ( ( finite_finite_o @ B4 )
% 13.77/7.70 => ( ord_less_eq_o @ ( lattic1973801136483472281_Min_o @ B4 ) @ ( lattic1973801136483472281_Min_o @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2173_Min_Osubset__imp,axiom,
% 13.77/7.70 ! [A4: set_rat,B4: set_rat] :
% 13.77/7.70 ( ( ord_less_eq_set_rat @ A4 @ B4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.70 => ( ( finite_finite_rat @ B4 )
% 13.77/7.70 => ( ord_less_eq_rat @ ( lattic8086005427650270231in_rat @ B4 ) @ ( lattic8086005427650270231in_rat @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2174_Min_Osubset__imp,axiom,
% 13.77/7.70 ! [A4: set_num,B4: set_num] :
% 13.77/7.70 ( ( ord_less_eq_set_num @ A4 @ B4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_num )
% 13.77/7.70 => ( ( finite_finite_num @ B4 )
% 13.77/7.70 => ( ord_less_eq_num @ ( lattic5278467273892544601in_num @ B4 ) @ ( lattic5278467273892544601in_num @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2175_Min_Osubset__imp,axiom,
% 13.77/7.70 ! [A4: set_int,B4: set_int] :
% 13.77/7.70 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_int )
% 13.77/7.70 => ( ( finite_finite_int @ B4 )
% 13.77/7.70 => ( ord_less_eq_int @ ( lattic8718645017227715691in_int @ B4 ) @ ( lattic8718645017227715691in_int @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2176_Min_Osubset__imp,axiom,
% 13.77/7.70 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.70 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.70 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.70 => ( ( finite_finite_nat @ B4 )
% 13.77/7.70 => ( ord_less_eq_nat @ ( lattic8721135487736765967in_nat @ B4 ) @ ( lattic8721135487736765967in_nat @ A4 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2177_Max__mono,axiom,
% 13.77/7.70 ! [M7: set_Code_integer,N8: set_Code_integer] :
% 13.77/7.70 ( ( ord_le7084787975880047091nteger @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bo3990330152332043303nteger )
% 13.77/7.70 => ( ( finite6017078050557962740nteger @ N8 )
% 13.77/7.70 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ M7 ) @ ( lattic4901227151466704046nteger @ N8 ) ) ) ) ) ).
% 13.77/7.70
% 13.77/7.70 thf(fact_2178_Max__mono,axiom,
% 13.77/7.70 ! [M7: set_o,N8: set_o] :
% 13.77/7.70 ( ( ord_less_eq_set_o @ M7 @ N8 )
% 13.77/7.70 => ( ( M7 != bot_bot_set_o )
% 13.77/7.70 => ( ( finite_finite_o @ N8 )
% 13.77/7.70 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ M7 ) @ ( lattic1921953407002678535_Max_o @ N8 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2179_Max__mono,axiom,
% 13.77/7.71 ! [M7: set_rat,N8: set_rat] :
% 13.77/7.71 ( ( ord_less_eq_set_rat @ M7 @ N8 )
% 13.77/7.71 => ( ( M7 != bot_bot_set_rat )
% 13.77/7.71 => ( ( finite_finite_rat @ N8 )
% 13.77/7.71 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ M7 ) @ ( lattic7630753665789217321ax_rat @ N8 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2180_Max__mono,axiom,
% 13.77/7.71 ! [M7: set_num,N8: set_num] :
% 13.77/7.71 ( ( ord_less_eq_set_num @ M7 @ N8 )
% 13.77/7.71 => ( ( M7 != bot_bot_set_num )
% 13.77/7.71 => ( ( finite_finite_num @ N8 )
% 13.77/7.71 => ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ M7 ) @ ( lattic4823215512031491691ax_num @ N8 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2181_Max__mono,axiom,
% 13.77/7.71 ! [M7: set_int,N8: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ M7 @ N8 )
% 13.77/7.71 => ( ( M7 != bot_bot_set_int )
% 13.77/7.71 => ( ( finite_finite_int @ N8 )
% 13.77/7.71 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ M7 ) @ ( lattic8263393255366662781ax_int @ N8 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2182_Max__mono,axiom,
% 13.77/7.71 ! [M7: set_nat,N8: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ M7 @ N8 )
% 13.77/7.71 => ( ( M7 != bot_bot_set_nat )
% 13.77/7.71 => ( ( finite_finite_nat @ N8 )
% 13.77/7.71 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ M7 ) @ ( lattic8265883725875713057ax_nat @ N8 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2183_Max_Osubset__imp,axiom,
% 13.77/7.71 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.77/7.71 ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.71 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.71 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.71 => ( ord_le3102999989581377725nteger @ ( lattic4901227151466704046nteger @ A4 ) @ ( lattic4901227151466704046nteger @ B4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2184_Max_Osubset__imp,axiom,
% 13.77/7.71 ! [A4: set_o,B4: set_o] :
% 13.77/7.71 ( ( ord_less_eq_set_o @ A4 @ B4 )
% 13.77/7.71 => ( ( A4 != bot_bot_set_o )
% 13.77/7.71 => ( ( finite_finite_o @ B4 )
% 13.77/7.71 => ( ord_less_eq_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ ( lattic1921953407002678535_Max_o @ B4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2185_Max_Osubset__imp,axiom,
% 13.77/7.71 ! [A4: set_rat,B4: set_rat] :
% 13.77/7.71 ( ( ord_less_eq_set_rat @ A4 @ B4 )
% 13.77/7.71 => ( ( A4 != bot_bot_set_rat )
% 13.77/7.71 => ( ( finite_finite_rat @ B4 )
% 13.77/7.71 => ( ord_less_eq_rat @ ( lattic7630753665789217321ax_rat @ A4 ) @ ( lattic7630753665789217321ax_rat @ B4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2186_Max_Osubset__imp,axiom,
% 13.77/7.71 ! [A4: set_num,B4: set_num] :
% 13.77/7.71 ( ( ord_less_eq_set_num @ A4 @ B4 )
% 13.77/7.71 => ( ( A4 != bot_bot_set_num )
% 13.77/7.71 => ( ( finite_finite_num @ B4 )
% 13.77/7.71 => ( ord_less_eq_num @ ( lattic4823215512031491691ax_num @ A4 ) @ ( lattic4823215512031491691ax_num @ B4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2187_Max_Osubset__imp,axiom,
% 13.77/7.71 ! [A4: set_int,B4: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.71 => ( ( A4 != bot_bot_set_int )
% 13.77/7.71 => ( ( finite_finite_int @ B4 )
% 13.77/7.71 => ( ord_less_eq_int @ ( lattic8263393255366662781ax_int @ A4 ) @ ( lattic8263393255366662781ax_int @ B4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2188_Max_Osubset__imp,axiom,
% 13.77/7.71 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.71 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.71 => ( ( finite_finite_nat @ B4 )
% 13.77/7.71 => ( ord_less_eq_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ B4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2189_greater__shift,axiom,
% 13.77/7.71 ( ord_less_nat
% 13.77/7.71 = ( ^ [Y4: nat,X4: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2190_less__shift,axiom,
% 13.77/7.71 ( ord_less_nat
% 13.77/7.71 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_less @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2191_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 13.77/7.71 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2192_the__elem__eq,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT] :
% 13.77/7.71 ( ( the_elem_VEBT_VEBT @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) )
% 13.77/7.71 = X ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2193_the__elem__eq,axiom,
% 13.77/7.71 ! [X: nat] :
% 13.77/7.71 ( ( the_elem_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.71 = X ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2194_the__elem__eq,axiom,
% 13.77/7.71 ! [X: int] :
% 13.77/7.71 ( ( the_elem_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.71 = X ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2195_the__elem__eq,axiom,
% 13.77/7.71 ! [X: $o] :
% 13.77/7.71 ( ( the_elem_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.71 = X ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2196_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.71 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 13.77/7.71 = Y )
% 13.77/7.71 => ( ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ $false @ $false ) )
% 13.77/7.71 => ( Y != one_one_nat ) )
% 13.77/7.71 => ( ( ? [Uv: $o] :
% 13.77/7.71 ( X
% 13.77/7.71 = ( vEBT_Leaf @ $true @ Uv ) )
% 13.77/7.71 => ( Y != one_one_nat ) )
% 13.77/7.71 => ( ( ? [Uu: $o] :
% 13.77/7.71 ( X
% 13.77/7.71 = ( vEBT_Leaf @ Uu @ $true ) )
% 13.77/7.71 => ( Y != one_one_nat ) )
% 13.77/7.71 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.71 ( X
% 13.77/7.71 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 13.77/7.71 => ( Y != one_one_nat ) )
% 13.77/7.71 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.71 ( X
% 13.77/7.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 13.77/7.71 => ( Y != one_one_nat ) ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2197_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2198_is__singletonI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT] : ( is_sin24926331636114728T_VEBT @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2199_is__singletonI,axiom,
% 13.77/7.71 ! [X: nat] : ( is_singleton_nat @ ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2200_is__singletonI,axiom,
% 13.77/7.71 ! [X: int] : ( is_singleton_int @ ( insert_int @ X @ bot_bot_set_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2201_is__singletonI,axiom,
% 13.77/7.71 ! [X: $o] : ( is_singleton_o @ ( insert_o @ X @ bot_bot_set_o ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2202_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2203_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2204_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2205_is__singleton__the__elem,axiom,
% 13.77/7.71 ( is_sin24926331636114728T_VEBT
% 13.77/7.71 = ( ^ [A6: set_VEBT_VEBT] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_VEBT_VEBT @ ( the_elem_VEBT_VEBT @ A6 ) @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2206_is__singleton__the__elem,axiom,
% 13.77/7.71 ( is_singleton_nat
% 13.77/7.71 = ( ^ [A6: set_nat] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_nat @ ( the_elem_nat @ A6 ) @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2207_is__singleton__the__elem,axiom,
% 13.77/7.71 ( is_singleton_int
% 13.77/7.71 = ( ^ [A6: set_int] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_int @ ( the_elem_int @ A6 ) @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2208_is__singleton__the__elem,axiom,
% 13.77/7.71 ( is_singleton_o
% 13.77/7.71 = ( ^ [A6: set_o] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_o @ ( the_elem_o @ A6 ) @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2209_is__singletonI_H,axiom,
% 13.77/7.71 ! [A4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( A4 != bot_bo8194388402131092736T_VEBT )
% 13.77/7.71 => ( ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.71 => ( ( member_VEBT_VEBT @ Y3 @ A4 )
% 13.77/7.71 => ( X3 = Y3 ) ) )
% 13.77/7.71 => ( is_sin24926331636114728T_VEBT @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2210_is__singletonI_H,axiom,
% 13.77/7.71 ! [A4: set_real] :
% 13.77/7.71 ( ( A4 != bot_bot_set_real )
% 13.77/7.71 => ( ! [X3: real,Y3: real] :
% 13.77/7.71 ( ( member_real @ X3 @ A4 )
% 13.77/7.71 => ( ( member_real @ Y3 @ A4 )
% 13.77/7.71 => ( X3 = Y3 ) ) )
% 13.77/7.71 => ( is_singleton_real @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2211_is__singletonI_H,axiom,
% 13.77/7.71 ! [A4: set_set_nat] :
% 13.77/7.71 ( ( A4 != bot_bot_set_set_nat )
% 13.77/7.71 => ( ! [X3: set_nat,Y3: set_nat] :
% 13.77/7.71 ( ( member_set_nat @ X3 @ A4 )
% 13.77/7.71 => ( ( member_set_nat @ Y3 @ A4 )
% 13.77/7.71 => ( X3 = Y3 ) ) )
% 13.77/7.71 => ( is_singleton_set_nat @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2212_is__singletonI_H,axiom,
% 13.77/7.71 ! [A4: set_nat] :
% 13.77/7.71 ( ( A4 != bot_bot_set_nat )
% 13.77/7.71 => ( ! [X3: nat,Y3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ A4 )
% 13.77/7.71 => ( ( member_nat @ Y3 @ A4 )
% 13.77/7.71 => ( X3 = Y3 ) ) )
% 13.77/7.71 => ( is_singleton_nat @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2213_is__singletonI_H,axiom,
% 13.77/7.71 ! [A4: set_int] :
% 13.77/7.71 ( ( A4 != bot_bot_set_int )
% 13.77/7.71 => ( ! [X3: int,Y3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ A4 )
% 13.77/7.71 => ( ( member_int @ Y3 @ A4 )
% 13.77/7.71 => ( X3 = Y3 ) ) )
% 13.77/7.71 => ( is_singleton_int @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2214_is__singletonI_H,axiom,
% 13.77/7.71 ! [A4: set_o] :
% 13.77/7.71 ( ( A4 != bot_bot_set_o )
% 13.77/7.71 => ( ! [X3: $o,Y3: $o] :
% 13.77/7.71 ( ( member_o @ X3 @ A4 )
% 13.77/7.71 => ( ( member_o @ Y3 @ A4 )
% 13.77/7.71 => ( X3 = Y3 ) ) )
% 13.77/7.71 => ( is_singleton_o @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2215_minNull__bound,axiom,
% 13.77/7.71 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_N_u_l_l @ T ) @ one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2216_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J,axiom,
% 13.77/7.71 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $false @ $false ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2217_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J,axiom,
% 13.77/7.71 ! [Uv2: $o] :
% 13.77/7.71 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ $true @ Uv2 ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2218_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J,axiom,
% 13.77/7.71 ! [Uu2: $o] :
% 13.77/7.71 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Leaf @ Uu2 @ $true ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2219_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 13.77/7.71 ! [A: $o,B: $o,X: nat] :
% 13.77/7.71 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2220_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J,axiom,
% 13.77/7.71 ! [Uu2: $o,Uv2: $o] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2221_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J,axiom,
% 13.77/7.71 ! [Uv2: $o,Uw2: $o,N: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2222_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I3_J,axiom,
% 13.77/7.71 ! [A: $o,B: $o,Va2: nat] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2223_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J,axiom,
% 13.77/7.71 ! [Uu2: $o,Uv2: $o] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2224_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J,axiom,
% 13.77/7.71 ! [Uy2: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz @ Va2 ) @ Vb )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2225_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J,axiom,
% 13.77/7.71 ! [Uv2: $o,Uw2: $o,N: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2226_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J,axiom,
% 13.77/7.71 ! [Uy2: nat,Uz: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb: nat] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz @ Va2 ) @ Vb )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2227_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J,axiom,
% 13.77/7.71 ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz ) @ Va2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2228_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J,axiom,
% 13.77/7.71 ! [Uu2: $o,B: $o] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2229_is__singletonE,axiom,
% 13.77/7.71 ! [A4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( is_sin24926331636114728T_VEBT @ A4 )
% 13.77/7.71 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.71 ( A4
% 13.77/7.71 != ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2230_is__singletonE,axiom,
% 13.77/7.71 ! [A4: set_nat] :
% 13.77/7.71 ( ( is_singleton_nat @ A4 )
% 13.77/7.71 => ~ ! [X3: nat] :
% 13.77/7.71 ( A4
% 13.77/7.71 != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2231_is__singletonE,axiom,
% 13.77/7.71 ! [A4: set_int] :
% 13.77/7.71 ( ( is_singleton_int @ A4 )
% 13.77/7.71 => ~ ! [X3: int] :
% 13.77/7.71 ( A4
% 13.77/7.71 != ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2232_is__singletonE,axiom,
% 13.77/7.71 ! [A4: set_o] :
% 13.77/7.71 ( ( is_singleton_o @ A4 )
% 13.77/7.71 => ~ ! [X3: $o] :
% 13.77/7.71 ( A4
% 13.77/7.71 != ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2233_is__singleton__def,axiom,
% 13.77/7.71 ( is_sin24926331636114728T_VEBT
% 13.77/7.71 = ( ^ [A6: set_VEBT_VEBT] :
% 13.77/7.71 ? [X4: vEBT_VEBT] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2234_is__singleton__def,axiom,
% 13.77/7.71 ( is_singleton_nat
% 13.77/7.71 = ( ^ [A6: set_nat] :
% 13.77/7.71 ? [X4: nat] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2235_is__singleton__def,axiom,
% 13.77/7.71 ( is_singleton_int
% 13.77/7.71 = ( ^ [A6: set_int] :
% 13.77/7.71 ? [X4: int] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2236_is__singleton__def,axiom,
% 13.77/7.71 ( is_singleton_o
% 13.77/7.71 = ( ^ [A6: set_o] :
% 13.77/7.71 ? [X4: $o] :
% 13.77/7.71 ( A6
% 13.77/7.71 = ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2237_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J,axiom,
% 13.77/7.71 ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,Va2: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz ) @ Va2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2238_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J,axiom,
% 13.77/7.71 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 13.77/7.71 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2239_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J,axiom,
% 13.77/7.71 ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 13.77/7.71 ( ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2240_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 13.77/7.71 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X: nat] :
% 13.77/7.71 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2241_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2242_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J,axiom,
% 13.77/7.71 ! [A: $o,Uw2: $o] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2243_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2244_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 13.77/7.71 ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2245_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 13.77/7.71 ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2246_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 13.77/7.71 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 13.77/7.71 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2247_set__removeAll,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.71 ( ( set_VEBT_VEBT2 @ ( removeAll_VEBT_VEBT @ X @ Xs ) )
% 13.77/7.71 = ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2248_set__removeAll,axiom,
% 13.77/7.71 ! [X: real,Xs: list_real] :
% 13.77/7.71 ( ( set_real2 @ ( removeAll_real @ X @ Xs ) )
% 13.77/7.71 = ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2249_set__removeAll,axiom,
% 13.77/7.71 ! [X: int,Xs: list_int] :
% 13.77/7.71 ( ( set_int2 @ ( removeAll_int @ X @ Xs ) )
% 13.77/7.71 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2250_set__removeAll,axiom,
% 13.77/7.71 ! [X: $o,Xs: list_o] :
% 13.77/7.71 ( ( set_o2 @ ( removeAll_o @ X @ Xs ) )
% 13.77/7.71 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2251_set__removeAll,axiom,
% 13.77/7.71 ! [X: nat,Xs: list_nat] :
% 13.77/7.71 ( ( set_nat2 @ ( removeAll_nat @ X @ Xs ) )
% 13.77/7.71 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2252_vebt__maxt_Opelims,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,Y: option_nat] :
% 13.77/7.71 ( ( ( vEBT_vebt_maxt @ X )
% 13.77/7.71 = Y )
% 13.77/7.71 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 13.77/7.71 => ( ! [A3: $o,B3: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.71 => ( ( ( B3
% 13.77/7.71 => ( Y
% 13.77/7.71 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.71 & ( ~ B3
% 13.77/7.71 => ( ( A3
% 13.77/7.71 => ( Y
% 13.77/7.71 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.71 & ( ~ A3
% 13.77/7.71 => ( Y = none_nat ) ) ) ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.71 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.71 => ( ( Y = none_nat )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 13.77/7.71 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.71 => ( ( Y
% 13.77/7.71 = ( some_nat @ Ma2 ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2253_vebt__mint_Opelims,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,Y: option_nat] :
% 13.77/7.71 ( ( ( vEBT_vebt_mint @ X )
% 13.77/7.71 = Y )
% 13.77/7.71 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 13.77/7.71 => ( ! [A3: $o,B3: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.71 => ( ( ( A3
% 13.77/7.71 => ( Y
% 13.77/7.71 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.71 & ( ~ A3
% 13.77/7.71 => ( ( B3
% 13.77/7.71 => ( Y
% 13.77/7.71 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.71 & ( ~ B3
% 13.77/7.71 => ( Y = none_nat ) ) ) ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.71 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.71 => ( ( Y = none_nat )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 13.77/7.71 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.71 => ( ( Y
% 13.77/7.71 = ( some_nat @ Mi2 ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2254_height__node,axiom,
% 13.77/7.71 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 13.77/7.71 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 13.77/7.71 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2255_insertsimp_H,axiom,
% 13.77/7.71 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 13.77/7.71 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.71 => ( ( vEBT_VEBT_minNull @ T )
% 13.77/7.71 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ L ) @ one_one_nat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2256_insersimp_H,axiom,
% 13.77/7.71 ! [T: vEBT_VEBT,N: nat,Y: nat] :
% 13.77/7.71 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.71 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 13.77/7.71 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ Y ) @ one_one_nat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2257_frac__unique__iff,axiom,
% 13.77/7.71 ! [X: real,A: real] :
% 13.77/7.71 ( ( ( archim2898591450579166408c_real @ X )
% 13.77/7.71 = A )
% 13.77/7.71 = ( ( member_real @ ( minus_minus_real @ X @ A ) @ ring_1_Ints_real )
% 13.77/7.71 & ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.71 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2258_frac__unique__iff,axiom,
% 13.77/7.71 ! [X: rat,A: rat] :
% 13.77/7.71 ( ( ( archimedean_frac_rat @ X )
% 13.77/7.71 = A )
% 13.77/7.71 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 13.77/7.71 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.71 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2259_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J,axiom,
% 13.77/7.71 ! [V2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.71 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2260_remove__def,axiom,
% 13.77/7.71 ( remove_VEBT_VEBT
% 13.77/7.71 = ( ^ [X4: vEBT_VEBT,A6: set_VEBT_VEBT] : ( minus_5127226145743854075T_VEBT @ A6 @ ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2261_remove__def,axiom,
% 13.77/7.71 ( remove_int
% 13.77/7.71 = ( ^ [X4: int,A6: set_int] : ( minus_minus_set_int @ A6 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2262_remove__def,axiom,
% 13.77/7.71 ( remove_o
% 13.77/7.71 = ( ^ [X4: $o,A6: set_o] : ( minus_minus_set_o @ A6 @ ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2263_remove__def,axiom,
% 13.77/7.71 ( remove_nat
% 13.77/7.71 = ( ^ [X4: nat,A6: set_nat] : ( minus_minus_set_nat @ A6 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2264_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J,axiom,
% 13.77/7.71 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 13.77/7.71 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2265_member__remove,axiom,
% 13.77/7.71 ! [X: nat,Y: nat,A4: set_nat] :
% 13.77/7.71 ( ( member_nat @ X @ ( remove_nat @ Y @ A4 ) )
% 13.77/7.71 = ( ( member_nat @ X @ A4 )
% 13.77/7.71 & ( X != Y ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2266_member__remove,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,Y: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ ( remove_VEBT_VEBT @ Y @ A4 ) )
% 13.77/7.71 = ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 & ( X != Y ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2267_member__remove,axiom,
% 13.77/7.71 ! [X: real,Y: real,A4: set_real] :
% 13.77/7.71 ( ( member_real @ X @ ( remove_real @ Y @ A4 ) )
% 13.77/7.71 = ( ( member_real @ X @ A4 )
% 13.77/7.71 & ( X != Y ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2268_member__remove,axiom,
% 13.77/7.71 ! [X: int,Y: int,A4: set_int] :
% 13.77/7.71 ( ( member_int @ X @ ( remove_int @ Y @ A4 ) )
% 13.77/7.71 = ( ( member_int @ X @ A4 )
% 13.77/7.71 & ( X != Y ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2269_member__remove,axiom,
% 13.77/7.71 ! [X: set_nat,Y: set_nat,A4: set_set_nat] :
% 13.77/7.71 ( ( member_set_nat @ X @ ( remove_set_nat @ Y @ A4 ) )
% 13.77/7.71 = ( ( member_set_nat @ X @ A4 )
% 13.77/7.71 & ( X != Y ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2270_frac__eq__0__iff,axiom,
% 13.77/7.71 ! [X: real] :
% 13.77/7.71 ( ( ( archim2898591450579166408c_real @ X )
% 13.77/7.71 = zero_zero_real )
% 13.77/7.71 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2271_frac__eq__0__iff,axiom,
% 13.77/7.71 ! [X: rat] :
% 13.77/7.71 ( ( ( archimedean_frac_rat @ X )
% 13.77/7.71 = zero_zero_rat )
% 13.77/7.71 = ( member_rat @ X @ ring_1_Ints_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2272_frac__gt__0__iff,axiom,
% 13.77/7.71 ! [X: real] :
% 13.77/7.71 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X ) )
% 13.77/7.71 = ( ~ ( member_real @ X @ ring_1_Ints_real ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2273_frac__gt__0__iff,axiom,
% 13.77/7.71 ! [X: rat] :
% 13.77/7.71 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) )
% 13.77/7.71 = ( ~ ( member_rat @ X @ ring_1_Ints_rat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2274_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 13.77/7.71 ! [A: $o,B: $o] :
% 13.77/7.71 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.71 = zero_zero_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2275_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J,axiom,
% 13.77/7.71 ! [A: $o,B: $o,X: nat] :
% 13.77/7.71 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2276_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J,axiom,
% 13.77/7.71 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 13.77/7.71 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X )
% 13.77/7.71 = one_one_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2277_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Opelims,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.71 ( ( ( vEBT_T_m_i_n_N_u_l_l @ X )
% 13.77/7.71 = Y )
% 13.77/7.71 => ( ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ X )
% 13.77/7.71 => ( ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ $false @ $false ) )
% 13.77/7.71 => ( ( Y = one_one_nat )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 13.77/7.71 => ( ! [Uv: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ $true @ Uv ) )
% 13.77/7.71 => ( ( Y = one_one_nat )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ $true @ Uv ) ) ) )
% 13.77/7.71 => ( ! [Uu: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ Uu @ $true ) )
% 13.77/7.71 => ( ( Y = one_one_nat )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Leaf @ Uu @ $true ) ) ) )
% 13.77/7.71 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 13.77/7.71 => ( ( Y = one_one_nat )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) )
% 13.77/7.71 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 13.77/7.71 => ( ( Y = one_one_nat )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_T5462971552011256508_l_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2278_delete__bound__height_H,axiom,
% 13.77/7.71 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.71 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.71 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2279_height__compose__child,axiom,
% 13.77/7.71 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2280_height__compose__list,axiom,
% 13.77/7.71 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.71 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2281_height__compose__summary,axiom,
% 13.77/7.71 ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2282_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,Y: $o] :
% 13.77/7.71 ( ( ( vEBT_VEBT_minNull @ X )
% 13.77/7.71 = Y )
% 13.77/7.71 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 13.77/7.71 => ( ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ $false @ $false ) )
% 13.77/7.71 => ( Y
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 13.77/7.71 => ( ! [Uv: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ $true @ Uv ) )
% 13.77/7.71 => ( ~ Y
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) ) )
% 13.77/7.71 => ( ! [Uu: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ Uu @ $true ) )
% 13.77/7.71 => ( ~ Y
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) ) )
% 13.77/7.71 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 13.77/7.71 => ( Y
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) )
% 13.77/7.71 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 13.77/7.71 => ( ~ Y
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2283_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT] :
% 13.77/7.71 ( ( vEBT_VEBT_minNull @ X )
% 13.77/7.71 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 13.77/7.71 => ( ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ $false @ $false ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 13.77/7.71 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2284_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT] :
% 13.77/7.71 ( ~ ( vEBT_VEBT_minNull @ X )
% 13.77/7.71 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 13.77/7.71 => ( ! [Uv: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ $true @ Uv ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) )
% 13.77/7.71 => ( ! [Uu: $o] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Leaf @ Uu @ $true ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) )
% 13.77/7.71 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.71 ( ( X
% 13.77/7.71 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 13.77/7.71 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2285_Ints__0,axiom,
% 13.77/7.71 member_uint32 @ zero_zero_uint32 @ ring_1_Ints_uint32 ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2286_Ints__0,axiom,
% 13.77/7.71 member_real @ zero_zero_real @ ring_1_Ints_real ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2287_Ints__0,axiom,
% 13.77/7.71 member_rat @ zero_zero_rat @ ring_1_Ints_rat ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2288_Ints__0,axiom,
% 13.77/7.71 member_int @ zero_zero_int @ ring_1_Ints_int ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2289_enumerate__Suc_H,axiom,
% 13.77/7.71 ! [S3: set_nat,N: nat] :
% 13.77/7.71 ( ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) )
% 13.77/7.71 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ ( infini8530281810654367211te_nat @ S3 @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2290_even__odd__cases,axiom,
% 13.77/7.71 ! [X: nat] :
% 13.77/7.71 ( ! [N2: nat] :
% 13.77/7.71 ( X
% 13.77/7.71 != ( plus_plus_nat @ N2 @ N2 ) )
% 13.77/7.71 => ~ ! [N2: nat] :
% 13.77/7.71 ( X
% 13.77/7.71 != ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2291_add__right__cancel,axiom,
% 13.77/7.71 ! [B: real,A: real,C2: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ B @ A )
% 13.77/7.71 = ( plus_plus_real @ C2 @ A ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2292_add__right__cancel,axiom,
% 13.77/7.71 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ B @ A )
% 13.77/7.71 = ( plus_plus_rat @ C2 @ A ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2293_add__right__cancel,axiom,
% 13.77/7.71 ! [B: nat,A: nat,C2: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ B @ A )
% 13.77/7.71 = ( plus_plus_nat @ C2 @ A ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2294_add__right__cancel,axiom,
% 13.77/7.71 ! [B: int,A: int,C2: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ B @ A )
% 13.77/7.71 = ( plus_plus_int @ C2 @ A ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2295_add__left__cancel,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ A @ B )
% 13.77/7.71 = ( plus_plus_real @ A @ C2 ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2296_add__left__cancel,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ A @ B )
% 13.77/7.71 = ( plus_plus_rat @ A @ C2 ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2297_add__left__cancel,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ A @ B )
% 13.77/7.71 = ( plus_plus_nat @ A @ C2 ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2298_add__left__cancel,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ A @ B )
% 13.77/7.71 = ( plus_plus_int @ A @ C2 ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2299_image__eqI,axiom,
% 13.77/7.71 ! [B: nat,F: nat > nat,X: nat,A4: set_nat] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2300_image__eqI,axiom,
% 13.77/7.71 ! [B: vEBT_VEBT,F: nat > vEBT_VEBT,X: nat,A4: set_nat] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ B @ ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2301_image__eqI,axiom,
% 13.77/7.71 ! [B: real,F: nat > real,X: nat,A4: set_nat] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_real @ B @ ( image_nat_real @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2302_image__eqI,axiom,
% 13.77/7.71 ! [B: int,F: nat > int,X: nat,A4: set_nat] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2303_image__eqI,axiom,
% 13.77/7.71 ! [B: nat,F: vEBT_VEBT > nat,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_nat @ B @ ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2304_image__eqI,axiom,
% 13.77/7.71 ! [B: vEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ B @ ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2305_image__eqI,axiom,
% 13.77/7.71 ! [B: real,F: vEBT_VEBT > real,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_real @ B @ ( image_VEBT_VEBT_real @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2306_image__eqI,axiom,
% 13.77/7.71 ! [B: int,F: vEBT_VEBT > int,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_int @ B @ ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2307_image__eqI,axiom,
% 13.77/7.71 ! [B: nat,F: real > nat,X: real,A4: set_real] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( member_nat @ B @ ( image_real_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2308_image__eqI,axiom,
% 13.77/7.71 ! [B: vEBT_VEBT,F: real > vEBT_VEBT,X: real,A4: set_real] :
% 13.77/7.71 ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ B @ ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2309_double__eq__0__iff,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ A @ A )
% 13.77/7.71 = zero_zero_real )
% 13.77/7.71 = ( A = zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2310_double__eq__0__iff,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ A @ A )
% 13.77/7.71 = zero_zero_rat )
% 13.77/7.71 = ( A = zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2311_double__eq__0__iff,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ A @ A )
% 13.77/7.71 = zero_zero_int )
% 13.77/7.71 = ( A = zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2312_add_Oright__neutral,axiom,
% 13.77/7.71 ! [A: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ A @ zero_zero_uint32 )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2313_add_Oright__neutral,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( plus_plus_real @ A @ zero_zero_real )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2314_add_Oright__neutral,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2315_add_Oright__neutral,axiom,
% 13.77/7.71 ! [A: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2316_add_Oright__neutral,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( plus_plus_int @ A @ zero_zero_int )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2317_double__zero__sym,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( zero_zero_real
% 13.77/7.71 = ( plus_plus_real @ A @ A ) )
% 13.77/7.71 = ( A = zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2318_double__zero__sym,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( zero_zero_rat
% 13.77/7.71 = ( plus_plus_rat @ A @ A ) )
% 13.77/7.71 = ( A = zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2319_double__zero__sym,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( zero_zero_int
% 13.77/7.71 = ( plus_plus_int @ A @ A ) )
% 13.77/7.71 = ( A = zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2320_add__cancel__left__left,axiom,
% 13.77/7.71 ! [B: uint32,A: uint32] :
% 13.77/7.71 ( ( ( plus_plus_uint32 @ B @ A )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_uint32 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2321_add__cancel__left__left,axiom,
% 13.77/7.71 ! [B: real,A: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ B @ A )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2322_add__cancel__left__left,axiom,
% 13.77/7.71 ! [B: rat,A: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ B @ A )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2323_add__cancel__left__left,axiom,
% 13.77/7.71 ! [B: nat,A: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ B @ A )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2324_add__cancel__left__left,axiom,
% 13.77/7.71 ! [B: int,A: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ B @ A )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2325_add__cancel__left__right,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32] :
% 13.77/7.71 ( ( ( plus_plus_uint32 @ A @ B )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_uint32 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2326_add__cancel__left__right,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ A @ B )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2327_add__cancel__left__right,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ A @ B )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2328_add__cancel__left__right,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ A @ B )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2329_add__cancel__left__right,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ A @ B )
% 13.77/7.71 = A )
% 13.77/7.71 = ( B = zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2330_add__cancel__right__left,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_uint32 @ B @ A ) )
% 13.77/7.71 = ( B = zero_zero_uint32 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2331_add__cancel__right__left,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_real @ B @ A ) )
% 13.77/7.71 = ( B = zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2332_add__cancel__right__left,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_rat @ B @ A ) )
% 13.77/7.71 = ( B = zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2333_add__cancel__right__left,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_nat @ B @ A ) )
% 13.77/7.71 = ( B = zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2334_add__cancel__right__left,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_int @ B @ A ) )
% 13.77/7.71 = ( B = zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2335_add__cancel__right__right,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_uint32 @ A @ B ) )
% 13.77/7.71 = ( B = zero_zero_uint32 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2336_add__cancel__right__right,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_real @ A @ B ) )
% 13.77/7.71 = ( B = zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2337_add__cancel__right__right,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_rat @ A @ B ) )
% 13.77/7.71 = ( B = zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2338_add__cancel__right__right,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_nat @ A @ B ) )
% 13.77/7.71 = ( B = zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2339_add__cancel__right__right,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( plus_plus_int @ A @ B ) )
% 13.77/7.71 = ( B = zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2340_add__eq__0__iff__both__eq__0,axiom,
% 13.77/7.71 ! [X: nat,Y: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ X @ Y )
% 13.77/7.71 = zero_zero_nat )
% 13.77/7.71 = ( ( X = zero_zero_nat )
% 13.77/7.71 & ( Y = zero_zero_nat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2341_zero__eq__add__iff__both__eq__0,axiom,
% 13.77/7.71 ! [X: nat,Y: nat] :
% 13.77/7.71 ( ( zero_zero_nat
% 13.77/7.71 = ( plus_plus_nat @ X @ Y ) )
% 13.77/7.71 = ( ( X = zero_zero_nat )
% 13.77/7.71 & ( Y = zero_zero_nat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2342_add__0,axiom,
% 13.77/7.71 ! [A: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ zero_zero_uint32 @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2343_add__0,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( plus_plus_real @ zero_zero_real @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2344_add__0,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2345_add__0,axiom,
% 13.77/7.71 ! [A: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2346_add__0,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( plus_plus_int @ zero_zero_int @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2347_add__le__cancel__right,axiom,
% 13.77/7.71 ! [A: real,C2: real,B: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_eq_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2348_add__le__cancel__right,axiom,
% 13.77/7.71 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_eq_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2349_add__le__cancel__right,axiom,
% 13.77/7.71 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_eq_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2350_add__le__cancel__right,axiom,
% 13.77/7.71 ! [A: int,C2: int,B: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_eq_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2351_add__le__cancel__left,axiom,
% 13.77/7.71 ! [C2: real,A: real,B: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_eq_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2352_add__le__cancel__left,axiom,
% 13.77/7.71 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_eq_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2353_add__le__cancel__left,axiom,
% 13.77/7.71 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_eq_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2354_add__le__cancel__left,axiom,
% 13.77/7.71 ! [C2: int,A: int,B: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_eq_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2355_add__less__cancel__left,axiom,
% 13.77/7.71 ! [C2: real,A: real,B: real] :
% 13.77/7.71 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2356_add__less__cancel__left,axiom,
% 13.77/7.71 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2357_add__less__cancel__left,axiom,
% 13.77/7.71 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2358_add__less__cancel__left,axiom,
% 13.77/7.71 ! [C2: int,A: int,B: int] :
% 13.77/7.71 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 13.77/7.71 = ( ord_less_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2359_add__less__cancel__right,axiom,
% 13.77/7.71 ! [A: real,C2: real,B: real] :
% 13.77/7.71 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2360_add__less__cancel__right,axiom,
% 13.77/7.71 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2361_add__less__cancel__right,axiom,
% 13.77/7.71 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2362_add__less__cancel__right,axiom,
% 13.77/7.71 ! [A: int,C2: int,B: int] :
% 13.77/7.71 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 13.77/7.71 = ( ord_less_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2363_add__diff__cancel__right_H,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2364_add__diff__cancel__right_H,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2365_add__diff__cancel__right_H,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2366_add__diff__cancel__right_H,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2367_add__diff__cancel__right_H,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2368_add__diff__cancel__right,axiom,
% 13.77/7.71 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2369_add__diff__cancel__right,axiom,
% 13.77/7.71 ! [A: uint32,C2: uint32,B: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ C2 ) @ ( plus_plus_uint32 @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_uint32 @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2370_add__diff__cancel__right,axiom,
% 13.77/7.71 ! [A: real,C2: real,B: real] :
% 13.77/7.71 ( ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2371_add__diff__cancel__right,axiom,
% 13.77/7.71 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2372_add__diff__cancel__right,axiom,
% 13.77/7.71 ! [A: int,C2: int,B: int] :
% 13.77/7.71 ( ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2373_add__diff__cancel__left_H,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 13.77/7.71 = B ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2374_add__diff__cancel__left_H,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ A )
% 13.77/7.71 = B ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2375_add__diff__cancel__left_H,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 13.77/7.71 = B ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2376_add__diff__cancel__left_H,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 13.77/7.71 = B ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2377_add__diff__cancel__left_H,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 13.77/7.71 = B ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2378_add__diff__cancel__left,axiom,
% 13.77/7.71 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 13.77/7.71 = ( minus_minus_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2379_add__diff__cancel__left,axiom,
% 13.77/7.71 ! [C2: uint32,A: uint32,B: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ C2 @ A ) @ ( plus_plus_uint32 @ C2 @ B ) )
% 13.77/7.71 = ( minus_minus_uint32 @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2380_add__diff__cancel__left,axiom,
% 13.77/7.71 ! [C2: real,A: real,B: real] :
% 13.77/7.71 ( ( minus_minus_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 13.77/7.71 = ( minus_minus_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2381_add__diff__cancel__left,axiom,
% 13.77/7.71 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 13.77/7.71 = ( minus_minus_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2382_add__diff__cancel__left,axiom,
% 13.77/7.71 ! [C2: int,A: int,B: int] :
% 13.77/7.71 ( ( minus_minus_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 13.77/7.71 = ( minus_minus_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2383_diff__add__cancel,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2384_diff__add__cancel,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2385_diff__add__cancel,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2386_diff__add__cancel,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2387_add__diff__cancel,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2388_add__diff__cancel,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2389_add__diff__cancel,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2390_add__diff__cancel,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2391_image__empty,axiom,
% 13.77/7.71 ! [F: nat > set_nat] :
% 13.77/7.71 ( ( image_nat_set_nat @ F @ bot_bot_set_nat )
% 13.77/7.71 = bot_bot_set_set_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2392_image__empty,axiom,
% 13.77/7.71 ! [F: nat > nat] :
% 13.77/7.71 ( ( image_nat_nat @ F @ bot_bot_set_nat )
% 13.77/7.71 = bot_bot_set_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2393_image__empty,axiom,
% 13.77/7.71 ! [F: nat > int] :
% 13.77/7.71 ( ( image_nat_int @ F @ bot_bot_set_nat )
% 13.77/7.71 = bot_bot_set_int ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2394_image__empty,axiom,
% 13.77/7.71 ! [F: nat > $o] :
% 13.77/7.71 ( ( image_nat_o @ F @ bot_bot_set_nat )
% 13.77/7.71 = bot_bot_set_o ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2395_image__empty,axiom,
% 13.77/7.71 ! [F: int > nat] :
% 13.77/7.71 ( ( image_int_nat @ F @ bot_bot_set_int )
% 13.77/7.71 = bot_bot_set_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2396_image__empty,axiom,
% 13.77/7.71 ! [F: int > int] :
% 13.77/7.71 ( ( image_int_int @ F @ bot_bot_set_int )
% 13.77/7.71 = bot_bot_set_int ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2397_image__empty,axiom,
% 13.77/7.71 ! [F: int > $o] :
% 13.77/7.71 ( ( image_int_o @ F @ bot_bot_set_int )
% 13.77/7.71 = bot_bot_set_o ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2398_image__empty,axiom,
% 13.77/7.71 ! [F: $o > nat] :
% 13.77/7.71 ( ( image_o_nat @ F @ bot_bot_set_o )
% 13.77/7.71 = bot_bot_set_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2399_image__empty,axiom,
% 13.77/7.71 ! [F: $o > int] :
% 13.77/7.71 ( ( image_o_int @ F @ bot_bot_set_o )
% 13.77/7.71 = bot_bot_set_int ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2400_image__empty,axiom,
% 13.77/7.71 ! [F: $o > $o] :
% 13.77/7.71 ( ( image_o_o @ F @ bot_bot_set_o )
% 13.77/7.71 = bot_bot_set_o ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2401_empty__is__image,axiom,
% 13.77/7.71 ! [F: nat > set_nat,A4: set_nat] :
% 13.77/7.71 ( ( bot_bot_set_set_nat
% 13.77/7.71 = ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2402_empty__is__image,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat] :
% 13.77/7.71 ( ( bot_bot_set_nat
% 13.77/7.71 = ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2403_empty__is__image,axiom,
% 13.77/7.71 ! [F: int > nat,A4: set_int] :
% 13.77/7.71 ( ( bot_bot_set_nat
% 13.77/7.71 = ( image_int_nat @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2404_empty__is__image,axiom,
% 13.77/7.71 ! [F: $o > nat,A4: set_o] :
% 13.77/7.71 ( ( bot_bot_set_nat
% 13.77/7.71 = ( image_o_nat @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_o ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2405_empty__is__image,axiom,
% 13.77/7.71 ! [F: nat > int,A4: set_nat] :
% 13.77/7.71 ( ( bot_bot_set_int
% 13.77/7.71 = ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2406_empty__is__image,axiom,
% 13.77/7.71 ! [F: int > int,A4: set_int] :
% 13.77/7.71 ( ( bot_bot_set_int
% 13.77/7.71 = ( image_int_int @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2407_empty__is__image,axiom,
% 13.77/7.71 ! [F: $o > int,A4: set_o] :
% 13.77/7.71 ( ( bot_bot_set_int
% 13.77/7.71 = ( image_o_int @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_o ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2408_empty__is__image,axiom,
% 13.77/7.71 ! [F: nat > $o,A4: set_nat] :
% 13.77/7.71 ( ( bot_bot_set_o
% 13.77/7.71 = ( image_nat_o @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2409_empty__is__image,axiom,
% 13.77/7.71 ! [F: int > $o,A4: set_int] :
% 13.77/7.71 ( ( bot_bot_set_o
% 13.77/7.71 = ( image_int_o @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2410_empty__is__image,axiom,
% 13.77/7.71 ! [F: $o > $o,A4: set_o] :
% 13.77/7.71 ( ( bot_bot_set_o
% 13.77/7.71 = ( image_o_o @ F @ A4 ) )
% 13.77/7.71 = ( A4 = bot_bot_set_o ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2411_image__is__empty,axiom,
% 13.77/7.71 ! [F: nat > set_nat,A4: set_nat] :
% 13.77/7.71 ( ( ( image_nat_set_nat @ F @ A4 )
% 13.77/7.71 = bot_bot_set_set_nat )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2412_image__is__empty,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat] :
% 13.77/7.71 ( ( ( image_nat_nat @ F @ A4 )
% 13.77/7.71 = bot_bot_set_nat )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2413_image__is__empty,axiom,
% 13.77/7.71 ! [F: int > nat,A4: set_int] :
% 13.77/7.71 ( ( ( image_int_nat @ F @ A4 )
% 13.77/7.71 = bot_bot_set_nat )
% 13.77/7.71 = ( A4 = bot_bot_set_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2414_image__is__empty,axiom,
% 13.77/7.71 ! [F: $o > nat,A4: set_o] :
% 13.77/7.71 ( ( ( image_o_nat @ F @ A4 )
% 13.77/7.71 = bot_bot_set_nat )
% 13.77/7.71 = ( A4 = bot_bot_set_o ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2415_image__is__empty,axiom,
% 13.77/7.71 ! [F: nat > int,A4: set_nat] :
% 13.77/7.71 ( ( ( image_nat_int @ F @ A4 )
% 13.77/7.71 = bot_bot_set_int )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2416_image__is__empty,axiom,
% 13.77/7.71 ! [F: int > int,A4: set_int] :
% 13.77/7.71 ( ( ( image_int_int @ F @ A4 )
% 13.77/7.71 = bot_bot_set_int )
% 13.77/7.71 = ( A4 = bot_bot_set_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2417_image__is__empty,axiom,
% 13.77/7.71 ! [F: $o > int,A4: set_o] :
% 13.77/7.71 ( ( ( image_o_int @ F @ A4 )
% 13.77/7.71 = bot_bot_set_int )
% 13.77/7.71 = ( A4 = bot_bot_set_o ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2418_image__is__empty,axiom,
% 13.77/7.71 ! [F: nat > $o,A4: set_nat] :
% 13.77/7.71 ( ( ( image_nat_o @ F @ A4 )
% 13.77/7.71 = bot_bot_set_o )
% 13.77/7.71 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2419_image__is__empty,axiom,
% 13.77/7.71 ! [F: int > $o,A4: set_int] :
% 13.77/7.71 ( ( ( image_int_o @ F @ A4 )
% 13.77/7.71 = bot_bot_set_o )
% 13.77/7.71 = ( A4 = bot_bot_set_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2420_image__is__empty,axiom,
% 13.77/7.71 ! [F: $o > $o,A4: set_o] :
% 13.77/7.71 ( ( ( image_o_o @ F @ A4 )
% 13.77/7.71 = bot_bot_set_o )
% 13.77/7.71 = ( A4 = bot_bot_set_o ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2421_add__Suc__right,axiom,
% 13.77/7.71 ! [M: nat,N: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 13.77/7.71 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2422_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_nat,H2: nat > nat] :
% 13.77/7.71 ( ( finite_finite_nat @ F2 )
% 13.77/7.71 => ( finite_finite_nat @ ( image_nat_nat @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2423_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_nat,H2: nat > int] :
% 13.77/7.71 ( ( finite_finite_nat @ F2 )
% 13.77/7.71 => ( finite_finite_int @ ( image_nat_int @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2424_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_nat,H2: nat > complex] :
% 13.77/7.71 ( ( finite_finite_nat @ F2 )
% 13.77/7.71 => ( finite3207457112153483333omplex @ ( image_nat_complex @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2425_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_nat,H2: nat > code_integer] :
% 13.77/7.71 ( ( finite_finite_nat @ F2 )
% 13.77/7.71 => ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2426_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_int,H2: int > nat] :
% 13.77/7.71 ( ( finite_finite_int @ F2 )
% 13.77/7.71 => ( finite_finite_nat @ ( image_int_nat @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2427_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_int,H2: int > int] :
% 13.77/7.71 ( ( finite_finite_int @ F2 )
% 13.77/7.71 => ( finite_finite_int @ ( image_int_int @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2428_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_int,H2: int > complex] :
% 13.77/7.71 ( ( finite_finite_int @ F2 )
% 13.77/7.71 => ( finite3207457112153483333omplex @ ( image_int_complex @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2429_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_int,H2: int > code_integer] :
% 13.77/7.71 ( ( finite_finite_int @ F2 )
% 13.77/7.71 => ( finite6017078050557962740nteger @ ( image_1587234942943678608nteger @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2430_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_complex,H2: complex > nat] :
% 13.77/7.71 ( ( finite3207457112153483333omplex @ F2 )
% 13.77/7.71 => ( finite_finite_nat @ ( image_complex_nat @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2431_finite__imageI,axiom,
% 13.77/7.71 ! [F2: set_complex,H2: complex > int] :
% 13.77/7.71 ( ( finite3207457112153483333omplex @ F2 )
% 13.77/7.71 => ( finite_finite_int @ ( image_complex_int @ H2 @ F2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2432_add__is__0,axiom,
% 13.77/7.71 ! [M: nat,N: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ M @ N )
% 13.77/7.71 = zero_zero_nat )
% 13.77/7.71 = ( ( M = zero_zero_nat )
% 13.77/7.71 & ( N = zero_zero_nat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2433_Nat_Oadd__0__right,axiom,
% 13.77/7.71 ! [M: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 13.77/7.71 = M ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2434_nat__add__left__cancel__less,axiom,
% 13.77/7.71 ! [K: nat,M: nat,N: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 13.77/7.71 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2435_insert__image,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > nat] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( insert_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 = ( image_nat_nat @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2436_insert__image,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > vEBT_VEBT] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( insert_VEBT_VEBT @ ( F @ X ) @ ( image_nat_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.71 = ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2437_insert__image,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > int] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( insert_int @ ( F @ X ) @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 = ( image_nat_int @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2438_insert__image,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > $o] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( insert_o @ ( F @ X ) @ ( image_nat_o @ F @ A4 ) )
% 13.77/7.71 = ( image_nat_o @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2439_insert__image,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( insert_nat @ ( F @ X ) @ ( image_VEBT_VEBT_nat @ F @ A4 ) )
% 13.77/7.71 = ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2440_insert__image,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( insert_VEBT_VEBT @ ( F @ X ) @ ( image_3375948659692109573T_VEBT @ F @ A4 ) )
% 13.77/7.71 = ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2441_insert__image,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( insert_int @ ( F @ X ) @ ( image_VEBT_VEBT_int @ F @ A4 ) )
% 13.77/7.71 = ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2442_insert__image,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > $o] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( insert_o @ ( F @ X ) @ ( image_VEBT_VEBT_o @ F @ A4 ) )
% 13.77/7.71 = ( image_VEBT_VEBT_o @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2443_insert__image,axiom,
% 13.77/7.71 ! [X: real,A4: set_real,F: real > nat] :
% 13.77/7.71 ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( ( insert_nat @ ( F @ X ) @ ( image_real_nat @ F @ A4 ) )
% 13.77/7.71 = ( image_real_nat @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2444_insert__image,axiom,
% 13.77/7.71 ! [X: real,A4: set_real,F: real > vEBT_VEBT] :
% 13.77/7.71 ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( ( insert_VEBT_VEBT @ ( F @ X ) @ ( image_real_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.71 = ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2445_image__insert,axiom,
% 13.77/7.71 ! [F: nat > nat,A: nat,B4: set_nat] :
% 13.77/7.71 ( ( image_nat_nat @ F @ ( insert_nat @ A @ B4 ) )
% 13.77/7.71 = ( insert_nat @ ( F @ A ) @ ( image_nat_nat @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2446_image__insert,axiom,
% 13.77/7.71 ! [F: nat > vEBT_VEBT,A: nat,B4: set_nat] :
% 13.77/7.71 ( ( image_nat_VEBT_VEBT @ F @ ( insert_nat @ A @ B4 ) )
% 13.77/7.71 = ( insert_VEBT_VEBT @ ( F @ A ) @ ( image_nat_VEBT_VEBT @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2447_image__insert,axiom,
% 13.77/7.71 ! [F: nat > int,A: nat,B4: set_nat] :
% 13.77/7.71 ( ( image_nat_int @ F @ ( insert_nat @ A @ B4 ) )
% 13.77/7.71 = ( insert_int @ ( F @ A ) @ ( image_nat_int @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2448_image__insert,axiom,
% 13.77/7.71 ! [F: nat > $o,A: nat,B4: set_nat] :
% 13.77/7.71 ( ( image_nat_o @ F @ ( insert_nat @ A @ B4 ) )
% 13.77/7.71 = ( insert_o @ ( F @ A ) @ ( image_nat_o @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2449_image__insert,axiom,
% 13.77/7.71 ! [F: vEBT_VEBT > nat,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( image_VEBT_VEBT_nat @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 13.77/7.71 = ( insert_nat @ ( F @ A ) @ ( image_VEBT_VEBT_nat @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2450_image__insert,axiom,
% 13.77/7.71 ! [F: vEBT_VEBT > vEBT_VEBT,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( image_3375948659692109573T_VEBT @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 13.77/7.71 = ( insert_VEBT_VEBT @ ( F @ A ) @ ( image_3375948659692109573T_VEBT @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2451_image__insert,axiom,
% 13.77/7.71 ! [F: vEBT_VEBT > int,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( image_VEBT_VEBT_int @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 13.77/7.71 = ( insert_int @ ( F @ A ) @ ( image_VEBT_VEBT_int @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2452_image__insert,axiom,
% 13.77/7.71 ! [F: vEBT_VEBT > $o,A: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.71 ( ( image_VEBT_VEBT_o @ F @ ( insert_VEBT_VEBT @ A @ B4 ) )
% 13.77/7.71 = ( insert_o @ ( F @ A ) @ ( image_VEBT_VEBT_o @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2453_image__insert,axiom,
% 13.77/7.71 ! [F: int > nat,A: int,B4: set_int] :
% 13.77/7.71 ( ( image_int_nat @ F @ ( insert_int @ A @ B4 ) )
% 13.77/7.71 = ( insert_nat @ ( F @ A ) @ ( image_int_nat @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2454_image__insert,axiom,
% 13.77/7.71 ! [F: int > vEBT_VEBT,A: int,B4: set_int] :
% 13.77/7.71 ( ( image_int_VEBT_VEBT @ F @ ( insert_int @ A @ B4 ) )
% 13.77/7.71 = ( insert_VEBT_VEBT @ ( F @ A ) @ ( image_int_VEBT_VEBT @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2455_nat__add__left__cancel__le,axiom,
% 13.77/7.71 ! [K: nat,M: nat,N: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 13.77/7.71 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2456_diff__diff__left,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 13.77/7.71 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2457_zero__le__double__add__iff__zero__le__single__add,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 13.77/7.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2458_zero__le__double__add__iff__zero__le__single__add,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 13.77/7.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2459_zero__le__double__add__iff__zero__le__single__add,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 13.77/7.71 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2460_double__add__le__zero__iff__single__add__le__zero,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 13.77/7.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2461_double__add__le__zero__iff__single__add__le__zero,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 13.77/7.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2462_double__add__le__zero__iff__single__add__le__zero,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 13.77/7.71 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2463_le__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 13.77/7.71 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2464_le__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 13.77/7.71 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2465_le__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 13.77/7.71 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2466_le__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 13.77/7.71 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2467_le__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 13.77/7.71 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2468_le__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 13.77/7.71 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2469_le__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 13.77/7.71 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2470_le__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 13.77/7.71 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2471_add__le__same__cancel2,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2472_add__le__same__cancel2,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2473_add__le__same__cancel2,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2474_add__le__same__cancel2,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2475_add__le__same__cancel1,axiom,
% 13.77/7.71 ! [B: real,A: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2476_add__le__same__cancel1,axiom,
% 13.77/7.71 ! [B: rat,A: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2477_add__le__same__cancel1,axiom,
% 13.77/7.71 ! [B: nat,A: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2478_add__le__same__cancel1,axiom,
% 13.77/7.71 ! [B: int,A: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2479_zero__less__double__add__iff__zero__less__single__add,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 13.77/7.71 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2480_zero__less__double__add__iff__zero__less__single__add,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 13.77/7.71 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2481_zero__less__double__add__iff__zero__less__single__add,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 13.77/7.71 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2482_double__add__less__zero__iff__single__add__less__zero,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 13.77/7.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2483_double__add__less__zero__iff__single__add__less__zero,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 13.77/7.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2484_double__add__less__zero__iff__single__add__less__zero,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 13.77/7.71 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2485_less__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 13.77/7.71 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2486_less__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 13.77/7.71 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2487_less__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 13.77/7.71 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2488_less__add__same__cancel2,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 13.77/7.71 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2489_less__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 13.77/7.71 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2490_less__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 13.77/7.71 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2491_less__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 13.77/7.71 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2492_less__add__same__cancel1,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 13.77/7.71 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2493_add__less__same__cancel2,axiom,
% 13.77/7.71 ! [A: real,B: real] :
% 13.77/7.71 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2494_add__less__same__cancel2,axiom,
% 13.77/7.71 ! [A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2495_add__less__same__cancel2,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2496_add__less__same__cancel2,axiom,
% 13.77/7.71 ! [A: int,B: int] :
% 13.77/7.71 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 13.77/7.71 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2497_add__less__same__cancel1,axiom,
% 13.77/7.71 ! [B: real,A: real] :
% 13.77/7.71 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2498_add__less__same__cancel1,axiom,
% 13.77/7.71 ! [B: rat,A: rat] :
% 13.77/7.71 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2499_add__less__same__cancel1,axiom,
% 13.77/7.71 ! [B: nat,A: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2500_add__less__same__cancel1,axiom,
% 13.77/7.71 ! [B: int,A: int] :
% 13.77/7.71 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 13.77/7.71 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2501_diff__add__zero,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 13.77/7.71 = zero_zero_nat ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2502_le__add__diff__inverse2,axiom,
% 13.77/7.71 ! [B: real,A: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ B @ A )
% 13.77/7.71 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2503_le__add__diff__inverse2,axiom,
% 13.77/7.71 ! [B: rat,A: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.71 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2504_le__add__diff__inverse2,axiom,
% 13.77/7.71 ! [B: nat,A: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.71 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2505_le__add__diff__inverse2,axiom,
% 13.77/7.71 ! [B: int,A: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.71 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2506_le__add__diff__inverse,axiom,
% 13.77/7.71 ! [B: real,A: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ B @ A )
% 13.77/7.71 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2507_le__add__diff__inverse,axiom,
% 13.77/7.71 ! [B: rat,A: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.71 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2508_le__add__diff__inverse,axiom,
% 13.77/7.71 ! [B: nat,A: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.71 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2509_le__add__diff__inverse,axiom,
% 13.77/7.71 ! [B: int,A: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.71 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 13.77/7.71 = A ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2510_image__add__0,axiom,
% 13.77/7.71 ! [S3: set_uint32] :
% 13.77/7.71 ( ( image_uint32_uint32 @ ( plus_plus_uint32 @ zero_zero_uint32 ) @ S3 )
% 13.77/7.71 = S3 ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2511_image__add__0,axiom,
% 13.77/7.71 ! [S3: set_real] :
% 13.77/7.71 ( ( image_real_real @ ( plus_plus_real @ zero_zero_real ) @ S3 )
% 13.77/7.71 = S3 ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2512_image__add__0,axiom,
% 13.77/7.71 ! [S3: set_rat] :
% 13.77/7.71 ( ( image_rat_rat @ ( plus_plus_rat @ zero_zero_rat ) @ S3 )
% 13.77/7.71 = S3 ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2513_image__add__0,axiom,
% 13.77/7.71 ! [S3: set_nat] :
% 13.77/7.71 ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S3 )
% 13.77/7.71 = S3 ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2514_image__add__0,axiom,
% 13.77/7.71 ! [S3: set_int] :
% 13.77/7.71 ( ( image_int_int @ ( plus_plus_int @ zero_zero_int ) @ S3 )
% 13.77/7.71 = S3 ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2515_add__gr__0,axiom,
% 13.77/7.71 ! [M: nat,N: nat] :
% 13.77/7.71 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 13.77/7.71 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.71 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2516_Nat_Odiff__diff__right,axiom,
% 13.77/7.71 ! [K: nat,J: nat,I: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.71 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 13.77/7.71 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2517_Nat_Oadd__diff__assoc2,axiom,
% 13.77/7.71 ! [K: nat,J: nat,I: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.71 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 13.77/7.71 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2518_Nat_Oadd__diff__assoc,axiom,
% 13.77/7.71 ! [K: nat,J: nat,I: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.71 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 13.77/7.71 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2519_diff__Suc__diff__eq1,axiom,
% 13.77/7.71 ! [K: nat,J: nat,I: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.71 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 13.77/7.71 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2520_diff__Suc__diff__eq2,axiom,
% 13.77/7.71 ! [K: nat,J: nat,I: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.71 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 13.77/7.71 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2521_enumerate__mono__iff,axiom,
% 13.77/7.71 ! [S3: set_nat,M: nat,N: nat] :
% 13.77/7.71 ( ~ ( finite_finite_nat @ S3 )
% 13.77/7.71 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) )
% 13.77/7.71 = ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2522_add__right__imp__eq,axiom,
% 13.77/7.71 ! [B: real,A: real,C2: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ B @ A )
% 13.77/7.71 = ( plus_plus_real @ C2 @ A ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2523_add__right__imp__eq,axiom,
% 13.77/7.71 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ B @ A )
% 13.77/7.71 = ( plus_plus_rat @ C2 @ A ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2524_add__right__imp__eq,axiom,
% 13.77/7.71 ! [B: nat,A: nat,C2: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ B @ A )
% 13.77/7.71 = ( plus_plus_nat @ C2 @ A ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2525_add__right__imp__eq,axiom,
% 13.77/7.71 ! [B: int,A: int,C2: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ B @ A )
% 13.77/7.71 = ( plus_plus_int @ C2 @ A ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2526_add__left__imp__eq,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ A @ B )
% 13.77/7.71 = ( plus_plus_real @ A @ C2 ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2527_add__left__imp__eq,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ A @ B )
% 13.77/7.71 = ( plus_plus_rat @ A @ C2 ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2528_add__left__imp__eq,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ A @ B )
% 13.77/7.71 = ( plus_plus_nat @ A @ C2 ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2529_add__left__imp__eq,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ A @ B )
% 13.77/7.71 = ( plus_plus_int @ A @ C2 ) )
% 13.77/7.71 => ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2530_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 13.77/7.71 ! [B: real,A: real,C2: real] :
% 13.77/7.71 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C2 ) )
% 13.77/7.71 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2531_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 13.77/7.71 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C2 ) )
% 13.77/7.71 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2532_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 13.77/7.71 ! [B: nat,A: nat,C2: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 13.77/7.71 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2533_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 13.77/7.71 ! [B: int,A: int,C2: int] :
% 13.77/7.71 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C2 ) )
% 13.77/7.71 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2534_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 13.77/7.71 ( plus_plus_real
% 13.77/7.71 = ( ^ [A7: real,B7: real] : ( plus_plus_real @ B7 @ A7 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2535_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 13.77/7.71 ( plus_plus_rat
% 13.77/7.71 = ( ^ [A7: rat,B7: rat] : ( plus_plus_rat @ B7 @ A7 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2536_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 13.77/7.71 ( plus_plus_nat
% 13.77/7.71 = ( ^ [A7: nat,B7: nat] : ( plus_plus_nat @ B7 @ A7 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2537_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 13.77/7.71 ( plus_plus_int
% 13.77/7.71 = ( ^ [A7: int,B7: int] : ( plus_plus_int @ B7 @ A7 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2538_add_Oright__cancel,axiom,
% 13.77/7.71 ! [B: real,A: real,C2: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ B @ A )
% 13.77/7.71 = ( plus_plus_real @ C2 @ A ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2539_add_Oright__cancel,axiom,
% 13.77/7.71 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ B @ A )
% 13.77/7.71 = ( plus_plus_rat @ C2 @ A ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2540_add_Oright__cancel,axiom,
% 13.77/7.71 ! [B: int,A: int,C2: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ B @ A )
% 13.77/7.71 = ( plus_plus_int @ C2 @ A ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2541_add_Oleft__cancel,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ A @ B )
% 13.77/7.71 = ( plus_plus_real @ A @ C2 ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2542_add_Oleft__cancel,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ A @ B )
% 13.77/7.71 = ( plus_plus_rat @ A @ C2 ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2543_add_Oleft__cancel,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ A @ B )
% 13.77/7.71 = ( plus_plus_int @ A @ C2 ) )
% 13.77/7.71 = ( B = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2544_add_Oassoc,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 13.77/7.71 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2545_add_Oassoc,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 13.77/7.71 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2546_add_Oassoc,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 13.77/7.71 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2547_add_Oassoc,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 13.77/7.71 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2548_group__cancel_Oadd2,axiom,
% 13.77/7.71 ! [B4: real,K: real,B: real,A: real] :
% 13.77/7.71 ( ( B4
% 13.77/7.71 = ( plus_plus_real @ K @ B ) )
% 13.77/7.71 => ( ( plus_plus_real @ A @ B4 )
% 13.77/7.71 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2549_group__cancel_Oadd2,axiom,
% 13.77/7.71 ! [B4: rat,K: rat,B: rat,A: rat] :
% 13.77/7.71 ( ( B4
% 13.77/7.71 = ( plus_plus_rat @ K @ B ) )
% 13.77/7.71 => ( ( plus_plus_rat @ A @ B4 )
% 13.77/7.71 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2550_group__cancel_Oadd2,axiom,
% 13.77/7.71 ! [B4: nat,K: nat,B: nat,A: nat] :
% 13.77/7.71 ( ( B4
% 13.77/7.71 = ( plus_plus_nat @ K @ B ) )
% 13.77/7.71 => ( ( plus_plus_nat @ A @ B4 )
% 13.77/7.71 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2551_group__cancel_Oadd2,axiom,
% 13.77/7.71 ! [B4: int,K: int,B: int,A: int] :
% 13.77/7.71 ( ( B4
% 13.77/7.71 = ( plus_plus_int @ K @ B ) )
% 13.77/7.71 => ( ( plus_plus_int @ A @ B4 )
% 13.77/7.71 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2552_group__cancel_Oadd1,axiom,
% 13.77/7.71 ! [A4: real,K: real,A: real,B: real] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_real @ K @ A ) )
% 13.77/7.71 => ( ( plus_plus_real @ A4 @ B )
% 13.77/7.71 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2553_group__cancel_Oadd1,axiom,
% 13.77/7.71 ! [A4: rat,K: rat,A: rat,B: rat] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_rat @ K @ A ) )
% 13.77/7.71 => ( ( plus_plus_rat @ A4 @ B )
% 13.77/7.71 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2554_group__cancel_Oadd1,axiom,
% 13.77/7.71 ! [A4: nat,K: nat,A: nat,B: nat] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_nat @ K @ A ) )
% 13.77/7.71 => ( ( plus_plus_nat @ A4 @ B )
% 13.77/7.71 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2555_group__cancel_Oadd1,axiom,
% 13.77/7.71 ! [A4: int,K: int,A: int,B: int] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_int @ K @ A ) )
% 13.77/7.71 => ( ( plus_plus_int @ A4 @ B )
% 13.77/7.71 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2556_add__mono__thms__linordered__semiring_I4_J,axiom,
% 13.77/7.71 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ( plus_plus_real @ I @ K )
% 13.77/7.71 = ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2557_add__mono__thms__linordered__semiring_I4_J,axiom,
% 13.77/7.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ( plus_plus_rat @ I @ K )
% 13.77/7.71 = ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2558_add__mono__thms__linordered__semiring_I4_J,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ( plus_plus_nat @ I @ K )
% 13.77/7.71 = ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2559_add__mono__thms__linordered__semiring_I4_J,axiom,
% 13.77/7.71 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ( plus_plus_int @ I @ K )
% 13.77/7.71 = ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2560_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,B: nat,F: nat > nat] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2561_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,B: vEBT_VEBT,F: nat > vEBT_VEBT] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_VEBT_VEBT @ B @ ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2562_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,B: real,F: nat > real] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_real @ B @ ( image_nat_real @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2563_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,B: int,F: nat > int] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_int @ B @ ( image_nat_int @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2564_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: nat,F: vEBT_VEBT > nat] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_nat @ B @ ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2565_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_VEBT_VEBT @ B @ ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2566_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: real,F: vEBT_VEBT > real] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_real @ B @ ( image_VEBT_VEBT_real @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2567_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,B: int,F: vEBT_VEBT > int] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_int @ B @ ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2568_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: real,A4: set_real,B: nat,F: real > nat] :
% 13.77/7.71 ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_nat @ B @ ( image_real_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2569_rev__image__eqI,axiom,
% 13.77/7.71 ! [X: real,A4: set_real,B: vEBT_VEBT,F: real > vEBT_VEBT] :
% 13.77/7.71 ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( ( B
% 13.77/7.71 = ( F @ X ) )
% 13.77/7.71 => ( member_VEBT_VEBT @ B @ ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2570_ball__imageD,axiom,
% 13.77/7.71 ! [F: nat > set_nat,A4: set_nat,P2: set_nat > $o] :
% 13.77/7.71 ( ! [X3: set_nat] :
% 13.77/7.71 ( ( member_set_nat @ X3 @ ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ X3 ) )
% 13.77/7.71 => ! [X5: nat] :
% 13.77/7.71 ( ( member_nat @ X5 @ A4 )
% 13.77/7.71 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2571_ball__imageD,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 13.77/7.71 ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ X3 ) )
% 13.77/7.71 => ! [X5: nat] :
% 13.77/7.71 ( ( member_nat @ X5 @ A4 )
% 13.77/7.71 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2572_ball__imageD,axiom,
% 13.77/7.71 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 13.77/7.71 ( ! [X3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ X3 ) )
% 13.77/7.71 => ! [X5: nat] :
% 13.77/7.71 ( ( member_nat @ X5 @ A4 )
% 13.77/7.71 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2573_ball__imageD,axiom,
% 13.77/7.71 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 13.77/7.71 ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ X3 ) )
% 13.77/7.71 => ! [X5: int] :
% 13.77/7.71 ( ( member_int @ X5 @ A4 )
% 13.77/7.71 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2574_ball__imageD,axiom,
% 13.77/7.71 ! [F: int > int,A4: set_int,P2: int > $o] :
% 13.77/7.71 ( ! [X3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ ( image_int_int @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ X3 ) )
% 13.77/7.71 => ! [X5: int] :
% 13.77/7.71 ( ( member_int @ X5 @ A4 )
% 13.77/7.71 => ( P2 @ ( F @ X5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2575_image__cong,axiom,
% 13.77/7.71 ! [M7: set_nat,N8: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 13.77/7.71 ( ( M7 = N8 )
% 13.77/7.71 => ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ N8 )
% 13.77/7.71 => ( ( F @ X3 )
% 13.77/7.71 = ( G @ X3 ) ) )
% 13.77/7.71 => ( ( image_nat_set_nat @ F @ M7 )
% 13.77/7.71 = ( image_nat_set_nat @ G @ N8 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2576_image__cong,axiom,
% 13.77/7.71 ! [M7: set_nat,N8: set_nat,F: nat > nat,G: nat > nat] :
% 13.77/7.71 ( ( M7 = N8 )
% 13.77/7.71 => ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ N8 )
% 13.77/7.71 => ( ( F @ X3 )
% 13.77/7.71 = ( G @ X3 ) ) )
% 13.77/7.71 => ( ( image_nat_nat @ F @ M7 )
% 13.77/7.71 = ( image_nat_nat @ G @ N8 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2577_image__cong,axiom,
% 13.77/7.71 ! [M7: set_nat,N8: set_nat,F: nat > int,G: nat > int] :
% 13.77/7.71 ( ( M7 = N8 )
% 13.77/7.71 => ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ N8 )
% 13.77/7.71 => ( ( F @ X3 )
% 13.77/7.71 = ( G @ X3 ) ) )
% 13.77/7.71 => ( ( image_nat_int @ F @ M7 )
% 13.77/7.71 = ( image_nat_int @ G @ N8 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2578_image__cong,axiom,
% 13.77/7.71 ! [M7: set_int,N8: set_int,F: int > nat,G: int > nat] :
% 13.77/7.71 ( ( M7 = N8 )
% 13.77/7.71 => ( ! [X3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ N8 )
% 13.77/7.71 => ( ( F @ X3 )
% 13.77/7.71 = ( G @ X3 ) ) )
% 13.77/7.71 => ( ( image_int_nat @ F @ M7 )
% 13.77/7.71 = ( image_int_nat @ G @ N8 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2579_image__cong,axiom,
% 13.77/7.71 ! [M7: set_int,N8: set_int,F: int > int,G: int > int] :
% 13.77/7.71 ( ( M7 = N8 )
% 13.77/7.71 => ( ! [X3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ N8 )
% 13.77/7.71 => ( ( F @ X3 )
% 13.77/7.71 = ( G @ X3 ) ) )
% 13.77/7.71 => ( ( image_int_int @ F @ M7 )
% 13.77/7.71 = ( image_int_int @ G @ N8 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2580_bex__imageD,axiom,
% 13.77/7.71 ! [F: nat > set_nat,A4: set_nat,P2: set_nat > $o] :
% 13.77/7.71 ( ? [X5: set_nat] :
% 13.77/7.71 ( ( member_set_nat @ X5 @ ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ X5 ) )
% 13.77/7.71 => ? [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ A4 )
% 13.77/7.71 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2581_bex__imageD,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat,P2: nat > $o] :
% 13.77/7.71 ( ? [X5: nat] :
% 13.77/7.71 ( ( member_nat @ X5 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ X5 ) )
% 13.77/7.71 => ? [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ A4 )
% 13.77/7.71 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2582_bex__imageD,axiom,
% 13.77/7.71 ! [F: nat > int,A4: set_nat,P2: int > $o] :
% 13.77/7.71 ( ? [X5: int] :
% 13.77/7.71 ( ( member_int @ X5 @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ X5 ) )
% 13.77/7.71 => ? [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ A4 )
% 13.77/7.71 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2583_bex__imageD,axiom,
% 13.77/7.71 ! [F: int > nat,A4: set_int,P2: nat > $o] :
% 13.77/7.71 ( ? [X5: nat] :
% 13.77/7.71 ( ( member_nat @ X5 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ X5 ) )
% 13.77/7.71 => ? [X3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ A4 )
% 13.77/7.71 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2584_bex__imageD,axiom,
% 13.77/7.71 ! [F: int > int,A4: set_int,P2: int > $o] :
% 13.77/7.71 ( ? [X5: int] :
% 13.77/7.71 ( ( member_int @ X5 @ ( image_int_int @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ X5 ) )
% 13.77/7.71 => ? [X3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ A4 )
% 13.77/7.71 & ( P2 @ ( F @ X3 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2585_image__iff,axiom,
% 13.77/7.71 ! [Z: nat,F: nat > nat,A4: set_nat] :
% 13.77/7.71 ( ( member_nat @ Z @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 = ( ? [X4: nat] :
% 13.77/7.71 ( ( member_nat @ X4 @ A4 )
% 13.77/7.71 & ( Z
% 13.77/7.71 = ( F @ X4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2586_image__iff,axiom,
% 13.77/7.71 ! [Z: nat,F: int > nat,A4: set_int] :
% 13.77/7.71 ( ( member_nat @ Z @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.71 = ( ? [X4: int] :
% 13.77/7.71 ( ( member_int @ X4 @ A4 )
% 13.77/7.71 & ( Z
% 13.77/7.71 = ( F @ X4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2587_image__iff,axiom,
% 13.77/7.71 ! [Z: int,F: nat > int,A4: set_nat] :
% 13.77/7.71 ( ( member_int @ Z @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 = ( ? [X4: nat] :
% 13.77/7.71 ( ( member_nat @ X4 @ A4 )
% 13.77/7.71 & ( Z
% 13.77/7.71 = ( F @ X4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2588_image__iff,axiom,
% 13.77/7.71 ! [Z: int,F: int > int,A4: set_int] :
% 13.77/7.71 ( ( member_int @ Z @ ( image_int_int @ F @ A4 ) )
% 13.77/7.71 = ( ? [X4: int] :
% 13.77/7.71 ( ( member_int @ X4 @ A4 )
% 13.77/7.71 & ( Z
% 13.77/7.71 = ( F @ X4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2589_image__iff,axiom,
% 13.77/7.71 ! [Z: set_nat,F: nat > set_nat,A4: set_nat] :
% 13.77/7.71 ( ( member_set_nat @ Z @ ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.71 = ( ? [X4: nat] :
% 13.77/7.71 ( ( member_nat @ X4 @ A4 )
% 13.77/7.71 & ( Z
% 13.77/7.71 = ( F @ X4 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2590_imageI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > nat] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2591_imageI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > vEBT_VEBT] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ ( F @ X ) @ ( image_nat_VEBT_VEBT @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2592_imageI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > real] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_real @ ( F @ X ) @ ( image_nat_real @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2593_imageI,axiom,
% 13.77/7.71 ! [X: nat,A4: set_nat,F: nat > int] :
% 13.77/7.71 ( ( member_nat @ X @ A4 )
% 13.77/7.71 => ( member_int @ ( F @ X ) @ ( image_nat_int @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2594_imageI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X ) @ ( image_VEBT_VEBT_nat @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2595_imageI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ ( F @ X ) @ ( image_3375948659692109573T_VEBT @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2596_imageI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_real @ ( F @ X ) @ ( image_VEBT_VEBT_real @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2597_imageI,axiom,
% 13.77/7.71 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.71 => ( member_int @ ( F @ X ) @ ( image_VEBT_VEBT_int @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2598_imageI,axiom,
% 13.77/7.71 ! [X: real,A4: set_real,F: real > nat] :
% 13.77/7.71 ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X ) @ ( image_real_nat @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2599_imageI,axiom,
% 13.77/7.71 ! [X: real,A4: set_real,F: real > vEBT_VEBT] :
% 13.77/7.71 ( ( member_real @ X @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ ( F @ X ) @ ( image_real_VEBT_VEBT @ F @ A4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2600_image__mono,axiom,
% 13.77/7.71 ! [A4: set_nat,B4: set_nat,F: nat > set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.71 => ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A4 ) @ ( image_nat_set_nat @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2601_image__mono,axiom,
% 13.77/7.71 ! [A4: set_nat,B4: set_nat,F: nat > nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.71 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2602_image__mono,axiom,
% 13.77/7.71 ! [A4: set_nat,B4: set_nat,F: nat > int] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.71 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2603_image__mono,axiom,
% 13.77/7.71 ! [A4: set_int,B4: set_int,F: int > nat] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.71 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2604_image__mono,axiom,
% 13.77/7.71 ! [A4: set_int,B4: set_int,F: int > int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.71 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B4 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2605_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_nat,F: nat > nat,B4: set_nat] :
% 13.77/7.71 ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2606_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_nat,F: nat > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.71 ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_le4337996190870823476T_VEBT @ ( image_nat_VEBT_VEBT @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2607_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_nat,F: nat > real,B4: set_real] :
% 13.77/7.71 ( ! [X3: nat] :
% 13.77/7.71 ( ( member_nat @ X3 @ A4 )
% 13.77/7.71 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_less_eq_set_real @ ( image_nat_real @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2608_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat,B4: set_nat] :
% 13.77/7.71 ( ! [X3: vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_less_eq_set_nat @ ( image_VEBT_VEBT_nat @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2609_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.71 ( ! [X3: vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_le4337996190870823476T_VEBT @ ( image_3375948659692109573T_VEBT @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2610_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real,B4: set_real] :
% 13.77/7.71 ( ! [X3: vEBT_VEBT] :
% 13.77/7.71 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.71 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_less_eq_set_real @ ( image_VEBT_VEBT_real @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2611_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_real,F: real > nat,B4: set_nat] :
% 13.77/7.71 ( ! [X3: real] :
% 13.77/7.71 ( ( member_real @ X3 @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_less_eq_set_nat @ ( image_real_nat @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2612_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_real,F: real > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.71 ( ! [X3: real] :
% 13.77/7.71 ( ( member_real @ X3 @ A4 )
% 13.77/7.71 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_le4337996190870823476T_VEBT @ ( image_real_VEBT_VEBT @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2613_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_real,F: real > real,B4: set_real] :
% 13.77/7.71 ( ! [X3: real] :
% 13.77/7.71 ( ( member_real @ X3 @ A4 )
% 13.77/7.71 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_less_eq_set_real @ ( image_real_real @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2614_image__subsetI,axiom,
% 13.77/7.71 ! [A4: set_int,F: int > nat,B4: set_nat] :
% 13.77/7.71 ( ! [X3: int] :
% 13.77/7.71 ( ( member_int @ X3 @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 13.77/7.71 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B4 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2615_subset__imageE,axiom,
% 13.77/7.71 ! [B4: set_set_nat,F: nat > set_nat,A4: set_nat] :
% 13.77/7.71 ( ( ord_le6893508408891458716et_nat @ B4 @ ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.71 => ~ ! [C5: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 13.77/7.71 => ( B4
% 13.77/7.71 != ( image_nat_set_nat @ F @ C5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2616_subset__imageE,axiom,
% 13.77/7.71 ! [B4: set_nat,F: nat > nat,A4: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 => ~ ! [C5: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 13.77/7.71 => ( B4
% 13.77/7.71 != ( image_nat_nat @ F @ C5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2617_subset__imageE,axiom,
% 13.77/7.71 ! [B4: set_nat,F: int > nat,A4: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.71 => ~ ! [C5: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ C5 @ A4 )
% 13.77/7.71 => ( B4
% 13.77/7.71 != ( image_int_nat @ F @ C5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2618_subset__imageE,axiom,
% 13.77/7.71 ! [B4: set_int,F: nat > int,A4: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B4 @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 => ~ ! [C5: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 13.77/7.71 => ( B4
% 13.77/7.71 != ( image_nat_int @ F @ C5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2619_subset__imageE,axiom,
% 13.77/7.71 ! [B4: set_int,F: int > int,A4: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B4 @ ( image_int_int @ F @ A4 ) )
% 13.77/7.71 => ~ ! [C5: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ C5 @ A4 )
% 13.77/7.71 => ( B4
% 13.77/7.71 != ( image_int_int @ F @ C5 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2620_image__subset__iff,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat,B4: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B4 )
% 13.77/7.71 = ( ! [X4: nat] :
% 13.77/7.71 ( ( member_nat @ X4 @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2621_image__subset__iff,axiom,
% 13.77/7.71 ! [F: int > nat,A4: set_int,B4: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B4 )
% 13.77/7.71 = ( ! [X4: int] :
% 13.77/7.71 ( ( member_int @ X4 @ A4 )
% 13.77/7.71 => ( member_nat @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2622_image__subset__iff,axiom,
% 13.77/7.71 ! [F: nat > set_nat,A4: set_nat,B4: set_set_nat] :
% 13.77/7.71 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A4 ) @ B4 )
% 13.77/7.71 = ( ! [X4: nat] :
% 13.77/7.71 ( ( member_nat @ X4 @ A4 )
% 13.77/7.71 => ( member_set_nat @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2623_image__subset__iff,axiom,
% 13.77/7.71 ! [F: nat > int,A4: set_nat,B4: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B4 )
% 13.77/7.71 = ( ! [X4: nat] :
% 13.77/7.71 ( ( member_nat @ X4 @ A4 )
% 13.77/7.71 => ( member_int @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2624_image__subset__iff,axiom,
% 13.77/7.71 ! [F: int > int,A4: set_int,B4: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B4 )
% 13.77/7.71 = ( ! [X4: int] :
% 13.77/7.71 ( ( member_int @ X4 @ A4 )
% 13.77/7.71 => ( member_int @ ( F @ X4 ) @ B4 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2625_subset__image__iff,axiom,
% 13.77/7.71 ! [B4: set_set_nat,F: nat > set_nat,A4: set_nat] :
% 13.77/7.71 ( ( ord_le6893508408891458716et_nat @ B4 @ ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.71 = ( ? [AA: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 13.77/7.71 & ( B4
% 13.77/7.71 = ( image_nat_set_nat @ F @ AA ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2626_subset__image__iff,axiom,
% 13.77/7.71 ! [B4: set_nat,F: nat > nat,A4: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 = ( ? [AA: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 13.77/7.71 & ( B4
% 13.77/7.71 = ( image_nat_nat @ F @ AA ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2627_subset__image__iff,axiom,
% 13.77/7.71 ! [B4: set_nat,F: int > nat,A4: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.71 = ( ? [AA: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ AA @ A4 )
% 13.77/7.71 & ( B4
% 13.77/7.71 = ( image_int_nat @ F @ AA ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2628_subset__image__iff,axiom,
% 13.77/7.71 ! [B4: set_int,F: nat > int,A4: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B4 @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 = ( ? [AA: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ AA @ A4 )
% 13.77/7.71 & ( B4
% 13.77/7.71 = ( image_nat_int @ F @ AA ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2629_subset__image__iff,axiom,
% 13.77/7.71 ! [B4: set_int,F: int > int,A4: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B4 @ ( image_int_int @ F @ A4 ) )
% 13.77/7.71 = ( ? [AA: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ AA @ A4 )
% 13.77/7.71 & ( B4
% 13.77/7.71 = ( image_int_int @ F @ AA ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2630_all__subset__image,axiom,
% 13.77/7.71 ! [F: nat > set_nat,A4: set_nat,P2: set_set_nat > $o] :
% 13.77/7.71 ( ( ! [B6: set_set_nat] :
% 13.77/7.71 ( ( ord_le6893508408891458716et_nat @ B6 @ ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 13.77/7.71 => ( P2 @ ( image_nat_set_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2631_all__subset__image,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 13.77/7.71 ( ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 13.77/7.71 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2632_all__subset__image,axiom,
% 13.77/7.71 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 13.77/7.71 ( ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 13.77/7.71 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2633_all__subset__image,axiom,
% 13.77/7.71 ! [F: nat > int,A4: set_nat,P2: set_int > $o] :
% 13.77/7.71 ( ( ! [B6: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ord_less_eq_set_nat @ B6 @ A4 )
% 13.77/7.71 => ( P2 @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2634_all__subset__image,axiom,
% 13.77/7.71 ! [F: int > int,A4: set_int,P2: set_int > $o] :
% 13.77/7.71 ( ( ! [B6: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A4 ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_int] :
% 13.77/7.71 ( ( ord_less_eq_set_int @ B6 @ A4 )
% 13.77/7.71 => ( P2 @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2635_verit__sum__simplify,axiom,
% 13.77/7.71 ! [A: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ A @ zero_zero_uint32 )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2636_verit__sum__simplify,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( plus_plus_real @ A @ zero_zero_real )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2637_verit__sum__simplify,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2638_verit__sum__simplify,axiom,
% 13.77/7.71 ! [A: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2639_verit__sum__simplify,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( plus_plus_int @ A @ zero_zero_int )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2640_comm__monoid__add__class_Oadd__0,axiom,
% 13.77/7.71 ! [A: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ zero_zero_uint32 @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2641_comm__monoid__add__class_Oadd__0,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( plus_plus_real @ zero_zero_real @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2642_comm__monoid__add__class_Oadd__0,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2643_comm__monoid__add__class_Oadd__0,axiom,
% 13.77/7.71 ! [A: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2644_comm__monoid__add__class_Oadd__0,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( plus_plus_int @ zero_zero_int @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2645_add_Ocomm__neutral,axiom,
% 13.77/7.71 ! [A: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ A @ zero_zero_uint32 )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2646_add_Ocomm__neutral,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( plus_plus_real @ A @ zero_zero_real )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2647_add_Ocomm__neutral,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2648_add_Ocomm__neutral,axiom,
% 13.77/7.71 ! [A: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2649_add_Ocomm__neutral,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( plus_plus_int @ A @ zero_zero_int )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2650_add_Ogroup__left__neutral,axiom,
% 13.77/7.71 ! [A: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ zero_zero_uint32 @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2651_add_Ogroup__left__neutral,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( plus_plus_real @ zero_zero_real @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2652_add_Ogroup__left__neutral,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2653_add_Ogroup__left__neutral,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( plus_plus_int @ zero_zero_int @ A )
% 13.77/7.71 = A ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2654_add__le__imp__le__right,axiom,
% 13.77/7.71 ! [A: real,C2: real,B: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_eq_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2655_add__le__imp__le__right,axiom,
% 13.77/7.71 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_eq_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2656_add__le__imp__le__right,axiom,
% 13.77/7.71 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_eq_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2657_add__le__imp__le__right,axiom,
% 13.77/7.71 ! [A: int,C2: int,B: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_eq_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2658_add__le__imp__le__left,axiom,
% 13.77/7.71 ! [C2: real,A: real,B: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_eq_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2659_add__le__imp__le__left,axiom,
% 13.77/7.71 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_eq_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2660_add__le__imp__le__left,axiom,
% 13.77/7.71 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_eq_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2661_add__le__imp__le__left,axiom,
% 13.77/7.71 ! [C2: int,A: int,B: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_eq_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2662_le__iff__add,axiom,
% 13.77/7.71 ( ord_less_eq_nat
% 13.77/7.71 = ( ^ [A7: nat,B7: nat] :
% 13.77/7.71 ? [C6: nat] :
% 13.77/7.71 ( B7
% 13.77/7.71 = ( plus_plus_nat @ A7 @ C6 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2663_add__right__mono,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.71 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2664_add__right__mono,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2665_add__right__mono,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2666_add__right__mono,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.71 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2667_less__eqE,axiom,
% 13.77/7.71 ! [A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.71 => ~ ! [C: nat] :
% 13.77/7.71 ( B
% 13.77/7.71 != ( plus_plus_nat @ A @ C ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2668_add__left__mono,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.71 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2669_add__left__mono,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2670_add__left__mono,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2671_add__left__mono,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.71 => ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2672_add__mono,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.71 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.71 => ( ( ord_less_eq_real @ C2 @ D )
% 13.77/7.71 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2673_add__mono,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.71 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.71 => ( ( ord_less_eq_rat @ C2 @ D )
% 13.77/7.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2674_add__mono,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.71 => ( ( ord_less_eq_nat @ C2 @ D )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2675_add__mono,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.71 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.71 => ( ( ord_less_eq_int @ C2 @ D )
% 13.77/7.71 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2676_add__mono__thms__linordered__semiring_I1_J,axiom,
% 13.77/7.71 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.71 ( ( ( ord_less_eq_real @ I @ J )
% 13.77/7.71 & ( ord_less_eq_real @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2677_add__mono__thms__linordered__semiring_I1_J,axiom,
% 13.77/7.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.71 ( ( ( ord_less_eq_rat @ I @ J )
% 13.77/7.71 & ( ord_less_eq_rat @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2678_add__mono__thms__linordered__semiring_I1_J,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.71 & ( ord_less_eq_nat @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2679_add__mono__thms__linordered__semiring_I1_J,axiom,
% 13.77/7.71 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.71 ( ( ( ord_less_eq_int @ I @ J )
% 13.77/7.71 & ( ord_less_eq_int @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2680_add__mono__thms__linordered__semiring_I2_J,axiom,
% 13.77/7.71 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_eq_real @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2681_add__mono__thms__linordered__semiring_I2_J,axiom,
% 13.77/7.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_eq_rat @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2682_add__mono__thms__linordered__semiring_I2_J,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_eq_nat @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2683_add__mono__thms__linordered__semiring_I2_J,axiom,
% 13.77/7.71 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_eq_int @ K @ L ) )
% 13.77/7.71 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2684_add__mono__thms__linordered__semiring_I3_J,axiom,
% 13.77/7.71 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.71 ( ( ( ord_less_eq_real @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2685_add__mono__thms__linordered__semiring_I3_J,axiom,
% 13.77/7.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.71 ( ( ( ord_less_eq_rat @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2686_add__mono__thms__linordered__semiring_I3_J,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2687_add__mono__thms__linordered__semiring_I3_J,axiom,
% 13.77/7.71 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.71 ( ( ( ord_less_eq_int @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2688_add__mono__thms__linordered__field_I5_J,axiom,
% 13.77/7.71 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.71 ( ( ( ord_less_real @ I @ J )
% 13.77/7.71 & ( ord_less_real @ K @ L ) )
% 13.77/7.71 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2689_add__mono__thms__linordered__field_I5_J,axiom,
% 13.77/7.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.71 ( ( ( ord_less_rat @ I @ J )
% 13.77/7.71 & ( ord_less_rat @ K @ L ) )
% 13.77/7.71 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2690_add__mono__thms__linordered__field_I5_J,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ( ord_less_nat @ I @ J )
% 13.77/7.71 & ( ord_less_nat @ K @ L ) )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2691_add__mono__thms__linordered__field_I5_J,axiom,
% 13.77/7.71 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.71 ( ( ( ord_less_int @ I @ J )
% 13.77/7.71 & ( ord_less_int @ K @ L ) )
% 13.77/7.71 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2692_add__mono__thms__linordered__field_I2_J,axiom,
% 13.77/7.71 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_real @ K @ L ) )
% 13.77/7.71 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2693_add__mono__thms__linordered__field_I2_J,axiom,
% 13.77/7.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_rat @ K @ L ) )
% 13.77/7.71 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2694_add__mono__thms__linordered__field_I2_J,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_nat @ K @ L ) )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2695_add__mono__thms__linordered__field_I2_J,axiom,
% 13.77/7.71 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.71 ( ( ( I = J )
% 13.77/7.71 & ( ord_less_int @ K @ L ) )
% 13.77/7.71 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2696_add__mono__thms__linordered__field_I1_J,axiom,
% 13.77/7.71 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.71 ( ( ( ord_less_real @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2697_add__mono__thms__linordered__field_I1_J,axiom,
% 13.77/7.71 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.71 ( ( ( ord_less_rat @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2698_add__mono__thms__linordered__field_I1_J,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ( ord_less_nat @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2699_add__mono__thms__linordered__field_I1_J,axiom,
% 13.77/7.71 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.71 ( ( ( ord_less_int @ I @ J )
% 13.77/7.71 & ( K = L ) )
% 13.77/7.71 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2700_add__strict__mono,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.71 ( ( ord_less_real @ A @ B )
% 13.77/7.71 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.71 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2701_add__strict__mono,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.71 ( ( ord_less_rat @ A @ B )
% 13.77/7.71 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.71 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2702_add__strict__mono,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.71 ( ( ord_less_nat @ A @ B )
% 13.77/7.71 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2703_add__strict__mono,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.71 ( ( ord_less_int @ A @ B )
% 13.77/7.71 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.71 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2704_add__strict__left__mono,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ord_less_real @ A @ B )
% 13.77/7.71 => ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2705_add__strict__left__mono,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ord_less_rat @ A @ B )
% 13.77/7.71 => ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2706_add__strict__left__mono,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( ord_less_nat @ A @ B )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2707_add__strict__left__mono,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ord_less_int @ A @ B )
% 13.77/7.71 => ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2708_add__strict__right__mono,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ord_less_real @ A @ B )
% 13.77/7.71 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2709_add__strict__right__mono,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ord_less_rat @ A @ B )
% 13.77/7.71 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2710_add__strict__right__mono,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( ord_less_nat @ A @ B )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2711_add__strict__right__mono,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ord_less_int @ A @ B )
% 13.77/7.71 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2712_add__less__imp__less__left,axiom,
% 13.77/7.71 ! [C2: real,A: real,B: real] :
% 13.77/7.71 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2713_add__less__imp__less__left,axiom,
% 13.77/7.71 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2714_add__less__imp__less__left,axiom,
% 13.77/7.71 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2715_add__less__imp__less__left,axiom,
% 13.77/7.71 ! [C2: int,A: int,B: int] :
% 13.77/7.71 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 13.77/7.71 => ( ord_less_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2716_add__less__imp__less__right,axiom,
% 13.77/7.71 ! [A: real,C2: real,B: real] :
% 13.77/7.71 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_real @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2717_add__less__imp__less__right,axiom,
% 13.77/7.71 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.71 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_rat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2718_add__less__imp__less__right,axiom,
% 13.77/7.71 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_nat @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2719_add__less__imp__less__right,axiom,
% 13.77/7.71 ! [A: int,C2: int,B: int] :
% 13.77/7.71 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 13.77/7.71 => ( ord_less_int @ A @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2720_diff__diff__eq,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2721_diff__diff__eq,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32,C2: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_uint32 @ A @ ( plus_plus_uint32 @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2722_diff__diff__eq,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2723_diff__diff__eq,axiom,
% 13.77/7.71 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2724_diff__diff__eq,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2725_add__implies__diff,axiom,
% 13.77/7.71 ! [C2: rat,B: rat,A: rat] :
% 13.77/7.71 ( ( ( plus_plus_rat @ C2 @ B )
% 13.77/7.71 = A )
% 13.77/7.71 => ( C2
% 13.77/7.71 = ( minus_minus_rat @ A @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2726_add__implies__diff,axiom,
% 13.77/7.71 ! [C2: uint32,B: uint32,A: uint32] :
% 13.77/7.71 ( ( ( plus_plus_uint32 @ C2 @ B )
% 13.77/7.71 = A )
% 13.77/7.71 => ( C2
% 13.77/7.71 = ( minus_minus_uint32 @ A @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2727_add__implies__diff,axiom,
% 13.77/7.71 ! [C2: real,B: real,A: real] :
% 13.77/7.71 ( ( ( plus_plus_real @ C2 @ B )
% 13.77/7.71 = A )
% 13.77/7.71 => ( C2
% 13.77/7.71 = ( minus_minus_real @ A @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2728_add__implies__diff,axiom,
% 13.77/7.71 ! [C2: nat,B: nat,A: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ C2 @ B )
% 13.77/7.71 = A )
% 13.77/7.71 => ( C2
% 13.77/7.71 = ( minus_minus_nat @ A @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2729_add__implies__diff,axiom,
% 13.77/7.71 ! [C2: int,B: int,A: int] :
% 13.77/7.71 ( ( ( plus_plus_int @ C2 @ B )
% 13.77/7.71 = A )
% 13.77/7.71 => ( C2
% 13.77/7.71 = ( minus_minus_int @ A @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2730_diff__add__eq__diff__diff__swap,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2731_diff__add__eq__diff__diff__swap,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32,C2: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ A @ ( plus_plus_uint32 @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_uint32 @ ( minus_minus_uint32 @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2732_diff__add__eq__diff__diff__swap,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_real @ ( minus_minus_real @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2733_diff__add__eq__diff__diff__swap,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2734_diff__add__eq,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2735_diff__add__eq,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32,C2: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ ( minus_minus_uint32 @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2736_diff__add__eq,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2737_diff__add__eq,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 13.77/7.71 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2738_diff__diff__eq2,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2739_diff__diff__eq2,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32,C2: uint32] :
% 13.77/7.71 ( ( minus_minus_uint32 @ A @ ( minus_minus_uint32 @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2740_diff__diff__eq2,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2741_diff__diff__eq2,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2742_add__diff__eq,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2743_add__diff__eq,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32,C2: uint32] :
% 13.77/7.71 ( ( plus_plus_uint32 @ A @ ( minus_minus_uint32 @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_uint32 @ ( plus_plus_uint32 @ A @ B ) @ C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2744_add__diff__eq,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2745_add__diff__eq,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 13.77/7.71 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2746_eq__diff__eq,axiom,
% 13.77/7.71 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( minus_minus_rat @ C2 @ B ) )
% 13.77/7.71 = ( ( plus_plus_rat @ A @ B )
% 13.77/7.71 = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2747_eq__diff__eq,axiom,
% 13.77/7.71 ! [A: uint32,C2: uint32,B: uint32] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( minus_minus_uint32 @ C2 @ B ) )
% 13.77/7.71 = ( ( plus_plus_uint32 @ A @ B )
% 13.77/7.71 = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2748_eq__diff__eq,axiom,
% 13.77/7.71 ! [A: real,C2: real,B: real] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( minus_minus_real @ C2 @ B ) )
% 13.77/7.71 = ( ( plus_plus_real @ A @ B )
% 13.77/7.71 = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2749_eq__diff__eq,axiom,
% 13.77/7.71 ! [A: int,C2: int,B: int] :
% 13.77/7.71 ( ( A
% 13.77/7.71 = ( minus_minus_int @ C2 @ B ) )
% 13.77/7.71 = ( ( plus_plus_int @ A @ B )
% 13.77/7.71 = C2 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2750_diff__eq__eq,axiom,
% 13.77/7.71 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.71 ( ( ( minus_minus_rat @ A @ B )
% 13.77/7.71 = C2 )
% 13.77/7.71 = ( A
% 13.77/7.71 = ( plus_plus_rat @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2751_diff__eq__eq,axiom,
% 13.77/7.71 ! [A: uint32,B: uint32,C2: uint32] :
% 13.77/7.71 ( ( ( minus_minus_uint32 @ A @ B )
% 13.77/7.71 = C2 )
% 13.77/7.71 = ( A
% 13.77/7.71 = ( plus_plus_uint32 @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2752_diff__eq__eq,axiom,
% 13.77/7.71 ! [A: real,B: real,C2: real] :
% 13.77/7.71 ( ( ( minus_minus_real @ A @ B )
% 13.77/7.71 = C2 )
% 13.77/7.71 = ( A
% 13.77/7.71 = ( plus_plus_real @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2753_diff__eq__eq,axiom,
% 13.77/7.71 ! [A: int,B: int,C2: int] :
% 13.77/7.71 ( ( ( minus_minus_int @ A @ B )
% 13.77/7.71 = C2 )
% 13.77/7.71 = ( A
% 13.77/7.71 = ( plus_plus_int @ C2 @ B ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2754_group__cancel_Osub1,axiom,
% 13.77/7.71 ! [A4: rat,K: rat,A: rat,B: rat] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_rat @ K @ A ) )
% 13.77/7.71 => ( ( minus_minus_rat @ A4 @ B )
% 13.77/7.71 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2755_group__cancel_Osub1,axiom,
% 13.77/7.71 ! [A4: uint32,K: uint32,A: uint32,B: uint32] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_uint32 @ K @ A ) )
% 13.77/7.71 => ( ( minus_minus_uint32 @ A4 @ B )
% 13.77/7.71 = ( plus_plus_uint32 @ K @ ( minus_minus_uint32 @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2756_group__cancel_Osub1,axiom,
% 13.77/7.71 ! [A4: real,K: real,A: real,B: real] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_real @ K @ A ) )
% 13.77/7.71 => ( ( minus_minus_real @ A4 @ B )
% 13.77/7.71 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2757_group__cancel_Osub1,axiom,
% 13.77/7.71 ! [A4: int,K: int,A: int,B: int] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_int @ K @ A ) )
% 13.77/7.71 => ( ( minus_minus_int @ A4 @ B )
% 13.77/7.71 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2758_nat__arith_Osuc1,axiom,
% 13.77/7.71 ! [A4: nat,K: nat,A: nat] :
% 13.77/7.71 ( ( A4
% 13.77/7.71 = ( plus_plus_nat @ K @ A ) )
% 13.77/7.71 => ( ( suc @ A4 )
% 13.77/7.71 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2759_add__Suc,axiom,
% 13.77/7.71 ! [M: nat,N: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 13.77/7.71 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2760_add__Suc__shift,axiom,
% 13.77/7.71 ! [M: nat,N: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 13.77/7.71 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2761_plus__nat_Oadd__0,axiom,
% 13.77/7.71 ! [N: nat] :
% 13.77/7.71 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 13.77/7.71 = N ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2762_add__eq__self__zero,axiom,
% 13.77/7.71 ! [M: nat,N: nat] :
% 13.77/7.71 ( ( ( plus_plus_nat @ M @ N )
% 13.77/7.71 = M )
% 13.77/7.71 => ( N = zero_zero_nat ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2763_add__lessD1,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat] :
% 13.77/7.71 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 13.77/7.71 => ( ord_less_nat @ I @ K ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2764_add__less__mono,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ord_less_nat @ I @ J )
% 13.77/7.71 => ( ( ord_less_nat @ K @ L )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2765_not__add__less1,axiom,
% 13.77/7.71 ! [I: nat,J: nat] :
% 13.77/7.71 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2766_not__add__less2,axiom,
% 13.77/7.71 ! [J: nat,I: nat] :
% 13.77/7.71 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2767_add__less__mono1,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat] :
% 13.77/7.71 ( ( ord_less_nat @ I @ J )
% 13.77/7.71 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2768_trans__less__add1,axiom,
% 13.77/7.71 ! [I: nat,J: nat,M: nat] :
% 13.77/7.71 ( ( ord_less_nat @ I @ J )
% 13.77/7.71 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2769_trans__less__add2,axiom,
% 13.77/7.71 ! [I: nat,J: nat,M: nat] :
% 13.77/7.71 ( ( ord_less_nat @ I @ J )
% 13.77/7.71 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2770_less__add__eq__less,axiom,
% 13.77/7.71 ! [K: nat,L: nat,M: nat,N: nat] :
% 13.77/7.71 ( ( ord_less_nat @ K @ L )
% 13.77/7.71 => ( ( ( plus_plus_nat @ M @ L )
% 13.77/7.71 = ( plus_plus_nat @ K @ N ) )
% 13.77/7.71 => ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2771_nat__le__iff__add,axiom,
% 13.77/7.71 ( ord_less_eq_nat
% 13.77/7.71 = ( ^ [M5: nat,N6: nat] :
% 13.77/7.71 ? [K3: nat] :
% 13.77/7.71 ( N6
% 13.77/7.71 = ( plus_plus_nat @ M5 @ K3 ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2772_trans__le__add2,axiom,
% 13.77/7.71 ! [I: nat,J: nat,M: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.71 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2773_trans__le__add1,axiom,
% 13.77/7.71 ! [I: nat,J: nat,M: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.71 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2774_add__le__mono1,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2775_add__le__mono,axiom,
% 13.77/7.71 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.71 => ( ( ord_less_eq_nat @ K @ L )
% 13.77/7.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2776_le__Suc__ex,axiom,
% 13.77/7.71 ! [K: nat,L: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ K @ L )
% 13.77/7.71 => ? [N2: nat] :
% 13.77/7.71 ( L
% 13.77/7.71 = ( plus_plus_nat @ K @ N2 ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2777_add__leD2,axiom,
% 13.77/7.71 ! [M: nat,K: nat,N: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 13.77/7.71 => ( ord_less_eq_nat @ K @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2778_add__leD1,axiom,
% 13.77/7.71 ! [M: nat,K: nat,N: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 13.77/7.71 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2779_le__add2,axiom,
% 13.77/7.71 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2780_le__add1,axiom,
% 13.77/7.71 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2781_add__leE,axiom,
% 13.77/7.71 ! [M: nat,K: nat,N: nat] :
% 13.77/7.71 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 13.77/7.71 => ~ ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.71 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2782_diff__add__inverse2,axiom,
% 13.77/7.71 ! [M: nat,N: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 13.77/7.71 = M ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2783_diff__add__inverse,axiom,
% 13.77/7.71 ! [N: nat,M: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 13.77/7.71 = M ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2784_diff__cancel2,axiom,
% 13.77/7.71 ! [M: nat,K: nat,N: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 13.77/7.71 = ( minus_minus_nat @ M @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2785_Nat_Odiff__cancel,axiom,
% 13.77/7.71 ! [K: nat,M: nat,N: nat] :
% 13.77/7.71 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 13.77/7.71 = ( minus_minus_nat @ M @ N ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2786_enumerate__in__set,axiom,
% 13.77/7.71 ! [S3: set_nat,N: nat] :
% 13.77/7.71 ( ~ ( finite_finite_nat @ S3 )
% 13.77/7.71 => ( member_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ S3 ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2787_Ints__double__eq__0__iff,axiom,
% 13.77/7.71 ! [A: real] :
% 13.77/7.71 ( ( member_real @ A @ ring_1_Ints_real )
% 13.77/7.71 => ( ( ( plus_plus_real @ A @ A )
% 13.77/7.71 = zero_zero_real )
% 13.77/7.71 = ( A = zero_zero_real ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2788_Ints__double__eq__0__iff,axiom,
% 13.77/7.71 ! [A: rat] :
% 13.77/7.71 ( ( member_rat @ A @ ring_1_Ints_rat )
% 13.77/7.71 => ( ( ( plus_plus_rat @ A @ A )
% 13.77/7.71 = zero_zero_rat )
% 13.77/7.71 = ( A = zero_zero_rat ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2789_Ints__double__eq__0__iff,axiom,
% 13.77/7.71 ! [A: int] :
% 13.77/7.71 ( ( member_int @ A @ ring_1_Ints_int )
% 13.77/7.71 => ( ( ( plus_plus_int @ A @ A )
% 13.77/7.71 = zero_zero_int )
% 13.77/7.71 = ( A = zero_zero_int ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2790_enumerate__Ex,axiom,
% 13.77/7.71 ! [S3: set_nat,S: nat] :
% 13.77/7.71 ( ~ ( finite_finite_nat @ S3 )
% 13.77/7.71 => ( ( member_nat @ S @ S3 )
% 13.77/7.71 => ? [N2: nat] :
% 13.77/7.71 ( ( infini8530281810654367211te_nat @ S3 @ N2 )
% 13.77/7.71 = S ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2791_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 13.77/7.71 ( ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2792_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: complex > nat,A4: set_complex,P2: set_nat > $o] :
% 13.77/7.71 ( ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ ( image_complex_nat @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_complex] :
% 13.77/7.71 ( ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_complex_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2793_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: code_integer > nat,A4: set_Code_integer,P2: set_nat > $o] :
% 13.77/7.71 ( ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ ( image_951025933927791156er_nat @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_Code_integer] :
% 13.77/7.71 ( ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.71 & ( ord_le7084787975880047091nteger @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_951025933927791156er_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2794_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: nat > complex,A4: set_nat,P2: set_complex > $o] :
% 13.77/7.71 ( ( ! [B6: set_complex] :
% 13.77/7.71 ( ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ ( image_nat_complex @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_nat_complex @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2795_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: complex > complex,A4: set_complex,P2: set_complex > $o] :
% 13.77/7.71 ( ( ! [B6: set_complex] :
% 13.77/7.71 ( ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ ( image_1468599708987790691omplex @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_complex] :
% 13.77/7.71 ( ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_1468599708987790691omplex @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2796_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: code_integer > complex,A4: set_Code_integer,P2: set_complex > $o] :
% 13.77/7.71 ( ( ! [B6: set_complex] :
% 13.77/7.71 ( ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ ( image_3397630267976458002omplex @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_Code_integer] :
% 13.77/7.71 ( ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.71 & ( ord_le7084787975880047091nteger @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_3397630267976458002omplex @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2797_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: nat > code_integer,A4: set_nat,P2: set_Code_integer > $o] :
% 13.77/7.71 ( ( ! [B6: set_Code_integer] :
% 13.77/7.71 ( ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.71 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1215581382706833972nteger @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_1215581382706833972nteger @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2798_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: complex > code_integer,A4: set_complex,P2: set_Code_integer > $o] :
% 13.77/7.71 ( ( ! [B6: set_Code_integer] :
% 13.77/7.71 ( ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.71 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1994230757181692690nteger @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_complex] :
% 13.77/7.71 ( ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_1994230757181692690nteger @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2799_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: code_integer > code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.71 ( ( ! [B6: set_Code_integer] :
% 13.77/7.71 ( ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.71 & ( ord_le7084787975880047091nteger @ B6 @ ( image_4470545334726330049nteger @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_Code_integer] :
% 13.77/7.71 ( ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.71 & ( ord_le7084787975880047091nteger @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_4470545334726330049nteger @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2800_all__finite__subset__image,axiom,
% 13.77/7.71 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 13.77/7.71 ( ( ! [B6: set_nat] :
% 13.77/7.71 ( ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) ) )
% 13.77/7.71 => ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ! [B6: set_int] :
% 13.77/7.71 ( ( ( finite_finite_int @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_int @ B6 @ A4 ) )
% 13.77/7.71 => ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2801_ex__finite__subset__image,axiom,
% 13.77/7.71 ! [F: nat > nat,A4: set_nat,P2: set_nat > $o] :
% 13.77/7.71 ( ( ? [B6: set_nat] :
% 13.77/7.71 ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ? [B6: set_nat] :
% 13.77/7.71 ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 13.77/7.71 & ( P2 @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2802_ex__finite__subset__image,axiom,
% 13.77/7.71 ! [F: complex > nat,A4: set_complex,P2: set_nat > $o] :
% 13.77/7.71 ( ( ? [B6: set_nat] :
% 13.77/7.71 ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ ( image_complex_nat @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ? [B6: set_complex] :
% 13.77/7.71 ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ A4 )
% 13.77/7.71 & ( P2 @ ( image_complex_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2803_ex__finite__subset__image,axiom,
% 13.77/7.71 ! [F: code_integer > nat,A4: set_Code_integer,P2: set_nat > $o] :
% 13.77/7.71 ( ( ? [B6: set_nat] :
% 13.77/7.71 ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ ( image_951025933927791156er_nat @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ? [B6: set_Code_integer] :
% 13.77/7.71 ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.71 & ( ord_le7084787975880047091nteger @ B6 @ A4 )
% 13.77/7.71 & ( P2 @ ( image_951025933927791156er_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2804_ex__finite__subset__image,axiom,
% 13.77/7.71 ! [F: nat > complex,A4: set_nat,P2: set_complex > $o] :
% 13.77/7.71 ( ( ? [B6: set_complex] :
% 13.77/7.71 ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.71 & ( ord_le211207098394363844omplex @ B6 @ ( image_nat_complex @ F @ A4 ) )
% 13.77/7.71 & ( P2 @ B6 ) ) )
% 13.77/7.71 = ( ? [B6: set_nat] :
% 13.77/7.71 ( ( finite_finite_nat @ B6 )
% 13.77/7.71 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 13.77/7.71 & ( P2 @ ( image_nat_complex @ F @ B6 ) ) ) ) ) ).
% 13.77/7.71
% 13.77/7.71 thf(fact_2805_ex__finite__subset__image,axiom,
% 13.77/7.71 ! [F: complex > complex,A4: set_complex,P2: set_complex > $o] :
% 13.77/7.72 ( ( ? [B6: set_complex] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.72 & ( ord_le211207098394363844omplex @ B6 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 13.77/7.72 & ( P2 @ B6 ) ) )
% 13.77/7.72 = ( ? [B6: set_complex] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.72 & ( ord_le211207098394363844omplex @ B6 @ A4 )
% 13.77/7.72 & ( P2 @ ( image_1468599708987790691omplex @ F @ B6 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2806_ex__finite__subset__image,axiom,
% 13.77/7.72 ! [F: code_integer > complex,A4: set_Code_integer,P2: set_complex > $o] :
% 13.77/7.72 ( ( ? [B6: set_complex] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.72 & ( ord_le211207098394363844omplex @ B6 @ ( image_3397630267976458002omplex @ F @ A4 ) )
% 13.77/7.72 & ( P2 @ B6 ) ) )
% 13.77/7.72 = ( ? [B6: set_Code_integer] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.72 & ( ord_le7084787975880047091nteger @ B6 @ A4 )
% 13.77/7.72 & ( P2 @ ( image_3397630267976458002omplex @ F @ B6 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2807_ex__finite__subset__image,axiom,
% 13.77/7.72 ! [F: nat > code_integer,A4: set_nat,P2: set_Code_integer > $o] :
% 13.77/7.72 ( ( ? [B6: set_Code_integer] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.72 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1215581382706833972nteger @ F @ A4 ) )
% 13.77/7.72 & ( P2 @ B6 ) ) )
% 13.77/7.72 = ( ? [B6: set_nat] :
% 13.77/7.72 ( ( finite_finite_nat @ B6 )
% 13.77/7.72 & ( ord_less_eq_set_nat @ B6 @ A4 )
% 13.77/7.72 & ( P2 @ ( image_1215581382706833972nteger @ F @ B6 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2808_ex__finite__subset__image,axiom,
% 13.77/7.72 ! [F: complex > code_integer,A4: set_complex,P2: set_Code_integer > $o] :
% 13.77/7.72 ( ( ? [B6: set_Code_integer] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.72 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1994230757181692690nteger @ F @ A4 ) )
% 13.77/7.72 & ( P2 @ B6 ) ) )
% 13.77/7.72 = ( ? [B6: set_complex] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ B6 )
% 13.77/7.72 & ( ord_le211207098394363844omplex @ B6 @ A4 )
% 13.77/7.72 & ( P2 @ ( image_1994230757181692690nteger @ F @ B6 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2809_ex__finite__subset__image,axiom,
% 13.77/7.72 ! [F: code_integer > code_integer,A4: set_Code_integer,P2: set_Code_integer > $o] :
% 13.77/7.72 ( ( ? [B6: set_Code_integer] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.72 & ( ord_le7084787975880047091nteger @ B6 @ ( image_4470545334726330049nteger @ F @ A4 ) )
% 13.77/7.72 & ( P2 @ B6 ) ) )
% 13.77/7.72 = ( ? [B6: set_Code_integer] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B6 )
% 13.77/7.72 & ( ord_le7084787975880047091nteger @ B6 @ A4 )
% 13.77/7.72 & ( P2 @ ( image_4470545334726330049nteger @ F @ B6 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2810_ex__finite__subset__image,axiom,
% 13.77/7.72 ! [F: int > nat,A4: set_int,P2: set_nat > $o] :
% 13.77/7.72 ( ( ? [B6: set_nat] :
% 13.77/7.72 ( ( finite_finite_nat @ B6 )
% 13.77/7.72 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.72 & ( P2 @ B6 ) ) )
% 13.77/7.72 = ( ? [B6: set_int] :
% 13.77/7.72 ( ( finite_finite_int @ B6 )
% 13.77/7.72 & ( ord_less_eq_set_int @ B6 @ A4 )
% 13.77/7.72 & ( P2 @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2811_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_nat,F: nat > nat,A4: set_nat] :
% 13.77/7.72 ( ( finite_finite_nat @ B4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_nat] :
% 13.77/7.72 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 13.77/7.72 & ( finite_finite_nat @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_nat_nat @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2812_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_nat,F: complex > nat,A4: set_complex] :
% 13.77/7.72 ( ( finite_finite_nat @ B4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_complex_nat @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_complex] :
% 13.77/7.72 ( ( ord_le211207098394363844omplex @ C5 @ A4 )
% 13.77/7.72 & ( finite3207457112153483333omplex @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_complex_nat @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2813_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_nat,F: code_integer > nat,A4: set_Code_integer] :
% 13.77/7.72 ( ( finite_finite_nat @ B4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_951025933927791156er_nat @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_Code_integer] :
% 13.77/7.72 ( ( ord_le7084787975880047091nteger @ C5 @ A4 )
% 13.77/7.72 & ( finite6017078050557962740nteger @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_951025933927791156er_nat @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2814_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_complex,F: nat > complex,A4: set_nat] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.72 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_nat_complex @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_nat] :
% 13.77/7.72 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 13.77/7.72 & ( finite_finite_nat @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_nat_complex @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2815_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_complex,F: complex > complex,A4: set_complex] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.72 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_complex] :
% 13.77/7.72 ( ( ord_le211207098394363844omplex @ C5 @ A4 )
% 13.77/7.72 & ( finite3207457112153483333omplex @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_1468599708987790691omplex @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2816_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_complex,F: code_integer > complex,A4: set_Code_integer] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.72 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_3397630267976458002omplex @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_Code_integer] :
% 13.77/7.72 ( ( ord_le7084787975880047091nteger @ C5 @ A4 )
% 13.77/7.72 & ( finite6017078050557962740nteger @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_3397630267976458002omplex @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2817_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_Code_integer,F: nat > code_integer,A4: set_nat] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.72 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1215581382706833972nteger @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_nat] :
% 13.77/7.72 ( ( ord_less_eq_set_nat @ C5 @ A4 )
% 13.77/7.72 & ( finite_finite_nat @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_1215581382706833972nteger @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2818_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_Code_integer,F: complex > code_integer,A4: set_complex] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.72 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1994230757181692690nteger @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_complex] :
% 13.77/7.72 ( ( ord_le211207098394363844omplex @ C5 @ A4 )
% 13.77/7.72 & ( finite3207457112153483333omplex @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_1994230757181692690nteger @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2819_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_Code_integer,F: code_integer > code_integer,A4: set_Code_integer] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.72 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_4470545334726330049nteger @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_Code_integer] :
% 13.77/7.72 ( ( ord_le7084787975880047091nteger @ C5 @ A4 )
% 13.77/7.72 & ( finite6017078050557962740nteger @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_4470545334726330049nteger @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2820_finite__subset__image,axiom,
% 13.77/7.72 ! [B4: set_nat,F: int > nat,A4: set_int] :
% 13.77/7.72 ( ( finite_finite_nat @ B4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.72 => ? [C5: set_int] :
% 13.77/7.72 ( ( ord_less_eq_set_int @ C5 @ A4 )
% 13.77/7.72 & ( finite_finite_int @ C5 )
% 13.77/7.72 & ( B4
% 13.77/7.72 = ( image_int_nat @ F @ C5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2821_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_nat,B4: set_nat,F: nat > nat] :
% 13.77/7.72 ( ( finite_finite_nat @ A4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.72 => ( finite_finite_nat @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2822_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_nat,B4: set_complex,F: nat > complex] :
% 13.77/7.72 ( ( finite_finite_nat @ A4 )
% 13.77/7.72 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_nat_complex @ F @ A4 ) )
% 13.77/7.72 => ( finite3207457112153483333omplex @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2823_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_nat,B4: set_Code_integer,F: nat > code_integer] :
% 13.77/7.72 ( ( finite_finite_nat @ A4 )
% 13.77/7.72 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1215581382706833972nteger @ F @ A4 ) )
% 13.77/7.72 => ( finite6017078050557962740nteger @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2824_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_int,B4: set_nat,F: int > nat] :
% 13.77/7.72 ( ( finite_finite_int @ A4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.72 => ( finite_finite_nat @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2825_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_int,B4: set_complex,F: int > complex] :
% 13.77/7.72 ( ( finite_finite_int @ A4 )
% 13.77/7.72 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_int_complex @ F @ A4 ) )
% 13.77/7.72 => ( finite3207457112153483333omplex @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2826_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_int,B4: set_Code_integer,F: int > code_integer] :
% 13.77/7.72 ( ( finite_finite_int @ A4 )
% 13.77/7.72 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1587234942943678608nteger @ F @ A4 ) )
% 13.77/7.72 => ( finite6017078050557962740nteger @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2827_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_complex,B4: set_nat,F: complex > nat] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_complex_nat @ F @ A4 ) )
% 13.77/7.72 => ( finite_finite_nat @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2828_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_complex,B4: set_complex,F: complex > complex] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.72 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 13.77/7.72 => ( finite3207457112153483333omplex @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2829_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_complex,B4: set_Code_integer,F: complex > code_integer] :
% 13.77/7.72 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.72 => ( ( ord_le7084787975880047091nteger @ B4 @ ( image_1994230757181692690nteger @ F @ A4 ) )
% 13.77/7.72 => ( finite6017078050557962740nteger @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2830_finite__surj,axiom,
% 13.77/7.72 ! [A4: set_Code_integer,B4: set_nat,F: code_integer > nat] :
% 13.77/7.72 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.72 => ( ( ord_less_eq_set_nat @ B4 @ ( image_951025933927791156er_nat @ F @ A4 ) )
% 13.77/7.72 => ( finite_finite_nat @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2831_image__diff__subset,axiom,
% 13.77/7.72 ! [F: nat > set_nat,A4: set_nat,B4: set_nat] : ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ ( image_nat_set_nat @ F @ A4 ) @ ( image_nat_set_nat @ F @ B4 ) ) @ ( image_nat_set_nat @ F @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2832_image__diff__subset,axiom,
% 13.77/7.72 ! [F: int > nat,A4: set_int,B4: set_int] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_int_nat @ F @ A4 ) @ ( image_int_nat @ F @ B4 ) ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2833_image__diff__subset,axiom,
% 13.77/7.72 ! [F: nat > nat,A4: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_nat_nat @ F @ A4 ) @ ( image_nat_nat @ F @ B4 ) ) @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2834_image__diff__subset,axiom,
% 13.77/7.72 ! [F: int > int,A4: set_int,B4: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_int_int @ F @ A4 ) @ ( image_int_int @ F @ B4 ) ) @ ( image_int_int @ F @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2835_image__diff__subset,axiom,
% 13.77/7.72 ! [F: nat > int,A4: set_nat,B4: set_nat] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_nat_int @ F @ A4 ) @ ( image_nat_int @ F @ B4 ) ) @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2836_add__nonpos__eq__0__iff,axiom,
% 13.77/7.72 ! [X: real,Y: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 13.77/7.72 => ( ( ( plus_plus_real @ X @ Y )
% 13.77/7.72 = zero_zero_real )
% 13.77/7.72 = ( ( X = zero_zero_real )
% 13.77/7.72 & ( Y = zero_zero_real ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2837_add__nonpos__eq__0__iff,axiom,
% 13.77/7.72 ! [X: rat,Y: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 13.77/7.72 => ( ( ( plus_plus_rat @ X @ Y )
% 13.77/7.72 = zero_zero_rat )
% 13.77/7.72 = ( ( X = zero_zero_rat )
% 13.77/7.72 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2838_add__nonpos__eq__0__iff,axiom,
% 13.77/7.72 ! [X: nat,Y: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 13.77/7.72 => ( ( ( plus_plus_nat @ X @ Y )
% 13.77/7.72 = zero_zero_nat )
% 13.77/7.72 = ( ( X = zero_zero_nat )
% 13.77/7.72 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2839_add__nonpos__eq__0__iff,axiom,
% 13.77/7.72 ! [X: int,Y: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 13.77/7.72 => ( ( ( plus_plus_int @ X @ Y )
% 13.77/7.72 = zero_zero_int )
% 13.77/7.72 = ( ( X = zero_zero_int )
% 13.77/7.72 & ( Y = zero_zero_int ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2840_add__nonneg__eq__0__iff,axiom,
% 13.77/7.72 ! [X: real,Y: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.72 => ( ( ( plus_plus_real @ X @ Y )
% 13.77/7.72 = zero_zero_real )
% 13.77/7.72 = ( ( X = zero_zero_real )
% 13.77/7.72 & ( Y = zero_zero_real ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2841_add__nonneg__eq__0__iff,axiom,
% 13.77/7.72 ! [X: rat,Y: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 13.77/7.72 => ( ( ( plus_plus_rat @ X @ Y )
% 13.77/7.72 = zero_zero_rat )
% 13.77/7.72 = ( ( X = zero_zero_rat )
% 13.77/7.72 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2842_add__nonneg__eq__0__iff,axiom,
% 13.77/7.72 ! [X: nat,Y: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 13.77/7.72 => ( ( ( plus_plus_nat @ X @ Y )
% 13.77/7.72 = zero_zero_nat )
% 13.77/7.72 = ( ( X = zero_zero_nat )
% 13.77/7.72 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2843_add__nonneg__eq__0__iff,axiom,
% 13.77/7.72 ! [X: int,Y: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.72 => ( ( ( plus_plus_int @ X @ Y )
% 13.77/7.72 = zero_zero_int )
% 13.77/7.72 = ( ( X = zero_zero_int )
% 13.77/7.72 & ( Y = zero_zero_int ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2844_add__nonpos__nonpos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2845_add__nonpos__nonpos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2846_add__nonpos__nonpos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2847_add__nonpos__nonpos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2848_add__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2849_add__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2850_add__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2851_add__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2852_add__increasing2,axiom,
% 13.77/7.72 ! [C2: real,B: real,A: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ A )
% 13.77/7.72 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2853_add__increasing2,axiom,
% 13.77/7.72 ! [C2: rat,B: rat,A: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.72 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2854_add__increasing2,axiom,
% 13.77/7.72 ! [C2: nat,B: nat,A: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.72 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2855_add__increasing2,axiom,
% 13.77/7.72 ! [C2: int,B: int,A: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ A )
% 13.77/7.72 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2856_add__decreasing2,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_eq_real @ A @ B )
% 13.77/7.72 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2857_add__decreasing2,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.72 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2858_add__decreasing2,axiom,
% 13.77/7.72 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ C2 @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2859_add__decreasing2,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_eq_int @ A @ B )
% 13.77/7.72 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2860_add__increasing,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2861_add__increasing,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2862_add__increasing,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.77/7.72 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2863_add__increasing,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2864_add__decreasing,axiom,
% 13.77/7.72 ! [A: real,C2: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_eq_real @ C2 @ B )
% 13.77/7.72 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2865_add__decreasing,axiom,
% 13.77/7.72 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_eq_rat @ C2 @ B )
% 13.77/7.72 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2866_add__decreasing,axiom,
% 13.77/7.72 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_eq_nat @ C2 @ B )
% 13.77/7.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2867_add__decreasing,axiom,
% 13.77/7.72 ! [A: int,C2: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_eq_int @ C2 @ B )
% 13.77/7.72 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2868_pos__add__strict,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_real @ B @ C2 )
% 13.77/7.72 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2869_pos__add__strict,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_rat @ B @ C2 )
% 13.77/7.72 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2870_pos__add__strict,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_nat @ B @ C2 )
% 13.77/7.72 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2871_pos__add__strict,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_int @ B @ C2 )
% 13.77/7.72 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2872_canonically__ordered__monoid__add__class_OlessE,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ B )
% 13.77/7.72 => ~ ! [C: nat] :
% 13.77/7.72 ( ( B
% 13.77/7.72 = ( plus_plus_nat @ A @ C ) )
% 13.77/7.72 => ( C = zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2873_add__pos__pos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2874_add__pos__pos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2875_add__pos__pos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2876_add__pos__pos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2877_add__neg__neg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2878_add__neg__neg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2879_add__neg__neg,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2880_add__neg__neg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2881_add__less__zeroD,axiom,
% 13.77/7.72 ! [X: real,Y: real] :
% 13.77/7.72 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.72 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2882_add__less__zeroD,axiom,
% 13.77/7.72 ! [X: rat,Y: rat] :
% 13.77/7.72 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 13.77/7.72 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2883_add__less__zeroD,axiom,
% 13.77/7.72 ! [X: int,Y: int] :
% 13.77/7.72 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_int @ X @ zero_zero_int )
% 13.77/7.72 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2884_add__mono__thms__linordered__field_I4_J,axiom,
% 13.77/7.72 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.72 ( ( ( ord_less_eq_real @ I @ J )
% 13.77/7.72 & ( ord_less_real @ K @ L ) )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2885_add__mono__thms__linordered__field_I4_J,axiom,
% 13.77/7.72 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.72 ( ( ( ord_less_eq_rat @ I @ J )
% 13.77/7.72 & ( ord_less_rat @ K @ L ) )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2886_add__mono__thms__linordered__field_I4_J,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.72 ( ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.72 & ( ord_less_nat @ K @ L ) )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2887_add__mono__thms__linordered__field_I4_J,axiom,
% 13.77/7.72 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.72 ( ( ( ord_less_eq_int @ I @ J )
% 13.77/7.72 & ( ord_less_int @ K @ L ) )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2888_add__mono__thms__linordered__field_I3_J,axiom,
% 13.77/7.72 ! [I: real,J: real,K: real,L: real] :
% 13.77/7.72 ( ( ( ord_less_real @ I @ J )
% 13.77/7.72 & ( ord_less_eq_real @ K @ L ) )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2889_add__mono__thms__linordered__field_I3_J,axiom,
% 13.77/7.72 ! [I: rat,J: rat,K: rat,L: rat] :
% 13.77/7.72 ( ( ( ord_less_rat @ I @ J )
% 13.77/7.72 & ( ord_less_eq_rat @ K @ L ) )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2890_add__mono__thms__linordered__field_I3_J,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.72 ( ( ( ord_less_nat @ I @ J )
% 13.77/7.72 & ( ord_less_eq_nat @ K @ L ) )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2891_add__mono__thms__linordered__field_I3_J,axiom,
% 13.77/7.72 ! [I: int,J: int,K: int,L: int] :
% 13.77/7.72 ( ( ( ord_less_int @ I @ J )
% 13.77/7.72 & ( ord_less_eq_int @ K @ L ) )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2892_add__le__less__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2893_add__le__less__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2894_add__le__less__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2895_add__le__less__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2896_add__less__le__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ C2 @ D )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2897_add__less__le__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ C2 @ D )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2898_add__less__le__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ C2 @ D )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2899_add__less__le__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_int @ C2 @ D )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2900_add__mono1,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ B )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2901_add__mono1,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ B )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2902_add__mono1,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ B )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2903_add__mono1,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ B )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2904_less__add__one,axiom,
% 13.77/7.72 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2905_less__add__one,axiom,
% 13.77/7.72 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2906_less__add__one,axiom,
% 13.77/7.72 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2907_less__add__one,axiom,
% 13.77/7.72 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2908_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ( minus_minus_nat @ B @ A )
% 13.77/7.72 = C2 )
% 13.77/7.72 = ( B
% 13.77/7.72 = ( plus_plus_nat @ C2 @ A ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2909_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 13.77/7.72 = B ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2910_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( minus_minus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 13.77/7.72 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2911_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A )
% 13.77/7.72 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2912_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 )
% 13.77/7.72 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2913_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A )
% 13.77/7.72 = ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2914_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 13.77/7.72 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2915_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 13.77/7.72 = ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2916_le__add__diff,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2917_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 13.77/7.72 = B ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2918_le__diff__eq,axiom,
% 13.77/7.72 ! [A: real,C2: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2919_le__diff__eq,axiom,
% 13.77/7.72 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2920_le__diff__eq,axiom,
% 13.77/7.72 ! [A: int,C2: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2921_diff__le__eq,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 13.77/7.72 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2922_diff__le__eq,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 13.77/7.72 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2923_diff__le__eq,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 13.77/7.72 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2924_add__le__add__imp__diff__le,axiom,
% 13.77/7.72 ! [I: real,K: real,N: real,J: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 13.77/7.72 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 13.77/7.72 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2925_add__le__add__imp__diff__le,axiom,
% 13.77/7.72 ! [I: rat,K: rat,N: rat,J: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 13.77/7.72 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 13.77/7.72 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2926_add__le__add__imp__diff__le,axiom,
% 13.77/7.72 ! [I: nat,K: nat,N: nat,J: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 13.77/7.72 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 13.77/7.72 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2927_add__le__add__imp__diff__le,axiom,
% 13.77/7.72 ! [I: int,K: int,N: int,J: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 13.77/7.72 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 13.77/7.72 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 13.77/7.72 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2928_add__le__imp__le__diff,axiom,
% 13.77/7.72 ! [I: real,K: real,N: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 13.77/7.72 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2929_add__le__imp__le__diff,axiom,
% 13.77/7.72 ! [I: rat,K: rat,N: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 13.77/7.72 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2930_add__le__imp__le__diff,axiom,
% 13.77/7.72 ! [I: nat,K: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 13.77/7.72 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2931_add__le__imp__le__diff,axiom,
% 13.77/7.72 ! [I: int,K: int,N: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 13.77/7.72 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2932_diff__less__eq,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 13.77/7.72 = ( ord_less_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2933_diff__less__eq,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 13.77/7.72 = ( ord_less_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2934_diff__less__eq,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 13.77/7.72 = ( ord_less_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2935_less__diff__eq,axiom,
% 13.77/7.72 ! [A: real,C2: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2936_less__diff__eq,axiom,
% 13.77/7.72 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2937_less__diff__eq,axiom,
% 13.77/7.72 ! [A: int,C2: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2938_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ~ ( ord_less_real @ A @ B )
% 13.77/7.72 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 13.77/7.72 = A ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2939_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ~ ( ord_less_rat @ A @ B )
% 13.77/7.72 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 13.77/7.72 = A ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2940_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ~ ( ord_less_nat @ A @ B )
% 13.77/7.72 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 13.77/7.72 = A ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2941_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ~ ( ord_less_int @ A @ B )
% 13.77/7.72 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 13.77/7.72 = A ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2942_Ints__odd__nonzero,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( member_real @ A @ ring_1_Ints_real )
% 13.77/7.72 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 13.77/7.72 != zero_zero_real ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2943_Ints__odd__nonzero,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( member_rat @ A @ ring_1_Ints_rat )
% 13.77/7.72 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 13.77/7.72 != zero_zero_rat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2944_Ints__odd__nonzero,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( member_int @ A @ ring_1_Ints_int )
% 13.77/7.72 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 13.77/7.72 != zero_zero_int ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2945_one__is__add,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ( suc @ zero_zero_nat )
% 13.77/7.72 = ( plus_plus_nat @ M @ N ) )
% 13.77/7.72 = ( ( ( M
% 13.77/7.72 = ( suc @ zero_zero_nat ) )
% 13.77/7.72 & ( N = zero_zero_nat ) )
% 13.77/7.72 | ( ( M = zero_zero_nat )
% 13.77/7.72 & ( N
% 13.77/7.72 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2946_add__is__1,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ( plus_plus_nat @ M @ N )
% 13.77/7.72 = ( suc @ zero_zero_nat ) )
% 13.77/7.72 = ( ( ( M
% 13.77/7.72 = ( suc @ zero_zero_nat ) )
% 13.77/7.72 & ( N = zero_zero_nat ) )
% 13.77/7.72 | ( ( M = zero_zero_nat )
% 13.77/7.72 & ( N
% 13.77/7.72 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2947_less__natE,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_nat @ M @ N )
% 13.77/7.72 => ~ ! [Q5: nat] :
% 13.77/7.72 ( N
% 13.77/7.72 != ( suc @ ( plus_plus_nat @ M @ Q5 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2948_less__add__Suc1,axiom,
% 13.77/7.72 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2949_less__add__Suc2,axiom,
% 13.77/7.72 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2950_less__iff__Suc__add,axiom,
% 13.77/7.72 ( ord_less_nat
% 13.77/7.72 = ( ^ [M5: nat,N6: nat] :
% 13.77/7.72 ? [K3: nat] :
% 13.77/7.72 ( N6
% 13.77/7.72 = ( suc @ ( plus_plus_nat @ M5 @ K3 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2951_less__imp__Suc__add,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_nat @ M @ N )
% 13.77/7.72 => ? [K2: nat] :
% 13.77/7.72 ( N
% 13.77/7.72 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2952_less__imp__add__positive,axiom,
% 13.77/7.72 ! [I: nat,J: nat] :
% 13.77/7.72 ( ( ord_less_nat @ I @ J )
% 13.77/7.72 => ? [K2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 13.77/7.72 & ( ( plus_plus_nat @ I @ K2 )
% 13.77/7.72 = J ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2953_Suc__eq__plus1__left,axiom,
% 13.77/7.72 ( suc
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2954_plus__1__eq__Suc,axiom,
% 13.77/7.72 ( ( plus_plus_nat @ one_one_nat )
% 13.77/7.72 = suc ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2955_Suc__eq__plus1,axiom,
% 13.77/7.72 ( suc
% 13.77/7.72 = ( ^ [N6: nat] : ( plus_plus_nat @ N6 @ one_one_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2956_mono__nat__linear__lb,axiom,
% 13.77/7.72 ! [F: nat > nat,M: nat,K: nat] :
% 13.77/7.72 ( ! [M3: nat,N2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ M3 @ N2 )
% 13.77/7.72 => ( ord_less_nat @ ( F @ M3 ) @ ( F @ N2 ) ) )
% 13.77/7.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2957_diff__add__0,axiom,
% 13.77/7.72 ! [N: nat,M: nat] :
% 13.77/7.72 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 13.77/7.72 = zero_zero_nat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2958_add__diff__inverse__nat,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ~ ( ord_less_nat @ M @ N )
% 13.77/7.72 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.72 = M ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2959_less__diff__conv,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat] :
% 13.77/7.72 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 13.77/7.72 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2960_Nat_Ole__imp__diff__is__add,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.72 => ( ( ( minus_minus_nat @ J @ I )
% 13.77/7.72 = K )
% 13.77/7.72 = ( J
% 13.77/7.72 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2961_Nat_Odiff__add__assoc2,axiom,
% 13.77/7.72 ! [K: nat,J: nat,I: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.72 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 13.77/7.72 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2962_Nat_Odiff__add__assoc,axiom,
% 13.77/7.72 ! [K: nat,J: nat,I: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.72 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 13.77/7.72 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2963_Nat_Ole__diff__conv2,axiom,
% 13.77/7.72 ! [K: nat,J: nat,I: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.72 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 13.77/7.72 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2964_le__diff__conv,axiom,
% 13.77/7.72 ! [J: nat,K: nat,I: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 13.77/7.72 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2965_le__enumerate,axiom,
% 13.77/7.72 ! [S3: set_nat,N: nat] :
% 13.77/7.72 ( ~ ( finite_finite_nat @ S3 )
% 13.77/7.72 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2966_the__elem__image__unique,axiom,
% 13.77/7.72 ! [A4: set_nat,F: nat > set_nat,X: nat] :
% 13.77/7.72 ( ( A4 != bot_bot_set_nat )
% 13.77/7.72 => ( ! [Y3: nat] :
% 13.77/7.72 ( ( member_nat @ Y3 @ A4 )
% 13.77/7.72 => ( ( F @ Y3 )
% 13.77/7.72 = ( F @ X ) ) )
% 13.77/7.72 => ( ( the_elem_set_nat @ ( image_nat_set_nat @ F @ A4 ) )
% 13.77/7.72 = ( F @ X ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2967_the__elem__image__unique,axiom,
% 13.77/7.72 ! [A4: set_nat,F: nat > nat,X: nat] :
% 13.77/7.72 ( ( A4 != bot_bot_set_nat )
% 13.77/7.72 => ( ! [Y3: nat] :
% 13.77/7.72 ( ( member_nat @ Y3 @ A4 )
% 13.77/7.72 => ( ( F @ Y3 )
% 13.77/7.72 = ( F @ X ) ) )
% 13.77/7.72 => ( ( the_elem_nat @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.72 = ( F @ X ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2968_the__elem__image__unique,axiom,
% 13.77/7.72 ! [A4: set_nat,F: nat > int,X: nat] :
% 13.77/7.72 ( ( A4 != bot_bot_set_nat )
% 13.77/7.72 => ( ! [Y3: nat] :
% 13.77/7.72 ( ( member_nat @ Y3 @ A4 )
% 13.77/7.72 => ( ( F @ Y3 )
% 13.77/7.72 = ( F @ X ) ) )
% 13.77/7.72 => ( ( the_elem_int @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.72 = ( F @ X ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2969_the__elem__image__unique,axiom,
% 13.77/7.72 ! [A4: set_int,F: int > nat,X: int] :
% 13.77/7.72 ( ( A4 != bot_bot_set_int )
% 13.77/7.72 => ( ! [Y3: int] :
% 13.77/7.72 ( ( member_int @ Y3 @ A4 )
% 13.77/7.72 => ( ( F @ Y3 )
% 13.77/7.72 = ( F @ X ) ) )
% 13.77/7.72 => ( ( the_elem_nat @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.72 = ( F @ X ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2970_the__elem__image__unique,axiom,
% 13.77/7.72 ! [A4: set_int,F: int > int,X: int] :
% 13.77/7.72 ( ( A4 != bot_bot_set_int )
% 13.77/7.72 => ( ! [Y3: int] :
% 13.77/7.72 ( ( member_int @ Y3 @ A4 )
% 13.77/7.72 => ( ( F @ Y3 )
% 13.77/7.72 = ( F @ X ) ) )
% 13.77/7.72 => ( ( the_elem_int @ ( image_int_int @ F @ A4 ) )
% 13.77/7.72 = ( F @ X ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2971_Ints__odd__less__0,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( member_real @ A @ ring_1_Ints_real )
% 13.77/7.72 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 13.77/7.72 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2972_Ints__odd__less__0,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( member_rat @ A @ ring_1_Ints_rat )
% 13.77/7.72 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 13.77/7.72 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2973_Ints__odd__less__0,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( member_int @ A @ ring_1_Ints_int )
% 13.77/7.72 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 13.77/7.72 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2974_add__strict__increasing2,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_real @ B @ C2 )
% 13.77/7.72 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2975_add__strict__increasing2,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_rat @ B @ C2 )
% 13.77/7.72 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2976_add__strict__increasing2,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_nat @ B @ C2 )
% 13.77/7.72 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2977_add__strict__increasing2,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_int @ B @ C2 )
% 13.77/7.72 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2978_add__strict__increasing,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ C2 )
% 13.77/7.72 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2979_add__strict__increasing,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ C2 )
% 13.77/7.72 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2980_add__strict__increasing,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ C2 )
% 13.77/7.72 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2981_add__strict__increasing,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ C2 )
% 13.77/7.72 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2982_add__pos__nonneg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2983_add__pos__nonneg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2984_add__pos__nonneg,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2985_add__pos__nonneg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2986_add__nonpos__neg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2987_add__nonpos__neg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2988_add__nonpos__neg,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2989_add__nonpos__neg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2990_add__nonneg__pos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2991_add__nonneg__pos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2992_add__nonneg__pos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2993_add__nonneg__pos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2994_add__neg__nonpos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2995_add__neg__nonpos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2996_add__neg__nonpos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2997_add__neg__nonpos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2998_zero__less__two,axiom,
% 13.77/7.72 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_2999_zero__less__two,axiom,
% 13.77/7.72 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3000_zero__less__two,axiom,
% 13.77/7.72 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3001_zero__less__two,axiom,
% 13.77/7.72 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3002_discrete,axiom,
% 13.77/7.72 ( ord_less_nat
% 13.77/7.72 = ( ^ [A7: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A7 @ one_one_nat ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3003_discrete,axiom,
% 13.77/7.72 ( ord_less_int
% 13.77/7.72 = ( ^ [A7: int] : ( ord_less_eq_int @ ( plus_plus_int @ A7 @ one_one_int ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3004_nat__diff__split__asm,axiom,
% 13.77/7.72 ! [P2: nat > $o,A: nat,B: nat] :
% 13.77/7.72 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 13.77/7.72 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 13.77/7.72 & ~ ( P2 @ zero_zero_nat ) )
% 13.77/7.72 | ? [D5: nat] :
% 13.77/7.72 ( ( A
% 13.77/7.72 = ( plus_plus_nat @ B @ D5 ) )
% 13.77/7.72 & ~ ( P2 @ D5 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3005_nat__diff__split,axiom,
% 13.77/7.72 ! [P2: nat > $o,A: nat,B: nat] :
% 13.77/7.72 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 13.77/7.72 = ( ( ( ord_less_nat @ A @ B )
% 13.77/7.72 => ( P2 @ zero_zero_nat ) )
% 13.77/7.72 & ! [D5: nat] :
% 13.77/7.72 ( ( A
% 13.77/7.72 = ( plus_plus_nat @ B @ D5 ) )
% 13.77/7.72 => ( P2 @ D5 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3006_less__diff__conv2,axiom,
% 13.77/7.72 ! [K: nat,J: nat,I: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ K @ J )
% 13.77/7.72 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 13.77/7.72 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3007_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 13.77/7.72 ! [Uu2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.72 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu2 @ Deg @ TreeList @ Summary ) )
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3008_enumerate__step,axiom,
% 13.77/7.72 ! [S3: set_nat,N: nat] :
% 13.77/7.72 ( ~ ( finite_finite_nat @ S3 )
% 13.77/7.72 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3009_enumerate__mono,axiom,
% 13.77/7.72 ! [M: nat,N: nat,S3: set_nat] :
% 13.77/7.72 ( ( ord_less_nat @ M @ N )
% 13.77/7.72 => ( ~ ( finite_finite_nat @ S3 )
% 13.77/7.72 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3010_add__eq__if,axiom,
% 13.77/7.72 ( plus_plus_nat
% 13.77/7.72 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N6 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N6 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3011_frac__add,axiom,
% 13.77/7.72 ! [X: real,Y: real] :
% 13.77/7.72 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 13.77/7.72 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 13.77/7.72 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 13.77/7.72 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 13.77/7.72 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X @ Y ) )
% 13.77/7.72 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3012_frac__add,axiom,
% 13.77/7.72 ! [X: rat,Y: rat] :
% 13.77/7.72 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 13.77/7.72 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 13.77/7.72 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 13.77/7.72 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 13.77/7.72 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 13.77/7.72 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3013_VEBT__internal_Oheight_Oelims,axiom,
% 13.77/7.72 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.72 ( ( ( vEBT_VEBT_height @ X )
% 13.77/7.72 = Y )
% 13.77/7.72 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.72 ( X
% 13.77/7.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.72 => ( Y != zero_zero_nat ) )
% 13.77/7.72 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.72 => ( Y
% 13.77/7.72 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3014_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I3_J,axiom,
% 13.77/7.72 ! [A: $o,B: $o,Va2: nat] :
% 13.77/7.72 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3015_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J,axiom,
% 13.77/7.72 ! [Uu2: $o,B: $o] :
% 13.77/7.72 ( ( vEBT_T_s_u_c_c @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3016_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J,axiom,
% 13.77/7.72 ! [A: $o,Uw2: $o] :
% 13.77/7.72 ( ( vEBT_T_p_r_e_d @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3017_pred__bound__height_H,axiom,
% 13.77/7.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.72 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.72 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3018_succ_H__bound__height,axiom,
% 13.77/7.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.72 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.72 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3019_insert_H__bound__height,axiom,
% 13.77/7.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.72 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.72 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3020_member__bound__height_H,axiom,
% 13.77/7.72 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.72 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.72 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ T @ X ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3021_VEBT__internal_Oheight_Opelims,axiom,
% 13.77/7.72 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.72 ( ( ( vEBT_VEBT_height @ X )
% 13.77/7.72 = Y )
% 13.77/7.72 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X )
% 13.77/7.72 => ( ! [A3: $o,B3: $o] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.72 => ( ( Y = zero_zero_nat )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.72 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.72 => ( ( Y
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3022_max__ins__scaled,axiom,
% 13.77/7.72 ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3023_field__le__epsilon,axiom,
% 13.77/7.72 ! [X: real,Y: real] :
% 13.77/7.72 ( ! [E: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ E )
% 13.77/7.72 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E ) ) )
% 13.77/7.72 => ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3024_field__le__epsilon,axiom,
% 13.77/7.72 ! [X: rat,Y: rat] :
% 13.77/7.72 ( ! [E: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ E )
% 13.77/7.72 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E ) ) )
% 13.77/7.72 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3025_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims,axiom,
% 13.77/7.72 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.72 ( ( ( vEBT_T_m_i_n_t @ X )
% 13.77/7.72 = Y )
% 13.77/7.72 => ( ! [A3: $o] :
% 13.77/7.72 ( ? [B3: $o] :
% 13.77/7.72 ( X
% 13.77/7.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.72 => ( Y
% 13.77/7.72 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 13.77/7.72 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.72 ( X
% 13.77/7.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.72 => ( Y != one_one_nat ) )
% 13.77/7.72 => ~ ( ? [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.72 ( X
% 13.77/7.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.72 => ( Y != one_one_nat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3026_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims,axiom,
% 13.77/7.72 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.72 ( ( ( vEBT_T_m_a_x_t @ X )
% 13.77/7.72 = Y )
% 13.77/7.72 => ( ! [A3: $o,B3: $o] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.72 => ( Y
% 13.77/7.72 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 13.77/7.72 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.72 ( X
% 13.77/7.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.72 => ( Y != one_one_nat ) )
% 13.77/7.72 => ~ ( ? [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.72 ( X
% 13.77/7.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.72 => ( Y != one_one_nat ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3027_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims,axiom,
% 13.77/7.72 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.72 ( ( ( vEBT_T_m_i_n_t @ X )
% 13.77/7.72 = Y )
% 13.77/7.72 => ( ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ X )
% 13.77/7.72 => ( ! [A3: $o,B3: $o] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.72 => ( ( Y
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A3 @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.72 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.72 => ( ( Y = one_one_nat )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 13.77/7.72 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.72 => ( ( Y = one_one_nat )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3028_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims,axiom,
% 13.77/7.72 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.72 ( ( ( vEBT_T_m_a_x_t @ X )
% 13.77/7.72 = Y )
% 13.77/7.72 => ( ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ X )
% 13.77/7.72 => ( ! [A3: $o,B3: $o] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.72 => ( ( Y
% 13.77/7.72 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.72 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.72 => ( ( Y = one_one_nat )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 13.77/7.72 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.72 ( ( X
% 13.77/7.72 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.72 => ( ( Y = one_one_nat )
% 13.77/7.72 => ~ ( accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3029_Euclid__induct,axiom,
% 13.77/7.72 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 13.77/7.72 ( ! [A3: nat,B3: nat] :
% 13.77/7.72 ( ( P2 @ A3 @ B3 )
% 13.77/7.72 = ( P2 @ B3 @ A3 ) )
% 13.77/7.72 => ( ! [A3: nat] : ( P2 @ A3 @ zero_zero_nat )
% 13.77/7.72 => ( ! [A3: nat,B3: nat] :
% 13.77/7.72 ( ( P2 @ A3 @ B3 )
% 13.77/7.72 => ( P2 @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 13.77/7.72 => ( P2 @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3030_triangle__Suc,axiom,
% 13.77/7.72 ! [N: nat] :
% 13.77/7.72 ( ( nat_triangle @ ( suc @ N ) )
% 13.77/7.72 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3031_mult__cancel__right,axiom,
% 13.77/7.72 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.72 ( ( ( times_times_rat @ A @ C2 )
% 13.77/7.72 = ( times_times_rat @ B @ C2 ) )
% 13.77/7.72 = ( ( C2 = zero_zero_rat )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3032_mult__cancel__right,axiom,
% 13.77/7.72 ! [A: real,C2: real,B: real] :
% 13.77/7.72 ( ( ( times_times_real @ A @ C2 )
% 13.77/7.72 = ( times_times_real @ B @ C2 ) )
% 13.77/7.72 = ( ( C2 = zero_zero_real )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3033_mult__cancel__right,axiom,
% 13.77/7.72 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ A @ C2 )
% 13.77/7.72 = ( times_times_nat @ B @ C2 ) )
% 13.77/7.72 = ( ( C2 = zero_zero_nat )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3034_mult__cancel__right,axiom,
% 13.77/7.72 ! [A: int,C2: int,B: int] :
% 13.77/7.72 ( ( ( times_times_int @ A @ C2 )
% 13.77/7.72 = ( times_times_int @ B @ C2 ) )
% 13.77/7.72 = ( ( C2 = zero_zero_int )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3035_mult__cancel__left,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( ( times_times_rat @ C2 @ A )
% 13.77/7.72 = ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 = ( ( C2 = zero_zero_rat )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3036_mult__cancel__left,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( ( times_times_real @ C2 @ A )
% 13.77/7.72 = ( times_times_real @ C2 @ B ) )
% 13.77/7.72 = ( ( C2 = zero_zero_real )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3037_mult__cancel__left,axiom,
% 13.77/7.72 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ C2 @ A )
% 13.77/7.72 = ( times_times_nat @ C2 @ B ) )
% 13.77/7.72 = ( ( C2 = zero_zero_nat )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3038_mult__cancel__left,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( ( times_times_int @ C2 @ A )
% 13.77/7.72 = ( times_times_int @ C2 @ B ) )
% 13.77/7.72 = ( ( C2 = zero_zero_int )
% 13.77/7.72 | ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3039_mult__eq__0__iff,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ( times_times_rat @ A @ B )
% 13.77/7.72 = zero_zero_rat )
% 13.77/7.72 = ( ( A = zero_zero_rat )
% 13.77/7.72 | ( B = zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3040_mult__eq__0__iff,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ( times_times_real @ A @ B )
% 13.77/7.72 = zero_zero_real )
% 13.77/7.72 = ( ( A = zero_zero_real )
% 13.77/7.72 | ( B = zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3041_mult__eq__0__iff,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ A @ B )
% 13.77/7.72 = zero_zero_nat )
% 13.77/7.72 = ( ( A = zero_zero_nat )
% 13.77/7.72 | ( B = zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3042_mult__eq__0__iff,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ( times_times_int @ A @ B )
% 13.77/7.72 = zero_zero_int )
% 13.77/7.72 = ( ( A = zero_zero_int )
% 13.77/7.72 | ( B = zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3043_mult__zero__right,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( times_times_rat @ A @ zero_zero_rat )
% 13.77/7.72 = zero_zero_rat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3044_mult__zero__right,axiom,
% 13.77/7.72 ! [A: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ A @ zero_zero_uint32 )
% 13.77/7.72 = zero_zero_uint32 ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3045_mult__zero__right,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( times_times_real @ A @ zero_zero_real )
% 13.77/7.72 = zero_zero_real ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3046_mult__zero__right,axiom,
% 13.77/7.72 ! [A: nat] :
% 13.77/7.72 ( ( times_times_nat @ A @ zero_zero_nat )
% 13.77/7.72 = zero_zero_nat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3047_mult__zero__right,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( times_times_int @ A @ zero_zero_int )
% 13.77/7.72 = zero_zero_int ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3048_mult__zero__left,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( times_times_rat @ zero_zero_rat @ A )
% 13.77/7.72 = zero_zero_rat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3049_mult__zero__left,axiom,
% 13.77/7.72 ! [A: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ zero_zero_uint32 @ A )
% 13.77/7.72 = zero_zero_uint32 ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3050_mult__zero__left,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( times_times_real @ zero_zero_real @ A )
% 13.77/7.72 = zero_zero_real ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3051_mult__zero__left,axiom,
% 13.77/7.72 ! [A: nat] :
% 13.77/7.72 ( ( times_times_nat @ zero_zero_nat @ A )
% 13.77/7.72 = zero_zero_nat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3052_mult__zero__left,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( times_times_int @ zero_zero_int @ A )
% 13.77/7.72 = zero_zero_int ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3053_mult_Oright__neutral,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( times_times_rat @ A @ one_one_rat )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3054_mult_Oright__neutral,axiom,
% 13.77/7.72 ! [A: assn] :
% 13.77/7.72 ( ( times_times_assn @ A @ one_one_assn )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3055_mult_Oright__neutral,axiom,
% 13.77/7.72 ! [A: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ A @ one_one_uint32 )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3056_mult_Oright__neutral,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( times_times_real @ A @ one_one_real )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3057_mult_Oright__neutral,axiom,
% 13.77/7.72 ! [A: nat] :
% 13.77/7.72 ( ( times_times_nat @ A @ one_one_nat )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3058_mult_Oright__neutral,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( times_times_int @ A @ one_one_int )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3059_mult__1,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( times_times_rat @ one_one_rat @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3060_mult__1,axiom,
% 13.77/7.72 ! [A: assn] :
% 13.77/7.72 ( ( times_times_assn @ one_one_assn @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3061_mult__1,axiom,
% 13.77/7.72 ! [A: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ one_one_uint32 @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3062_mult__1,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( times_times_real @ one_one_real @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3063_mult__1,axiom,
% 13.77/7.72 ! [A: nat] :
% 13.77/7.72 ( ( times_times_nat @ one_one_nat @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3064_mult__1,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( times_times_int @ one_one_int @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3065_mult__cancel2,axiom,
% 13.77/7.72 ! [M: nat,K: nat,N: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ M @ K )
% 13.77/7.72 = ( times_times_nat @ N @ K ) )
% 13.77/7.72 = ( ( M = N )
% 13.77/7.72 | ( K = zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3066_mult__cancel1,axiom,
% 13.77/7.72 ! [K: nat,M: nat,N: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ K @ M )
% 13.77/7.72 = ( times_times_nat @ K @ N ) )
% 13.77/7.72 = ( ( M = N )
% 13.77/7.72 | ( K = zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3067_mult__0__right,axiom,
% 13.77/7.72 ! [M: nat] :
% 13.77/7.72 ( ( times_times_nat @ M @ zero_zero_nat )
% 13.77/7.72 = zero_zero_nat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3068_mult__is__0,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ M @ N )
% 13.77/7.72 = zero_zero_nat )
% 13.77/7.72 = ( ( M = zero_zero_nat )
% 13.77/7.72 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3069_nat__1__eq__mult__iff,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( one_one_nat
% 13.77/7.72 = ( times_times_nat @ M @ N ) )
% 13.77/7.72 = ( ( M = one_one_nat )
% 13.77/7.72 & ( N = one_one_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3070_nat__mult__eq__1__iff,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ M @ N )
% 13.77/7.72 = one_one_nat )
% 13.77/7.72 = ( ( M = one_one_nat )
% 13.77/7.72 & ( N = one_one_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3071_triangle__0,axiom,
% 13.77/7.72 ( ( nat_triangle @ zero_zero_nat )
% 13.77/7.72 = zero_zero_nat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3072_mult__cancel__right2,axiom,
% 13.77/7.72 ! [A: rat,C2: rat] :
% 13.77/7.72 ( ( ( times_times_rat @ A @ C2 )
% 13.77/7.72 = C2 )
% 13.77/7.72 = ( ( C2 = zero_zero_rat )
% 13.77/7.72 | ( A = one_one_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3073_mult__cancel__right2,axiom,
% 13.77/7.72 ! [A: real,C2: real] :
% 13.77/7.72 ( ( ( times_times_real @ A @ C2 )
% 13.77/7.72 = C2 )
% 13.77/7.72 = ( ( C2 = zero_zero_real )
% 13.77/7.72 | ( A = one_one_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3074_mult__cancel__right2,axiom,
% 13.77/7.72 ! [A: int,C2: int] :
% 13.77/7.72 ( ( ( times_times_int @ A @ C2 )
% 13.77/7.72 = C2 )
% 13.77/7.72 = ( ( C2 = zero_zero_int )
% 13.77/7.72 | ( A = one_one_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3075_mult__cancel__right1,axiom,
% 13.77/7.72 ! [C2: rat,B: rat] :
% 13.77/7.72 ( ( C2
% 13.77/7.72 = ( times_times_rat @ B @ C2 ) )
% 13.77/7.72 = ( ( C2 = zero_zero_rat )
% 13.77/7.72 | ( B = one_one_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3076_mult__cancel__right1,axiom,
% 13.77/7.72 ! [C2: real,B: real] :
% 13.77/7.72 ( ( C2
% 13.77/7.72 = ( times_times_real @ B @ C2 ) )
% 13.77/7.72 = ( ( C2 = zero_zero_real )
% 13.77/7.72 | ( B = one_one_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3077_mult__cancel__right1,axiom,
% 13.77/7.72 ! [C2: int,B: int] :
% 13.77/7.72 ( ( C2
% 13.77/7.72 = ( times_times_int @ B @ C2 ) )
% 13.77/7.72 = ( ( C2 = zero_zero_int )
% 13.77/7.72 | ( B = one_one_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3078_mult__cancel__left2,axiom,
% 13.77/7.72 ! [C2: rat,A: rat] :
% 13.77/7.72 ( ( ( times_times_rat @ C2 @ A )
% 13.77/7.72 = C2 )
% 13.77/7.72 = ( ( C2 = zero_zero_rat )
% 13.77/7.72 | ( A = one_one_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3079_mult__cancel__left2,axiom,
% 13.77/7.72 ! [C2: real,A: real] :
% 13.77/7.72 ( ( ( times_times_real @ C2 @ A )
% 13.77/7.72 = C2 )
% 13.77/7.72 = ( ( C2 = zero_zero_real )
% 13.77/7.72 | ( A = one_one_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3080_mult__cancel__left2,axiom,
% 13.77/7.72 ! [C2: int,A: int] :
% 13.77/7.72 ( ( ( times_times_int @ C2 @ A )
% 13.77/7.72 = C2 )
% 13.77/7.72 = ( ( C2 = zero_zero_int )
% 13.77/7.72 | ( A = one_one_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3081_mult__cancel__left1,axiom,
% 13.77/7.72 ! [C2: rat,B: rat] :
% 13.77/7.72 ( ( C2
% 13.77/7.72 = ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 = ( ( C2 = zero_zero_rat )
% 13.77/7.72 | ( B = one_one_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3082_mult__cancel__left1,axiom,
% 13.77/7.72 ! [C2: real,B: real] :
% 13.77/7.72 ( ( C2
% 13.77/7.72 = ( times_times_real @ C2 @ B ) )
% 13.77/7.72 = ( ( C2 = zero_zero_real )
% 13.77/7.72 | ( B = one_one_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3083_mult__cancel__left1,axiom,
% 13.77/7.72 ! [C2: int,B: int] :
% 13.77/7.72 ( ( C2
% 13.77/7.72 = ( times_times_int @ C2 @ B ) )
% 13.77/7.72 = ( ( C2 = zero_zero_int )
% 13.77/7.72 | ( B = one_one_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3084_mult__eq__1__iff,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ M @ N )
% 13.77/7.72 = ( suc @ zero_zero_nat ) )
% 13.77/7.72 = ( ( M
% 13.77/7.72 = ( suc @ zero_zero_nat ) )
% 13.77/7.72 & ( N
% 13.77/7.72 = ( suc @ zero_zero_nat ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3085_one__eq__mult__iff,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ( suc @ zero_zero_nat )
% 13.77/7.72 = ( times_times_nat @ M @ N ) )
% 13.77/7.72 = ( ( M
% 13.77/7.72 = ( suc @ zero_zero_nat ) )
% 13.77/7.72 & ( N
% 13.77/7.72 = ( suc @ zero_zero_nat ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3086_mult__less__cancel2,axiom,
% 13.77/7.72 ! [M: nat,K: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 13.77/7.72 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.72 & ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3087_nat__0__less__mult__iff,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 13.77/7.72 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.72 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3088_mult__Suc__right,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( times_times_nat @ M @ ( suc @ N ) )
% 13.77/7.72 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3089_one__le__mult__iff,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 13.77/7.72 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 13.77/7.72 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3090_mult__le__cancel2,axiom,
% 13.77/7.72 ! [M: nat,K: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 13.77/7.72 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.72 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3091_mult_Oassoc,axiom,
% 13.77/7.72 ! [A: assn,B: assn,C2: assn] :
% 13.77/7.72 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C2 )
% 13.77/7.72 = ( times_times_assn @ A @ ( times_times_assn @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3092_mult_Oassoc,axiom,
% 13.77/7.72 ! [A: uint32,B: uint32,C2: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ ( times_times_uint32 @ A @ B ) @ C2 )
% 13.77/7.72 = ( times_times_uint32 @ A @ ( times_times_uint32 @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3093_mult_Oassoc,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 13.77/7.72 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3094_mult_Oassoc,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 13.77/7.72 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3095_mult_Oassoc,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 13.77/7.72 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3096_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 13.77/7.72 ( times_times_assn
% 13.77/7.72 = ( ^ [A7: assn,B7: assn] : ( times_times_assn @ B7 @ A7 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3097_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 13.77/7.72 ( times_times_uint32
% 13.77/7.72 = ( ^ [A7: uint32,B7: uint32] : ( times_times_uint32 @ B7 @ A7 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3098_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 13.77/7.72 ( times_times_real
% 13.77/7.72 = ( ^ [A7: real,B7: real] : ( times_times_real @ B7 @ A7 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3099_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 13.77/7.72 ( times_times_nat
% 13.77/7.72 = ( ^ [A7: nat,B7: nat] : ( times_times_nat @ B7 @ A7 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3100_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 13.77/7.72 ( times_times_int
% 13.77/7.72 = ( ^ [A7: int,B7: int] : ( times_times_int @ B7 @ A7 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3101_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 13.77/7.72 ! [B: assn,A: assn,C2: assn] :
% 13.77/7.72 ( ( times_times_assn @ B @ ( times_times_assn @ A @ C2 ) )
% 13.77/7.72 = ( times_times_assn @ A @ ( times_times_assn @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3102_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 13.77/7.72 ! [B: uint32,A: uint32,C2: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ B @ ( times_times_uint32 @ A @ C2 ) )
% 13.77/7.72 = ( times_times_uint32 @ A @ ( times_times_uint32 @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3103_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 13.77/7.72 ! [B: real,A: real,C2: real] :
% 13.77/7.72 ( ( times_times_real @ B @ ( times_times_real @ A @ C2 ) )
% 13.77/7.72 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3104_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 13.77/7.72 ! [B: nat,A: nat,C2: nat] :
% 13.77/7.72 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C2 ) )
% 13.77/7.72 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3105_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 13.77/7.72 ! [B: int,A: int,C2: int] :
% 13.77/7.72 ( ( times_times_int @ B @ ( times_times_int @ A @ C2 ) )
% 13.77/7.72 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3106_mult__right__cancel,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( C2 != zero_zero_rat )
% 13.77/7.72 => ( ( ( times_times_rat @ A @ C2 )
% 13.77/7.72 = ( times_times_rat @ B @ C2 ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3107_mult__right__cancel,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( C2 != zero_zero_real )
% 13.77/7.72 => ( ( ( times_times_real @ A @ C2 )
% 13.77/7.72 = ( times_times_real @ B @ C2 ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3108_mult__right__cancel,axiom,
% 13.77/7.72 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.72 ( ( C2 != zero_zero_nat )
% 13.77/7.72 => ( ( ( times_times_nat @ A @ C2 )
% 13.77/7.72 = ( times_times_nat @ B @ C2 ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3109_mult__right__cancel,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( C2 != zero_zero_int )
% 13.77/7.72 => ( ( ( times_times_int @ A @ C2 )
% 13.77/7.72 = ( times_times_int @ B @ C2 ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3110_mult__left__cancel,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( C2 != zero_zero_rat )
% 13.77/7.72 => ( ( ( times_times_rat @ C2 @ A )
% 13.77/7.72 = ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3111_mult__left__cancel,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( C2 != zero_zero_real )
% 13.77/7.72 => ( ( ( times_times_real @ C2 @ A )
% 13.77/7.72 = ( times_times_real @ C2 @ B ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3112_mult__left__cancel,axiom,
% 13.77/7.72 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.72 ( ( C2 != zero_zero_nat )
% 13.77/7.72 => ( ( ( times_times_nat @ C2 @ A )
% 13.77/7.72 = ( times_times_nat @ C2 @ B ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3113_mult__left__cancel,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( C2 != zero_zero_int )
% 13.77/7.72 => ( ( ( times_times_int @ C2 @ A )
% 13.77/7.72 = ( times_times_int @ C2 @ B ) )
% 13.77/7.72 = ( A = B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3114_no__zero__divisors,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( A != zero_zero_rat )
% 13.77/7.72 => ( ( B != zero_zero_rat )
% 13.77/7.72 => ( ( times_times_rat @ A @ B )
% 13.77/7.72 != zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3115_no__zero__divisors,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( A != zero_zero_real )
% 13.77/7.72 => ( ( B != zero_zero_real )
% 13.77/7.72 => ( ( times_times_real @ A @ B )
% 13.77/7.72 != zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3116_no__zero__divisors,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( A != zero_zero_nat )
% 13.77/7.72 => ( ( B != zero_zero_nat )
% 13.77/7.72 => ( ( times_times_nat @ A @ B )
% 13.77/7.72 != zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3117_no__zero__divisors,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( A != zero_zero_int )
% 13.77/7.72 => ( ( B != zero_zero_int )
% 13.77/7.72 => ( ( times_times_int @ A @ B )
% 13.77/7.72 != zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3118_divisors__zero,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ( times_times_rat @ A @ B )
% 13.77/7.72 = zero_zero_rat )
% 13.77/7.72 => ( ( A = zero_zero_rat )
% 13.77/7.72 | ( B = zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3119_divisors__zero,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ( times_times_real @ A @ B )
% 13.77/7.72 = zero_zero_real )
% 13.77/7.72 => ( ( A = zero_zero_real )
% 13.77/7.72 | ( B = zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3120_divisors__zero,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ A @ B )
% 13.77/7.72 = zero_zero_nat )
% 13.77/7.72 => ( ( A = zero_zero_nat )
% 13.77/7.72 | ( B = zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3121_divisors__zero,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ( times_times_int @ A @ B )
% 13.77/7.72 = zero_zero_int )
% 13.77/7.72 => ( ( A = zero_zero_int )
% 13.77/7.72 | ( B = zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3122_mult__not__zero,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ( times_times_rat @ A @ B )
% 13.77/7.72 != zero_zero_rat )
% 13.77/7.72 => ( ( A != zero_zero_rat )
% 13.77/7.72 & ( B != zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3123_mult__not__zero,axiom,
% 13.77/7.72 ! [A: uint32,B: uint32] :
% 13.77/7.72 ( ( ( times_times_uint32 @ A @ B )
% 13.77/7.72 != zero_zero_uint32 )
% 13.77/7.72 => ( ( A != zero_zero_uint32 )
% 13.77/7.72 & ( B != zero_zero_uint32 ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3124_mult__not__zero,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ( times_times_real @ A @ B )
% 13.77/7.72 != zero_zero_real )
% 13.77/7.72 => ( ( A != zero_zero_real )
% 13.77/7.72 & ( B != zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3125_mult__not__zero,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ A @ B )
% 13.77/7.72 != zero_zero_nat )
% 13.77/7.72 => ( ( A != zero_zero_nat )
% 13.77/7.72 & ( B != zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3126_mult__not__zero,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ( times_times_int @ A @ B )
% 13.77/7.72 != zero_zero_int )
% 13.77/7.72 => ( ( A != zero_zero_int )
% 13.77/7.72 & ( B != zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3127_comm__monoid__mult__class_Omult__1,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( times_times_rat @ one_one_rat @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3128_comm__monoid__mult__class_Omult__1,axiom,
% 13.77/7.72 ! [A: assn] :
% 13.77/7.72 ( ( times_times_assn @ one_one_assn @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3129_comm__monoid__mult__class_Omult__1,axiom,
% 13.77/7.72 ! [A: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ one_one_uint32 @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3130_comm__monoid__mult__class_Omult__1,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( times_times_real @ one_one_real @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3131_comm__monoid__mult__class_Omult__1,axiom,
% 13.77/7.72 ! [A: nat] :
% 13.77/7.72 ( ( times_times_nat @ one_one_nat @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3132_comm__monoid__mult__class_Omult__1,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( times_times_int @ one_one_int @ A )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3133_mult_Ocomm__neutral,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ( ( times_times_rat @ A @ one_one_rat )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3134_mult_Ocomm__neutral,axiom,
% 13.77/7.72 ! [A: assn] :
% 13.77/7.72 ( ( times_times_assn @ A @ one_one_assn )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3135_mult_Ocomm__neutral,axiom,
% 13.77/7.72 ! [A: uint32] :
% 13.77/7.72 ( ( times_times_uint32 @ A @ one_one_uint32 )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3136_mult_Ocomm__neutral,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ( ( times_times_real @ A @ one_one_real )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3137_mult_Ocomm__neutral,axiom,
% 13.77/7.72 ! [A: nat] :
% 13.77/7.72 ( ( times_times_nat @ A @ one_one_nat )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3138_mult_Ocomm__neutral,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ( ( times_times_int @ A @ one_one_int )
% 13.77/7.72 = A ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3139_Suc__mult__cancel1,axiom,
% 13.77/7.72 ! [K: nat,M: nat,N: nat] :
% 13.77/7.72 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 13.77/7.72 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 13.77/7.72 = ( M = N ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3140_mult__0,axiom,
% 13.77/7.72 ! [N: nat] :
% 13.77/7.72 ( ( times_times_nat @ zero_zero_nat @ N )
% 13.77/7.72 = zero_zero_nat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3141_add__mult__distrib,axiom,
% 13.77/7.72 ! [M: nat,N: nat,K: nat] :
% 13.77/7.72 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 13.77/7.72 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3142_add__mult__distrib2,axiom,
% 13.77/7.72 ! [K: nat,M: nat,N: nat] :
% 13.77/7.72 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 13.77/7.72 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3143_le__cube,axiom,
% 13.77/7.72 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3144_le__square,axiom,
% 13.77/7.72 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3145_mult__le__mono,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat,L: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.72 => ( ( ord_less_eq_nat @ K @ L )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3146_mult__le__mono1,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3147_mult__le__mono2,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3148_nat__mult__1,axiom,
% 13.77/7.72 ! [N: nat] :
% 13.77/7.72 ( ( times_times_nat @ one_one_nat @ N )
% 13.77/7.72 = N ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3149_nat__mult__1__right,axiom,
% 13.77/7.72 ! [N: nat] :
% 13.77/7.72 ( ( times_times_nat @ N @ one_one_nat )
% 13.77/7.72 = N ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3150_diff__mult__distrib,axiom,
% 13.77/7.72 ! [M: nat,N: nat,K: nat] :
% 13.77/7.72 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 13.77/7.72 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3151_diff__mult__distrib2,axiom,
% 13.77/7.72 ! [K: nat,M: nat,N: nat] :
% 13.77/7.72 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.72 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3152_zero__notin__Suc__image,axiom,
% 13.77/7.72 ! [A4: set_nat] :
% 13.77/7.72 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3153_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3154_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3155_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3156_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3157_zero__le__mult__iff,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 13.77/7.72 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 13.77/7.72 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3158_zero__le__mult__iff,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 13.77/7.72 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 13.77/7.72 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3159_zero__le__mult__iff,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 13.77/7.72 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 13.77/7.72 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3160_mult__nonneg__nonpos2,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3161_mult__nonneg__nonpos2,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3162_mult__nonneg__nonpos2,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3163_mult__nonneg__nonpos2,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3164_mult__nonpos__nonneg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3165_mult__nonpos__nonneg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3166_mult__nonpos__nonneg,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3167_mult__nonpos__nonneg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3168_mult__nonneg__nonpos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3169_mult__nonneg__nonpos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3170_mult__nonneg__nonpos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3171_mult__nonneg__nonpos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3172_mult__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3173_mult__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3174_mult__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3175_mult__nonneg__nonneg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3176_split__mult__neg__le,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 13.77/7.72 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3177_split__mult__neg__le,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 13.77/7.72 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3178_split__mult__neg__le,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 13.77/7.72 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 13.77/7.72 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3179_split__mult__neg__le,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 13.77/7.72 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3180_mult__le__0__iff,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 13.77/7.72 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 13.77/7.72 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3181_mult__le__0__iff,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 13.77/7.72 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 13.77/7.72 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3182_mult__le__0__iff,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 13.77/7.72 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 13.77/7.72 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3183_mult__right__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3184_mult__right__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3185_mult__right__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3186_mult__right__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3187_mult__right__mono__neg,axiom,
% 13.77/7.72 ! [B: real,A: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ B @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3188_mult__right__mono__neg,axiom,
% 13.77/7.72 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3189_mult__right__mono__neg,axiom,
% 13.77/7.72 ! [B: int,A: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3190_mult__left__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3191_mult__left__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3192_mult__left__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3193_mult__left__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3194_mult__nonpos__nonpos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3195_mult__nonpos__nonpos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3196_mult__nonpos__nonpos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3197_mult__left__mono__neg,axiom,
% 13.77/7.72 ! [B: real,A: real,C2: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ B @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3198_mult__left__mono__neg,axiom,
% 13.77/7.72 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3199_mult__left__mono__neg,axiom,
% 13.77/7.72 ! [B: int,A: int,C2: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3200_split__mult__pos__le,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 13.77/7.72 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.72 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 13.77/7.72 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3201_split__mult__pos__le,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 13.77/7.72 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 13.77/7.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3202_split__mult__pos__le,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 13.77/7.72 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.72 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 13.77/7.72 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3203_zero__le__square,axiom,
% 13.77/7.72 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3204_zero__le__square,axiom,
% 13.77/7.72 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3205_zero__le__square,axiom,
% 13.77/7.72 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3206_mult__mono_H,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3207_mult__mono_H,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3208_mult__mono_H,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3209_mult__mono_H,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_int @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3210_mult__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3211_mult__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3212_mult__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3213_mult__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_eq_int @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3214_mult__neg__neg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3215_mult__neg__neg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3216_mult__neg__neg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3217_not__square__less__zero,axiom,
% 13.77/7.72 ! [A: real] :
% 13.77/7.72 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3218_not__square__less__zero,axiom,
% 13.77/7.72 ! [A: rat] :
% 13.77/7.72 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3219_not__square__less__zero,axiom,
% 13.77/7.72 ! [A: int] :
% 13.77/7.72 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3220_mult__less__0__iff,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 13.77/7.72 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 & ( ord_less_real @ B @ zero_zero_real ) )
% 13.77/7.72 | ( ( ord_less_real @ A @ zero_zero_real )
% 13.77/7.72 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3221_mult__less__0__iff,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 13.77/7.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 13.77/7.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3222_mult__less__0__iff,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 13.77/7.72 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 & ( ord_less_int @ B @ zero_zero_int ) )
% 13.77/7.72 | ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.72 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3223_mult__neg__pos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3224_mult__neg__pos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3225_mult__neg__pos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ zero_zero_nat )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3226_mult__neg__pos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3227_mult__pos__neg,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3228_mult__pos__neg,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3229_mult__pos__neg,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3230_mult__pos__neg,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3231_mult__pos__pos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3232_mult__pos__pos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3233_mult__pos__pos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.72 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3234_mult__pos__pos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.72 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3235_mult__pos__neg2,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ( ord_less_real @ B @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3236_mult__pos__neg2,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3237_mult__pos__neg2,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3238_mult__pos__neg2,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3239_zero__less__mult__iff,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 13.77/7.72 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 & ( ord_less_real @ zero_zero_real @ B ) )
% 13.77/7.72 | ( ( ord_less_real @ A @ zero_zero_real )
% 13.77/7.72 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3240_zero__less__mult__iff,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 13.77/7.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 13.77/7.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3241_zero__less__mult__iff,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 13.77/7.72 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 & ( ord_less_int @ zero_zero_int @ B ) )
% 13.77/7.72 | ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.72 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3242_zero__less__mult__pos,axiom,
% 13.77/7.72 ! [A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3243_zero__less__mult__pos,axiom,
% 13.77/7.72 ! [A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3244_zero__less__mult__pos,axiom,
% 13.77/7.72 ! [A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3245_zero__less__mult__pos,axiom,
% 13.77/7.72 ! [A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3246_zero__less__mult__pos2,axiom,
% 13.77/7.72 ! [B: real,A: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.72 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3247_zero__less__mult__pos2,axiom,
% 13.77/7.72 ! [B: rat,A: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.72 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3248_zero__less__mult__pos2,axiom,
% 13.77/7.72 ! [B: nat,A: nat] :
% 13.77/7.72 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.72 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3249_zero__less__mult__pos2,axiom,
% 13.77/7.72 ! [B: int,A: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.72 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3250_mult__less__cancel__left__neg,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_real @ B @ A ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3251_mult__less__cancel__left__neg,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_rat @ B @ A ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3252_mult__less__cancel__left__neg,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_int @ B @ A ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3253_mult__less__cancel__left__pos,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3254_mult__less__cancel__left__pos,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_rat @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3255_mult__less__cancel__left__pos,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.72 = ( ord_less_int @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3256_mult__strict__left__mono__neg,axiom,
% 13.77/7.72 ! [B: real,A: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ B @ A )
% 13.77/7.72 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3257_mult__strict__left__mono__neg,axiom,
% 13.77/7.72 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ B @ A )
% 13.77/7.72 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3258_mult__strict__left__mono__neg,axiom,
% 13.77/7.72 ! [B: int,A: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ B @ A )
% 13.77/7.72 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3259_mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3260_mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3261_mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3262_mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3263_mult__less__cancel__left__disj,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.72 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 & ( ord_less_real @ A @ B ) )
% 13.77/7.72 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.72 & ( ord_less_real @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3264_mult__less__cancel__left__disj,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 & ( ord_less_rat @ A @ B ) )
% 13.77/7.72 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3265_mult__less__cancel__left__disj,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.72 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 & ( ord_less_int @ A @ B ) )
% 13.77/7.72 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.72 & ( ord_less_int @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3266_mult__strict__right__mono__neg,axiom,
% 13.77/7.72 ! [B: real,A: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ B @ A )
% 13.77/7.72 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3267_mult__strict__right__mono__neg,axiom,
% 13.77/7.72 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ B @ A )
% 13.77/7.72 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3268_mult__strict__right__mono__neg,axiom,
% 13.77/7.72 ! [B: int,A: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ B @ A )
% 13.77/7.72 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3269_mult__strict__right__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3270_mult__strict__right__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3271_mult__strict__right__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3272_mult__strict__right__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3273_mult__less__cancel__right__disj,axiom,
% 13.77/7.72 ! [A: real,C2: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 13.77/7.72 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 & ( ord_less_real @ A @ B ) )
% 13.77/7.72 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.72 & ( ord_less_real @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3274_mult__less__cancel__right__disj,axiom,
% 13.77/7.72 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 13.77/7.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 & ( ord_less_rat @ A @ B ) )
% 13.77/7.72 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3275_mult__less__cancel__right__disj,axiom,
% 13.77/7.72 ! [A: int,C2: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 13.77/7.72 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 & ( ord_less_int @ A @ B ) )
% 13.77/7.72 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.72 & ( ord_less_int @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3276_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3277_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3278_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: nat,B: nat,C2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ B )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3279_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 13.77/7.72 ! [A: int,B: int,C2: int] :
% 13.77/7.72 ( ( ord_less_int @ A @ B )
% 13.77/7.72 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3280_less__1__mult,axiom,
% 13.77/7.72 ! [M: real,N: real] :
% 13.77/7.72 ( ( ord_less_real @ one_one_real @ M )
% 13.77/7.72 => ( ( ord_less_real @ one_one_real @ N )
% 13.77/7.72 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3281_less__1__mult,axiom,
% 13.77/7.72 ! [M: rat,N: rat] :
% 13.77/7.72 ( ( ord_less_rat @ one_one_rat @ M )
% 13.77/7.72 => ( ( ord_less_rat @ one_one_rat @ N )
% 13.77/7.72 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3282_less__1__mult,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_nat @ one_one_nat @ M )
% 13.77/7.72 => ( ( ord_less_nat @ one_one_nat @ N )
% 13.77/7.72 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3283_less__1__mult,axiom,
% 13.77/7.72 ! [M: int,N: int] :
% 13.77/7.72 ( ( ord_less_int @ one_one_int @ M )
% 13.77/7.72 => ( ( ord_less_int @ one_one_int @ N )
% 13.77/7.72 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3284_Suc__mult__less__cancel1,axiom,
% 13.77/7.72 ! [K: nat,M: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 13.77/7.72 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3285_mult__less__mono1,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat] :
% 13.77/7.72 ( ( ord_less_nat @ I @ J )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3286_mult__less__mono2,axiom,
% 13.77/7.72 ! [I: nat,J: nat,K: nat] :
% 13.77/7.72 ( ( ord_less_nat @ I @ J )
% 13.77/7.72 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.72 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3287_mult__Suc,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( times_times_nat @ ( suc @ M ) @ N )
% 13.77/7.72 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3288_Suc__mult__le__cancel1,axiom,
% 13.77/7.72 ! [K: nat,M: nat,N: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 13.77/7.72 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3289_mult__eq__self__implies__10,axiom,
% 13.77/7.72 ! [M: nat,N: nat] :
% 13.77/7.72 ( ( M
% 13.77/7.72 = ( times_times_nat @ M @ N ) )
% 13.77/7.72 => ( ( N = one_one_nat )
% 13.77/7.72 | ( M = zero_zero_nat ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3290_mlex__snd__decrI,axiom,
% 13.77/7.72 ! [A: nat,A2: nat,B: nat,B2: nat,N8: nat] :
% 13.77/7.72 ( ( A = A2 )
% 13.77/7.72 => ( ( ord_less_nat @ B @ B2 )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N8 ) @ B2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3291_mlex__fst__decrI,axiom,
% 13.77/7.72 ! [A: nat,A2: nat,B: nat,N8: nat,B2: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ A2 )
% 13.77/7.72 => ( ( ord_less_nat @ B @ N8 )
% 13.77/7.72 => ( ( ord_less_nat @ B2 @ N8 )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N8 ) @ B2 ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3292_mlex__bound,axiom,
% 13.77/7.72 ! [A: nat,A4: nat,B: nat,N8: nat] :
% 13.77/7.72 ( ( ord_less_nat @ A @ A4 )
% 13.77/7.72 => ( ( ord_less_nat @ B @ N8 )
% 13.77/7.72 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( times_times_nat @ A4 @ N8 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3293_mlex__leI,axiom,
% 13.77/7.72 ! [A: nat,A2: nat,B: nat,B2: nat,N8: nat] :
% 13.77/7.72 ( ( ord_less_eq_nat @ A @ A2 )
% 13.77/7.72 => ( ( ord_less_eq_nat @ B @ B2 )
% 13.77/7.72 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N8 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N8 ) @ B2 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3294_field__le__mult__one__interval,axiom,
% 13.77/7.72 ! [X: real,Y: real] :
% 13.77/7.72 ( ! [Z3: real] :
% 13.77/7.72 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 13.77/7.72 => ( ( ord_less_real @ Z3 @ one_one_real )
% 13.77/7.72 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ Y ) ) )
% 13.77/7.72 => ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3295_field__le__mult__one__interval,axiom,
% 13.77/7.72 ! [X: rat,Y: rat] :
% 13.77/7.72 ( ! [Z3: rat] :
% 13.77/7.72 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 13.77/7.72 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ Y ) ) )
% 13.77/7.72 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3296_in__image__insert__iff,axiom,
% 13.77/7.72 ! [B4: set_set_VEBT_VEBT,X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.72 ( ! [C5: set_VEBT_VEBT] :
% 13.77/7.72 ( ( member_set_VEBT_VEBT @ C5 @ B4 )
% 13.77/7.72 => ~ ( member_VEBT_VEBT @ X @ C5 ) )
% 13.77/7.72 => ( ( member_set_VEBT_VEBT @ A4 @ ( image_1661326939266726661T_VEBT @ ( insert_VEBT_VEBT @ X ) @ B4 ) )
% 13.77/7.72 = ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.72 & ( member_set_VEBT_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3297_in__image__insert__iff,axiom,
% 13.77/7.72 ! [B4: set_set_real,X: real,A4: set_real] :
% 13.77/7.72 ( ! [C5: set_real] :
% 13.77/7.72 ( ( member_set_real @ C5 @ B4 )
% 13.77/7.72 => ~ ( member_real @ X @ C5 ) )
% 13.77/7.72 => ( ( member_set_real @ A4 @ ( image_2436557299294012491t_real @ ( insert_real @ X ) @ B4 ) )
% 13.77/7.72 = ( ( member_real @ X @ A4 )
% 13.77/7.72 & ( member_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B4 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3298_in__image__insert__iff,axiom,
% 13.77/7.72 ! [B4: set_set_set_nat,X: set_nat,A4: set_set_nat] :
% 13.77/7.72 ( ! [C5: set_set_nat] :
% 13.77/7.72 ( ( member_set_set_nat @ C5 @ B4 )
% 13.77/7.72 => ~ ( member_set_nat @ X @ C5 ) )
% 13.77/7.72 => ( ( member_set_set_nat @ A4 @ ( image_7884819252390400639et_nat @ ( insert_set_nat @ X ) @ B4 ) )
% 13.77/7.72 = ( ( member_set_nat @ X @ A4 )
% 13.77/7.72 & ( member_set_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B4 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3299_in__image__insert__iff,axiom,
% 13.77/7.72 ! [B4: set_set_int,X: int,A4: set_int] :
% 13.77/7.72 ( ! [C5: set_int] :
% 13.77/7.72 ( ( member_set_int @ C5 @ B4 )
% 13.77/7.72 => ~ ( member_int @ X @ C5 ) )
% 13.77/7.72 => ( ( member_set_int @ A4 @ ( image_524474410958335435et_int @ ( insert_int @ X ) @ B4 ) )
% 13.77/7.72 = ( ( member_int @ X @ A4 )
% 13.77/7.72 & ( member_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B4 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3300_in__image__insert__iff,axiom,
% 13.77/7.72 ! [B4: set_set_o,X: $o,A4: set_o] :
% 13.77/7.72 ( ! [C5: set_o] :
% 13.77/7.72 ( ( member_set_o @ C5 @ B4 )
% 13.77/7.72 => ~ ( member_o @ X @ C5 ) )
% 13.77/7.72 => ( ( member_set_o @ A4 @ ( image_set_o_set_o @ ( insert_o @ X ) @ B4 ) )
% 13.77/7.72 = ( ( member_o @ X @ A4 )
% 13.77/7.72 & ( member_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B4 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3301_in__image__insert__iff,axiom,
% 13.77/7.72 ! [B4: set_set_nat,X: nat,A4: set_nat] :
% 13.77/7.72 ( ! [C5: set_nat] :
% 13.77/7.72 ( ( member_set_nat @ C5 @ B4 )
% 13.77/7.72 => ~ ( member_nat @ X @ C5 ) )
% 13.77/7.72 => ( ( member_set_nat @ A4 @ ( image_7916887816326733075et_nat @ ( insert_nat @ X ) @ B4 ) )
% 13.77/7.72 = ( ( member_nat @ X @ A4 )
% 13.77/7.72 & ( member_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B4 ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3302_mult__le__cancel__left,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.72 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ A @ B ) )
% 13.77/7.72 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3303_mult__le__cancel__left,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ A @ B ) )
% 13.77/7.72 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3304_mult__le__cancel__left,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.72 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ A @ B ) )
% 13.77/7.72 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3305_mult__le__cancel__right,axiom,
% 13.77/7.72 ! [A: real,C2: real,B: real] :
% 13.77/7.72 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 13.77/7.72 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_eq_real @ A @ B ) )
% 13.77/7.72 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.72 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3306_mult__le__cancel__right,axiom,
% 13.77/7.72 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 13.77/7.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_eq_rat @ A @ B ) )
% 13.77/7.72 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.72 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3307_mult__le__cancel__right,axiom,
% 13.77/7.72 ! [A: int,C2: int,B: int] :
% 13.77/7.72 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 13.77/7.72 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_eq_int @ A @ B ) )
% 13.77/7.72 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.72 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3308_mult__left__less__imp__less,axiom,
% 13.77/7.72 ! [C2: real,A: real,B: real] :
% 13.77/7.72 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3309_mult__left__less__imp__less,axiom,
% 13.77/7.72 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.72 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_rat @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3310_mult__left__less__imp__less,axiom,
% 13.77/7.72 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.72 ( ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 13.77/7.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.72 => ( ord_less_nat @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3311_mult__left__less__imp__less,axiom,
% 13.77/7.72 ! [C2: int,A: int,B: int] :
% 13.77/7.72 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.72 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.72 => ( ord_less_int @ A @ B ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3312_mult__strict__mono,axiom,
% 13.77/7.72 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.72 ( ( ord_less_real @ A @ B )
% 13.77/7.72 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.72 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.72 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 13.77/7.72
% 13.77/7.72 thf(fact_3313_mult__strict__mono,axiom,
% 13.77/7.72 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.72 ( ( ord_less_rat @ A @ B )
% 13.77/7.72 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.72 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 13.77/7.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.72 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3314_mult__strict__mono,axiom,
% 13.77/7.73 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.73 ( ( ord_less_nat @ A @ B )
% 13.77/7.73 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.73 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3315_mult__strict__mono,axiom,
% 13.77/7.73 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.73 ( ( ord_less_int @ A @ B )
% 13.77/7.73 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3316_mult__less__cancel__left,axiom,
% 13.77/7.73 ! [C2: real,A: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ A @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_real @ B @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3317_mult__less__cancel__left,axiom,
% 13.77/7.73 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ A @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3318_mult__less__cancel__left,axiom,
% 13.77/7.73 ! [C2: int,A: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ A @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_int @ B @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3319_mult__right__less__imp__less,axiom,
% 13.77/7.73 ! [A: real,C2: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3320_mult__right__less__imp__less,axiom,
% 13.77/7.73 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3321_mult__right__less__imp__less,axiom,
% 13.77/7.73 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.73 ( ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.73 => ( ord_less_nat @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3322_mult__right__less__imp__less,axiom,
% 13.77/7.73 ! [A: int,C2: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3323_mult__strict__mono_H,axiom,
% 13.77/7.73 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.73 ( ( ord_less_real @ A @ B )
% 13.77/7.73 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3324_mult__strict__mono_H,axiom,
% 13.77/7.73 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.73 ( ( ord_less_rat @ A @ B )
% 13.77/7.73 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3325_mult__strict__mono_H,axiom,
% 13.77/7.73 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.73 ( ( ord_less_nat @ A @ B )
% 13.77/7.73 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.73 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3326_mult__strict__mono_H,axiom,
% 13.77/7.73 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.73 ( ( ord_less_int @ A @ B )
% 13.77/7.73 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3327_mult__less__cancel__right,axiom,
% 13.77/7.73 ! [A: real,C2: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ A @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_real @ B @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3328_mult__less__cancel__right,axiom,
% 13.77/7.73 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ A @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3329_mult__less__cancel__right,axiom,
% 13.77/7.73 ! [A: int,C2: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ A @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_int @ B @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3330_mult__le__cancel__left__neg,axiom,
% 13.77/7.73 ! [C2: real,A: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.73 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3331_mult__le__cancel__left__neg,axiom,
% 13.77/7.73 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.73 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3332_mult__le__cancel__left__neg,axiom,
% 13.77/7.73 ! [C2: int,A: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.73 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3333_mult__le__cancel__left__pos,axiom,
% 13.77/7.73 ! [C2: real,A: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.73 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3334_mult__le__cancel__left__pos,axiom,
% 13.77/7.73 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.73 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3335_mult__le__cancel__left__pos,axiom,
% 13.77/7.73 ! [C2: int,A: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.73 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3336_mult__left__le__imp__le,axiom,
% 13.77/7.73 ! [C2: real,A: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 13.77/7.73 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3337_mult__left__le__imp__le,axiom,
% 13.77/7.73 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.73 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3338_mult__left__le__imp__le,axiom,
% 13.77/7.73 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.73 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3339_mult__left__le__imp__le,axiom,
% 13.77/7.73 ! [C2: int,A: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 13.77/7.73 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3340_mult__right__le__imp__le,axiom,
% 13.77/7.73 ! [A: real,C2: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3341_mult__right__le__imp__le,axiom,
% 13.77/7.73 ! [A: rat,C2: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3342_mult__right__le__imp__le,axiom,
% 13.77/7.73 ! [A: nat,C2: nat,B: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.73 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3343_mult__right__le__imp__le,axiom,
% 13.77/7.73 ! [A: int,C2: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 13.77/7.73 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3344_mult__le__less__imp__less,axiom,
% 13.77/7.73 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.73 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3345_mult__le__less__imp__less,axiom,
% 13.77/7.73 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.73 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3346_mult__le__less__imp__less,axiom,
% 13.77/7.73 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.73 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 13.77/7.73 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3347_mult__le__less__imp__less,axiom,
% 13.77/7.73 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.73 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3348_mult__less__le__imp__less,axiom,
% 13.77/7.73 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.73 ( ( ord_less_real @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_real @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3349_mult__less__le__imp__less,axiom,
% 13.77/7.73 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.73 ( ( ord_less_rat @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_rat @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3350_mult__less__le__imp__less,axiom,
% 13.77/7.73 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.73 ( ( ord_less_nat @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_nat @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.73 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3351_mult__less__le__imp__less,axiom,
% 13.77/7.73 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.73 ( ( ord_less_int @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_int @ C2 @ D )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3352_sum__squares__ge__zero,axiom,
% 13.77/7.73 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3353_sum__squares__ge__zero,axiom,
% 13.77/7.73 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3354_sum__squares__ge__zero,axiom,
% 13.77/7.73 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3355_mult__left__le,axiom,
% 13.77/7.73 ! [C2: real,A: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ C2 @ one_one_real )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3356_mult__left__le,axiom,
% 13.77/7.73 ! [C2: rat,A: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ C2 @ one_one_rat )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3357_mult__left__le,axiom,
% 13.77/7.73 ! [C2: nat,A: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ C2 @ one_one_nat )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3358_mult__left__le,axiom,
% 13.77/7.73 ! [C2: int,A: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ C2 @ one_one_int )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3359_mult__le__one,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ A @ one_one_real )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.73 => ( ( ord_less_eq_real @ B @ one_one_real )
% 13.77/7.73 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3360_mult__le__one,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.73 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3361_mult__le__one,axiom,
% 13.77/7.73 ! [A: nat,B: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.73 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 13.77/7.73 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3362_mult__le__one,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ A @ one_one_int )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.73 => ( ( ord_less_eq_int @ B @ one_one_int )
% 13.77/7.73 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3363_mult__right__le__one__le,axiom,
% 13.77/7.73 ! [X: real,Y: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.73 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.73 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3364_mult__right__le__one__le,axiom,
% 13.77/7.73 ! [X: rat,Y: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 13.77/7.73 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3365_mult__right__le__one__le,axiom,
% 13.77/7.73 ! [X: int,Y: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.73 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 13.77/7.73 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3366_mult__left__le__one__le,axiom,
% 13.77/7.73 ! [X: real,Y: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.73 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.73 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3367_mult__left__le__one__le,axiom,
% 13.77/7.73 ! [X: rat,Y: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 13.77/7.73 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3368_mult__left__le__one__le,axiom,
% 13.77/7.73 ! [X: int,Y: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.73 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 13.77/7.73 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3369_not__sum__squares__lt__zero,axiom,
% 13.77/7.73 ! [X: real,Y: real] :
% 13.77/7.73 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3370_not__sum__squares__lt__zero,axiom,
% 13.77/7.73 ! [X: rat,Y: rat] :
% 13.77/7.73 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3371_not__sum__squares__lt__zero,axiom,
% 13.77/7.73 ! [X: int,Y: int] :
% 13.77/7.73 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3372_ordered__ring__class_Ole__add__iff1,axiom,
% 13.77/7.73 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3373_ordered__ring__class_Ole__add__iff1,axiom,
% 13.77/7.73 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3374_ordered__ring__class_Ole__add__iff1,axiom,
% 13.77/7.73 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3375_ordered__ring__class_Ole__add__iff2,axiom,
% 13.77/7.73 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_eq_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3376_ordered__ring__class_Ole__add__iff2,axiom,
% 13.77/7.73 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_eq_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3377_ordered__ring__class_Ole__add__iff2,axiom,
% 13.77/7.73 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_eq_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3378_less__add__iff2,axiom,
% 13.77/7.73 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 13.77/7.73 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3379_less__add__iff2,axiom,
% 13.77/7.73 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3380_less__add__iff2,axiom,
% 13.77/7.73 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 13.77/7.73 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3381_less__add__iff1,axiom,
% 13.77/7.73 ! [A: real,E2: real,C2: real,B: real,D: real] :
% 13.77/7.73 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3382_less__add__iff1,axiom,
% 13.77/7.73 ! [A: rat,E2: rat,C2: rat,B: rat,D: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3383_less__add__iff1,axiom,
% 13.77/7.73 ! [A: int,E2: int,C2: int,B: int,D: int] :
% 13.77/7.73 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 13.77/7.73 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C2 ) @ D ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3384_one__less__mult,axiom,
% 13.77/7.73 ! [N: nat,M: nat] :
% 13.77/7.73 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.73 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 13.77/7.73 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3385_n__less__m__mult__n,axiom,
% 13.77/7.73 ! [N: nat,M: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 13.77/7.73 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3386_n__less__n__mult__m,axiom,
% 13.77/7.73 ! [N: nat,M: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 13.77/7.73 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3387_linordered__field__no__ub,axiom,
% 13.77/7.73 ! [X5: real] :
% 13.77/7.73 ? [X_1: real] : ( ord_less_real @ X5 @ X_1 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3388_linordered__field__no__ub,axiom,
% 13.77/7.73 ! [X5: rat] :
% 13.77/7.73 ? [X_1: rat] : ( ord_less_rat @ X5 @ X_1 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3389_linordered__field__no__lb,axiom,
% 13.77/7.73 ! [X5: real] :
% 13.77/7.73 ? [Y3: real] : ( ord_less_real @ Y3 @ X5 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3390_linordered__field__no__lb,axiom,
% 13.77/7.73 ! [X5: rat] :
% 13.77/7.73 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X5 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3391_mult__le__cancel__left1,axiom,
% 13.77/7.73 ! [C2: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_eq_real @ one_one_real @ B ) )
% 13.77/7.73 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3392_mult__le__cancel__left1,axiom,
% 13.77/7.73 ! [C2: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 13.77/7.73 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3393_mult__le__cancel__left1,axiom,
% 13.77/7.73 ! [C2: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_eq_int @ one_one_int @ B ) )
% 13.77/7.73 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3394_mult__le__cancel__left2,axiom,
% 13.77/7.73 ! [C2: real,A: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_eq_real @ A @ one_one_real ) )
% 13.77/7.73 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3395_mult__le__cancel__left2,axiom,
% 13.77/7.73 ! [C2: rat,A: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 13.77/7.73 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3396_mult__le__cancel__left2,axiom,
% 13.77/7.73 ! [C2: int,A: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_eq_int @ A @ one_one_int ) )
% 13.77/7.73 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3397_mult__le__cancel__right1,axiom,
% 13.77/7.73 ! [C2: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_eq_real @ one_one_real @ B ) )
% 13.77/7.73 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3398_mult__le__cancel__right1,axiom,
% 13.77/7.73 ! [C2: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 13.77/7.73 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3399_mult__le__cancel__right1,axiom,
% 13.77/7.73 ! [C2: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_eq_int @ one_one_int @ B ) )
% 13.77/7.73 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3400_mult__le__cancel__right2,axiom,
% 13.77/7.73 ! [A: real,C2: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_eq_real @ A @ one_one_real ) )
% 13.77/7.73 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3401_mult__le__cancel__right2,axiom,
% 13.77/7.73 ! [A: rat,C2: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 13.77/7.73 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3402_mult__le__cancel__right2,axiom,
% 13.77/7.73 ! [A: int,C2: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_eq_int @ A @ one_one_int ) )
% 13.77/7.73 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3403_mult__less__cancel__left1,axiom,
% 13.77/7.73 ! [C2: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ one_one_real @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3404_mult__less__cancel__left1,axiom,
% 13.77/7.73 ! [C2: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ one_one_rat @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3405_mult__less__cancel__left1,axiom,
% 13.77/7.73 ! [C2: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 13.77/7.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ one_one_int @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3406_mult__less__cancel__left2,axiom,
% 13.77/7.73 ! [C2: real,A: real] :
% 13.77/7.73 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ A @ one_one_real ) )
% 13.77/7.73 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3407_mult__less__cancel__left2,axiom,
% 13.77/7.73 ! [C2: rat,A: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ A @ one_one_rat ) )
% 13.77/7.73 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3408_mult__less__cancel__left2,axiom,
% 13.77/7.73 ! [C2: int,A: int] :
% 13.77/7.73 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ A @ one_one_int ) )
% 13.77/7.73 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3409_mult__less__cancel__right1,axiom,
% 13.77/7.73 ! [C2: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ one_one_real @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3410_mult__less__cancel__right1,axiom,
% 13.77/7.73 ! [C2: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ one_one_rat @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3411_mult__less__cancel__right1,axiom,
% 13.77/7.73 ! [C2: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 13.77/7.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ one_one_int @ B ) )
% 13.77/7.73 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3412_mult__less__cancel__right2,axiom,
% 13.77/7.73 ! [A: real,C2: real] :
% 13.77/7.73 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.73 => ( ord_less_real @ A @ one_one_real ) )
% 13.77/7.73 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 13.77/7.73 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3413_mult__less__cancel__right2,axiom,
% 13.77/7.73 ! [A: rat,C2: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 13.77/7.73 => ( ord_less_rat @ A @ one_one_rat ) )
% 13.77/7.73 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 13.77/7.73 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3414_mult__less__cancel__right2,axiom,
% 13.77/7.73 ! [A: int,C2: int] :
% 13.77/7.73 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 13.77/7.73 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.73 => ( ord_less_int @ A @ one_one_int ) )
% 13.77/7.73 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 13.77/7.73 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3415_convex__bound__le,axiom,
% 13.77/7.73 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ X @ A )
% 13.77/7.73 => ( ( ord_less_eq_real @ Y @ A )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 13.77/7.73 => ( ( ( plus_plus_real @ U @ V2 )
% 13.77/7.73 = one_one_real )
% 13.77/7.73 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3416_convex__bound__le,axiom,
% 13.77/7.73 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ X @ A )
% 13.77/7.73 => ( ( ord_less_eq_rat @ Y @ A )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 13.77/7.73 => ( ( ( plus_plus_rat @ U @ V2 )
% 13.77/7.73 = one_one_rat )
% 13.77/7.73 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3417_convex__bound__le,axiom,
% 13.77/7.73 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ X @ A )
% 13.77/7.73 => ( ( ord_less_eq_int @ Y @ A )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 13.77/7.73 => ( ( ( plus_plus_int @ U @ V2 )
% 13.77/7.73 = one_one_int )
% 13.77/7.73 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3418_mult__eq__if,axiom,
% 13.77/7.73 ( times_times_nat
% 13.77/7.73 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N6 @ ( times_times_nat @ ( minus_minus_nat @ M5 @ one_one_nat ) @ N6 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3419_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J,axiom,
% 13.77/7.73 ! [A: $o,B: $o] :
% 13.77/7.73 ( ( vEBT_T_m_a_x_t @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.73 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3420_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J,axiom,
% 13.77/7.73 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 13.77/7.73 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 13.77/7.73 = one_one_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3421_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J,axiom,
% 13.77/7.73 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 13.77/7.73 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 13.77/7.73 = one_one_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3422_convex__bound__lt,axiom,
% 13.77/7.73 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 13.77/7.73 ( ( ord_less_real @ X @ A )
% 13.77/7.73 => ( ( ord_less_real @ Y @ A )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 13.77/7.73 => ( ( ( plus_plus_real @ U @ V2 )
% 13.77/7.73 = one_one_real )
% 13.77/7.73 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3423_convex__bound__lt,axiom,
% 13.77/7.73 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 13.77/7.73 ( ( ord_less_rat @ X @ A )
% 13.77/7.73 => ( ( ord_less_rat @ Y @ A )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 13.77/7.73 => ( ( ( plus_plus_rat @ U @ V2 )
% 13.77/7.73 = one_one_rat )
% 13.77/7.73 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3424_convex__bound__lt,axiom,
% 13.77/7.73 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 13.77/7.73 ( ( ord_less_int @ X @ A )
% 13.77/7.73 => ( ( ord_less_int @ Y @ A )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 13.77/7.73 => ( ( ( plus_plus_int @ U @ V2 )
% 13.77/7.73 = one_one_int )
% 13.77/7.73 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3425_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J,axiom,
% 13.77/7.73 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 13.77/7.73 ( ( vEBT_T_m_a_x_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 13.77/7.73 = one_one_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3426_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J,axiom,
% 13.77/7.73 ! [A: $o,B: $o] :
% 13.77/7.73 ( ( vEBT_T_m_i_n_t @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.73 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ A @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3427_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J,axiom,
% 13.77/7.73 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 13.77/7.73 ( ( vEBT_T_m_i_n_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 13.77/7.73 = one_one_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3428_nat__mult__le__cancel__disj,axiom,
% 13.77/7.73 ! [K: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.73 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.73 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3429_nat__mult__less__cancel__disj,axiom,
% 13.77/7.73 ! [K: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.73 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.73 & ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3430_sum__squares__eq__zero__iff,axiom,
% 13.77/7.73 ! [X: rat,Y: rat] :
% 13.77/7.73 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 13.77/7.73 = zero_zero_rat )
% 13.77/7.73 = ( ( X = zero_zero_rat )
% 13.77/7.73 & ( Y = zero_zero_rat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3431_sum__squares__eq__zero__iff,axiom,
% 13.77/7.73 ! [X: real,Y: real] :
% 13.77/7.73 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 13.77/7.73 = zero_zero_real )
% 13.77/7.73 = ( ( X = zero_zero_real )
% 13.77/7.73 & ( Y = zero_zero_real ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3432_sum__squares__eq__zero__iff,axiom,
% 13.77/7.73 ! [X: int,Y: int] :
% 13.77/7.73 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 13.77/7.73 = zero_zero_int )
% 13.77/7.73 = ( ( X = zero_zero_int )
% 13.77/7.73 & ( Y = zero_zero_int ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3433_nat__less__add__iff2,axiom,
% 13.77/7.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.73 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3434_nat__less__add__iff1,axiom,
% 13.77/7.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ J @ I )
% 13.77/7.73 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3435_nat__diff__add__eq2,axiom,
% 13.77/7.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3436_nat__diff__add__eq1,axiom,
% 13.77/7.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ J @ I )
% 13.77/7.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3437_nat__le__add__iff2,axiom,
% 13.77/7.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3438_nat__le__add__iff1,axiom,
% 13.77/7.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ J @ I )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3439_star__false__left,axiom,
% 13.77/7.73 ! [P2: assn] :
% 13.77/7.73 ( ( times_times_assn @ bot_bot_assn @ P2 )
% 13.77/7.73 = bot_bot_assn ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3440_star__false__right,axiom,
% 13.77/7.73 ! [P2: assn] :
% 13.77/7.73 ( ( times_times_assn @ P2 @ bot_bot_assn )
% 13.77/7.73 = bot_bot_assn ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3441_snga__same__false,axiom,
% 13.77/7.73 ! [P3: array_VEBT_VEBTi,X: list_VEBT_VEBTi,Y: list_VEBT_VEBTi] :
% 13.77/7.73 ( ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ P3 @ X ) @ ( snga_assn_VEBT_VEBTi @ P3 @ Y ) )
% 13.77/7.73 = bot_bot_assn ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3442_mod__h__bot__iff_I5_J,axiom,
% 13.77/7.73 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 13.77/7.73 ( ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.77/7.73 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.77/7.73 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3443_mod__starE,axiom,
% 13.77/7.73 ! [A: assn,B: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.73 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H2 )
% 13.77/7.73 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 13.77/7.73 => ! [H_2: produc3658429121746597890et_nat] :
% 13.77/7.73 ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3444_mod__starD,axiom,
% 13.77/7.73 ! [A4: assn,B4: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.73 ( ( rep_assn @ ( times_times_assn @ A4 @ B4 ) @ H2 )
% 13.77/7.73 => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 13.77/7.73 ( ( rep_assn @ A4 @ H1 )
% 13.77/7.73 & ( rep_assn @ B4 @ H22 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3445_assn__one__left,axiom,
% 13.77/7.73 ! [P2: assn] :
% 13.77/7.73 ( ( times_times_assn @ one_one_assn @ P2 )
% 13.77/7.73 = P2 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3446_nat__mult__eq__cancel__disj,axiom,
% 13.77/7.73 ! [K: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ( times_times_nat @ K @ M )
% 13.77/7.73 = ( times_times_nat @ K @ N ) )
% 13.77/7.73 = ( ( K = zero_zero_nat )
% 13.77/7.73 | ( M = N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3447_nat__mult__less__cancel1,axiom,
% 13.77/7.73 ! [K: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.73 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.73 = ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3448_nat__mult__eq__cancel1,axiom,
% 13.77/7.73 ! [K: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.73 => ( ( ( times_times_nat @ K @ M )
% 13.77/7.73 = ( times_times_nat @ K @ N ) )
% 13.77/7.73 = ( M = N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3449_sum__squares__le__zero__iff,axiom,
% 13.77/7.73 ! [X: real,Y: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 13.77/7.73 = ( ( X = zero_zero_real )
% 13.77/7.73 & ( Y = zero_zero_real ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3450_sum__squares__le__zero__iff,axiom,
% 13.77/7.73 ! [X: rat,Y: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 13.77/7.73 = ( ( X = zero_zero_rat )
% 13.77/7.73 & ( Y = zero_zero_rat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3451_sum__squares__le__zero__iff,axiom,
% 13.77/7.73 ! [X: int,Y: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 13.77/7.73 = ( ( X = zero_zero_int )
% 13.77/7.73 & ( Y = zero_zero_int ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3452_sum__squares__gt__zero__iff,axiom,
% 13.77/7.73 ! [X: real,Y: real] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 13.77/7.73 = ( ( X != zero_zero_real )
% 13.77/7.73 | ( Y != zero_zero_real ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3453_sum__squares__gt__zero__iff,axiom,
% 13.77/7.73 ! [X: rat,Y: rat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 13.77/7.73 = ( ( X != zero_zero_rat )
% 13.77/7.73 | ( Y != zero_zero_rat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3454_sum__squares__gt__zero__iff,axiom,
% 13.77/7.73 ! [X: int,Y: int] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 13.77/7.73 = ( ( X != zero_zero_int )
% 13.77/7.73 | ( Y != zero_zero_int ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3455_nat__mult__le__cancel1,axiom,
% 13.77/7.73 ! [K: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3456_nat__eq__add__iff1,axiom,
% 13.77/7.73 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ J @ I )
% 13.77/7.73 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 13.77/7.73 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 13.77/7.73 = N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3457_nat__eq__add__iff2,axiom,
% 13.77/7.73 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.73 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 13.77/7.73 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 13.77/7.73 = ( M
% 13.77/7.73 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3458_mult__le__cancel__iff2,axiom,
% 13.77/7.73 ! [Z: real,X: real,Y: real] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ Z )
% 13.77/7.73 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 13.77/7.73 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3459_mult__le__cancel__iff2,axiom,
% 13.77/7.73 ! [Z: rat,X: rat,Y: rat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 13.77/7.73 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 13.77/7.73 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3460_mult__le__cancel__iff2,axiom,
% 13.77/7.73 ! [Z: int,X: int,Y: int] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ Z )
% 13.77/7.73 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 13.77/7.73 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3461_mult__le__cancel__iff1,axiom,
% 13.77/7.73 ! [Z: real,X: real,Y: real] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ Z )
% 13.77/7.73 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 13.77/7.73 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3462_mult__le__cancel__iff1,axiom,
% 13.77/7.73 ! [Z: rat,X: rat,Y: rat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 13.77/7.73 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 13.77/7.73 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3463_mult__le__cancel__iff1,axiom,
% 13.77/7.73 ! [Z: int,X: int,Y: int] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ Z )
% 13.77/7.73 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 13.77/7.73 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3464_add__scale__eq__noteq,axiom,
% 13.77/7.73 ! [R: rat,A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.73 ( ( R != zero_zero_rat )
% 13.77/7.73 => ( ( ( A = B )
% 13.77/7.73 & ( C2 != D ) )
% 13.77/7.73 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C2 ) )
% 13.77/7.73 != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3465_add__scale__eq__noteq,axiom,
% 13.77/7.73 ! [R: real,A: real,B: real,C2: real,D: real] :
% 13.77/7.73 ( ( R != zero_zero_real )
% 13.77/7.73 => ( ( ( A = B )
% 13.77/7.73 & ( C2 != D ) )
% 13.77/7.73 => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C2 ) )
% 13.77/7.73 != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3466_add__scale__eq__noteq,axiom,
% 13.77/7.73 ! [R: nat,A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.73 ( ( R != zero_zero_nat )
% 13.77/7.73 => ( ( ( A = B )
% 13.77/7.73 & ( C2 != D ) )
% 13.77/7.73 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C2 ) )
% 13.77/7.73 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3467_add__scale__eq__noteq,axiom,
% 13.77/7.73 ! [R: int,A: int,B: int,C2: int,D: int] :
% 13.77/7.73 ( ( R != zero_zero_int )
% 13.77/7.73 => ( ( ( A = B )
% 13.77/7.73 & ( C2 != D ) )
% 13.77/7.73 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C2 ) )
% 13.77/7.73 != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3468_mult__less__iff1,axiom,
% 13.77/7.73 ! [Z: real,X: real,Y: real] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ Z )
% 13.77/7.73 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 13.77/7.73 = ( ord_less_real @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3469_mult__less__iff1,axiom,
% 13.77/7.73 ! [Z: rat,X: rat,Y: rat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 13.77/7.73 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 13.77/7.73 = ( ord_less_rat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3470_mult__less__iff1,axiom,
% 13.77/7.73 ! [Z: int,X: int,Y: int] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ Z )
% 13.77/7.73 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 13.77/7.73 = ( ord_less_int @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3471_add__0__iff,axiom,
% 13.77/7.73 ! [B: real,A: real] :
% 13.77/7.73 ( ( B
% 13.77/7.73 = ( plus_plus_real @ B @ A ) )
% 13.77/7.73 = ( A = zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3472_add__0__iff,axiom,
% 13.77/7.73 ! [B: rat,A: rat] :
% 13.77/7.73 ( ( B
% 13.77/7.73 = ( plus_plus_rat @ B @ A ) )
% 13.77/7.73 = ( A = zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3473_add__0__iff,axiom,
% 13.77/7.73 ! [B: nat,A: nat] :
% 13.77/7.73 ( ( B
% 13.77/7.73 = ( plus_plus_nat @ B @ A ) )
% 13.77/7.73 = ( A = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3474_add__0__iff,axiom,
% 13.77/7.73 ! [B: int,A: int] :
% 13.77/7.73 ( ( B
% 13.77/7.73 = ( plus_plus_int @ B @ A ) )
% 13.77/7.73 = ( A = zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3475_mul__shift,axiom,
% 13.77/7.73 ! [X: nat,Y: nat,Z: nat] :
% 13.77/7.73 ( ( ( times_times_nat @ X @ Y )
% 13.77/7.73 = Z )
% 13.77/7.73 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 13.77/7.73 = ( some_nat @ Z ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3476_minus__Max__eq__Min,axiom,
% 13.77/7.73 ! [S3: set_Code_integer] :
% 13.77/7.73 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.73 => ( ( uminus1351360451143612070nteger @ ( lattic4901227151466704046nteger @ S3 ) )
% 13.77/7.73 = ( lattic1063845414844153500nteger @ ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3477_minus__Max__eq__Min,axiom,
% 13.77/7.73 ! [S3: set_real] :
% 13.77/7.73 ( ( finite_finite_real @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bot_set_real )
% 13.77/7.73 => ( ( uminus_uminus_real @ ( lattic4275903605611617917x_real @ S3 ) )
% 13.77/7.73 = ( lattic3629708407755379051n_real @ ( image_real_real @ uminus_uminus_real @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3478_minus__Max__eq__Min,axiom,
% 13.77/7.73 ! [S3: set_rat] :
% 13.77/7.73 ( ( finite_finite_rat @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bot_set_rat )
% 13.77/7.73 => ( ( uminus_uminus_rat @ ( lattic7630753665789217321ax_rat @ S3 ) )
% 13.77/7.73 = ( lattic8086005427650270231in_rat @ ( image_rat_rat @ uminus_uminus_rat @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3479_minus__Max__eq__Min,axiom,
% 13.77/7.73 ! [S3: set_int] :
% 13.77/7.73 ( ( finite_finite_int @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bot_set_int )
% 13.77/7.73 => ( ( uminus_uminus_int @ ( lattic8263393255366662781ax_int @ S3 ) )
% 13.77/7.73 = ( lattic8718645017227715691in_int @ ( image_int_int @ uminus_uminus_int @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3480_minus__Min__eq__Max,axiom,
% 13.77/7.73 ! [S3: set_Code_integer] :
% 13.77/7.73 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.73 => ( ( uminus1351360451143612070nteger @ ( lattic1063845414844153500nteger @ S3 ) )
% 13.77/7.73 = ( lattic4901227151466704046nteger @ ( image_4470545334726330049nteger @ uminus1351360451143612070nteger @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3481_minus__Min__eq__Max,axiom,
% 13.77/7.73 ! [S3: set_real] :
% 13.77/7.73 ( ( finite_finite_real @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bot_set_real )
% 13.77/7.73 => ( ( uminus_uminus_real @ ( lattic3629708407755379051n_real @ S3 ) )
% 13.77/7.73 = ( lattic4275903605611617917x_real @ ( image_real_real @ uminus_uminus_real @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3482_minus__Min__eq__Max,axiom,
% 13.77/7.73 ! [S3: set_rat] :
% 13.77/7.73 ( ( finite_finite_rat @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bot_set_rat )
% 13.77/7.73 => ( ( uminus_uminus_rat @ ( lattic8086005427650270231in_rat @ S3 ) )
% 13.77/7.73 = ( lattic7630753665789217321ax_rat @ ( image_rat_rat @ uminus_uminus_rat @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3483_minus__Min__eq__Max,axiom,
% 13.77/7.73 ! [S3: set_int] :
% 13.77/7.73 ( ( finite_finite_int @ S3 )
% 13.77/7.73 => ( ( S3 != bot_bot_set_int )
% 13.77/7.73 => ( ( uminus_uminus_int @ ( lattic8718645017227715691in_int @ S3 ) )
% 13.77/7.73 = ( lattic8263393255366662781ax_int @ ( image_int_int @ uminus_uminus_int @ S3 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3484_add__shift,axiom,
% 13.77/7.73 ! [X: nat,Y: nat,Z: nat] :
% 13.77/7.73 ( ( ( plus_plus_nat @ X @ Y )
% 13.77/7.73 = Z )
% 13.77/7.73 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 13.77/7.73 = ( some_nat @ Z ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3485_add_Oinverse__inverse,axiom,
% 13.77/7.73 ! [A: uint32] :
% 13.77/7.73 ( ( uminus_uminus_uint32 @ ( uminus_uminus_uint32 @ A ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3486_add_Oinverse__inverse,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3487_add_Oinverse__inverse,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3488_add_Oinverse__inverse,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3489_neg__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( ( uminus_uminus_uint32 @ A )
% 13.77/7.73 = ( uminus_uminus_uint32 @ B ) )
% 13.77/7.73 = ( A = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3490_neg__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ( uminus_uminus_real @ A )
% 13.77/7.73 = ( uminus_uminus_real @ B ) )
% 13.77/7.73 = ( A = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3491_neg__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ( uminus_uminus_rat @ A )
% 13.77/7.73 = ( uminus_uminus_rat @ B ) )
% 13.77/7.73 = ( A = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3492_neg__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ( uminus_uminus_int @ A )
% 13.77/7.73 = ( uminus_uminus_int @ B ) )
% 13.77/7.73 = ( A = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3493_Compl__subset__Compl__iff,axiom,
% 13.77/7.73 ! [A4: set_int,B4: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A4 ) @ ( uminus1532241313380277803et_int @ B4 ) )
% 13.77/7.73 = ( ord_less_eq_set_int @ B4 @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3494_Compl__anti__mono,axiom,
% 13.77/7.73 ! [A4: set_int,B4: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.73 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B4 ) @ ( uminus1532241313380277803et_int @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3495_neg__equal__zero,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ( uminus_uminus_real @ A )
% 13.77/7.73 = A )
% 13.77/7.73 = ( A = zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3496_neg__equal__zero,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ( uminus_uminus_rat @ A )
% 13.77/7.73 = A )
% 13.77/7.73 = ( A = zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3497_neg__equal__zero,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ( uminus_uminus_int @ A )
% 13.77/7.73 = A )
% 13.77/7.73 = ( A = zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3498_equal__neg__zero,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( A = zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3499_equal__neg__zero,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( A = zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3500_equal__neg__zero,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( A = zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3501_neg__equal__0__iff__equal,axiom,
% 13.77/7.73 ! [A: uint32] :
% 13.77/7.73 ( ( ( uminus_uminus_uint32 @ A )
% 13.77/7.73 = zero_zero_uint32 )
% 13.77/7.73 = ( A = zero_zero_uint32 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3502_neg__equal__0__iff__equal,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ( uminus_uminus_real @ A )
% 13.77/7.73 = zero_zero_real )
% 13.77/7.73 = ( A = zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3503_neg__equal__0__iff__equal,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ( uminus_uminus_rat @ A )
% 13.77/7.73 = zero_zero_rat )
% 13.77/7.73 = ( A = zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3504_neg__equal__0__iff__equal,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ( uminus_uminus_int @ A )
% 13.77/7.73 = zero_zero_int )
% 13.77/7.73 = ( A = zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3505_neg__0__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: uint32] :
% 13.77/7.73 ( ( zero_zero_uint32
% 13.77/7.73 = ( uminus_uminus_uint32 @ A ) )
% 13.77/7.73 = ( zero_zero_uint32 = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3506_neg__0__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( zero_zero_real
% 13.77/7.73 = ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( zero_zero_real = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3507_neg__0__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( zero_zero_rat
% 13.77/7.73 = ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( zero_zero_rat = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3508_neg__0__equal__iff__equal,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( zero_zero_int
% 13.77/7.73 = ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( zero_zero_int = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3509_add_Oinverse__neutral,axiom,
% 13.77/7.73 ( ( uminus_uminus_uint32 @ zero_zero_uint32 )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3510_add_Oinverse__neutral,axiom,
% 13.77/7.73 ( ( uminus_uminus_real @ zero_zero_real )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3511_add_Oinverse__neutral,axiom,
% 13.77/7.73 ( ( uminus_uminus_rat @ zero_zero_rat )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3512_add_Oinverse__neutral,axiom,
% 13.77/7.73 ( ( uminus_uminus_int @ zero_zero_int )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3513_neg__le__iff__le,axiom,
% 13.77/7.73 ! [B: real,A: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( ord_less_eq_real @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3514_neg__le__iff__le,axiom,
% 13.77/7.73 ! [B: rat,A: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( ord_less_eq_rat @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3515_neg__le__iff__le,axiom,
% 13.77/7.73 ! [B: int,A: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( ord_less_eq_int @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3516_compl__le__compl__iff,axiom,
% 13.77/7.73 ! [X: assn,Y: assn] :
% 13.77/7.73 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 13.77/7.73 = ( ord_less_eq_assn @ Y @ X ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3517_compl__le__compl__iff,axiom,
% 13.77/7.73 ! [X: set_int,Y: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 13.77/7.73 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3518_neg__less__iff__less,axiom,
% 13.77/7.73 ! [B: real,A: real] :
% 13.77/7.73 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( ord_less_real @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3519_neg__less__iff__less,axiom,
% 13.77/7.73 ! [B: rat,A: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( ord_less_rat @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3520_neg__less__iff__less,axiom,
% 13.77/7.73 ! [B: int,A: int] :
% 13.77/7.73 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( ord_less_int @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3521_compl__less__compl__iff,axiom,
% 13.77/7.73 ! [X: assn,Y: assn] :
% 13.77/7.73 ( ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 13.77/7.73 = ( ord_less_assn @ Y @ X ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3522_add__minus__cancel,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( plus_plus_uint32 @ A @ ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3523_add__minus__cancel,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3524_add__minus__cancel,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3525_add__minus__cancel,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3526_minus__add__cancel,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ ( plus_plus_uint32 @ A @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3527_minus__add__cancel,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3528_minus__add__cancel,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3529_minus__add__cancel,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 13.77/7.73 = B ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3530_minus__add__distrib,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( uminus_uminus_uint32 @ ( plus_plus_uint32 @ A @ B ) )
% 13.77/7.73 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ ( uminus_uminus_uint32 @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3531_minus__add__distrib,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 13.77/7.73 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3532_minus__add__distrib,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 13.77/7.73 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3533_minus__add__distrib,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 13.77/7.73 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3534_minus__diff__eq,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( uminus_uminus_uint32 @ ( minus_minus_uint32 @ A @ B ) )
% 13.77/7.73 = ( minus_minus_uint32 @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3535_minus__diff__eq,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 13.77/7.73 = ( minus_minus_real @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3536_minus__diff__eq,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 13.77/7.73 = ( minus_minus_rat @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3537_minus__diff__eq,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 13.77/7.73 = ( minus_minus_int @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3538_neg__0__le__iff__le,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3539_neg__0__le__iff__le,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3540_neg__0__le__iff__le,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3541_neg__le__0__iff__le,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 13.77/7.73 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3542_neg__le__0__iff__le,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 13.77/7.73 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3543_neg__le__0__iff__le,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 13.77/7.73 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3544_less__eq__neg__nonpos,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3545_less__eq__neg__nonpos,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3546_less__eq__neg__nonpos,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3547_neg__less__eq__nonneg,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 13.77/7.73 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3548_neg__less__eq__nonneg,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 13.77/7.73 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3549_neg__less__eq__nonneg,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 13.77/7.73 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3550_less__neg__neg,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3551_less__neg__neg,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3552_less__neg__neg,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3553_neg__less__pos,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 13.77/7.73 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3554_neg__less__pos,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 13.77/7.73 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3555_neg__less__pos,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 13.77/7.73 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3556_neg__0__less__iff__less,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3557_neg__0__less__iff__less,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3558_neg__0__less__iff__less,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3559_neg__less__0__iff__less,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 13.77/7.73 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3560_neg__less__0__iff__less,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 13.77/7.73 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3561_neg__less__0__iff__less,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 13.77/7.73 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3562_ab__left__minus,axiom,
% 13.77/7.73 ! [A: uint32] :
% 13.77/7.73 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ A )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3563_ab__left__minus,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3564_ab__left__minus,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3565_ab__left__minus,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3566_add_Oright__inverse,axiom,
% 13.77/7.73 ! [A: uint32] :
% 13.77/7.73 ( ( plus_plus_uint32 @ A @ ( uminus_uminus_uint32 @ A ) )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3567_add_Oright__inverse,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3568_add_Oright__inverse,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3569_add_Oright__inverse,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3570_diff__0,axiom,
% 13.77/7.73 ! [A: uint32] :
% 13.77/7.73 ( ( minus_minus_uint32 @ zero_zero_uint32 @ A )
% 13.77/7.73 = ( uminus_uminus_uint32 @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3571_diff__0,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( minus_minus_real @ zero_zero_real @ A )
% 13.77/7.73 = ( uminus_uminus_real @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3572_diff__0,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 13.77/7.73 = ( uminus_uminus_rat @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3573_diff__0,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( minus_minus_int @ zero_zero_int @ A )
% 13.77/7.73 = ( uminus_uminus_int @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3574_verit__minus__simplify_I3_J,axiom,
% 13.77/7.73 ! [B: uint32] :
% 13.77/7.73 ( ( minus_minus_uint32 @ zero_zero_uint32 @ B )
% 13.77/7.73 = ( uminus_uminus_uint32 @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3575_verit__minus__simplify_I3_J,axiom,
% 13.77/7.73 ! [B: real] :
% 13.77/7.73 ( ( minus_minus_real @ zero_zero_real @ B )
% 13.77/7.73 = ( uminus_uminus_real @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3576_verit__minus__simplify_I3_J,axiom,
% 13.77/7.73 ! [B: rat] :
% 13.77/7.73 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 13.77/7.73 = ( uminus_uminus_rat @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3577_verit__minus__simplify_I3_J,axiom,
% 13.77/7.73 ! [B: int] :
% 13.77/7.73 ( ( minus_minus_int @ zero_zero_int @ B )
% 13.77/7.73 = ( uminus_uminus_int @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3578_uminus__add__conv__diff,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ B )
% 13.77/7.73 = ( minus_minus_uint32 @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3579_uminus__add__conv__diff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 13.77/7.73 = ( minus_minus_real @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3580_uminus__add__conv__diff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 13.77/7.73 = ( minus_minus_rat @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3581_uminus__add__conv__diff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 13.77/7.73 = ( minus_minus_int @ B @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3582_diff__minus__eq__add,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( minus_minus_uint32 @ A @ ( uminus_uminus_uint32 @ B ) )
% 13.77/7.73 = ( plus_plus_uint32 @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3583_diff__minus__eq__add,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 13.77/7.73 = ( plus_plus_real @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3584_diff__minus__eq__add,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 13.77/7.73 = ( plus_plus_rat @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3585_diff__minus__eq__add,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 13.77/7.73 = ( plus_plus_int @ A @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3586_subset__Compl__singleton,axiom,
% 13.77/7.73 ! [A4: set_VEBT_VEBT,B: vEBT_VEBT] :
% 13.77/7.73 ( ( ord_le4337996190870823476T_VEBT @ A4 @ ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ B @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.73 = ( ~ ( member_VEBT_VEBT @ B @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3587_subset__Compl__singleton,axiom,
% 13.77/7.73 ! [A4: set_real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_set_real @ A4 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 13.77/7.73 = ( ~ ( member_real @ B @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3588_subset__Compl__singleton,axiom,
% 13.77/7.73 ! [A4: set_set_nat,B: set_nat] :
% 13.77/7.73 ( ( ord_le6893508408891458716et_nat @ A4 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 13.77/7.73 = ( ~ ( member_set_nat @ B @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3589_subset__Compl__singleton,axiom,
% 13.77/7.73 ! [A4: set_nat,B: nat] :
% 13.77/7.73 ( ( ord_less_eq_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 13.77/7.73 = ( ~ ( member_nat @ B @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3590_subset__Compl__singleton,axiom,
% 13.77/7.73 ! [A4: set_o,B: $o] :
% 13.77/7.73 ( ( ord_less_eq_set_o @ A4 @ ( uminus_uminus_set_o @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 13.77/7.73 = ( ~ ( member_o @ B @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3591_subset__Compl__singleton,axiom,
% 13.77/7.73 ! [A4: set_int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 13.77/7.73 = ( ~ ( member_int @ B @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3592_add__neg__numeral__special_I7_J,axiom,
% 13.77/7.73 ( ( plus_plus_uint32 @ one_one_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3593_add__neg__numeral__special_I7_J,axiom,
% 13.77/7.73 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3594_add__neg__numeral__special_I7_J,axiom,
% 13.77/7.73 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3595_add__neg__numeral__special_I7_J,axiom,
% 13.77/7.73 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3596_add__neg__numeral__special_I8_J,axiom,
% 13.77/7.73 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ one_one_uint32 )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3597_add__neg__numeral__special_I8_J,axiom,
% 13.77/7.73 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3598_add__neg__numeral__special_I8_J,axiom,
% 13.77/7.73 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3599_add__neg__numeral__special_I8_J,axiom,
% 13.77/7.73 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3600_diff__numeral__special_I12_J,axiom,
% 13.77/7.73 ( ( minus_minus_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ ( uminus_uminus_uint32 @ one_one_uint32 ) )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3601_diff__numeral__special_I12_J,axiom,
% 13.77/7.73 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3602_diff__numeral__special_I12_J,axiom,
% 13.77/7.73 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3603_diff__numeral__special_I12_J,axiom,
% 13.77/7.73 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3604_add__def,axiom,
% 13.77/7.73 ( vEBT_VEBT_add
% 13.77/7.73 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3605_mul__def,axiom,
% 13.77/7.73 ( vEBT_VEBT_mul
% 13.77/7.73 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3606_assn__times__comm,axiom,
% 13.77/7.73 ( times_times_assn
% 13.77/7.73 = ( ^ [P5: assn,Q6: assn] : ( times_times_assn @ Q6 @ P5 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3607_assn__times__assoc,axiom,
% 13.77/7.73 ! [P2: assn,Q2: assn,R2: assn] :
% 13.77/7.73 ( ( times_times_assn @ ( times_times_assn @ P2 @ Q2 ) @ R2 )
% 13.77/7.73 = ( times_times_assn @ P2 @ ( times_times_assn @ Q2 @ R2 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3608_equation__minus__iff,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_uint32 @ B ) )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_uint32 @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3609_equation__minus__iff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_real @ B ) )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_real @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3610_equation__minus__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_rat @ B ) )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_rat @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3611_equation__minus__iff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_int @ B ) )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_int @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3612_minus__equation__iff,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( ( uminus_uminus_uint32 @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( uminus_uminus_uint32 @ B )
% 13.77/7.73 = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3613_minus__equation__iff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ( uminus_uminus_real @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( uminus_uminus_real @ B )
% 13.77/7.73 = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3614_minus__equation__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ( uminus_uminus_rat @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( uminus_uminus_rat @ B )
% 13.77/7.73 = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3615_minus__equation__iff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ( uminus_uminus_int @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( uminus_uminus_int @ B )
% 13.77/7.73 = A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3616_le__minus__iff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 13.77/7.73 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3617_le__minus__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 13.77/7.73 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3618_le__minus__iff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 13.77/7.73 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3619_minus__le__iff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 13.77/7.73 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3620_minus__le__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 13.77/7.73 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3621_minus__le__iff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 13.77/7.73 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3622_le__imp__neg__le,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.73 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3623_le__imp__neg__le,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.73 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3624_le__imp__neg__le,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.73 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3625_compl__le__swap2,axiom,
% 13.77/7.73 ! [Y: assn,X: assn] :
% 13.77/7.73 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 13.77/7.73 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3626_compl__le__swap2,axiom,
% 13.77/7.73 ! [Y: set_int,X: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 13.77/7.73 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3627_compl__le__swap1,axiom,
% 13.77/7.73 ! [Y: assn,X: assn] :
% 13.77/7.73 ( ( ord_less_eq_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 13.77/7.73 => ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3628_compl__le__swap1,axiom,
% 13.77/7.73 ! [Y: set_int,X: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 13.77/7.73 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3629_compl__mono,axiom,
% 13.77/7.73 ! [X: assn,Y: assn] :
% 13.77/7.73 ( ( ord_less_eq_assn @ X @ Y )
% 13.77/7.73 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ ( uminus_uminus_assn @ X ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3630_compl__mono,axiom,
% 13.77/7.73 ! [X: set_int,Y: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ X @ Y )
% 13.77/7.73 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3631_minus__less__iff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 13.77/7.73 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3632_minus__less__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 13.77/7.73 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3633_minus__less__iff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 13.77/7.73 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3634_less__minus__iff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 13.77/7.73 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3635_less__minus__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 13.77/7.73 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3636_less__minus__iff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 13.77/7.73 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3637_verit__negate__coefficient_I2_J,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ord_less_real @ A @ B )
% 13.77/7.73 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3638_verit__negate__coefficient_I2_J,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ord_less_rat @ A @ B )
% 13.77/7.73 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3639_verit__negate__coefficient_I2_J,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ord_less_int @ A @ B )
% 13.77/7.73 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3640_compl__less__swap2,axiom,
% 13.77/7.73 ! [Y: assn,X: assn] :
% 13.77/7.73 ( ( ord_less_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 13.77/7.73 => ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3641_compl__less__swap1,axiom,
% 13.77/7.73 ! [Y: assn,X: assn] :
% 13.77/7.73 ( ( ord_less_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 13.77/7.73 => ( ord_less_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3642_group__cancel_Oneg1,axiom,
% 13.77/7.73 ! [A4: uint32,K: uint32,A: uint32] :
% 13.77/7.73 ( ( A4
% 13.77/7.73 = ( plus_plus_uint32 @ K @ A ) )
% 13.77/7.73 => ( ( uminus_uminus_uint32 @ A4 )
% 13.77/7.73 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ K ) @ ( uminus_uminus_uint32 @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3643_group__cancel_Oneg1,axiom,
% 13.77/7.73 ! [A4: real,K: real,A: real] :
% 13.77/7.73 ( ( A4
% 13.77/7.73 = ( plus_plus_real @ K @ A ) )
% 13.77/7.73 => ( ( uminus_uminus_real @ A4 )
% 13.77/7.73 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3644_group__cancel_Oneg1,axiom,
% 13.77/7.73 ! [A4: rat,K: rat,A: rat] :
% 13.77/7.73 ( ( A4
% 13.77/7.73 = ( plus_plus_rat @ K @ A ) )
% 13.77/7.73 => ( ( uminus_uminus_rat @ A4 )
% 13.77/7.73 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3645_group__cancel_Oneg1,axiom,
% 13.77/7.73 ! [A4: int,K: int,A: int] :
% 13.77/7.73 ( ( A4
% 13.77/7.73 = ( plus_plus_int @ K @ A ) )
% 13.77/7.73 => ( ( uminus_uminus_int @ A4 )
% 13.77/7.73 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3646_add_Oinverse__distrib__swap,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( uminus_uminus_uint32 @ ( plus_plus_uint32 @ A @ B ) )
% 13.77/7.73 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ B ) @ ( uminus_uminus_uint32 @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3647_add_Oinverse__distrib__swap,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 13.77/7.73 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3648_add_Oinverse__distrib__swap,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 13.77/7.73 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3649_add_Oinverse__distrib__swap,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 13.77/7.73 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3650_minus__diff__commute,axiom,
% 13.77/7.73 ! [B: uint32,A: uint32] :
% 13.77/7.73 ( ( minus_minus_uint32 @ ( uminus_uminus_uint32 @ B ) @ A )
% 13.77/7.73 = ( minus_minus_uint32 @ ( uminus_uminus_uint32 @ A ) @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3651_minus__diff__commute,axiom,
% 13.77/7.73 ! [B: real,A: real] :
% 13.77/7.73 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 13.77/7.73 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3652_minus__diff__commute,axiom,
% 13.77/7.73 ! [B: rat,A: rat] :
% 13.77/7.73 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 13.77/7.73 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3653_minus__diff__commute,axiom,
% 13.77/7.73 ! [B: int,A: int] :
% 13.77/7.73 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 13.77/7.73 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3654_neg__eq__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( ( uminus_uminus_uint32 @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( plus_plus_uint32 @ A @ B )
% 13.77/7.73 = zero_zero_uint32 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3655_neg__eq__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ( uminus_uminus_real @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( plus_plus_real @ A @ B )
% 13.77/7.73 = zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3656_neg__eq__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ( uminus_uminus_rat @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( plus_plus_rat @ A @ B )
% 13.77/7.73 = zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3657_neg__eq__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ( uminus_uminus_int @ A )
% 13.77/7.73 = B )
% 13.77/7.73 = ( ( plus_plus_int @ A @ B )
% 13.77/7.73 = zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3658_eq__neg__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_uint32 @ B ) )
% 13.77/7.73 = ( ( plus_plus_uint32 @ A @ B )
% 13.77/7.73 = zero_zero_uint32 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3659_eq__neg__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_real @ B ) )
% 13.77/7.73 = ( ( plus_plus_real @ A @ B )
% 13.77/7.73 = zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3660_eq__neg__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_rat @ B ) )
% 13.77/7.73 = ( ( plus_plus_rat @ A @ B )
% 13.77/7.73 = zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3661_eq__neg__iff__add__eq__0,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( A
% 13.77/7.73 = ( uminus_uminus_int @ B ) )
% 13.77/7.73 = ( ( plus_plus_int @ A @ B )
% 13.77/7.73 = zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3662_add_Oinverse__unique,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( ( plus_plus_uint32 @ A @ B )
% 13.77/7.73 = zero_zero_uint32 )
% 13.77/7.73 => ( ( uminus_uminus_uint32 @ A )
% 13.77/7.73 = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3663_add_Oinverse__unique,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ( plus_plus_real @ A @ B )
% 13.77/7.73 = zero_zero_real )
% 13.77/7.73 => ( ( uminus_uminus_real @ A )
% 13.77/7.73 = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3664_add_Oinverse__unique,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ( plus_plus_rat @ A @ B )
% 13.77/7.73 = zero_zero_rat )
% 13.77/7.73 => ( ( uminus_uminus_rat @ A )
% 13.77/7.73 = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3665_add_Oinverse__unique,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ( plus_plus_int @ A @ B )
% 13.77/7.73 = zero_zero_int )
% 13.77/7.73 => ( ( uminus_uminus_int @ A )
% 13.77/7.73 = B ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3666_ab__group__add__class_Oab__left__minus,axiom,
% 13.77/7.73 ! [A: uint32] :
% 13.77/7.73 ( ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ A ) @ A )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3667_ab__group__add__class_Oab__left__minus,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3668_ab__group__add__class_Oab__left__minus,axiom,
% 13.77/7.73 ! [A: rat] :
% 13.77/7.73 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3669_ab__group__add__class_Oab__left__minus,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3670_add__eq__0__iff,axiom,
% 13.77/7.73 ! [A: uint32,B: uint32] :
% 13.77/7.73 ( ( ( plus_plus_uint32 @ A @ B )
% 13.77/7.73 = zero_zero_uint32 )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_uint32 @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3671_add__eq__0__iff,axiom,
% 13.77/7.73 ! [A: real,B: real] :
% 13.77/7.73 ( ( ( plus_plus_real @ A @ B )
% 13.77/7.73 = zero_zero_real )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_real @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3672_add__eq__0__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat] :
% 13.77/7.73 ( ( ( plus_plus_rat @ A @ B )
% 13.77/7.73 = zero_zero_rat )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_rat @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3673_add__eq__0__iff,axiom,
% 13.77/7.73 ! [A: int,B: int] :
% 13.77/7.73 ( ( ( plus_plus_int @ A @ B )
% 13.77/7.73 = zero_zero_int )
% 13.77/7.73 = ( B
% 13.77/7.73 = ( uminus_uminus_int @ A ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3674_zero__neq__neg__one,axiom,
% 13.77/7.73 ( zero_zero_real
% 13.77/7.73 != ( uminus_uminus_real @ one_one_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3675_zero__neq__neg__one,axiom,
% 13.77/7.73 ( zero_zero_rat
% 13.77/7.73 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3676_zero__neq__neg__one,axiom,
% 13.77/7.73 ( zero_zero_int
% 13.77/7.73 != ( uminus_uminus_int @ one_one_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3677_le__minus__one__simps_I2_J,axiom,
% 13.77/7.73 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3678_le__minus__one__simps_I2_J,axiom,
% 13.77/7.73 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3679_le__minus__one__simps_I2_J,axiom,
% 13.77/7.73 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3680_le__minus__one__simps_I4_J,axiom,
% 13.77/7.73 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3681_le__minus__one__simps_I4_J,axiom,
% 13.77/7.73 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3682_le__minus__one__simps_I4_J,axiom,
% 13.77/7.73 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3683_less__minus__one__simps_I4_J,axiom,
% 13.77/7.73 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3684_less__minus__one__simps_I4_J,axiom,
% 13.77/7.73 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3685_less__minus__one__simps_I4_J,axiom,
% 13.77/7.73 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3686_less__minus__one__simps_I2_J,axiom,
% 13.77/7.73 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3687_less__minus__one__simps_I2_J,axiom,
% 13.77/7.73 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3688_less__minus__one__simps_I2_J,axiom,
% 13.77/7.73 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3689_group__cancel_Osub2,axiom,
% 13.77/7.73 ! [B4: uint32,K: uint32,B: uint32,A: uint32] :
% 13.77/7.73 ( ( B4
% 13.77/7.73 = ( plus_plus_uint32 @ K @ B ) )
% 13.77/7.73 => ( ( minus_minus_uint32 @ A @ B4 )
% 13.77/7.73 = ( plus_plus_uint32 @ ( uminus_uminus_uint32 @ K ) @ ( minus_minus_uint32 @ A @ B ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3690_group__cancel_Osub2,axiom,
% 13.77/7.73 ! [B4: real,K: real,B: real,A: real] :
% 13.77/7.73 ( ( B4
% 13.77/7.73 = ( plus_plus_real @ K @ B ) )
% 13.77/7.73 => ( ( minus_minus_real @ A @ B4 )
% 13.77/7.73 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3691_group__cancel_Osub2,axiom,
% 13.77/7.73 ! [B4: rat,K: rat,B: rat,A: rat] :
% 13.77/7.73 ( ( B4
% 13.77/7.73 = ( plus_plus_rat @ K @ B ) )
% 13.77/7.73 => ( ( minus_minus_rat @ A @ B4 )
% 13.77/7.73 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3692_group__cancel_Osub2,axiom,
% 13.77/7.73 ! [B4: int,K: int,B: int,A: int] :
% 13.77/7.73 ( ( B4
% 13.77/7.73 = ( plus_plus_int @ K @ B ) )
% 13.77/7.73 => ( ( minus_minus_int @ A @ B4 )
% 13.77/7.73 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3693_diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_uint32
% 13.77/7.73 = ( ^ [A7: uint32,B7: uint32] : ( plus_plus_uint32 @ A7 @ ( uminus_uminus_uint32 @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3694_diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_real
% 13.77/7.73 = ( ^ [A7: real,B7: real] : ( plus_plus_real @ A7 @ ( uminus_uminus_real @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3695_diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_rat
% 13.77/7.73 = ( ^ [A7: rat,B7: rat] : ( plus_plus_rat @ A7 @ ( uminus_uminus_rat @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3696_diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_int
% 13.77/7.73 = ( ^ [A7: int,B7: int] : ( plus_plus_int @ A7 @ ( uminus_uminus_int @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3697_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_uint32
% 13.77/7.73 = ( ^ [A7: uint32,B7: uint32] : ( plus_plus_uint32 @ A7 @ ( uminus_uminus_uint32 @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3698_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_real
% 13.77/7.73 = ( ^ [A7: real,B7: real] : ( plus_plus_real @ A7 @ ( uminus_uminus_real @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3699_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_rat
% 13.77/7.73 = ( ^ [A7: rat,B7: rat] : ( plus_plus_rat @ A7 @ ( uminus_uminus_rat @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3700_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 13.77/7.73 ( minus_minus_int
% 13.77/7.73 = ( ^ [A7: int,B7: int] : ( plus_plus_int @ A7 @ ( uminus_uminus_int @ B7 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3701_subset__Compl__self__eq,axiom,
% 13.77/7.73 ! [A4: set_nat] :
% 13.77/7.73 ( ( ord_less_eq_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 13.77/7.73 = ( A4 = bot_bot_set_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3702_subset__Compl__self__eq,axiom,
% 13.77/7.73 ! [A4: set_o] :
% 13.77/7.73 ( ( ord_less_eq_set_o @ A4 @ ( uminus_uminus_set_o @ A4 ) )
% 13.77/7.73 = ( A4 = bot_bot_set_o ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3703_subset__Compl__self__eq,axiom,
% 13.77/7.73 ! [A4: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ A4 @ ( uminus1532241313380277803et_int @ A4 ) )
% 13.77/7.73 = ( A4 = bot_bot_set_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3704_le__minus__one__simps_I1_J,axiom,
% 13.77/7.73 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3705_le__minus__one__simps_I1_J,axiom,
% 13.77/7.73 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3706_le__minus__one__simps_I1_J,axiom,
% 13.77/7.73 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3707_le__minus__one__simps_I3_J,axiom,
% 13.77/7.73 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3708_le__minus__one__simps_I3_J,axiom,
% 13.77/7.73 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3709_le__minus__one__simps_I3_J,axiom,
% 13.77/7.73 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3710_less__minus__one__simps_I3_J,axiom,
% 13.77/7.73 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3711_less__minus__one__simps_I3_J,axiom,
% 13.77/7.73 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3712_less__minus__one__simps_I3_J,axiom,
% 13.77/7.73 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3713_less__minus__one__simps_I1_J,axiom,
% 13.77/7.73 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3714_less__minus__one__simps_I1_J,axiom,
% 13.77/7.73 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3715_less__minus__one__simps_I1_J,axiom,
% 13.77/7.73 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3716_Compl__insert,axiom,
% 13.77/7.73 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.73 ( ( uminus8041839845116263051T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.73 = ( minus_5127226145743854075T_VEBT @ ( uminus8041839845116263051T_VEBT @ A4 ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3717_Compl__insert,axiom,
% 13.77/7.73 ! [X: int,A4: set_int] :
% 13.77/7.73 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.73 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A4 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3718_Compl__insert,axiom,
% 13.77/7.73 ! [X: $o,A4: set_o] :
% 13.77/7.73 ( ( uminus_uminus_set_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.73 = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A4 ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3719_Compl__insert,axiom,
% 13.77/7.73 ! [X: nat,A4: set_nat] :
% 13.77/7.73 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.73 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A4 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3720_frac__neg,axiom,
% 13.77/7.73 ! [X: real] :
% 13.77/7.73 ( ( ( member_real @ X @ ring_1_Ints_real )
% 13.77/7.73 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 13.77/7.73 = zero_zero_real ) )
% 13.77/7.73 & ( ~ ( member_real @ X @ ring_1_Ints_real )
% 13.77/7.73 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X ) )
% 13.77/7.73 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3721_frac__neg,axiom,
% 13.77/7.73 ! [X: rat] :
% 13.77/7.73 ( ( ( member_rat @ X @ ring_1_Ints_rat )
% 13.77/7.73 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 13.77/7.73 = zero_zero_rat ) )
% 13.77/7.73 & ( ~ ( member_rat @ X @ ring_1_Ints_rat )
% 13.77/7.73 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X ) )
% 13.77/7.73 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3722_dbl__dec__simps_I2_J,axiom,
% 13.77/7.73 ( ( neg_nu965353292909893953uint32 @ zero_zero_uint32 )
% 13.77/7.73 = ( uminus_uminus_uint32 @ one_one_uint32 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3723_dbl__dec__simps_I2_J,axiom,
% 13.77/7.73 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 13.77/7.73 = ( uminus_uminus_real @ one_one_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3724_dbl__dec__simps_I2_J,axiom,
% 13.77/7.73 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 13.77/7.73 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3725_dbl__dec__simps_I2_J,axiom,
% 13.77/7.73 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 13.77/7.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3726_foldr__one,axiom,
% 13.77/7.73 ! [D: nat,Ys: list_nat] : ( ord_less_eq_nat @ D @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3727_Gcd__remove0__nat,axiom,
% 13.77/7.73 ! [M7: set_nat] :
% 13.77/7.73 ( ( finite_finite_nat @ M7 )
% 13.77/7.73 => ( ( gcd_Gcd_nat @ M7 )
% 13.77/7.73 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3728_Gcd__0__iff,axiom,
% 13.77/7.73 ! [A4: set_nat] :
% 13.77/7.73 ( ( ( gcd_Gcd_nat @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3729_Gcd__0__iff,axiom,
% 13.77/7.73 ! [A4: set_int] :
% 13.77/7.73 ( ( ( gcd_Gcd_int @ A4 )
% 13.77/7.73 = zero_zero_int )
% 13.77/7.73 = ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3730_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J,axiom,
% 13.77/7.73 ! [A: $o,B: $o,X: nat] :
% 13.77/7.73 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.73 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3731_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J,axiom,
% 13.77/7.73 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 13.77/7.73 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X )
% 13.77/7.73 = one_one_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3732_the__dflt__None__empty,axiom,
% 13.77/7.73 ( ( dflt_None_set_nat @ bot_bot_set_nat )
% 13.77/7.73 = none_set_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3733_the__dflt__None__empty,axiom,
% 13.77/7.73 ( ( dflt_None_set_int @ bot_bot_set_int )
% 13.77/7.73 = none_set_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3734_the__dflt__None__empty,axiom,
% 13.77/7.73 ( ( dflt_None_set_o @ bot_bot_set_o )
% 13.77/7.73 = none_set_o ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3735_ComplI,axiom,
% 13.77/7.73 ! [C2: nat,A4: set_nat] :
% 13.77/7.73 ( ~ ( member_nat @ C2 @ A4 )
% 13.77/7.73 => ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3736_ComplI,axiom,
% 13.77/7.73 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.73 ( ~ ( member_VEBT_VEBT @ C2 @ A4 )
% 13.77/7.73 => ( member_VEBT_VEBT @ C2 @ ( uminus8041839845116263051T_VEBT @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3737_ComplI,axiom,
% 13.77/7.73 ! [C2: real,A4: set_real] :
% 13.77/7.73 ( ~ ( member_real @ C2 @ A4 )
% 13.77/7.73 => ( member_real @ C2 @ ( uminus612125837232591019t_real @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3738_ComplI,axiom,
% 13.77/7.73 ! [C2: int,A4: set_int] :
% 13.77/7.73 ( ~ ( member_int @ C2 @ A4 )
% 13.77/7.73 => ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3739_ComplI,axiom,
% 13.77/7.73 ! [C2: set_nat,A4: set_set_nat] :
% 13.77/7.73 ( ~ ( member_set_nat @ C2 @ A4 )
% 13.77/7.73 => ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3740_Compl__iff,axiom,
% 13.77/7.73 ! [C2: nat,A4: set_nat] :
% 13.77/7.73 ( ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 13.77/7.73 = ( ~ ( member_nat @ C2 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3741_Compl__iff,axiom,
% 13.77/7.73 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ C2 @ ( uminus8041839845116263051T_VEBT @ A4 ) )
% 13.77/7.73 = ( ~ ( member_VEBT_VEBT @ C2 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3742_Compl__iff,axiom,
% 13.77/7.73 ! [C2: real,A4: set_real] :
% 13.77/7.73 ( ( member_real @ C2 @ ( uminus612125837232591019t_real @ A4 ) )
% 13.77/7.73 = ( ~ ( member_real @ C2 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3743_Compl__iff,axiom,
% 13.77/7.73 ! [C2: int,A4: set_int] :
% 13.77/7.73 ( ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) )
% 13.77/7.73 = ( ~ ( member_int @ C2 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3744_Compl__iff,axiom,
% 13.77/7.73 ! [C2: set_nat,A4: set_set_nat] :
% 13.77/7.73 ( ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) )
% 13.77/7.73 = ( ~ ( member_set_nat @ C2 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3745_the__dflt__None__nonempty,axiom,
% 13.77/7.73 ! [S3: set_nat] :
% 13.77/7.73 ( ( S3 != bot_bot_set_nat )
% 13.77/7.73 => ( ( dflt_None_set_nat @ S3 )
% 13.77/7.73 = ( some_set_nat @ S3 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3746_the__dflt__None__nonempty,axiom,
% 13.77/7.73 ! [S3: set_int] :
% 13.77/7.73 ( ( S3 != bot_bot_set_int )
% 13.77/7.73 => ( ( dflt_None_set_int @ S3 )
% 13.77/7.73 = ( some_set_int @ S3 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3747_the__dflt__None__nonempty,axiom,
% 13.77/7.73 ! [S3: set_o] :
% 13.77/7.73 ( ( S3 != bot_bot_set_o )
% 13.77/7.73 => ( ( dflt_None_set_o @ S3 )
% 13.77/7.73 = ( some_set_o @ S3 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3748_Gcd__empty,axiom,
% 13.77/7.73 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3749_Gcd__empty,axiom,
% 13.77/7.73 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3750_ComplD,axiom,
% 13.77/7.73 ! [C2: nat,A4: set_nat] :
% 13.77/7.73 ( ( member_nat @ C2 @ ( uminus5710092332889474511et_nat @ A4 ) )
% 13.77/7.73 => ~ ( member_nat @ C2 @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3751_ComplD,axiom,
% 13.77/7.73 ! [C2: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ C2 @ ( uminus8041839845116263051T_VEBT @ A4 ) )
% 13.77/7.73 => ~ ( member_VEBT_VEBT @ C2 @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3752_ComplD,axiom,
% 13.77/7.73 ! [C2: real,A4: set_real] :
% 13.77/7.73 ( ( member_real @ C2 @ ( uminus612125837232591019t_real @ A4 ) )
% 13.77/7.73 => ~ ( member_real @ C2 @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3753_ComplD,axiom,
% 13.77/7.73 ! [C2: int,A4: set_int] :
% 13.77/7.73 ( ( member_int @ C2 @ ( uminus1532241313380277803et_int @ A4 ) )
% 13.77/7.73 => ~ ( member_int @ C2 @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3754_ComplD,axiom,
% 13.77/7.73 ! [C2: set_nat,A4: set_set_nat] :
% 13.77/7.73 ( ( member_set_nat @ C2 @ ( uminus613421341184616069et_nat @ A4 ) )
% 13.77/7.73 => ~ ( member_set_nat @ C2 @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3755_dflt__None__set__def,axiom,
% 13.77/7.73 ( dflt_None_set_nat
% 13.77/7.73 = ( ^ [S6: set_nat] : ( if_option_set_nat @ ( S6 = bot_bot_set_nat ) @ none_set_nat @ ( some_set_nat @ S6 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3756_dflt__None__set__def,axiom,
% 13.77/7.73 ( dflt_None_set_int
% 13.77/7.73 = ( ^ [S6: set_int] : ( if_option_set_int @ ( S6 = bot_bot_set_int ) @ none_set_int @ ( some_set_int @ S6 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3757_dflt__None__set__def,axiom,
% 13.77/7.73 ( dflt_None_set_o
% 13.77/7.73 = ( ^ [S6: set_o] : ( if_option_set_o @ ( S6 = bot_bot_set_o ) @ none_set_o @ ( some_set_o @ S6 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3758_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J,axiom,
% 13.77/7.73 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 13.77/7.73 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X )
% 13.77/7.73 = one_one_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3759_the__dflt__None__set,axiom,
% 13.77/7.73 ! [X: set_nat] :
% 13.77/7.73 ( ( the_default_set_nat @ bot_bot_set_nat @ ( dflt_None_set_nat @ X ) )
% 13.77/7.73 = X ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3760_the__dflt__None__set,axiom,
% 13.77/7.73 ! [X: set_int] :
% 13.77/7.73 ( ( the_default_set_int @ bot_bot_set_int @ ( dflt_None_set_int @ X ) )
% 13.77/7.73 = X ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3761_the__dflt__None__set,axiom,
% 13.77/7.73 ! [X: set_o] :
% 13.77/7.73 ( ( the_default_set_o @ bot_bot_set_o @ ( dflt_None_set_o @ X ) )
% 13.77/7.73 = X ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3762_foldr__same__int,axiom,
% 13.77/7.73 ! [Xs: list_nat,Y: nat] :
% 13.77/7.73 ( ! [X3: nat,Y3: nat] :
% 13.77/7.73 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 13.77/7.73 => ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 13.77/7.73 => ( X3 = Y3 ) ) )
% 13.77/7.73 => ( ! [X3: nat] :
% 13.77/7.73 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 13.77/7.73 => ( X3 = Y ) )
% 13.77/7.73 => ( ( foldr_nat_nat @ plus_plus_nat @ Xs @ zero_zero_nat )
% 13.77/7.73 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ Y ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3763_Gcd__fin__0__iff,axiom,
% 13.77/7.73 ! [A4: set_nat] :
% 13.77/7.73 ( ( ( semiri4258706085729940814in_nat @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 13.77/7.73 & ( finite_finite_nat @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3764_Gcd__fin__0__iff,axiom,
% 13.77/7.73 ! [A4: set_int] :
% 13.77/7.73 ( ( ( semiri4256215615220890538in_int @ A4 )
% 13.77/7.73 = zero_zero_int )
% 13.77/7.73 = ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) )
% 13.77/7.73 & ( finite_finite_int @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3765_power__decreasing__iff,axiom,
% 13.77/7.73 ! [B: real,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.73 => ( ( ord_less_real @ B @ one_one_real )
% 13.77/7.73 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3766_power__decreasing__iff,axiom,
% 13.77/7.73 ! [B: rat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ B )
% 13.77/7.73 => ( ( ord_less_rat @ B @ one_one_rat )
% 13.77/7.73 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3767_power__decreasing__iff,axiom,
% 13.77/7.73 ! [B: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.73 => ( ( ord_less_nat @ B @ one_one_nat )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3768_power__decreasing__iff,axiom,
% 13.77/7.73 ! [B: int,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.73 => ( ( ord_less_int @ B @ one_one_int )
% 13.77/7.73 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3769_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3770_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_int,X: int] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3771_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_o,X: $o] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite_card_o @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_o @ ( insert_o @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3772_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_complex,X: complex] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite_card_complex @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_complex @ ( insert_complex @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3773_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_literal,X: literal] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite_card_literal @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_literal @ ( insert_literal @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3774_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_list_nat,X: list_nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3775_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_set_nat,X: set_nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3776_card__insert__le__m1,axiom,
% 13.77/7.73 ! [N: nat,Y: set_nat,X: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3777_count__notin,axiom,
% 13.77/7.73 ! [X: int,Xs: list_int] :
% 13.77/7.73 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.73 => ( ( count_list_int @ Xs @ X )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3778_count__notin,axiom,
% 13.77/7.73 ! [X: set_nat,Xs: list_set_nat] :
% 13.77/7.73 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 13.77/7.73 => ( ( count_list_set_nat @ Xs @ X )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3779_count__notin,axiom,
% 13.77/7.73 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.73 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.73 => ( ( count_list_VEBT_VEBT @ Xs @ X )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3780_count__notin,axiom,
% 13.77/7.73 ! [X: nat,Xs: list_nat] :
% 13.77/7.73 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.73 => ( ( count_list_nat @ Xs @ X )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3781_count__notin,axiom,
% 13.77/7.73 ! [X: real,Xs: list_real] :
% 13.77/7.73 ( ~ ( member_real @ X @ ( set_real2 @ Xs ) )
% 13.77/7.73 => ( ( count_list_real @ Xs @ X )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3782_count__notin,axiom,
% 13.77/7.73 ! [X: $o,Xs: list_o] :
% 13.77/7.73 ( ~ ( member_o @ X @ ( set_o2 @ Xs ) )
% 13.77/7.73 => ( ( count_list_o @ Xs @ X )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3783_image__Fpow__mono,axiom,
% 13.77/7.73 ! [F: nat > set_nat,A4: set_nat,B4: set_set_nat] :
% 13.77/7.73 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A4 ) @ B4 )
% 13.77/7.73 => ( ord_le9131159989063066194et_nat @ ( image_6725021117256019401et_nat @ ( image_nat_set_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_set_nat @ B4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3784_image__Fpow__mono,axiom,
% 13.77/7.73 ! [F: nat > nat,A4: set_nat,B4: set_nat] :
% 13.77/7.73 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A4 ) @ B4 )
% 13.77/7.73 => ( ord_le6893508408891458716et_nat @ ( image_7916887816326733075et_nat @ ( image_nat_nat @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_nat @ B4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3785_image__Fpow__mono,axiom,
% 13.77/7.73 ! [F: int > nat,A4: set_int,B4: set_nat] :
% 13.77/7.73 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A4 ) @ B4 )
% 13.77/7.73 => ( ord_le6893508408891458716et_nat @ ( image_4702325430467532143et_nat @ ( image_int_nat @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_nat @ B4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3786_image__Fpow__mono,axiom,
% 13.77/7.73 ! [F: nat > int,A4: set_nat,B4: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A4 ) @ B4 )
% 13.77/7.73 => ( ord_le4403425263959731960et_int @ ( image_3739036796817536367et_int @ ( image_nat_int @ F ) @ ( finite_Fpow_nat @ A4 ) ) @ ( finite_Fpow_int @ B4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3787_image__Fpow__mono,axiom,
% 13.77/7.73 ! [F: int > int,A4: set_int,B4: set_int] :
% 13.77/7.73 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A4 ) @ B4 )
% 13.77/7.73 => ( ord_le4403425263959731960et_int @ ( image_524474410958335435et_int @ ( image_int_int @ F ) @ ( finite_Fpow_int @ A4 ) ) @ ( finite_Fpow_int @ B4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3788_power__shift,axiom,
% 13.77/7.73 ! [X: nat,Y: nat,Z: nat] :
% 13.77/7.73 ( ( ( power_power_nat @ X @ Y )
% 13.77/7.73 = Z )
% 13.77/7.73 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 13.77/7.73 = ( some_nat @ Z ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3789_local_Opower__def,axiom,
% 13.77/7.73 ( vEBT_VEBT_power
% 13.77/7.73 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3790_power__Suc__0,axiom,
% 13.77/7.73 ! [N: nat] :
% 13.77/7.73 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.73 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3791_nat__power__eq__Suc__0__iff,axiom,
% 13.77/7.73 ! [X: nat,M: nat] :
% 13.77/7.73 ( ( ( power_power_nat @ X @ M )
% 13.77/7.73 = ( suc @ zero_zero_nat ) )
% 13.77/7.73 = ( ( M = zero_zero_nat )
% 13.77/7.73 | ( X
% 13.77/7.73 = ( suc @ zero_zero_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3792_nat__zero__less__power__iff,axiom,
% 13.77/7.73 ! [X: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 13.77/7.73 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 13.77/7.73 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3793_power__inject__exp,axiom,
% 13.77/7.73 ! [A: real,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.73 => ( ( ( power_power_real @ A @ M )
% 13.77/7.73 = ( power_power_real @ A @ N ) )
% 13.77/7.73 = ( M = N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3794_power__inject__exp,axiom,
% 13.77/7.73 ! [A: rat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.73 => ( ( ( power_power_rat @ A @ M )
% 13.77/7.73 = ( power_power_rat @ A @ N ) )
% 13.77/7.73 = ( M = N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3795_power__inject__exp,axiom,
% 13.77/7.73 ! [A: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.73 => ( ( ( power_power_nat @ A @ M )
% 13.77/7.73 = ( power_power_nat @ A @ N ) )
% 13.77/7.73 = ( M = N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3796_power__inject__exp,axiom,
% 13.77/7.73 ! [A: int,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.73 => ( ( ( power_power_int @ A @ M )
% 13.77/7.73 = ( power_power_int @ A @ N ) )
% 13.77/7.73 = ( M = N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3797_power__0__Suc,axiom,
% 13.77/7.73 ! [N: nat] :
% 13.77/7.73 ( ( power_power_uint32 @ zero_zero_uint32 @ ( suc @ N ) )
% 13.77/7.73 = zero_zero_uint32 ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3798_power__0__Suc,axiom,
% 13.77/7.73 ! [N: nat] :
% 13.77/7.73 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 13.77/7.73 = zero_zero_rat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3799_power__0__Suc,axiom,
% 13.77/7.73 ! [N: nat] :
% 13.77/7.73 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3800_power__0__Suc,axiom,
% 13.77/7.73 ! [N: nat] :
% 13.77/7.73 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 13.77/7.73 = zero_zero_real ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3801_power__0__Suc,axiom,
% 13.77/7.73 ! [N: nat] :
% 13.77/7.73 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 13.77/7.73 = zero_zero_complex ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3802_power__0__Suc,axiom,
% 13.77/7.73 ! [N: nat] :
% 13.77/7.73 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3803_power__Suc0__right,axiom,
% 13.77/7.73 ! [A: nat] :
% 13.77/7.73 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3804_power__Suc0__right,axiom,
% 13.77/7.73 ! [A: real] :
% 13.77/7.73 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3805_power__Suc0__right,axiom,
% 13.77/7.73 ! [A: complex] :
% 13.77/7.73 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3806_power__Suc0__right,axiom,
% 13.77/7.73 ! [A: int] :
% 13.77/7.73 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 13.77/7.73 = A ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3807_card_Oempty,axiom,
% 13.77/7.73 ( ( finite_card_complex @ bot_bot_set_complex )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3808_card_Oempty,axiom,
% 13.77/7.73 ( ( finite_card_literal @ bot_bot_set_literal )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3809_card_Oempty,axiom,
% 13.77/7.73 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3810_card_Oempty,axiom,
% 13.77/7.73 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3811_card_Oempty,axiom,
% 13.77/7.73 ( ( finite_card_nat @ bot_bot_set_nat )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3812_card_Oempty,axiom,
% 13.77/7.73 ( ( finite_card_int @ bot_bot_set_int )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3813_card_Oempty,axiom,
% 13.77/7.73 ( ( finite_card_o @ bot_bot_set_o )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3814_card_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_literal] :
% 13.77/7.73 ( ~ ( finite5847741373460823677iteral @ A4 )
% 13.77/7.73 => ( ( finite_card_literal @ A4 )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3815_card_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_list_nat] :
% 13.77/7.73 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.73 => ( ( finite_card_list_nat @ A4 )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3816_card_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_set_nat] :
% 13.77/7.73 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.73 => ( ( finite_card_set_nat @ A4 )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3817_card_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_nat] :
% 13.77/7.73 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.73 => ( ( finite_card_nat @ A4 )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3818_card_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_int] :
% 13.77/7.73 ( ~ ( finite_finite_int @ A4 )
% 13.77/7.73 => ( ( finite_card_int @ A4 )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3819_card_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_complex] :
% 13.77/7.73 ( ~ ( finite3207457112153483333omplex @ A4 )
% 13.77/7.73 => ( ( finite_card_complex @ A4 )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3820_card_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_Code_integer] :
% 13.77/7.73 ( ~ ( finite6017078050557962740nteger @ A4 )
% 13.77/7.73 => ( ( finite4902975817058060853nteger @ A4 )
% 13.77/7.73 = zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3821_Gcd__fin_Oempty,axiom,
% 13.77/7.73 ( ( semiri4258706085729940814in_nat @ bot_bot_set_nat )
% 13.77/7.73 = zero_zero_nat ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3822_Gcd__fin_Oempty,axiom,
% 13.77/7.73 ( ( semiri4256215615220890538in_int @ bot_bot_set_int )
% 13.77/7.73 = zero_zero_int ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3823_Gcd__fin_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_nat] :
% 13.77/7.73 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.73 => ( ( semiri4258706085729940814in_nat @ A4 )
% 13.77/7.73 = one_one_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3824_Gcd__fin_Oinfinite,axiom,
% 13.77/7.73 ! [A4: set_int] :
% 13.77/7.73 ( ~ ( finite_finite_int @ A4 )
% 13.77/7.73 => ( ( semiri4256215615220890538in_int @ A4 )
% 13.77/7.73 = one_one_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3825_Gcd__fin__eq__Gcd,axiom,
% 13.77/7.73 ! [A4: set_nat] :
% 13.77/7.73 ( ( finite_finite_nat @ A4 )
% 13.77/7.73 => ( ( semiri4258706085729940814in_nat @ A4 )
% 13.77/7.73 = ( gcd_Gcd_nat @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3826_Gcd__fin__eq__Gcd,axiom,
% 13.77/7.73 ! [A4: set_int] :
% 13.77/7.73 ( ( finite_finite_int @ A4 )
% 13.77/7.73 => ( ( semiri4256215615220890538in_int @ A4 )
% 13.77/7.73 = ( gcd_Gcd_int @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3827_power__strict__increasing__iff,axiom,
% 13.77/7.73 ! [B: real,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.73 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 13.77/7.73 = ( ord_less_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3828_power__strict__increasing__iff,axiom,
% 13.77/7.73 ! [B: rat,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_rat @ one_one_rat @ B )
% 13.77/7.73 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 13.77/7.73 = ( ord_less_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3829_power__strict__increasing__iff,axiom,
% 13.77/7.73 ! [B: nat,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_nat @ one_one_nat @ B )
% 13.77/7.73 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 13.77/7.73 = ( ord_less_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3830_power__strict__increasing__iff,axiom,
% 13.77/7.73 ! [B: int,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_int @ one_one_int @ B )
% 13.77/7.73 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 13.77/7.73 = ( ord_less_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3831_power__eq__0__iff,axiom,
% 13.77/7.73 ! [A: rat,N: nat] :
% 13.77/7.73 ( ( ( power_power_rat @ A @ N )
% 13.77/7.73 = zero_zero_rat )
% 13.77/7.73 = ( ( A = zero_zero_rat )
% 13.77/7.73 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3832_power__eq__0__iff,axiom,
% 13.77/7.73 ! [A: nat,N: nat] :
% 13.77/7.73 ( ( ( power_power_nat @ A @ N )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( ( A = zero_zero_nat )
% 13.77/7.73 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3833_power__eq__0__iff,axiom,
% 13.77/7.73 ! [A: real,N: nat] :
% 13.77/7.73 ( ( ( power_power_real @ A @ N )
% 13.77/7.73 = zero_zero_real )
% 13.77/7.73 = ( ( A = zero_zero_real )
% 13.77/7.73 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3834_power__eq__0__iff,axiom,
% 13.77/7.73 ! [A: complex,N: nat] :
% 13.77/7.73 ( ( ( power_power_complex @ A @ N )
% 13.77/7.73 = zero_zero_complex )
% 13.77/7.73 = ( ( A = zero_zero_complex )
% 13.77/7.73 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3835_power__eq__0__iff,axiom,
% 13.77/7.73 ! [A: int,N: nat] :
% 13.77/7.73 ( ( ( power_power_int @ A @ N )
% 13.77/7.73 = zero_zero_int )
% 13.77/7.73 = ( ( A = zero_zero_int )
% 13.77/7.73 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3836_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_literal] :
% 13.77/7.73 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.73 => ( ( ( finite_card_literal @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bot_set_literal ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3837_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_list_nat] :
% 13.77/7.73 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.73 => ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bot_set_list_nat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3838_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_set_nat] :
% 13.77/7.73 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.73 => ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bot_set_set_nat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3839_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_complex] :
% 13.77/7.73 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.73 => ( ( ( finite_card_complex @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bot_set_complex ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3840_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_Code_integer] :
% 13.77/7.73 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.73 => ( ( ( finite4902975817058060853nteger @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bo3990330152332043303nteger ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3841_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_nat] :
% 13.77/7.73 ( ( finite_finite_nat @ A4 )
% 13.77/7.73 => ( ( ( finite_card_nat @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bot_set_nat ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3842_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_int] :
% 13.77/7.73 ( ( finite_finite_int @ A4 )
% 13.77/7.73 => ( ( ( finite_card_int @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bot_set_int ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3843_card__0__eq,axiom,
% 13.77/7.73 ! [A4: set_o] :
% 13.77/7.73 ( ( finite_finite_o @ A4 )
% 13.77/7.73 => ( ( ( finite_card_o @ A4 )
% 13.77/7.73 = zero_zero_nat )
% 13.77/7.73 = ( A4 = bot_bot_set_o ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3844_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_o,X: $o] :
% 13.77/7.73 ( ( finite_finite_o @ A4 )
% 13.77/7.73 => ( ~ ( member_o @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_o @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3845_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.73 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.73 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.73 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3846_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_real,X: real] :
% 13.77/7.73 ( ( finite_finite_real @ A4 )
% 13.77/7.73 => ( ~ ( member_real @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3847_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_literal,X: literal] :
% 13.77/7.73 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.73 => ( ~ ( member_literal @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_literal @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3848_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.73 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.73 => ( ~ ( member_list_nat @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3849_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.73 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.73 => ( ~ ( member_set_nat @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3850_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_nat,X: nat] :
% 13.77/7.73 ( ( finite_finite_nat @ A4 )
% 13.77/7.73 => ( ~ ( member_nat @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3851_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_int,X: int] :
% 13.77/7.73 ( ( finite_finite_int @ A4 )
% 13.77/7.73 => ( ~ ( member_int @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3852_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_complex,X: complex] :
% 13.77/7.73 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.73 => ( ~ ( member_complex @ X @ A4 )
% 13.77/7.73 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3853_card__insert__disjoint,axiom,
% 13.77/7.73 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.73 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.73 => ( ~ ( member_Code_integer @ X @ A4 )
% 13.77/7.73 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.73 = ( suc @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3854_power__strict__decreasing__iff,axiom,
% 13.77/7.73 ! [B: real,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.73 => ( ( ord_less_real @ B @ one_one_real )
% 13.77/7.73 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 13.77/7.73 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3855_power__strict__decreasing__iff,axiom,
% 13.77/7.73 ! [B: rat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ B )
% 13.77/7.73 => ( ( ord_less_rat @ B @ one_one_rat )
% 13.77/7.73 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 13.77/7.73 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3856_power__strict__decreasing__iff,axiom,
% 13.77/7.73 ! [B: nat,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.73 => ( ( ord_less_nat @ B @ one_one_nat )
% 13.77/7.73 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 13.77/7.73 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3857_power__strict__decreasing__iff,axiom,
% 13.77/7.73 ! [B: int,M: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.73 => ( ( ord_less_int @ B @ one_one_int )
% 13.77/7.73 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 13.77/7.73 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3858_power__mono__iff,axiom,
% 13.77/7.73 ! [A: real,B: real,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3859_power__mono__iff,axiom,
% 13.77/7.73 ! [A: rat,B: rat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3860_power__mono__iff,axiom,
% 13.77/7.73 ! [A: nat,B: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3861_power__mono__iff,axiom,
% 13.77/7.73 ! [A: int,B: int,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.73 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 13.77/7.73 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3862_power__increasing__iff,axiom,
% 13.77/7.73 ! [B: real,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.73 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 13.77/7.73 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3863_power__increasing__iff,axiom,
% 13.77/7.73 ! [B: rat,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_rat @ one_one_rat @ B )
% 13.77/7.73 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 13.77/7.73 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3864_power__increasing__iff,axiom,
% 13.77/7.73 ! [B: nat,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_nat @ one_one_nat @ B )
% 13.77/7.73 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 13.77/7.73 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3865_power__increasing__iff,axiom,
% 13.77/7.73 ! [B: int,X: nat,Y: nat] :
% 13.77/7.73 ( ( ord_less_int @ one_one_int @ B )
% 13.77/7.73 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 13.77/7.73 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3866_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: $o,A4: set_o,B4: set_o] :
% 13.77/7.73 ( ( member_o @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_o @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3867_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_VEBT_VEBT @ A @ B4 )
% 13.77/7.73 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3868_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: real,A4: set_real,B4: set_real] :
% 13.77/7.73 ( ( member_real @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_real @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3869_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: int,A4: set_int,B4: set_int] :
% 13.77/7.73 ( ( member_int @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_int @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3870_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: complex,A4: set_complex,B4: set_complex] :
% 13.77/7.73 ( ( member_complex @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_complex @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3871_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: literal,A4: set_literal,B4: set_literal] :
% 13.77/7.73 ( ( member_literal @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_literal @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3872_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: list_nat,A4: set_list_nat,B4: set_list_nat] :
% 13.77/7.73 ( ( member_list_nat @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_list_nat @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3873_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: set_nat,A4: set_set_nat,B4: set_set_nat] :
% 13.77/7.73 ( ( member_set_nat @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_set_nat @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3874_card__Diff__insert,axiom,
% 13.77/7.73 ! [A: nat,A4: set_nat,B4: set_nat] :
% 13.77/7.73 ( ( member_nat @ A @ A4 )
% 13.77/7.73 => ( ~ ( member_nat @ A @ B4 )
% 13.77/7.73 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ B4 ) ) )
% 13.77/7.73 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ one_one_nat ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3875_finite__enumerate__mono__iff,axiom,
% 13.77/7.73 ! [S3: set_nat,M: nat,N: nat] :
% 13.77/7.73 ( ( finite_finite_nat @ S3 )
% 13.77/7.73 => ( ( ord_less_nat @ M @ ( finite_card_nat @ S3 ) )
% 13.77/7.73 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 13.77/7.73 => ( ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) )
% 13.77/7.73 = ( ord_less_nat @ M @ N ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3876_size__neq__size__imp__neq,axiom,
% 13.77/7.73 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 13.77/7.73 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 13.77/7.73 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 13.77/7.73 => ( X != Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3877_size__neq__size__imp__neq,axiom,
% 13.77/7.73 ! [X: list_real,Y: list_real] :
% 13.77/7.73 ( ( ( size_size_list_real @ X )
% 13.77/7.73 != ( size_size_list_real @ Y ) )
% 13.77/7.73 => ( X != Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3878_size__neq__size__imp__neq,axiom,
% 13.77/7.73 ! [X: list_o,Y: list_o] :
% 13.77/7.73 ( ( ( size_size_list_o @ X )
% 13.77/7.73 != ( size_size_list_o @ Y ) )
% 13.77/7.73 => ( X != Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3879_size__neq__size__imp__neq,axiom,
% 13.77/7.73 ! [X: list_nat,Y: list_nat] :
% 13.77/7.73 ( ( ( size_size_list_nat @ X )
% 13.77/7.73 != ( size_size_list_nat @ Y ) )
% 13.77/7.73 => ( X != Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3880_size__neq__size__imp__neq,axiom,
% 13.77/7.73 ! [X: num,Y: num] :
% 13.77/7.73 ( ( ( size_size_num @ X )
% 13.77/7.73 != ( size_size_num @ Y ) )
% 13.77/7.73 => ( X != Y ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3881_count__le__length,axiom,
% 13.77/7.73 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs @ X ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3882_count__le__length,axiom,
% 13.77/7.73 ! [Xs: list_real,X: real] : ( ord_less_eq_nat @ ( count_list_real @ Xs @ X ) @ ( size_size_list_real @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3883_count__le__length,axiom,
% 13.77/7.73 ! [Xs: list_o,X: $o] : ( ord_less_eq_nat @ ( count_list_o @ Xs @ X ) @ ( size_size_list_o @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3884_count__le__length,axiom,
% 13.77/7.73 ! [Xs: list_nat,X: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs @ X ) @ ( size_size_list_nat @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3885_card__length,axiom,
% 13.77/7.73 ! [Xs: list_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( set_complex2 @ Xs ) ) @ ( size_s3451745648224563538omplex @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3886_card__length,axiom,
% 13.77/7.73 ! [Xs: list_literal] : ( ord_less_eq_nat @ ( finite_card_literal @ ( set_literal2 @ Xs ) ) @ ( size_s2501651207091587910iteral @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3887_card__length,axiom,
% 13.77/7.73 ! [Xs: list_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( set_list_nat2 @ Xs ) ) @ ( size_s3023201423986296836st_nat @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3888_card__length,axiom,
% 13.77/7.73 ! [Xs: list_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( set_set_nat2 @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3889_card__length,axiom,
% 13.77/7.73 ! [Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3890_card__length,axiom,
% 13.77/7.73 ! [Xs: list_real] : ( ord_less_eq_nat @ ( finite_card_real @ ( set_real2 @ Xs ) ) @ ( size_size_list_real @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3891_card__length,axiom,
% 13.77/7.73 ! [Xs: list_o] : ( ord_less_eq_nat @ ( finite_card_o @ ( set_o2 @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3892_card__length,axiom,
% 13.77/7.73 ! [Xs: list_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( set_nat2 @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3893_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 13.77/7.73 ! [A: rat,N: nat] :
% 13.77/7.73 ( ( A != zero_zero_rat )
% 13.77/7.73 => ( ( power_power_rat @ A @ N )
% 13.77/7.73 != zero_zero_rat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3894_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 13.77/7.73 ! [A: nat,N: nat] :
% 13.77/7.73 ( ( A != zero_zero_nat )
% 13.77/7.73 => ( ( power_power_nat @ A @ N )
% 13.77/7.73 != zero_zero_nat ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3895_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 13.77/7.73 ! [A: real,N: nat] :
% 13.77/7.73 ( ( A != zero_zero_real )
% 13.77/7.73 => ( ( power_power_real @ A @ N )
% 13.77/7.73 != zero_zero_real ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3896_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 13.77/7.73 ! [A: complex,N: nat] :
% 13.77/7.73 ( ( A != zero_zero_complex )
% 13.77/7.73 => ( ( power_power_complex @ A @ N )
% 13.77/7.73 != zero_zero_complex ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3897_semiring__1__no__zero__divisors__class_Opower__not__zero,axiom,
% 13.77/7.73 ! [A: int,N: nat] :
% 13.77/7.73 ( ( A != zero_zero_int )
% 13.77/7.73 => ( ( power_power_int @ A @ N )
% 13.77/7.73 != zero_zero_int ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3898_length__induct,axiom,
% 13.77/7.73 ! [P2: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 13.77/7.73 ( ! [Xs3: list_VEBT_VEBT] :
% 13.77/7.73 ( ! [Ys2: list_VEBT_VEBT] :
% 13.77/7.73 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Ys2 ) )
% 13.77/7.73 => ( P2 @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3899_length__induct,axiom,
% 13.77/7.73 ! [P2: list_real > $o,Xs: list_real] :
% 13.77/7.73 ( ! [Xs3: list_real] :
% 13.77/7.73 ( ! [Ys2: list_real] :
% 13.77/7.73 ( ( ord_less_nat @ ( size_size_list_real @ Ys2 ) @ ( size_size_list_real @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Ys2 ) )
% 13.77/7.73 => ( P2 @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3900_length__induct,axiom,
% 13.77/7.73 ! [P2: list_o > $o,Xs: list_o] :
% 13.77/7.73 ( ! [Xs3: list_o] :
% 13.77/7.73 ( ! [Ys2: list_o] :
% 13.77/7.73 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Ys2 ) )
% 13.77/7.73 => ( P2 @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3901_length__induct,axiom,
% 13.77/7.73 ! [P2: list_nat > $o,Xs: list_nat] :
% 13.77/7.73 ( ! [Xs3: list_nat] :
% 13.77/7.73 ( ! [Ys2: list_nat] :
% 13.77/7.73 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Ys2 ) )
% 13.77/7.73 => ( P2 @ Xs3 ) )
% 13.77/7.73 => ( P2 @ Xs ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3902_finite__maxlen,axiom,
% 13.77/7.73 ! [M7: set_list_VEBT_VEBT] :
% 13.77/7.73 ( ( finite3004134309566078307T_VEBT @ M7 )
% 13.77/7.73 => ? [N2: nat] :
% 13.77/7.73 ! [X5: list_VEBT_VEBT] :
% 13.77/7.73 ( ( member2936631157270082147T_VEBT @ X5 @ M7 )
% 13.77/7.73 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N2 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3903_finite__maxlen,axiom,
% 13.77/7.73 ! [M7: set_list_real] :
% 13.77/7.73 ( ( finite306553202115118035t_real @ M7 )
% 13.77/7.73 => ? [N2: nat] :
% 13.77/7.73 ! [X5: list_real] :
% 13.77/7.73 ( ( member_list_real @ X5 @ M7 )
% 13.77/7.73 => ( ord_less_nat @ ( size_size_list_real @ X5 ) @ N2 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3904_finite__maxlen,axiom,
% 13.77/7.73 ! [M7: set_list_o] :
% 13.77/7.73 ( ( finite_finite_list_o @ M7 )
% 13.77/7.73 => ? [N2: nat] :
% 13.77/7.73 ! [X5: list_o] :
% 13.77/7.73 ( ( member_list_o @ X5 @ M7 )
% 13.77/7.73 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N2 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3905_finite__maxlen,axiom,
% 13.77/7.73 ! [M7: set_list_nat] :
% 13.77/7.73 ( ( finite8100373058378681591st_nat @ M7 )
% 13.77/7.73 => ? [N2: nat] :
% 13.77/7.73 ! [X5: list_nat] :
% 13.77/7.73 ( ( member_list_nat @ X5 @ M7 )
% 13.77/7.73 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N2 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3906_zero__le__power,axiom,
% 13.77/7.73 ! [A: real,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3907_zero__le__power,axiom,
% 13.77/7.73 ! [A: rat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3908_zero__le__power,axiom,
% 13.77/7.73 ! [A: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3909_zero__le__power,axiom,
% 13.77/7.73 ! [A: int,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3910_power__mono,axiom,
% 13.77/7.73 ! [A: real,B: real,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3911_power__mono,axiom,
% 13.77/7.73 ! [A: rat,B: rat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3912_power__mono,axiom,
% 13.77/7.73 ! [A: nat,B: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3913_power__mono,axiom,
% 13.77/7.73 ! [A: int,B: int,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.73 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3914_zero__less__power,axiom,
% 13.77/7.73 ! [A: real,N: nat] :
% 13.77/7.73 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.73 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3915_zero__less__power,axiom,
% 13.77/7.73 ! [A: rat,N: nat] :
% 13.77/7.73 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.73 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3916_zero__less__power,axiom,
% 13.77/7.73 ! [A: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.73 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3917_zero__less__power,axiom,
% 13.77/7.73 ! [A: int,N: nat] :
% 13.77/7.73 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.73 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3918_one__le__power,axiom,
% 13.77/7.73 ! [A: real,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_real @ one_one_real @ A )
% 13.77/7.73 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3919_one__le__power,axiom,
% 13.77/7.73 ! [A: rat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 13.77/7.73 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3920_one__le__power,axiom,
% 13.77/7.73 ! [A: nat,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 13.77/7.73 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3921_one__le__power,axiom,
% 13.77/7.73 ! [A: int,N: nat] :
% 13.77/7.73 ( ( ord_less_eq_int @ one_one_int @ A )
% 13.77/7.73 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3922_card__subset__eq,axiom,
% 13.77/7.73 ! [B4: set_literal,A4: set_literal] :
% 13.77/7.73 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.73 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 13.77/7.73 => ( ( ( finite_card_literal @ A4 )
% 13.77/7.73 = ( finite_card_literal @ B4 ) )
% 13.77/7.73 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3923_card__subset__eq,axiom,
% 13.77/7.73 ! [B4: set_list_nat,A4: set_list_nat] :
% 13.77/7.73 ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.73 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 13.77/7.73 => ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.73 = ( finite_card_list_nat @ B4 ) )
% 13.77/7.73 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3924_card__subset__eq,axiom,
% 13.77/7.73 ! [B4: set_set_nat,A4: set_set_nat] :
% 13.77/7.73 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.73 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 13.77/7.73 => ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.73 = ( finite_card_set_nat @ B4 ) )
% 13.77/7.73 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3925_card__subset__eq,axiom,
% 13.77/7.73 ! [B4: set_nat,A4: set_nat] :
% 13.77/7.73 ( ( finite_finite_nat @ B4 )
% 13.77/7.73 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.73 => ( ( ( finite_card_nat @ A4 )
% 13.77/7.73 = ( finite_card_nat @ B4 ) )
% 13.77/7.73 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3926_card__subset__eq,axiom,
% 13.77/7.73 ! [B4: set_complex,A4: set_complex] :
% 13.77/7.73 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.73 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.73 => ( ( ( finite_card_complex @ A4 )
% 13.77/7.73 = ( finite_card_complex @ B4 ) )
% 13.77/7.73 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3927_card__subset__eq,axiom,
% 13.77/7.73 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.77/7.73 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.73 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.73 => ( ( ( finite4902975817058060853nteger @ A4 )
% 13.77/7.73 = ( finite4902975817058060853nteger @ B4 ) )
% 13.77/7.73 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3928_card__subset__eq,axiom,
% 13.77/7.73 ! [B4: set_int,A4: set_int] :
% 13.77/7.73 ( ( finite_finite_int @ B4 )
% 13.77/7.73 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.73 => ( ( ( finite_card_int @ A4 )
% 13.77/7.73 = ( finite_card_int @ B4 ) )
% 13.77/7.73 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3929_infinite__arbitrarily__large,axiom,
% 13.77/7.73 ! [A4: set_literal,N: nat] :
% 13.77/7.73 ( ~ ( finite5847741373460823677iteral @ A4 )
% 13.77/7.73 => ? [B8: set_literal] :
% 13.77/7.73 ( ( finite5847741373460823677iteral @ B8 )
% 13.77/7.73 & ( ( finite_card_literal @ B8 )
% 13.77/7.73 = N )
% 13.77/7.73 & ( ord_le7307670543136651348iteral @ B8 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3930_infinite__arbitrarily__large,axiom,
% 13.77/7.73 ! [A4: set_list_nat,N: nat] :
% 13.77/7.73 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.73 => ? [B8: set_list_nat] :
% 13.77/7.73 ( ( finite8100373058378681591st_nat @ B8 )
% 13.77/7.73 & ( ( finite_card_list_nat @ B8 )
% 13.77/7.73 = N )
% 13.77/7.73 & ( ord_le6045566169113846134st_nat @ B8 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3931_infinite__arbitrarily__large,axiom,
% 13.77/7.73 ! [A4: set_set_nat,N: nat] :
% 13.77/7.73 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.73 => ? [B8: set_set_nat] :
% 13.77/7.73 ( ( finite1152437895449049373et_nat @ B8 )
% 13.77/7.73 & ( ( finite_card_set_nat @ B8 )
% 13.77/7.73 = N )
% 13.77/7.73 & ( ord_le6893508408891458716et_nat @ B8 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3932_infinite__arbitrarily__large,axiom,
% 13.77/7.73 ! [A4: set_nat,N: nat] :
% 13.77/7.73 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.73 => ? [B8: set_nat] :
% 13.77/7.73 ( ( finite_finite_nat @ B8 )
% 13.77/7.73 & ( ( finite_card_nat @ B8 )
% 13.77/7.73 = N )
% 13.77/7.73 & ( ord_less_eq_set_nat @ B8 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3933_infinite__arbitrarily__large,axiom,
% 13.77/7.73 ! [A4: set_complex,N: nat] :
% 13.77/7.73 ( ~ ( finite3207457112153483333omplex @ A4 )
% 13.77/7.73 => ? [B8: set_complex] :
% 13.77/7.73 ( ( finite3207457112153483333omplex @ B8 )
% 13.77/7.73 & ( ( finite_card_complex @ B8 )
% 13.77/7.73 = N )
% 13.77/7.73 & ( ord_le211207098394363844omplex @ B8 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3934_infinite__arbitrarily__large,axiom,
% 13.77/7.73 ! [A4: set_Code_integer,N: nat] :
% 13.77/7.73 ( ~ ( finite6017078050557962740nteger @ A4 )
% 13.77/7.73 => ? [B8: set_Code_integer] :
% 13.77/7.73 ( ( finite6017078050557962740nteger @ B8 )
% 13.77/7.73 & ( ( finite4902975817058060853nteger @ B8 )
% 13.77/7.73 = N )
% 13.77/7.73 & ( ord_le7084787975880047091nteger @ B8 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3935_infinite__arbitrarily__large,axiom,
% 13.77/7.73 ! [A4: set_int,N: nat] :
% 13.77/7.73 ( ~ ( finite_finite_int @ A4 )
% 13.77/7.73 => ? [B8: set_int] :
% 13.77/7.73 ( ( finite_finite_int @ B8 )
% 13.77/7.73 & ( ( finite_card_int @ B8 )
% 13.77/7.73 = N )
% 13.77/7.73 & ( ord_less_eq_set_int @ B8 @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3936_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,R: vEBT_VEBT > vEBT_VEBT > $o] :
% 13.77/7.73 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.73 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.73 => ? [B9: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: vEBT_VEBT,A22: vEBT_VEBT,B3: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ A1 @ A4 )
% 13.77/7.73 => ( ( member_VEBT_VEBT @ A22 @ A4 )
% 13.77/7.73 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3937_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_real,A4: set_VEBT_VEBT,R: vEBT_VEBT > real > $o] :
% 13.77/7.73 ( ( finite_finite_real @ B4 )
% 13.77/7.73 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.73 => ? [B9: real] :
% 13.77/7.73 ( ( member_real @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: vEBT_VEBT,A22: vEBT_VEBT,B3: real] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ A1 @ A4 )
% 13.77/7.73 => ( ( member_VEBT_VEBT @ A22 @ A4 )
% 13.77/7.73 => ( ( member_real @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite_card_real @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3938_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_VEBT_VEBT,A4: set_real,R: real > vEBT_VEBT > $o] :
% 13.77/7.73 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.73 => ( ! [A3: real] :
% 13.77/7.73 ( ( member_real @ A3 @ A4 )
% 13.77/7.73 => ? [B9: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: real,A22: real,B3: vEBT_VEBT] :
% 13.77/7.73 ( ( member_real @ A1 @ A4 )
% 13.77/7.73 => ( ( member_real @ A22 @ A4 )
% 13.77/7.73 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3939_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_real,A4: set_real,R: real > real > $o] :
% 13.77/7.73 ( ( finite_finite_real @ B4 )
% 13.77/7.73 => ( ! [A3: real] :
% 13.77/7.73 ( ( member_real @ A3 @ A4 )
% 13.77/7.73 => ? [B9: real] :
% 13.77/7.73 ( ( member_real @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: real,A22: real,B3: real] :
% 13.77/7.73 ( ( member_real @ A1 @ A4 )
% 13.77/7.73 => ( ( member_real @ A22 @ A4 )
% 13.77/7.73 => ( ( member_real @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3940_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_VEBT_VEBT,A4: set_int,R: int > vEBT_VEBT > $o] :
% 13.77/7.73 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.73 => ( ! [A3: int] :
% 13.77/7.73 ( ( member_int @ A3 @ A4 )
% 13.77/7.73 => ? [B9: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: int,A22: int,B3: vEBT_VEBT] :
% 13.77/7.73 ( ( member_int @ A1 @ A4 )
% 13.77/7.73 => ( ( member_int @ A22 @ A4 )
% 13.77/7.73 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3941_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_real,A4: set_int,R: int > real > $o] :
% 13.77/7.73 ( ( finite_finite_real @ B4 )
% 13.77/7.73 => ( ! [A3: int] :
% 13.77/7.73 ( ( member_int @ A3 @ A4 )
% 13.77/7.73 => ? [B9: real] :
% 13.77/7.73 ( ( member_real @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: int,A22: int,B3: real] :
% 13.77/7.73 ( ( member_int @ A1 @ A4 )
% 13.77/7.73 => ( ( member_int @ A22 @ A4 )
% 13.77/7.73 => ( ( member_real @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_real @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3942_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_literal,A4: set_VEBT_VEBT,R: vEBT_VEBT > literal > $o] :
% 13.77/7.73 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.73 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.73 => ? [B9: literal] :
% 13.77/7.73 ( ( member_literal @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: vEBT_VEBT,A22: vEBT_VEBT,B3: literal] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ A1 @ A4 )
% 13.77/7.73 => ( ( member_VEBT_VEBT @ A22 @ A4 )
% 13.77/7.73 => ( ( member_literal @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3943_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_literal,A4: set_real,R: real > literal > $o] :
% 13.77/7.73 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.73 => ( ! [A3: real] :
% 13.77/7.73 ( ( member_real @ A3 @ A4 )
% 13.77/7.73 => ? [B9: literal] :
% 13.77/7.73 ( ( member_literal @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: real,A22: real,B3: literal] :
% 13.77/7.73 ( ( member_real @ A1 @ A4 )
% 13.77/7.73 => ( ( member_real @ A22 @ A4 )
% 13.77/7.73 => ( ( member_literal @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3944_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_literal,A4: set_int,R: int > literal > $o] :
% 13.77/7.73 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.73 => ( ! [A3: int] :
% 13.77/7.73 ( ( member_int @ A3 @ A4 )
% 13.77/7.73 => ? [B9: literal] :
% 13.77/7.73 ( ( member_literal @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: int,A22: int,B3: literal] :
% 13.77/7.73 ( ( member_int @ A1 @ A4 )
% 13.77/7.73 => ( ( member_int @ A22 @ A4 )
% 13.77/7.73 => ( ( member_literal @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3945_card__le__if__inj__on__rel,axiom,
% 13.77/7.73 ! [B4: set_VEBT_VEBT,A4: set_complex,R: complex > vEBT_VEBT > $o] :
% 13.77/7.73 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.73 => ( ! [A3: complex] :
% 13.77/7.73 ( ( member_complex @ A3 @ A4 )
% 13.77/7.73 => ? [B9: vEBT_VEBT] :
% 13.77/7.73 ( ( member_VEBT_VEBT @ B9 @ B4 )
% 13.77/7.73 & ( R @ A3 @ B9 ) ) )
% 13.77/7.73 => ( ! [A1: complex,A22: complex,B3: vEBT_VEBT] :
% 13.77/7.73 ( ( member_complex @ A1 @ A4 )
% 13.77/7.73 => ( ( member_complex @ A22 @ A4 )
% 13.77/7.73 => ( ( member_VEBT_VEBT @ B3 @ B4 )
% 13.77/7.73 => ( ( R @ A1 @ B3 )
% 13.77/7.73 => ( ( R @ A22 @ B3 )
% 13.77/7.73 => ( A1 = A22 ) ) ) ) ) )
% 13.77/7.73 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite7802652506058667612T_VEBT @ B4 ) ) ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3946_empty__in__Fpow,axiom,
% 13.77/7.73 ! [A4: set_nat] : ( member_set_nat @ bot_bot_set_nat @ ( finite_Fpow_nat @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3947_empty__in__Fpow,axiom,
% 13.77/7.73 ! [A4: set_int] : ( member_set_int @ bot_bot_set_int @ ( finite_Fpow_int @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3948_empty__in__Fpow,axiom,
% 13.77/7.73 ! [A4: set_o] : ( member_set_o @ bot_bot_set_o @ ( finite_Fpow_o @ A4 ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3949_card__insert__le,axiom,
% 13.77/7.73 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3950_card__insert__le,axiom,
% 13.77/7.73 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3951_card__insert__le,axiom,
% 13.77/7.73 ! [A4: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ A4 ) @ ( finite_card_o @ ( insert_o @ X @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3952_card__insert__le,axiom,
% 13.77/7.73 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ ( insert_complex @ X @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3953_card__insert__le,axiom,
% 13.77/7.73 ! [A4: set_literal,X: literal] : ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ ( insert_literal @ X @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3954_card__insert__le,axiom,
% 13.77/7.73 ! [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 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3955_card__insert__le,axiom,
% 13.77/7.73 ! [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 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3956_card__insert__le,axiom,
% 13.77/7.73 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3957_power__Suc,axiom,
% 13.77/7.73 ! [A: complex,N: nat] :
% 13.77/7.73 ( ( power_power_complex @ A @ ( suc @ N ) )
% 13.77/7.73 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 13.77/7.73
% 13.77/7.73 thf(fact_3958_power__Suc,axiom,
% 13.77/7.73 ! [A: assn,N: nat] :
% 13.77/7.73 ( ( power_power_assn @ A @ ( suc @ N ) )
% 13.77/7.73 = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3959_power__Suc,axiom,
% 13.77/7.74 ! [A: uint32,N: nat] :
% 13.77/7.74 ( ( power_power_uint32 @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_uint32 @ A @ ( power_power_uint32 @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3960_power__Suc,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( power_power_real @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3961_power__Suc,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( power_power_nat @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3962_power__Suc,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( power_power_int @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3963_power__Suc2,axiom,
% 13.77/7.74 ! [A: complex,N: nat] :
% 13.77/7.74 ( ( power_power_complex @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3964_power__Suc2,axiom,
% 13.77/7.74 ! [A: assn,N: nat] :
% 13.77/7.74 ( ( power_power_assn @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_assn @ ( power_power_assn @ A @ N ) @ A ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3965_power__Suc2,axiom,
% 13.77/7.74 ! [A: uint32,N: nat] :
% 13.77/7.74 ( ( power_power_uint32 @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_uint32 @ ( power_power_uint32 @ A @ N ) @ A ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3966_power__Suc2,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( power_power_real @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3967_power__Suc2,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( power_power_nat @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3968_power__Suc2,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( power_power_int @ A @ ( suc @ N ) )
% 13.77/7.74 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3969_Fpow__mono,axiom,
% 13.77/7.74 ! [A4: set_int,B4: set_int] :
% 13.77/7.74 ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.74 => ( ord_le4403425263959731960et_int @ ( finite_Fpow_int @ A4 ) @ ( finite_Fpow_int @ B4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3970_power__0,axiom,
% 13.77/7.74 ! [A: uint32] :
% 13.77/7.74 ( ( power_power_uint32 @ A @ zero_zero_nat )
% 13.77/7.74 = one_one_uint32 ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3971_power__0,axiom,
% 13.77/7.74 ! [A: rat] :
% 13.77/7.74 ( ( power_power_rat @ A @ zero_zero_nat )
% 13.77/7.74 = one_one_rat ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3972_power__0,axiom,
% 13.77/7.74 ! [A: nat] :
% 13.77/7.74 ( ( power_power_nat @ A @ zero_zero_nat )
% 13.77/7.74 = one_one_nat ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3973_power__0,axiom,
% 13.77/7.74 ! [A: real] :
% 13.77/7.74 ( ( power_power_real @ A @ zero_zero_nat )
% 13.77/7.74 = one_one_real ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3974_power__0,axiom,
% 13.77/7.74 ! [A: complex] :
% 13.77/7.74 ( ( power_power_complex @ A @ zero_zero_nat )
% 13.77/7.74 = one_one_complex ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3975_power__0,axiom,
% 13.77/7.74 ! [A: int] :
% 13.77/7.74 ( ( power_power_int @ A @ zero_zero_nat )
% 13.77/7.74 = one_one_int ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3976_nat__power__less__imp__less,axiom,
% 13.77/7.74 ! [I: nat,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ I )
% 13.77/7.74 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 13.77/7.74 => ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3977_length__removeAll__less__eq,axiom,
% 13.77/7.74 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3978_length__removeAll__less__eq,axiom,
% 13.77/7.74 ! [X: real,Xs: list_real] : ( ord_less_eq_nat @ ( size_size_list_real @ ( removeAll_real @ X @ Xs ) ) @ ( size_size_list_real @ Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3979_length__removeAll__less__eq,axiom,
% 13.77/7.74 ! [X: $o,Xs: list_o] : ( ord_less_eq_nat @ ( size_size_list_o @ ( removeAll_o @ X @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3980_length__removeAll__less__eq,axiom,
% 13.77/7.74 ! [X: nat,Xs: list_nat] : ( ord_less_eq_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3981_is__singleton__altdef,axiom,
% 13.77/7.74 ( is_singleton_complex
% 13.77/7.74 = ( ^ [A6: set_complex] :
% 13.77/7.74 ( ( finite_card_complex @ A6 )
% 13.77/7.74 = one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3982_is__singleton__altdef,axiom,
% 13.77/7.74 ( is_singleton_literal
% 13.77/7.74 = ( ^ [A6: set_literal] :
% 13.77/7.74 ( ( finite_card_literal @ A6 )
% 13.77/7.74 = one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3983_is__singleton__altdef,axiom,
% 13.77/7.74 ( is_sin2641923865335537900st_nat
% 13.77/7.74 = ( ^ [A6: set_list_nat] :
% 13.77/7.74 ( ( finite_card_list_nat @ A6 )
% 13.77/7.74 = one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3984_is__singleton__altdef,axiom,
% 13.77/7.74 ( is_singleton_set_nat
% 13.77/7.74 = ( ^ [A6: set_set_nat] :
% 13.77/7.74 ( ( finite_card_set_nat @ A6 )
% 13.77/7.74 = one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3985_is__singleton__altdef,axiom,
% 13.77/7.74 ( is_singleton_nat
% 13.77/7.74 = ( ^ [A6: set_nat] :
% 13.77/7.74 ( ( finite_card_nat @ A6 )
% 13.77/7.74 = one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3986_power__less__imp__less__base,axiom,
% 13.77/7.74 ! [A: real,N: nat,B: real] :
% 13.77/7.74 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.74 => ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3987_power__less__imp__less__base,axiom,
% 13.77/7.74 ! [A: rat,N: nat,B: rat] :
% 13.77/7.74 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.74 => ( ord_less_rat @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3988_power__less__imp__less__base,axiom,
% 13.77/7.74 ! [A: nat,N: nat,B: nat] :
% 13.77/7.74 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.74 => ( ord_less_nat @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3989_power__less__imp__less__base,axiom,
% 13.77/7.74 ! [A: int,N: nat,B: int] :
% 13.77/7.74 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.74 => ( ord_less_int @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3990_card__ge__0__finite,axiom,
% 13.77/7.74 ! [A4: set_literal] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 13.77/7.74 => ( finite5847741373460823677iteral @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3991_card__ge__0__finite,axiom,
% 13.77/7.74 ! [A4: set_list_nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 13.77/7.74 => ( finite8100373058378681591st_nat @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3992_card__ge__0__finite,axiom,
% 13.77/7.74 ! [A4: set_set_nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 13.77/7.74 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3993_card__ge__0__finite,axiom,
% 13.77/7.74 ! [A4: set_nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 13.77/7.74 => ( finite_finite_nat @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3994_card__ge__0__finite,axiom,
% 13.77/7.74 ! [A4: set_int] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 13.77/7.74 => ( finite_finite_int @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3995_card__ge__0__finite,axiom,
% 13.77/7.74 ! [A4: set_complex] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 13.77/7.74 => ( finite3207457112153483333omplex @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3996_card__ge__0__finite,axiom,
% 13.77/7.74 ! [A4: set_Code_integer] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A4 ) )
% 13.77/7.74 => ( finite6017078050557962740nteger @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3997_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_literal] :
% 13.77/7.74 ( ( ( finite_card_literal @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bot_set_literal )
% 13.77/7.74 | ~ ( finite5847741373460823677iteral @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3998_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_list_nat] :
% 13.77/7.74 ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bot_set_list_nat )
% 13.77/7.74 | ~ ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_3999_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_set_nat] :
% 13.77/7.74 ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bot_set_set_nat )
% 13.77/7.74 | ~ ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4000_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_complex] :
% 13.77/7.74 ( ( ( finite_card_complex @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bot_set_complex )
% 13.77/7.74 | ~ ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4001_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_Code_integer] :
% 13.77/7.74 ( ( ( finite4902975817058060853nteger @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bo3990330152332043303nteger )
% 13.77/7.74 | ~ ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4002_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_nat] :
% 13.77/7.74 ( ( ( finite_card_nat @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bot_set_nat )
% 13.77/7.74 | ~ ( finite_finite_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4003_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_int] :
% 13.77/7.74 ( ( ( finite_card_int @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bot_set_int )
% 13.77/7.74 | ~ ( finite_finite_int @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4004_card__eq__0__iff,axiom,
% 13.77/7.74 ! [A4: set_o] :
% 13.77/7.74 ( ( ( finite_card_o @ A4 )
% 13.77/7.74 = zero_zero_nat )
% 13.77/7.74 = ( ( A4 = bot_bot_set_o )
% 13.77/7.74 | ~ ( finite_finite_o @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4005_power__le__one,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_eq_real @ A @ one_one_real )
% 13.77/7.74 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4006_power__le__one,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 13.77/7.74 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4007_power__le__one,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 13.77/7.74 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4008_power__le__one,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_eq_int @ A @ one_one_int )
% 13.77/7.74 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4009_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] :
% 13.77/7.74 ( ( finite_finite_o @ A4 )
% 13.77/7.74 => ( ( ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_o @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_o @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4010_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.74 = ( finite7802652506058667612T_VEBT @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4011_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_real,X: real] :
% 13.77/7.74 ( ( finite_finite_real @ A4 )
% 13.77/7.74 => ( ( ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_real @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4012_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_literal @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_literal @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4013_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_list_nat @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4014_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_set_nat @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4015_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_nat @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4016_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_int,X: int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_int @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4017_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 13.77/7.74 = ( finite_card_complex @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4018_card__insert__if,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( ( member_Code_integer @ X @ A4 )
% 13.77/7.74 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.74 = ( finite4902975817058060853nteger @ A4 ) ) )
% 13.77/7.74 & ( ~ ( member_Code_integer @ X @ A4 )
% 13.77/7.74 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4019_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_o,K: nat] :
% 13.77/7.74 ( ( ( finite_card_o @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: $o,B6: set_o] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_o @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_o @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_o @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite_finite_o @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4020_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,K: nat] :
% 13.77/7.74 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_VEBT_VEBT @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_VEBT_VEBT @ B7 @ B6 )
% 13.77/7.74 & ( ( finite7802652506058667612T_VEBT @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite5795047828879050333T_VEBT @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4021_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_real,K: nat] :
% 13.77/7.74 ( ( ( finite_card_real @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: real,B6: set_real] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_real @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_real @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_real @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite_finite_real @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4022_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_literal,K: nat] :
% 13.77/7.74 ( ( ( finite_card_literal @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: literal,B6: set_literal] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_literal @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_literal @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_literal @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite5847741373460823677iteral @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4023_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_list_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: list_nat,B6: set_list_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_list_nat @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_list_nat @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_list_nat @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4024_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_set_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: set_nat,B6: set_set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_set_nat @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_set_nat @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_set_nat @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4025_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: nat,B6: set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_nat @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_nat @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_nat @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4026_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_int,K: nat] :
% 13.77/7.74 ( ( ( finite_card_int @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: int,B6: set_int] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_int @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_int @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_int @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite_finite_int @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4027_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_complex,K: nat] :
% 13.77/7.74 ( ( ( finite_card_complex @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: complex,B6: set_complex] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_complex @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_complex @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_complex @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4028_card__Suc__eq__finite,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,K: nat] :
% 13.77/7.74 ( ( ( finite4902975817058060853nteger @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: code_integer,B6: set_Code_integer] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_Code_integer @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_Code_integer @ B7 @ B6 )
% 13.77/7.74 & ( ( finite4902975817058060853nteger @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( finite6017078050557962740nteger @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4029_power__inject__base,axiom,
% 13.77/7.74 ! [A: real,N: nat,B: real] :
% 13.77/7.74 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 13.77/7.74 = ( power_power_real @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.74 => ( A = B ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4030_power__inject__base,axiom,
% 13.77/7.74 ! [A: rat,N: nat,B: rat] :
% 13.77/7.74 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 13.77/7.74 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.74 => ( A = B ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4031_power__inject__base,axiom,
% 13.77/7.74 ! [A: nat,N: nat,B: nat] :
% 13.77/7.74 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 13.77/7.74 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.74 => ( A = B ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4032_power__inject__base,axiom,
% 13.77/7.74 ! [A: int,N: nat,B: int] :
% 13.77/7.74 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 13.77/7.74 = ( power_power_int @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.74 => ( A = B ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4033_power__le__imp__le__base,axiom,
% 13.77/7.74 ! [A: real,N: nat,B: real] :
% 13.77/7.74 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.74 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4034_power__le__imp__le__base,axiom,
% 13.77/7.74 ! [A: rat,N: nat,B: rat] :
% 13.77/7.74 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.74 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4035_power__le__imp__le__base,axiom,
% 13.77/7.74 ! [A: nat,N: nat,B: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.74 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4036_power__le__imp__le__base,axiom,
% 13.77/7.74 ! [A: int,N: nat,B: int] :
% 13.77/7.74 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.74 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4037_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_literal,F: literal > complex] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ ( image_5274195009022015549omplex @ F @ A4 ) ) @ ( finite_card_literal @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4038_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_literal,F: literal > literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ ( image_8195128725298311301iteral @ F @ A4 ) ) @ ( finite_card_literal @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4039_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_literal,F: literal > nat] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_literal_nat @ F @ A4 ) ) @ ( finite_card_literal @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4040_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_nat,F: nat > int] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_nat_int @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4041_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_nat,F: nat > complex] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ ( image_nat_complex @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4042_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_nat,F: nat > literal] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ ( image_nat_literal @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4043_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_nat,F: nat > nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_nat @ F @ A4 ) ) @ ( finite_card_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4044_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_int,F: int > int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_int_int @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4045_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_int,F: int > complex] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ ( image_int_complex @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4046_card__image__le,axiom,
% 13.77/7.74 ! [A4: set_int,F: int > literal] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ ( image_int_literal @ F @ A4 ) ) @ ( finite_card_int @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4047_power__gt1__lemma,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.74 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4048_power__gt1__lemma,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4049_power__gt1__lemma,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4050_power__gt1__lemma,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.74 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4051_power__less__power__Suc,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.74 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4052_power__less__power__Suc,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4053_power__less__power__Suc,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4054_power__less__power__Suc,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.74 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4055_finite__if__finite__subsets__card__bdd,axiom,
% 13.77/7.74 ! [F2: set_literal,C3: nat] :
% 13.77/7.74 ( ! [G2: set_literal] :
% 13.77/7.74 ( ( ord_le7307670543136651348iteral @ G2 @ F2 )
% 13.77/7.74 => ( ( finite5847741373460823677iteral @ G2 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ G2 ) @ C3 ) ) )
% 13.77/7.74 => ( ( finite5847741373460823677iteral @ F2 )
% 13.77/7.74 & ( ord_less_eq_nat @ ( finite_card_literal @ F2 ) @ C3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4056_finite__if__finite__subsets__card__bdd,axiom,
% 13.77/7.74 ! [F2: set_list_nat,C3: nat] :
% 13.77/7.74 ( ! [G2: set_list_nat] :
% 13.77/7.74 ( ( ord_le6045566169113846134st_nat @ G2 @ F2 )
% 13.77/7.74 => ( ( finite8100373058378681591st_nat @ G2 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G2 ) @ C3 ) ) )
% 13.77/7.74 => ( ( finite8100373058378681591st_nat @ F2 )
% 13.77/7.74 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F2 ) @ C3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4057_finite__if__finite__subsets__card__bdd,axiom,
% 13.77/7.74 ! [F2: set_set_nat,C3: nat] :
% 13.77/7.74 ( ! [G2: set_set_nat] :
% 13.77/7.74 ( ( ord_le6893508408891458716et_nat @ G2 @ F2 )
% 13.77/7.74 => ( ( finite1152437895449049373et_nat @ G2 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G2 ) @ C3 ) ) )
% 13.77/7.74 => ( ( finite1152437895449049373et_nat @ F2 )
% 13.77/7.74 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F2 ) @ C3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4058_finite__if__finite__subsets__card__bdd,axiom,
% 13.77/7.74 ! [F2: set_nat,C3: nat] :
% 13.77/7.74 ( ! [G2: set_nat] :
% 13.77/7.74 ( ( ord_less_eq_set_nat @ G2 @ F2 )
% 13.77/7.74 => ( ( finite_finite_nat @ G2 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ G2 ) @ C3 ) ) )
% 13.77/7.74 => ( ( finite_finite_nat @ F2 )
% 13.77/7.74 & ( ord_less_eq_nat @ ( finite_card_nat @ F2 ) @ C3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4059_finite__if__finite__subsets__card__bdd,axiom,
% 13.77/7.74 ! [F2: set_complex,C3: nat] :
% 13.77/7.74 ( ! [G2: set_complex] :
% 13.77/7.74 ( ( ord_le211207098394363844omplex @ G2 @ F2 )
% 13.77/7.74 => ( ( finite3207457112153483333omplex @ G2 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ G2 ) @ C3 ) ) )
% 13.77/7.74 => ( ( finite3207457112153483333omplex @ F2 )
% 13.77/7.74 & ( ord_less_eq_nat @ ( finite_card_complex @ F2 ) @ C3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4060_finite__if__finite__subsets__card__bdd,axiom,
% 13.77/7.74 ! [F2: set_Code_integer,C3: nat] :
% 13.77/7.74 ( ! [G2: set_Code_integer] :
% 13.77/7.74 ( ( ord_le7084787975880047091nteger @ G2 @ F2 )
% 13.77/7.74 => ( ( finite6017078050557962740nteger @ G2 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ G2 ) @ C3 ) ) )
% 13.77/7.74 => ( ( finite6017078050557962740nteger @ F2 )
% 13.77/7.74 & ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ F2 ) @ C3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4061_finite__if__finite__subsets__card__bdd,axiom,
% 13.77/7.74 ! [F2: set_int,C3: nat] :
% 13.77/7.74 ( ! [G2: set_int] :
% 13.77/7.74 ( ( ord_less_eq_set_int @ G2 @ F2 )
% 13.77/7.74 => ( ( finite_finite_int @ G2 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_int @ G2 ) @ C3 ) ) )
% 13.77/7.74 => ( ( finite_finite_int @ F2 )
% 13.77/7.74 & ( ord_less_eq_nat @ ( finite_card_int @ F2 ) @ C3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4062_card__seteq,axiom,
% 13.77/7.74 ! [B4: set_literal,A4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_literal @ A4 ) )
% 13.77/7.74 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4063_card__seteq,axiom,
% 13.77/7.74 ! [B4: set_list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B4 ) @ ( finite_card_list_nat @ A4 ) )
% 13.77/7.74 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4064_card__seteq,axiom,
% 13.77/7.74 ! [B4: set_set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B4 ) @ ( finite_card_set_nat @ A4 ) )
% 13.77/7.74 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4065_card__seteq,axiom,
% 13.77/7.74 ! [B4: set_nat,A4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_nat @ A4 ) )
% 13.77/7.74 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4066_card__seteq,axiom,
% 13.77/7.74 ! [B4: set_complex,A4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_complex @ A4 ) )
% 13.77/7.74 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4067_card__seteq,axiom,
% 13.77/7.74 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ B4 ) @ ( finite4902975817058060853nteger @ A4 ) )
% 13.77/7.74 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4068_card__seteq,axiom,
% 13.77/7.74 ! [B4: set_int,A4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_int @ B4 ) @ ( finite_card_int @ A4 ) )
% 13.77/7.74 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4069_card__mono,axiom,
% 13.77/7.74 ! [B4: set_literal,A4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4070_card__mono,axiom,
% 13.77/7.74 ! [B4: set_list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4071_card__mono,axiom,
% 13.77/7.74 ! [B4: set_set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4072_card__mono,axiom,
% 13.77/7.74 ! [B4: set_nat,A4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4073_card__mono,axiom,
% 13.77/7.74 ! [B4: set_complex,A4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4074_card__mono,axiom,
% 13.77/7.74 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4075_card__mono,axiom,
% 13.77/7.74 ! [B4: set_int,A4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4076_obtain__subset__with__card__n,axiom,
% 13.77/7.74 ! [N: nat,S3: set_literal] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ ( finite_card_literal @ S3 ) )
% 13.77/7.74 => ~ ! [T4: set_literal] :
% 13.77/7.74 ( ( ord_le7307670543136651348iteral @ T4 @ S3 )
% 13.77/7.74 => ( ( ( finite_card_literal @ T4 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ( finite5847741373460823677iteral @ T4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4077_obtain__subset__with__card__n,axiom,
% 13.77/7.74 ! [N: nat,S3: set_list_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ S3 ) )
% 13.77/7.74 => ~ ! [T4: set_list_nat] :
% 13.77/7.74 ( ( ord_le6045566169113846134st_nat @ T4 @ S3 )
% 13.77/7.74 => ( ( ( finite_card_list_nat @ T4 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ( finite8100373058378681591st_nat @ T4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4078_obtain__subset__with__card__n,axiom,
% 13.77/7.74 ! [N: nat,S3: set_set_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ S3 ) )
% 13.77/7.74 => ~ ! [T4: set_set_nat] :
% 13.77/7.74 ( ( ord_le6893508408891458716et_nat @ T4 @ S3 )
% 13.77/7.74 => ( ( ( finite_card_set_nat @ T4 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ( finite1152437895449049373et_nat @ T4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4079_obtain__subset__with__card__n,axiom,
% 13.77/7.74 ! [N: nat,S3: set_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S3 ) )
% 13.77/7.74 => ~ ! [T4: set_nat] :
% 13.77/7.74 ( ( ord_less_eq_set_nat @ T4 @ S3 )
% 13.77/7.74 => ( ( ( finite_card_nat @ T4 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ( finite_finite_nat @ T4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4080_obtain__subset__with__card__n,axiom,
% 13.77/7.74 ! [N: nat,S3: set_complex] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ ( finite_card_complex @ S3 ) )
% 13.77/7.74 => ~ ! [T4: set_complex] :
% 13.77/7.74 ( ( ord_le211207098394363844omplex @ T4 @ S3 )
% 13.77/7.74 => ( ( ( finite_card_complex @ T4 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ( finite3207457112153483333omplex @ T4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4081_obtain__subset__with__card__n,axiom,
% 13.77/7.74 ! [N: nat,S3: set_Code_integer] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ ( finite4902975817058060853nteger @ S3 ) )
% 13.77/7.74 => ~ ! [T4: set_Code_integer] :
% 13.77/7.74 ( ( ord_le7084787975880047091nteger @ T4 @ S3 )
% 13.77/7.74 => ( ( ( finite4902975817058060853nteger @ T4 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ( finite6017078050557962740nteger @ T4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4082_obtain__subset__with__card__n,axiom,
% 13.77/7.74 ! [N: nat,S3: set_int] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ ( finite_card_int @ S3 ) )
% 13.77/7.74 => ~ ! [T4: set_int] :
% 13.77/7.74 ( ( ord_less_eq_set_int @ T4 @ S3 )
% 13.77/7.74 => ( ( ( finite_card_int @ T4 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ( finite_finite_int @ T4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4083_power__gt1,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.74 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4084_power__gt1,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4085_power__gt1,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4086_power__gt1,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.74 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4087_power__0__left,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ( N = zero_zero_nat )
% 13.77/7.74 => ( ( power_power_uint32 @ zero_zero_uint32 @ N )
% 13.77/7.74 = one_one_uint32 ) )
% 13.77/7.74 & ( ( N != zero_zero_nat )
% 13.77/7.74 => ( ( power_power_uint32 @ zero_zero_uint32 @ N )
% 13.77/7.74 = zero_zero_uint32 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4088_power__0__left,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ( N = zero_zero_nat )
% 13.77/7.74 => ( ( power_power_rat @ zero_zero_rat @ N )
% 13.77/7.74 = one_one_rat ) )
% 13.77/7.74 & ( ( N != zero_zero_nat )
% 13.77/7.74 => ( ( power_power_rat @ zero_zero_rat @ N )
% 13.77/7.74 = zero_zero_rat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4089_power__0__left,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ( N = zero_zero_nat )
% 13.77/7.74 => ( ( power_power_nat @ zero_zero_nat @ N )
% 13.77/7.74 = one_one_nat ) )
% 13.77/7.74 & ( ( N != zero_zero_nat )
% 13.77/7.74 => ( ( power_power_nat @ zero_zero_nat @ N )
% 13.77/7.74 = zero_zero_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4090_power__0__left,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ( N = zero_zero_nat )
% 13.77/7.74 => ( ( power_power_real @ zero_zero_real @ N )
% 13.77/7.74 = one_one_real ) )
% 13.77/7.74 & ( ( N != zero_zero_nat )
% 13.77/7.74 => ( ( power_power_real @ zero_zero_real @ N )
% 13.77/7.74 = zero_zero_real ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4091_power__0__left,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ( N = zero_zero_nat )
% 13.77/7.74 => ( ( power_power_complex @ zero_zero_complex @ N )
% 13.77/7.74 = one_one_complex ) )
% 13.77/7.74 & ( ( N != zero_zero_nat )
% 13.77/7.74 => ( ( power_power_complex @ zero_zero_complex @ N )
% 13.77/7.74 = zero_zero_complex ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4092_power__0__left,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ( N = zero_zero_nat )
% 13.77/7.74 => ( ( power_power_int @ zero_zero_int @ N )
% 13.77/7.74 = one_one_int ) )
% 13.77/7.74 & ( ( N != zero_zero_nat )
% 13.77/7.74 => ( ( power_power_int @ zero_zero_int @ N )
% 13.77/7.74 = zero_zero_int ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4093_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT] :
% 13.77/7.74 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_VEBT_VEBT @ X3 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4094_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_complex] :
% 13.77/7.74 ( ( ( finite_card_complex @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: complex] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_complex @ X3 @ bot_bot_set_complex ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4095_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_literal] :
% 13.77/7.74 ( ( ( finite_card_literal @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: literal] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_literal @ X3 @ bot_bot_set_literal ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4096_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_list_nat] :
% 13.77/7.74 ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: list_nat] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_list_nat @ X3 @ bot_bot_set_list_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4097_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_set_nat] :
% 13.77/7.74 ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: set_nat] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_set_nat @ X3 @ bot_bot_set_set_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4098_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_nat] :
% 13.77/7.74 ( ( ( finite_card_nat @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: nat] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4099_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_int] :
% 13.77/7.74 ( ( ( finite_card_int @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: int] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_int @ X3 @ bot_bot_set_int ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4100_card__1__singletonE,axiom,
% 13.77/7.74 ! [A4: set_o] :
% 13.77/7.74 ( ( ( finite_card_o @ A4 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ~ ! [X3: $o] :
% 13.77/7.74 ( A4
% 13.77/7.74 != ( insert_o @ X3 @ bot_bot_set_o ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4101_power__strict__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: real] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.74 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4102_power__strict__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: rat] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4103_power__strict__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: nat] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4104_power__strict__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: int] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.74 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4105_power__less__imp__less__exp,axiom,
% 13.77/7.74 ! [A: real,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.74 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 13.77/7.74 => ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4106_power__less__imp__less__exp,axiom,
% 13.77/7.74 ! [A: rat,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 13.77/7.74 => ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4107_power__less__imp__less__exp,axiom,
% 13.77/7.74 ! [A: nat,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 13.77/7.74 => ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4108_power__less__imp__less__exp,axiom,
% 13.77/7.74 ! [A: int,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.74 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 13.77/7.74 => ( ord_less_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4109_card__less__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_literal,B4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4110_card__less__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_list_nat,B4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4111_card__less__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_set_nat,B4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4112_card__less__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_int,B4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4113_card__less__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_complex,B4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4114_card__less__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) )
% 13.77/7.74 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4115_card__less__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4116_zero__power,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( power_power_uint32 @ zero_zero_uint32 @ N )
% 13.77/7.74 = zero_zero_uint32 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4117_zero__power,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( power_power_rat @ zero_zero_rat @ N )
% 13.77/7.74 = zero_zero_rat ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4118_zero__power,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( power_power_nat @ zero_zero_nat @ N )
% 13.77/7.74 = zero_zero_nat ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4119_zero__power,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( power_power_real @ zero_zero_real @ N )
% 13.77/7.74 = zero_zero_real ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4120_zero__power,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( power_power_complex @ zero_zero_complex @ N )
% 13.77/7.74 = zero_zero_complex ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4121_zero__power,axiom,
% 13.77/7.74 ! [N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( power_power_int @ zero_zero_int @ N )
% 13.77/7.74 = zero_zero_int ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4122_power__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: real] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_real @ one_one_real @ A )
% 13.77/7.74 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4123_power__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: rat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4124_power__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4125_power__increasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: int] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_int @ one_one_int @ A )
% 13.77/7.74 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N8 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4126_card__le__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_literal,B4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4127_card__le__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_list_nat,B4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4128_card__le__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_set_nat,B4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4129_card__le__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_int,B4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4130_card__le__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_complex,B4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4131_card__le__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4132_card__le__sym__Diff,axiom,
% 13.77/7.74 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B4 @ A4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4133_psubset__card__mono,axiom,
% 13.77/7.74 ! [B4: set_literal,A4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ( ord_less_set_literal @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4134_psubset__card__mono,axiom,
% 13.77/7.74 ! [B4: set_list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ( ord_le1190675801316882794st_nat @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4135_psubset__card__mono,axiom,
% 13.77/7.74 ! [B4: set_set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_set_set_nat @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4136_psubset__card__mono,axiom,
% 13.77/7.74 ! [B4: set_nat,A4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_set_nat @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4137_psubset__card__mono,axiom,
% 13.77/7.74 ! [B4: set_int,A4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ( ord_less_set_int @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4138_psubset__card__mono,axiom,
% 13.77/7.74 ! [B4: set_complex,A4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ( ord_less_set_complex @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4139_psubset__card__mono,axiom,
% 13.77/7.74 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ( ord_le1307284697595431911nteger @ A4 @ B4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4140_length__pos__if__in__set,axiom,
% 13.77/7.74 ! [X: int,Xs: list_int] :
% 13.77/7.74 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4141_length__pos__if__in__set,axiom,
% 13.77/7.74 ! [X: set_nat,Xs: list_set_nat] :
% 13.77/7.74 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4142_length__pos__if__in__set,axiom,
% 13.77/7.74 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4143_length__pos__if__in__set,axiom,
% 13.77/7.74 ! [X: real,Xs: list_real] :
% 13.77/7.74 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4144_length__pos__if__in__set,axiom,
% 13.77/7.74 ! [X: $o,Xs: list_o] :
% 13.77/7.74 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4145_length__pos__if__in__set,axiom,
% 13.77/7.74 ! [X: nat,Xs: list_nat] :
% 13.77/7.74 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4146_power__gt__expt,axiom,
% 13.77/7.74 ! [N: nat,K: nat] :
% 13.77/7.74 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.74 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4147_nat__one__le__power,axiom,
% 13.77/7.74 ! [I: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 13.77/7.74 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4148_finite__enum__ext,axiom,
% 13.77/7.74 ! [X6: set_nat,Y7: set_nat] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X6 ) )
% 13.77/7.74 => ( ( infini8530281810654367211te_nat @ X6 @ I2 )
% 13.77/7.74 = ( infini8530281810654367211te_nat @ Y7 @ I2 ) ) )
% 13.77/7.74 => ( ( finite_finite_nat @ X6 )
% 13.77/7.74 => ( ( finite_finite_nat @ Y7 )
% 13.77/7.74 => ( ( ( finite_card_nat @ X6 )
% 13.77/7.74 = ( finite_card_nat @ Y7 ) )
% 13.77/7.74 => ( X6 = Y7 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4149_finite__enumerate__Ex,axiom,
% 13.77/7.74 ! [S3: set_nat,S: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ S3 )
% 13.77/7.74 => ( ( member_nat @ S @ S3 )
% 13.77/7.74 => ? [N2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S3 ) )
% 13.77/7.74 & ( ( infini8530281810654367211te_nat @ S3 @ N2 )
% 13.77/7.74 = S ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4150_finite__enumerate__in__set,axiom,
% 13.77/7.74 ! [S3: set_nat,N: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ S3 )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 13.77/7.74 => ( member_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ S3 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4151_length__removeAll__less,axiom,
% 13.77/7.74 ! [X: int,Xs: list_int] :
% 13.77/7.74 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ ( size_size_list_int @ ( removeAll_int @ X @ Xs ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4152_length__removeAll__less,axiom,
% 13.77/7.74 ! [X: set_nat,Xs: list_set_nat] :
% 13.77/7.74 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ ( size_s3254054031482475050et_nat @ ( removeAll_set_nat @ X @ Xs ) ) @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4153_length__removeAll__less,axiom,
% 13.77/7.74 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.74 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ ( removeAll_VEBT_VEBT @ X @ Xs ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4154_length__removeAll__less,axiom,
% 13.77/7.74 ! [X: real,Xs: list_real] :
% 13.77/7.74 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ ( size_size_list_real @ ( removeAll_real @ X @ Xs ) ) @ ( size_size_list_real @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4155_length__removeAll__less,axiom,
% 13.77/7.74 ! [X: $o,Xs: list_o] :
% 13.77/7.74 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ ( size_size_list_o @ ( removeAll_o @ X @ Xs ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4156_length__removeAll__less,axiom,
% 13.77/7.74 ! [X: nat,Xs: list_nat] :
% 13.77/7.74 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.74 => ( ord_less_nat @ ( size_size_list_nat @ ( removeAll_nat @ X @ Xs ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4157_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_literal] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bot_set_literal )
% 13.77/7.74 & ( finite5847741373460823677iteral @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4158_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_list_nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bot_set_list_nat )
% 13.77/7.74 & ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4159_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_set_nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bot_set_set_nat )
% 13.77/7.74 & ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4160_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_complex] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bot_set_complex )
% 13.77/7.74 & ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4161_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_Code_integer] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.74 & ( finite6017078050557962740nteger @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4162_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bot_set_nat )
% 13.77/7.74 & ( finite_finite_nat @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4163_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_int] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bot_set_int )
% 13.77/7.74 & ( finite_finite_int @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4164_card__gt__0__iff,axiom,
% 13.77/7.74 ! [A4: set_o] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A4 ) )
% 13.77/7.74 = ( ( A4 != bot_bot_set_o )
% 13.77/7.74 & ( finite_finite_o @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4165_card__le__Suc0__iff__eq,axiom,
% 13.77/7.74 ! [A4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_literal @ A4 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ! [X4: literal] :
% 13.77/7.74 ( ( member_literal @ X4 @ A4 )
% 13.77/7.74 => ! [Y4: literal] :
% 13.77/7.74 ( ( member_literal @ Y4 @ A4 )
% 13.77/7.74 => ( X4 = Y4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4166_card__le__Suc0__iff__eq,axiom,
% 13.77/7.74 ! [A4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ! [X4: list_nat] :
% 13.77/7.74 ( ( member_list_nat @ X4 @ A4 )
% 13.77/7.74 => ! [Y4: list_nat] :
% 13.77/7.74 ( ( member_list_nat @ Y4 @ A4 )
% 13.77/7.74 => ( X4 = Y4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4167_card__le__Suc0__iff__eq,axiom,
% 13.77/7.74 ! [A4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ! [X4: set_nat] :
% 13.77/7.74 ( ( member_set_nat @ X4 @ A4 )
% 13.77/7.74 => ! [Y4: set_nat] :
% 13.77/7.74 ( ( member_set_nat @ Y4 @ A4 )
% 13.77/7.74 => ( X4 = Y4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4168_card__le__Suc0__iff__eq,axiom,
% 13.77/7.74 ! [A4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ! [X4: nat] :
% 13.77/7.74 ( ( member_nat @ X4 @ A4 )
% 13.77/7.74 => ! [Y4: nat] :
% 13.77/7.74 ( ( member_nat @ Y4 @ A4 )
% 13.77/7.74 => ( X4 = Y4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4169_card__le__Suc0__iff__eq,axiom,
% 13.77/7.74 ! [A4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ! [X4: int] :
% 13.77/7.74 ( ( member_int @ X4 @ A4 )
% 13.77/7.74 => ! [Y4: int] :
% 13.77/7.74 ( ( member_int @ Y4 @ A4 )
% 13.77/7.74 => ( X4 = Y4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4170_card__le__Suc0__iff__eq,axiom,
% 13.77/7.74 ! [A4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ! [X4: complex] :
% 13.77/7.74 ( ( member_complex @ X4 @ A4 )
% 13.77/7.74 => ! [Y4: complex] :
% 13.77/7.74 ( ( member_complex @ Y4 @ A4 )
% 13.77/7.74 => ( X4 = Y4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4171_card__le__Suc0__iff__eq,axiom,
% 13.77/7.74 ! [A4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ! [X4: code_integer] :
% 13.77/7.74 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.74 => ! [Y4: code_integer] :
% 13.77/7.74 ( ( member_Code_integer @ Y4 @ A4 )
% 13.77/7.74 => ( X4 = Y4 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4172_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,K: nat] :
% 13.77/7.74 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_VEBT_VEBT @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_VEBT_VEBT @ B7 @ B6 )
% 13.77/7.74 & ( ( finite7802652506058667612T_VEBT @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4173_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_real,K: nat] :
% 13.77/7.74 ( ( ( finite_card_real @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: real,B6: set_real] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_real @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_real @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_real @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_real ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4174_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_complex,K: nat] :
% 13.77/7.74 ( ( ( finite_card_complex @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: complex,B6: set_complex] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_complex @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_complex @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_complex @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_complex ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4175_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_literal,K: nat] :
% 13.77/7.74 ( ( ( finite_card_literal @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: literal,B6: set_literal] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_literal @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_literal @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_literal @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_literal ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4176_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_list_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: list_nat,B6: set_list_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_list_nat @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_list_nat @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_list_nat @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_list_nat ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4177_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_set_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: set_nat,B6: set_set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_set_nat @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_set_nat @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_set_nat @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_set_nat ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4178_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: nat,B6: set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_nat @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_nat @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_nat @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_nat ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4179_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_int,K: nat] :
% 13.77/7.74 ( ( ( finite_card_int @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: int,B6: set_int] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_int @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_int @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_int @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_int ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4180_card__Suc__eq,axiom,
% 13.77/7.74 ! [A4: set_o,K: nat] :
% 13.77/7.74 ( ( ( finite_card_o @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 = ( ? [B7: $o,B6: set_o] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_o @ B7 @ B6 ) )
% 13.77/7.74 & ~ ( member_o @ B7 @ B6 )
% 13.77/7.74 & ( ( finite_card_o @ B6 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B6 = bot_bot_set_o ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4181_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,K: nat] :
% 13.77/7.74 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: vEBT_VEBT,B8: set_VEBT_VEBT] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_VEBT_VEBT @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_VEBT_VEBT @ B3 @ B8 )
% 13.77/7.74 & ( ( finite7802652506058667612T_VEBT @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4182_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_real,K: nat] :
% 13.77/7.74 ( ( ( finite_card_real @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: real,B8: set_real] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_real @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_real @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_real @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_real ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4183_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_complex,K: nat] :
% 13.77/7.74 ( ( ( finite_card_complex @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: complex,B8: set_complex] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_complex @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_complex @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_complex @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_complex ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4184_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_literal,K: nat] :
% 13.77/7.74 ( ( ( finite_card_literal @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: literal,B8: set_literal] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_literal @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_literal @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_literal @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_literal ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4185_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_list_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: list_nat,B8: set_list_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_list_nat @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_list_nat @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_list_nat @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_list_nat ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4186_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_set_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: set_nat,B8: set_set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_set_nat @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_set_nat @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_set_nat @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_set_nat ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4187_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_nat,K: nat] :
% 13.77/7.74 ( ( ( finite_card_nat @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: nat,B8: set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_nat @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_nat @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_nat @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_nat ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4188_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_int,K: nat] :
% 13.77/7.74 ( ( ( finite_card_int @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: int,B8: set_int] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_int @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_int @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_int @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_int ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4189_card__eq__SucD,axiom,
% 13.77/7.74 ! [A4: set_o,K: nat] :
% 13.77/7.74 ( ( ( finite_card_o @ A4 )
% 13.77/7.74 = ( suc @ K ) )
% 13.77/7.74 => ? [B3: $o,B8: set_o] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_o @ B3 @ B8 ) )
% 13.77/7.74 & ~ ( member_o @ B3 @ B8 )
% 13.77/7.74 & ( ( finite_card_o @ B8 )
% 13.77/7.74 = K )
% 13.77/7.74 & ( ( K = zero_zero_nat )
% 13.77/7.74 => ( B8 = bot_bot_set_o ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4190_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT] :
% 13.77/7.74 ( ( ( finite7802652506058667612T_VEBT @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: vEBT_VEBT] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_VEBT_VEBT @ X4 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4191_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_complex] :
% 13.77/7.74 ( ( ( finite_card_complex @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: complex] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4192_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_literal] :
% 13.77/7.74 ( ( ( finite_card_literal @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: literal] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_literal @ X4 @ bot_bot_set_literal ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4193_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_list_nat] :
% 13.77/7.74 ( ( ( finite_card_list_nat @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: list_nat] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4194_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_set_nat] :
% 13.77/7.74 ( ( ( finite_card_set_nat @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: set_nat] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4195_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_nat] :
% 13.77/7.74 ( ( ( finite_card_nat @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: nat] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4196_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_int] :
% 13.77/7.74 ( ( ( finite_card_int @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: int] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4197_card__1__singleton__iff,axiom,
% 13.77/7.74 ! [A4: set_o] :
% 13.77/7.74 ( ( ( finite_card_o @ A4 )
% 13.77/7.74 = ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( ? [X4: $o] :
% 13.77/7.74 ( A4
% 13.77/7.74 = ( insert_o @ X4 @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4198_power__Suc__less,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_real @ A @ one_one_real )
% 13.77/7.74 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4199_power__Suc__less,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_rat @ A @ one_one_rat )
% 13.77/7.74 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4200_power__Suc__less,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ A @ one_one_nat )
% 13.77/7.74 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4201_power__Suc__less,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_int @ A @ one_one_int )
% 13.77/7.74 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4202_power__Suc__le__self,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_eq_real @ A @ one_one_real )
% 13.77/7.74 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4203_power__Suc__le__self,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 13.77/7.74 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4204_power__Suc__le__self,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 13.77/7.74 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4205_power__Suc__le__self,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_eq_int @ A @ one_one_int )
% 13.77/7.74 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4206_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_o] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_o @ A4 ) )
% 13.77/7.74 = ( ? [A7: $o,B6: set_o] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_o @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_o @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_o @ B6 ) )
% 13.77/7.74 & ( finite_finite_o @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4207_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_VEBT_VEBT] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 13.77/7.74 = ( ? [A7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_VEBT_VEBT @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_VEBT_VEBT @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite7802652506058667612T_VEBT @ B6 ) )
% 13.77/7.74 & ( finite5795047828879050333T_VEBT @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4208_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_real] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_real @ A4 ) )
% 13.77/7.74 = ( ? [A7: real,B6: set_real] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_real @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_real @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_real @ B6 ) )
% 13.77/7.74 & ( finite_finite_real @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4209_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_literal] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_literal @ A4 ) )
% 13.77/7.74 = ( ? [A7: literal,B6: set_literal] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_literal @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_literal @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_literal @ B6 ) )
% 13.77/7.74 & ( finite5847741373460823677iteral @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4210_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_list_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_list_nat @ A4 ) )
% 13.77/7.74 = ( ? [A7: list_nat,B6: set_list_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_list_nat @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_list_nat @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ B6 ) )
% 13.77/7.74 & ( finite8100373058378681591st_nat @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4211_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_set_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_set_nat @ A4 ) )
% 13.77/7.74 = ( ? [A7: set_nat,B6: set_set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_set_nat @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_set_nat @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ B6 ) )
% 13.77/7.74 & ( finite1152437895449049373et_nat @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4212_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_nat @ A4 ) )
% 13.77/7.74 = ( ? [A7: nat,B6: set_nat] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_nat @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_nat @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_nat @ B6 ) )
% 13.77/7.74 & ( finite_finite_nat @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4213_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_int] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_int @ A4 ) )
% 13.77/7.74 = ( ? [A7: int,B6: set_int] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_int @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_int @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_int @ B6 ) )
% 13.77/7.74 & ( finite_finite_int @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4214_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_complex] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_complex @ A4 ) )
% 13.77/7.74 = ( ? [A7: complex,B6: set_complex] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_complex @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_complex @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite_card_complex @ B6 ) )
% 13.77/7.74 & ( finite3207457112153483333omplex @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4215_card__le__Suc__iff,axiom,
% 13.77/7.74 ! [N: nat,A4: set_Code_integer] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite4902975817058060853nteger @ A4 ) )
% 13.77/7.74 = ( ? [A7: code_integer,B6: set_Code_integer] :
% 13.77/7.74 ( ( A4
% 13.77/7.74 = ( insert_Code_integer @ A7 @ B6 ) )
% 13.77/7.74 & ~ ( member_Code_integer @ A7 @ B6 )
% 13.77/7.74 & ( ord_less_eq_nat @ N @ ( finite4902975817058060853nteger @ B6 ) )
% 13.77/7.74 & ( finite6017078050557962740nteger @ B6 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4216_power__Suc__less__one,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_real @ A @ one_one_real )
% 13.77/7.74 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4217_power__Suc__less__one,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_rat @ A @ one_one_rat )
% 13.77/7.74 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4218_power__Suc__less__one,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ A @ one_one_nat )
% 13.77/7.74 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4219_power__Suc__less__one,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_int @ A @ one_one_int )
% 13.77/7.74 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4220_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_literal,B4: set_complex,F: literal > complex] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_5274195009022015549omplex @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4221_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_literal,B4: set_literal,F: literal > literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( ord_le7307670543136651348iteral @ B4 @ ( image_8195128725298311301iteral @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4222_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_literal,B4: set_nat,F: literal > nat] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_set_nat @ B4 @ ( image_literal_nat @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4223_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_nat,B4: set_complex,F: nat > complex] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_nat_complex @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4224_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_nat,B4: set_literal,F: nat > literal] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( ord_le7307670543136651348iteral @ B4 @ ( image_nat_literal @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4225_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_nat,B4: set_nat,F: nat > nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_set_nat @ B4 @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4226_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_int,B4: set_complex,F: int > complex] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_int_complex @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4227_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_int,B4: set_literal,F: int > literal] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( ord_le7307670543136651348iteral @ B4 @ ( image_int_literal @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_literal @ B4 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4228_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_int,B4: set_nat,F: int > nat] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( ord_less_eq_set_nat @ B4 @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ B4 ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4229_surj__card__le,axiom,
% 13.77/7.74 ! [A4: set_complex,B4: set_complex,F: complex > complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ B4 @ ( image_1468599708987790691omplex @ F @ A4 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_complex @ B4 ) @ ( finite_card_complex @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4230_power__strict__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: real] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_real @ A @ one_one_real )
% 13.77/7.74 => ( ord_less_real @ ( power_power_real @ A @ N8 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4231_power__strict__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: rat] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_rat @ A @ one_one_rat )
% 13.77/7.74 => ( ord_less_rat @ ( power_power_rat @ A @ N8 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4232_power__strict__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: nat] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ A @ one_one_nat )
% 13.77/7.74 => ( ord_less_nat @ ( power_power_nat @ A @ N8 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4233_power__strict__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: int] :
% 13.77/7.74 ( ( ord_less_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_int @ A @ one_one_int )
% 13.77/7.74 => ( ord_less_int @ ( power_power_int @ A @ N8 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4234_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.74 => ( ( ( finite7802652506058667612T_VEBT @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_VEBT_VEBT @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4235_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_real,X: real] :
% 13.77/7.74 ( ( finite_finite_real @ S3 )
% 13.77/7.74 => ( ( ( finite_card_real @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_real @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4236_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_literal,X: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ S3 )
% 13.77/7.74 => ( ( ( finite_card_literal @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_literal @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_literal @ X @ bot_bot_set_literal ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4237_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ S3 )
% 13.77/7.74 => ( ( ( finite_card_list_nat @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_list_nat @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4238_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ S3 )
% 13.77/7.74 => ( ( ( finite_card_set_nat @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_set_nat @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4239_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_complex,X: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.74 => ( ( ( finite_card_complex @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_complex @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4240_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.74 => ( ( ( finite4902975817058060853nteger @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_Code_integer @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4241_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_nat,X: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ S3 )
% 13.77/7.74 => ( ( ( finite_card_nat @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_nat @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4242_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_int,X: int] :
% 13.77/7.74 ( ( finite_finite_int @ S3 )
% 13.77/7.74 => ( ( ( finite_card_int @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_int @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4243_card__1__singletonI,axiom,
% 13.77/7.74 ! [S3: set_o,X: $o] :
% 13.77/7.74 ( ( finite_finite_o @ S3 )
% 13.77/7.74 => ( ( ( finite_card_o @ S3 )
% 13.77/7.74 = one_one_nat )
% 13.77/7.74 => ( ( member_o @ X @ S3 )
% 13.77/7.74 => ( S3
% 13.77/7.74 = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4244_power__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: real] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_eq_real @ A @ one_one_real )
% 13.77/7.74 => ( ord_less_eq_real @ ( power_power_real @ A @ N8 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4245_power__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: rat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 13.77/7.74 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N8 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4246_power__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 13.77/7.74 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N8 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4247_power__decreasing,axiom,
% 13.77/7.74 ! [N: nat,N8: nat,A: int] :
% 13.77/7.74 ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_eq_int @ A @ one_one_int )
% 13.77/7.74 => ( ord_less_eq_int @ ( power_power_int @ A @ N8 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4248_power__eq__imp__eq__base,axiom,
% 13.77/7.74 ! [A: real,N: nat,B: real] :
% 13.77/7.74 ( ( ( power_power_real @ A @ N )
% 13.77/7.74 = ( power_power_real @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4249_power__eq__imp__eq__base,axiom,
% 13.77/7.74 ! [A: rat,N: nat,B: rat] :
% 13.77/7.74 ( ( ( power_power_rat @ A @ N )
% 13.77/7.74 = ( power_power_rat @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4250_power__eq__imp__eq__base,axiom,
% 13.77/7.74 ! [A: nat,N: nat,B: nat] :
% 13.77/7.74 ( ( ( power_power_nat @ A @ N )
% 13.77/7.74 = ( power_power_nat @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4251_power__eq__imp__eq__base,axiom,
% 13.77/7.74 ! [A: int,N: nat,B: int] :
% 13.77/7.74 ( ( ( power_power_int @ A @ N )
% 13.77/7.74 = ( power_power_int @ B @ N ) )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4252_power__eq__iff__eq__base,axiom,
% 13.77/7.74 ! [N: nat,A: real,B: real] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 13.77/7.74 => ( ( ( power_power_real @ A @ N )
% 13.77/7.74 = ( power_power_real @ B @ N ) )
% 13.77/7.74 = ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4253_power__eq__iff__eq__base,axiom,
% 13.77/7.74 ! [N: nat,A: rat,B: rat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 13.77/7.74 => ( ( ( power_power_rat @ A @ N )
% 13.77/7.74 = ( power_power_rat @ B @ N ) )
% 13.77/7.74 = ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4254_power__eq__iff__eq__base,axiom,
% 13.77/7.74 ! [N: nat,A: nat,B: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 13.77/7.74 => ( ( ( power_power_nat @ A @ N )
% 13.77/7.74 = ( power_power_nat @ B @ N ) )
% 13.77/7.74 = ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4255_power__eq__iff__eq__base,axiom,
% 13.77/7.74 ! [N: nat,A: int,B: int] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.74 => ( ( ( power_power_int @ A @ N )
% 13.77/7.74 = ( power_power_int @ B @ N ) )
% 13.77/7.74 = ( A = B ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4256_power__le__imp__le__exp,axiom,
% 13.77/7.74 ! [A: real,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.74 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 13.77/7.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4257_power__le__imp__le__exp,axiom,
% 13.77/7.74 ! [A: rat,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 13.77/7.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4258_power__le__imp__le__exp,axiom,
% 13.77/7.74 ! [A: nat,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 13.77/7.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4259_power__le__imp__le__exp,axiom,
% 13.77/7.74 ! [A: int,M: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.74 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 13.77/7.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4260_self__le__power,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_real @ one_one_real @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4261_self__le__power,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4262_self__le__power,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4263_self__le__power,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_int @ one_one_int @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4264_one__less__power,axiom,
% 13.77/7.74 ! [A: real,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4265_one__less__power,axiom,
% 13.77/7.74 ! [A: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ one_one_rat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4266_one__less__power,axiom,
% 13.77/7.74 ! [A: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ one_one_nat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4267_one__less__power,axiom,
% 13.77/7.74 ! [A: int,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4268_card__Diff1__le,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4269_card__Diff1__le,axiom,
% 13.77/7.74 ! [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 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4270_card__Diff1__le,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] : ( ord_less_eq_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4271_card__Diff1__le,axiom,
% 13.77/7.74 ! [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 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4272_card__Diff1__le,axiom,
% 13.77/7.74 ! [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 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4273_card__Diff1__le,axiom,
% 13.77/7.74 ! [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 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4274_card__Diff1__le,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] : ( ord_less_eq_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4275_card__Diff1__le,axiom,
% 13.77/7.74 ! [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 ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4276_card__Diff__subset,axiom,
% 13.77/7.74 ! [B4: set_literal,A4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ( ord_le7307670543136651348iteral @ B4 @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4277_card__Diff__subset,axiom,
% 13.77/7.74 ! [B4: set_list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6045566169113846134st_nat @ B4 @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4278_card__Diff__subset,axiom,
% 13.77/7.74 ! [B4: set_set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6893508408891458716et_nat @ B4 @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4279_card__Diff__subset,axiom,
% 13.77/7.74 ! [B4: set_complex,A4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4280_card__Diff__subset,axiom,
% 13.77/7.74 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.74 => ( ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4281_card__Diff__subset,axiom,
% 13.77/7.74 ! [B4: set_nat,A4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4282_card__Diff__subset,axiom,
% 13.77/7.74 ! [B4: set_int,A4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4283_diff__card__le__card__Diff,axiom,
% 13.77/7.74 ! [B4: set_literal,A4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) ) @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4284_diff__card__le__card__Diff,axiom,
% 13.77/7.74 ! [B4: set_list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4285_diff__card__le__card__Diff,axiom,
% 13.77/7.74 ! [B4: set_set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4286_diff__card__le__card__Diff,axiom,
% 13.77/7.74 ! [B4: set_int,A4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4287_diff__card__le__card__Diff,axiom,
% 13.77/7.74 ! [B4: set_complex,A4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4288_diff__card__le__card__Diff,axiom,
% 13.77/7.74 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4289_diff__card__le__card__Diff,axiom,
% 13.77/7.74 ! [B4: set_nat,A4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4290_card__psubset,axiom,
% 13.77/7.74 ! [B4: set_literal,A4: set_literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ B4 )
% 13.77/7.74 => ( ( ord_le7307670543136651348iteral @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_literal @ A4 ) @ ( finite_card_literal @ B4 ) )
% 13.77/7.74 => ( ord_less_set_literal @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4291_card__psubset,axiom,
% 13.77/7.74 ! [B4: set_list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6045566169113846134st_nat @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B4 ) )
% 13.77/7.74 => ( ord_le1190675801316882794st_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4292_card__psubset,axiom,
% 13.77/7.74 ! [B4: set_set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ B4 )
% 13.77/7.74 => ( ( ord_le6893508408891458716et_nat @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_set_set_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4293_card__psubset,axiom,
% 13.77/7.74 ! [B4: set_nat,A4: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B4 ) )
% 13.77/7.74 => ( ord_less_set_nat @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4294_card__psubset,axiom,
% 13.77/7.74 ! [B4: set_complex,A4: set_complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.74 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B4 ) )
% 13.77/7.74 => ( ord_less_set_complex @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4295_card__psubset,axiom,
% 13.77/7.74 ! [B4: set_Code_integer,A4: set_Code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.74 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( finite4902975817058060853nteger @ B4 ) )
% 13.77/7.74 => ( ord_le1307284697595431911nteger @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4296_card__psubset,axiom,
% 13.77/7.74 ! [B4: set_int,A4: set_int] :
% 13.77/7.74 ( ( finite_finite_int @ B4 )
% 13.77/7.74 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 13.77/7.74 => ( ( ord_less_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B4 ) )
% 13.77/7.74 => ( ord_less_set_int @ A4 @ B4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4297_finite__enumerate__mono,axiom,
% 13.77/7.74 ! [M: nat,N: nat,S3: set_nat] :
% 13.77/7.74 ( ( ord_less_nat @ M @ N )
% 13.77/7.74 => ( ( finite_finite_nat @ S3 )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 13.77/7.74 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ M ) @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4298_nat__mult__power__less__eq,axiom,
% 13.77/7.74 ! [B: nat,A: nat,N: nat,M: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ B )
% 13.77/7.74 => ( ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ B @ N ) ) @ ( power_power_nat @ B @ M ) )
% 13.77/7.74 = ( ord_less_nat @ A @ ( power_power_nat @ B @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4299_card__le__Suc__Max,axiom,
% 13.77/7.74 ! [S3: set_nat] :
% 13.77/7.74 ( ( finite_finite_nat @ S3 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4300_finite__le__enumerate,axiom,
% 13.77/7.74 ! [S3: set_nat,N: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ S3 )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 13.77/7.74 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4301_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] :
% 13.77/7.74 ( ( finite_finite_o @ A4 )
% 13.77/7.74 => ( ~ ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_o @ ( insert_o @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_o @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4302_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4303_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_real,X: real] :
% 13.77/7.74 ( ( finite_finite_real @ A4 )
% 13.77/7.74 => ( ~ ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_real @ ( insert_real @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_real @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4304_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ~ ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_literal @ ( insert_literal @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_literal @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4305_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ~ ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4306_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ~ ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4307_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ~ ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4308_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_int,X: int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ~ ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_int @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4309_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ~ ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite_card_complex @ ( insert_complex @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite_card_complex @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4310_card__insert__disjoint_H,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ~ ( member_Code_integer @ X @ A4 )
% 13.77/7.74 => ( ( minus_minus_nat @ ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.74 = ( finite4902975817058060853nteger @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4311_power__strict__mono,axiom,
% 13.77/7.74 ! [A: real,B: real,N: nat] :
% 13.77/7.74 ( ( ord_less_real @ A @ B )
% 13.77/7.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4312_power__strict__mono,axiom,
% 13.77/7.74 ! [A: rat,B: rat,N: nat] :
% 13.77/7.74 ( ( ord_less_rat @ A @ B )
% 13.77/7.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4313_power__strict__mono,axiom,
% 13.77/7.74 ! [A: nat,B: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_nat @ A @ B )
% 13.77/7.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4314_power__strict__mono,axiom,
% 13.77/7.74 ! [A: int,B: int,N: nat] :
% 13.77/7.74 ( ( ord_less_int @ A @ B )
% 13.77/7.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4315_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( finite7802652506058667612T_VEBT @ A4 )
% 13.77/7.74 = ( suc @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4316_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_real,X: real] :
% 13.77/7.74 ( ( finite_finite_real @ A4 )
% 13.77/7.74 => ( ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_real @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4317_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4318_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4319_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4320_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4321_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.74 => ( ( finite4902975817058060853nteger @ A4 )
% 13.77/7.74 = ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4322_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_int,X: int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4323_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] :
% 13.77/7.74 ( ( finite_finite_o @ A4 )
% 13.77/7.74 => ( ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_o @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4324_card_Oremove,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ A4 )
% 13.77/7.74 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4325_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 => ( ( finite7802652506058667612T_VEBT @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4326_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ ( insert_literal @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4327_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4328_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4329_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4330_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( finite4902975817058060853nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4331_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_int,X: int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4332_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] :
% 13.77/7.74 ( ( finite_finite_o @ A4 )
% 13.77/7.74 => ( ( finite_card_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4333_card_Oinsert__remove,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.74 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4334_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) )
% 13.77/7.74 = ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4335_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_real,X: real] :
% 13.77/7.74 ( ( finite_finite_real @ A4 )
% 13.77/7.74 => ( ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 13.77/7.74 = ( finite_card_real @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4336_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) )
% 13.77/7.74 = ( finite_card_literal @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4337_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) )
% 13.77/7.74 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4338_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 13.77/7.74 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4339_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 13.77/7.74 = ( finite_card_complex @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4340_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) )
% 13.77/7.74 = ( finite4902975817058060853nteger @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4341_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_int,X: int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 13.77/7.74 = ( finite_card_int @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4342_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] :
% 13.77/7.74 ( ( finite_finite_o @ A4 )
% 13.77/7.74 => ( ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) )
% 13.77/7.74 = ( finite_card_o @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4343_card__Suc__Diff1,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 13.77/7.74 = ( finite_card_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4344_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4345_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_real,X: real] :
% 13.77/7.74 ( ( finite_finite_real @ A4 )
% 13.77/7.74 => ( ( member_real @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4346_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4347_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4348_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4349_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4350_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4351_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_int,X: int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( member_int @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4352_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] :
% 13.77/7.74 ( ( finite_finite_o @ A4 )
% 13.77/7.74 => ( ( member_o @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4353_card__Diff1__less,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4354_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.74 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( member_VEBT_VEBT @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) @ ( insert_VEBT_VEBT @ Y @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4355_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_real,X: real,Y: real] :
% 13.77/7.74 ( ( finite_finite_real @ A4 )
% 13.77/7.74 => ( ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( member_real @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) @ ( insert_real @ Y @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4356_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal,Y: literal] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( member_literal @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) @ ( insert_literal @ Y @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4357_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat,Y: list_nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( member_list_nat @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) @ ( insert_list_nat @ Y @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4358_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat,Y: set_nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( member_set_nat @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ ( insert_set_nat @ Y @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4359_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex,Y: complex] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( member_complex @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ ( insert_complex @ Y @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4360_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer,Y: code_integer] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.74 => ( ( member_Code_integer @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) @ ( insert_Code_integer @ Y @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4361_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_int,X: int,Y: int] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( member_int @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) @ ( insert_int @ Y @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4362_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o,Y: $o] :
% 13.77/7.74 ( ( finite_finite_o @ A4 )
% 13.77/7.74 => ( ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( member_o @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) @ ( insert_o @ Y @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4363_card__Diff2__less,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat,Y: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( member_nat @ Y @ A4 )
% 13.77/7.74 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4364_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 13.77/7.74 = ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.74 & ( member_VEBT_VEBT @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4365_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_real,X: real] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) )
% 13.77/7.74 = ( ( finite_finite_real @ A4 )
% 13.77/7.74 & ( member_real @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4366_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_literal,X: literal] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) ) @ ( finite_card_literal @ A4 ) )
% 13.77/7.74 = ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 & ( member_literal @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4367_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_list_nat,X: list_nat] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) )
% 13.77/7.74 = ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 & ( member_list_nat @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4368_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_set_nat,X: set_nat] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) )
% 13.77/7.74 = ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 & ( member_set_nat @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4369_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_complex,X: complex] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) )
% 13.77/7.74 = ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 & ( member_complex @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4370_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) @ ( finite4902975817058060853nteger @ A4 ) )
% 13.77/7.74 = ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 & ( member_Code_integer @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4371_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_int,X: int] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) )
% 13.77/7.74 = ( ( finite_finite_int @ A4 )
% 13.77/7.74 & ( member_int @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4372_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_o,X: $o] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) @ ( finite_card_o @ A4 ) )
% 13.77/7.74 = ( ( finite_finite_o @ A4 )
% 13.77/7.74 & ( member_o @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4373_card__Diff1__less__iff,axiom,
% 13.77/7.74 ! [A4: set_nat,X: nat] :
% 13.77/7.74 ( ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) )
% 13.77/7.74 = ( ( finite_finite_nat @ A4 )
% 13.77/7.74 & ( member_nat @ X @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4374_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.74 ( ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.74 = ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4375_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: real,A4: set_real] :
% 13.77/7.74 ( ( ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_real @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 13.77/7.74 = ( finite_card_real @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4376_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: complex,A4: set_complex] :
% 13.77/7.74 ( ( ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 13.77/7.74 = ( finite_card_complex @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4377_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: literal,A4: set_literal] :
% 13.77/7.74 ( ( ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 13.77/7.74 = ( finite_card_literal @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4378_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 13.77/7.74 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4379_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 13.77/7.74 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4380_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: int,A4: set_int] :
% 13.77/7.74 ( ( ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_int @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 13.77/7.74 = ( finite_card_int @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4381_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: $o,A4: set_o] :
% 13.77/7.74 ( ( ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_o @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 13.77/7.74 = ( finite_card_o @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4382_card__Diff__singleton__if,axiom,
% 13.77/7.74 ! [X: nat,A4: set_nat] :
% 13.77/7.74 ( ( ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ one_one_nat ) ) )
% 13.77/7.74 & ( ~ ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 13.77/7.74 = ( finite_card_nat @ A4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4383_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.74 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.74 => ( ( finite7802652506058667612T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4384_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: real,A4: set_real] :
% 13.77/7.74 ( ( member_real @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_real @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4385_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: complex,A4: set_complex] :
% 13.77/7.74 ( ( member_complex @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4386_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: literal,A4: set_literal] :
% 13.77/7.74 ( ( member_literal @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_literal @ ( minus_7832829386415567259iteral @ A4 @ ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_literal @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4387_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: list_nat,A4: set_list_nat] :
% 13.77/7.74 ( ( member_list_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4388_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: set_nat,A4: set_set_nat] :
% 13.77/7.74 ( ( member_set_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4389_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: int,A4: set_int] :
% 13.77/7.74 ( ( member_int @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_int @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4390_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: $o,A4: set_o] :
% 13.77/7.74 ( ( member_o @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_o @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4391_card__Diff__singleton,axiom,
% 13.77/7.74 ! [X: nat,A4: set_nat] :
% 13.77/7.74 ( ( member_nat @ X @ A4 )
% 13.77/7.74 => ( ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 13.77/7.74 = ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ one_one_nat ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4392_the__default_Osimps_I1_J,axiom,
% 13.77/7.74 ! [Uu2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 13.77/7.74 ( ( the_de3812365490807259288at_nat @ Uu2 @ ( some_P7363390416028606310at_nat @ X ) )
% 13.77/7.74 = X ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4393_the__default_Osimps_I1_J,axiom,
% 13.77/7.74 ! [Uu2: nat,X: nat] :
% 13.77/7.74 ( ( the_default_nat @ Uu2 @ ( some_nat @ X ) )
% 13.77/7.74 = X ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4394_power__eq__if,axiom,
% 13.77/7.74 ( power_power_rat
% 13.77/7.74 = ( ^ [P7: rat,M5: nat] : ( if_rat @ ( M5 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P7 @ ( power_power_rat @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4395_power__eq__if,axiom,
% 13.77/7.74 ( power_power_complex
% 13.77/7.74 = ( ^ [P7: complex,M5: nat] : ( if_complex @ ( M5 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P7 @ ( power_power_complex @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4396_power__eq__if,axiom,
% 13.77/7.74 ( power_power_assn
% 13.77/7.74 = ( ^ [P7: assn,M5: nat] : ( if_assn @ ( M5 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P7 @ ( power_power_assn @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4397_power__eq__if,axiom,
% 13.77/7.74 ( power_power_uint32
% 13.77/7.74 = ( ^ [P7: uint32,M5: nat] : ( if_uint32 @ ( M5 = zero_zero_nat ) @ one_one_uint32 @ ( times_times_uint32 @ P7 @ ( power_power_uint32 @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4398_power__eq__if,axiom,
% 13.77/7.74 ( power_power_real
% 13.77/7.74 = ( ^ [P7: real,M5: nat] : ( if_real @ ( M5 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P7 @ ( power_power_real @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4399_power__eq__if,axiom,
% 13.77/7.74 ( power_power_nat
% 13.77/7.74 = ( ^ [P7: nat,M5: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P7 @ ( power_power_nat @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4400_power__eq__if,axiom,
% 13.77/7.74 ( power_power_int
% 13.77/7.74 = ( ^ [P7: int,M5: nat] : ( if_int @ ( M5 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P7 @ ( power_power_int @ P7 @ ( minus_minus_nat @ M5 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4401_the__default_Osimps_I2_J,axiom,
% 13.77/7.74 ! [X: product_prod_nat_nat] :
% 13.77/7.74 ( ( the_de3812365490807259288at_nat @ X @ none_P5556105721700978146at_nat )
% 13.77/7.74 = X ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4402_the__default_Osimps_I2_J,axiom,
% 13.77/7.74 ! [X: nat] :
% 13.77/7.74 ( ( the_default_nat @ X @ none_nat )
% 13.77/7.74 = X ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4403_power__minus__mult,axiom,
% 13.77/7.74 ! [N: nat,A: complex] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 13.77/7.74 = ( power_power_complex @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4404_power__minus__mult,axiom,
% 13.77/7.74 ! [N: nat,A: assn] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 13.77/7.74 = ( power_power_assn @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4405_power__minus__mult,axiom,
% 13.77/7.74 ! [N: nat,A: uint32] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( times_times_uint32 @ ( power_power_uint32 @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 13.77/7.74 = ( power_power_uint32 @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4406_power__minus__mult,axiom,
% 13.77/7.74 ! [N: nat,A: real] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 13.77/7.74 = ( power_power_real @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4407_power__minus__mult,axiom,
% 13.77/7.74 ! [N: nat,A: nat] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 13.77/7.74 = ( power_power_nat @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4408_power__minus__mult,axiom,
% 13.77/7.74 ! [N: nat,A: int] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 13.77/7.74 = ( power_power_int @ A @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4409_finite__enumerate__step,axiom,
% 13.77/7.74 ! [S3: set_nat,N: nat] :
% 13.77/7.74 ( ( finite_finite_nat @ S3 )
% 13.77/7.74 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite_card_nat @ S3 ) )
% 13.77/7.74 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4410_finite__enum__subset,axiom,
% 13.77/7.74 ! [X6: set_nat,Y7: set_nat] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( finite_card_nat @ X6 ) )
% 13.77/7.74 => ( ( infini8530281810654367211te_nat @ X6 @ I2 )
% 13.77/7.74 = ( infini8530281810654367211te_nat @ Y7 @ I2 ) ) )
% 13.77/7.74 => ( ( finite_finite_nat @ X6 )
% 13.77/7.74 => ( ( finite_finite_nat @ Y7 )
% 13.77/7.74 => ( ( ord_less_eq_nat @ ( finite_card_nat @ X6 ) @ ( finite_card_nat @ Y7 ) )
% 13.77/7.74 => ( ord_less_eq_set_nat @ X6 @ Y7 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4411_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 13.77/7.74 ! [K: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.74 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 13.77/7.74 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4412_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 13.77/7.74 ! [K: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.74 => ( ( power_power_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ ( plus_plus_nat @ N @ K ) )
% 13.77/7.74 = ( power_power_uint32 @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4413_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 13.77/7.74 ! [K: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.74 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 13.77/7.74 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4414_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 13.77/7.74 ! [K: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.74 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 13.77/7.74 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4415_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 13.77/7.74 ! [K: nat,N: nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.74 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 13.77/7.74 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4416_inthall,axiom,
% 13.77/7.74 ! [Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o,N: nat] :
% 13.77/7.74 ( ! [X3: vEBT_VEBTi] :
% 13.77/7.74 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 13.77/7.74 => ( P2 @ X3 ) )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.74 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4417_inthall,axiom,
% 13.77/7.74 ! [Xs: list_int,P2: int > $o,N: nat] :
% 13.77/7.74 ( ! [X3: int] :
% 13.77/7.74 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 13.77/7.74 => ( P2 @ X3 ) )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 13.77/7.74 => ( P2 @ ( nth_int @ Xs @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4418_inthall,axiom,
% 13.77/7.74 ! [Xs: list_set_nat,P2: set_nat > $o,N: nat] :
% 13.77/7.74 ( ! [X3: set_nat] :
% 13.77/7.74 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 13.77/7.74 => ( P2 @ X3 ) )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.74 => ( P2 @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4419_inthall,axiom,
% 13.77/7.74 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o,N: nat] :
% 13.77/7.74 ( ! [X3: vEBT_VEBT] :
% 13.77/7.74 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.74 => ( P2 @ X3 ) )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.74 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4420_inthall,axiom,
% 13.77/7.74 ! [Xs: list_real,P2: real > $o,N: nat] :
% 13.77/7.74 ( ! [X3: real] :
% 13.77/7.74 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 13.77/7.74 => ( P2 @ X3 ) )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.74 => ( P2 @ ( nth_real @ Xs @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4421_inthall,axiom,
% 13.77/7.74 ! [Xs: list_o,P2: $o > $o,N: nat] :
% 13.77/7.74 ( ! [X3: $o] :
% 13.77/7.74 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 13.77/7.74 => ( P2 @ X3 ) )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.74 => ( P2 @ ( nth_o @ Xs @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4422_inthall,axiom,
% 13.77/7.74 ! [Xs: list_nat,P2: nat > $o,N: nat] :
% 13.77/7.74 ( ! [X3: nat] :
% 13.77/7.74 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 13.77/7.74 => ( P2 @ X3 ) )
% 13.77/7.74 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.74 => ( P2 @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4423_slice__len,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.74 ( ( ord_less_eq_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.74 => ( ( size_s6755466524823107622T_VEBT @ ( slice_VEBT_VEBT @ From @ To @ Xs ) )
% 13.77/7.74 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4424_slice__len,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_real] :
% 13.77/7.74 ( ( ord_less_eq_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_size_list_real @ Xs ) )
% 13.77/7.74 => ( ( size_size_list_real @ ( slice_real @ From @ To @ Xs ) )
% 13.77/7.74 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4425_slice__len,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_o] :
% 13.77/7.74 ( ( ord_less_eq_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 13.77/7.74 => ( ( size_size_list_o @ ( slice_o @ From @ To @ Xs ) )
% 13.77/7.74 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4426_slice__len,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 13.77/7.74 => ( ( size_size_list_nat @ ( slice_nat @ From @ To @ Xs ) )
% 13.77/7.74 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4427_card__Min__le__sum,axiom,
% 13.77/7.74 ! [A4: set_literal,F: literal > nat] :
% 13.77/7.74 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_literal @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_literal_nat @ F @ A4 ) ) ) @ ( groups8652099787943017962al_nat @ F @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4428_card__Min__le__sum,axiom,
% 13.77/7.74 ! [A4: set_list_nat,F: list_nat > nat] :
% 13.77/7.74 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_list_nat @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_list_nat_nat @ F @ A4 ) ) ) @ ( groups4396056296759096172at_nat @ F @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4429_card__Min__le__sum,axiom,
% 13.77/7.74 ! [A4: set_set_nat,F: set_nat > nat] :
% 13.77/7.74 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_set_nat @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_set_nat_nat @ F @ A4 ) ) ) @ ( groups8294997508430121362at_nat @ F @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4430_card__Min__le__sum,axiom,
% 13.77/7.74 ! [A4: set_int,F: int > nat] :
% 13.77/7.74 ( ( finite_finite_int @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_int @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_int_nat @ F @ A4 ) ) ) @ ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4431_card__Min__le__sum,axiom,
% 13.77/7.74 ! [A4: set_complex,F: complex > nat] :
% 13.77/7.74 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_complex @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_complex_nat @ F @ A4 ) ) ) @ ( groups5693394587270226106ex_nat @ F @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4432_card__Min__le__sum,axiom,
% 13.77/7.74 ! [A4: set_Code_integer,F: code_integer > nat] :
% 13.77/7.74 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_951025933927791156er_nat @ F @ A4 ) ) ) @ ( groups7237345082560585321er_nat @ F @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4433_card__Min__le__sum,axiom,
% 13.77/7.74 ! [A4: set_nat,F: nat > nat] :
% 13.77/7.74 ( ( finite_finite_nat @ A4 )
% 13.77/7.74 => ( ord_less_eq_nat @ ( times_times_nat @ ( finite_card_nat @ A4 ) @ ( lattic8721135487736765967in_nat @ ( image_nat_nat @ F @ A4 ) ) ) @ ( groups3542108847815614940at_nat @ F @ A4 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4434_realpow__pos__nth,axiom,
% 13.77/7.74 ! [N: nat,A: real] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.74 => ? [R4: real] :
% 13.77/7.74 ( ( ord_less_real @ zero_zero_real @ R4 )
% 13.77/7.74 & ( ( power_power_real @ R4 @ N )
% 13.77/7.74 = A ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4435_realpow__pos__nth__unique,axiom,
% 13.77/7.74 ! [N: nat,A: real] :
% 13.77/7.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.74 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.74 => ? [X3: real] :
% 13.77/7.74 ( ( ord_less_real @ zero_zero_real @ X3 )
% 13.77/7.74 & ( ( power_power_real @ X3 @ N )
% 13.77/7.74 = A )
% 13.77/7.74 & ! [Y5: real] :
% 13.77/7.74 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 13.77/7.74 & ( ( power_power_real @ Y5 @ N )
% 13.77/7.74 = A ) )
% 13.77/7.74 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4436_length__mul__elem,axiom,
% 13.77/7.74 ! [Xs: list_list_VEBT_VEBT,N: nat] :
% 13.77/7.74 ( ! [X3: list_VEBT_VEBT] :
% 13.77/7.74 ( ( member2936631157270082147T_VEBT @ X3 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 13.77/7.74 => ( ( size_s6755466524823107622T_VEBT @ X3 )
% 13.77/7.74 = N ) )
% 13.77/7.74 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 13.77/7.74 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4437_length__mul__elem,axiom,
% 13.77/7.74 ! [Xs: list_list_real,N: nat] :
% 13.77/7.74 ( ! [X3: list_real] :
% 13.77/7.74 ( ( member_list_real @ X3 @ ( set_list_real2 @ Xs ) )
% 13.77/7.74 => ( ( size_size_list_real @ X3 )
% 13.77/7.74 = N ) )
% 13.77/7.74 => ( ( size_size_list_real @ ( concat_real @ Xs ) )
% 13.77/7.74 = ( times_times_nat @ ( size_s6660260683639930848t_real @ Xs ) @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4438_length__mul__elem,axiom,
% 13.77/7.74 ! [Xs: list_list_o,N: nat] :
% 13.77/7.74 ( ! [X3: list_o] :
% 13.77/7.74 ( ( member_list_o @ X3 @ ( set_list_o2 @ Xs ) )
% 13.77/7.74 => ( ( size_size_list_o @ X3 )
% 13.77/7.74 = N ) )
% 13.77/7.74 => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 13.77/7.74 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4439_length__mul__elem,axiom,
% 13.77/7.74 ! [Xs: list_list_nat,N: nat] :
% 13.77/7.74 ( ! [X3: list_nat] :
% 13.77/7.74 ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xs ) )
% 13.77/7.74 => ( ( size_size_list_nat @ X3 )
% 13.77/7.74 = N ) )
% 13.77/7.74 => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 13.77/7.74 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4440_rotate1__length01,axiom,
% 13.77/7.74 ! [Xs: list_VEBT_VEBT] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat )
% 13.77/7.74 => ( ( rotate1_VEBT_VEBT @ Xs )
% 13.77/7.74 = Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4441_rotate1__length01,axiom,
% 13.77/7.74 ! [Xs: list_real] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ one_one_nat )
% 13.77/7.74 => ( ( rotate1_real @ Xs )
% 13.77/7.74 = Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4442_rotate1__length01,axiom,
% 13.77/7.74 ! [Xs: list_o] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 13.77/7.74 => ( ( rotate1_o @ Xs )
% 13.77/7.74 = Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4443_rotate1__length01,axiom,
% 13.77/7.74 ! [Xs: list_nat] :
% 13.77/7.74 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 13.77/7.74 => ( ( rotate1_nat @ Xs )
% 13.77/7.74 = Xs ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4444_not__real__square__gt__zero,axiom,
% 13.77/7.74 ! [X: real] :
% 13.77/7.74 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 13.77/7.74 = ( X = zero_zero_real ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4445_slice__complete,axiom,
% 13.77/7.74 ! [Xs: list_VEBT_VEBT] :
% 13.77/7.74 ( ( slice_VEBT_VEBT @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ Xs )
% 13.77/7.74 = Xs ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4446_slice__complete,axiom,
% 13.77/7.74 ! [Xs: list_real] :
% 13.77/7.74 ( ( slice_real @ zero_zero_nat @ ( size_size_list_real @ Xs ) @ Xs )
% 13.77/7.74 = Xs ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4447_slice__complete,axiom,
% 13.77/7.74 ! [Xs: list_o] :
% 13.77/7.74 ( ( slice_o @ zero_zero_nat @ ( size_size_list_o @ Xs ) @ Xs )
% 13.77/7.74 = Xs ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4448_slice__complete,axiom,
% 13.77/7.74 ! [Xs: list_nat] :
% 13.77/7.74 ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) @ Xs )
% 13.77/7.74 = Xs ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4449_real__add__le__0__iff,axiom,
% 13.77/7.74 ! [X: real,Y: real] :
% 13.77/7.74 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 13.77/7.74 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4450_real__0__le__add__iff,axiom,
% 13.77/7.74 ! [X: real,Y: real] :
% 13.77/7.74 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 13.77/7.74 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4451_less__eq__real__def,axiom,
% 13.77/7.74 ( ord_less_eq_real
% 13.77/7.74 = ( ^ [X4: real,Y4: real] :
% 13.77/7.74 ( ( ord_less_real @ X4 @ Y4 )
% 13.77/7.74 | ( X4 = Y4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4452_real__arch__pow,axiom,
% 13.77/7.74 ! [X: real,Y: real] :
% 13.77/7.74 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.74 => ? [N2: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N2 ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4453_real__arch__pow__inv,axiom,
% 13.77/7.74 ! [Y: real,X: real] :
% 13.77/7.74 ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.74 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.74 => ? [N2: nat] : ( ord_less_real @ ( power_power_real @ X @ N2 ) @ Y ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4454_real__add__less__0__iff,axiom,
% 13.77/7.74 ! [X: real,Y: real] :
% 13.77/7.74 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 13.77/7.74 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4455_real__0__less__add__iff,axiom,
% 13.77/7.74 ! [X: real,Y: real] :
% 13.77/7.74 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 13.77/7.74 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4456_nth__equalityI,axiom,
% 13.77/7.74 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 13.77/7.74 ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.74 = ( size_s7982070591426661849_VEBTi @ Ys ) )
% 13.77/7.74 => ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.74 => ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.74 = ( nth_VEBT_VEBTi @ Ys @ I2 ) ) )
% 13.77/7.74 => ( Xs = Ys ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4457_nth__equalityI,axiom,
% 13.77/7.74 ! [Xs: list_int,Ys: list_int] :
% 13.77/7.74 ( ( ( size_size_list_int @ Xs )
% 13.77/7.74 = ( size_size_list_int @ Ys ) )
% 13.77/7.74 => ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.74 => ( ( nth_int @ Xs @ I2 )
% 13.77/7.74 = ( nth_int @ Ys @ I2 ) ) )
% 13.77/7.74 => ( Xs = Ys ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4458_nth__equalityI,axiom,
% 13.77/7.74 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 13.77/7.74 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.74 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.74 => ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.74 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 13.77/7.74 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 13.77/7.74 => ( Xs = Ys ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4459_nth__equalityI,axiom,
% 13.77/7.74 ! [Xs: list_real,Ys: list_real] :
% 13.77/7.74 ( ( ( size_size_list_real @ Xs )
% 13.77/7.74 = ( size_size_list_real @ Ys ) )
% 13.77/7.74 => ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 13.77/7.74 => ( ( nth_real @ Xs @ I2 )
% 13.77/7.74 = ( nth_real @ Ys @ I2 ) ) )
% 13.77/7.74 => ( Xs = Ys ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4460_nth__equalityI,axiom,
% 13.77/7.74 ! [Xs: list_o,Ys: list_o] :
% 13.77/7.74 ( ( ( size_size_list_o @ Xs )
% 13.77/7.74 = ( size_size_list_o @ Ys ) )
% 13.77/7.74 => ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 13.77/7.74 => ( ( nth_o @ Xs @ I2 )
% 13.77/7.74 = ( nth_o @ Ys @ I2 ) ) )
% 13.77/7.74 => ( Xs = Ys ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4461_nth__equalityI,axiom,
% 13.77/7.74 ! [Xs: list_nat,Ys: list_nat] :
% 13.77/7.74 ( ( ( size_size_list_nat @ Xs )
% 13.77/7.74 = ( size_size_list_nat @ Ys ) )
% 13.77/7.74 => ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.74 => ( ( nth_nat @ Xs @ I2 )
% 13.77/7.74 = ( nth_nat @ Ys @ I2 ) ) )
% 13.77/7.74 => ( Xs = Ys ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4462_Skolem__list__nth,axiom,
% 13.77/7.74 ! [K: nat,P2: nat > vEBT_VEBTi > $o] :
% 13.77/7.74 ( ( ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ? [X8: vEBT_VEBTi] : ( P2 @ I3 @ X8 ) ) )
% 13.77/7.74 = ( ? [Xs2: list_VEBT_VEBTi] :
% 13.77/7.74 ( ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 13.77/7.74 = K )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ( P2 @ I3 @ ( nth_VEBT_VEBTi @ Xs2 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4463_Skolem__list__nth,axiom,
% 13.77/7.74 ! [K: nat,P2: nat > int > $o] :
% 13.77/7.74 ( ( ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ? [X8: int] : ( P2 @ I3 @ X8 ) ) )
% 13.77/7.74 = ( ? [Xs2: list_int] :
% 13.77/7.74 ( ( ( size_size_list_int @ Xs2 )
% 13.77/7.74 = K )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ( P2 @ I3 @ ( nth_int @ Xs2 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4464_Skolem__list__nth,axiom,
% 13.77/7.74 ! [K: nat,P2: nat > vEBT_VEBT > $o] :
% 13.77/7.74 ( ( ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ? [X8: vEBT_VEBT] : ( P2 @ I3 @ X8 ) ) )
% 13.77/7.74 = ( ? [Xs2: list_VEBT_VEBT] :
% 13.77/7.74 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 13.77/7.74 = K )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ( P2 @ I3 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4465_Skolem__list__nth,axiom,
% 13.77/7.74 ! [K: nat,P2: nat > real > $o] :
% 13.77/7.74 ( ( ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ? [X8: real] : ( P2 @ I3 @ X8 ) ) )
% 13.77/7.74 = ( ? [Xs2: list_real] :
% 13.77/7.74 ( ( ( size_size_list_real @ Xs2 )
% 13.77/7.74 = K )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ( P2 @ I3 @ ( nth_real @ Xs2 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4466_Skolem__list__nth,axiom,
% 13.77/7.74 ! [K: nat,P2: nat > $o > $o] :
% 13.77/7.74 ( ( ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ? [X8: $o] : ( P2 @ I3 @ X8 ) ) )
% 13.77/7.74 = ( ? [Xs2: list_o] :
% 13.77/7.74 ( ( ( size_size_list_o @ Xs2 )
% 13.77/7.74 = K )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ( P2 @ I3 @ ( nth_o @ Xs2 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4467_Skolem__list__nth,axiom,
% 13.77/7.74 ! [K: nat,P2: nat > nat > $o] :
% 13.77/7.74 ( ( ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ? [X8: nat] : ( P2 @ I3 @ X8 ) ) )
% 13.77/7.74 = ( ? [Xs2: list_nat] :
% 13.77/7.74 ( ( ( size_size_list_nat @ Xs2 )
% 13.77/7.74 = K )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ K )
% 13.77/7.74 => ( P2 @ I3 @ ( nth_nat @ Xs2 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4468_list__eq__iff__nth__eq,axiom,
% 13.77/7.74 ( ( ^ [Y6: list_VEBT_VEBTi,Z4: list_VEBT_VEBTi] : ( Y6 = Z4 ) )
% 13.77/7.74 = ( ^ [Xs2: list_VEBT_VEBTi,Ys3: list_VEBT_VEBTi] :
% 13.77/7.74 ( ( ( size_s7982070591426661849_VEBTi @ Xs2 )
% 13.77/7.74 = ( size_s7982070591426661849_VEBTi @ Ys3 ) )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 13.77/7.74 => ( ( nth_VEBT_VEBTi @ Xs2 @ I3 )
% 13.77/7.74 = ( nth_VEBT_VEBTi @ Ys3 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4469_list__eq__iff__nth__eq,axiom,
% 13.77/7.74 ( ( ^ [Y6: list_int,Z4: list_int] : ( Y6 = Z4 ) )
% 13.77/7.74 = ( ^ [Xs2: list_int,Ys3: list_int] :
% 13.77/7.74 ( ( ( size_size_list_int @ Xs2 )
% 13.77/7.74 = ( size_size_list_int @ Ys3 ) )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 13.77/7.74 => ( ( nth_int @ Xs2 @ I3 )
% 13.77/7.74 = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4470_list__eq__iff__nth__eq,axiom,
% 13.77/7.74 ( ( ^ [Y6: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y6 = Z4 ) )
% 13.77/7.74 = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 13.77/7.74 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 13.77/7.74 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 13.77/7.74 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 13.77/7.74 = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4471_list__eq__iff__nth__eq,axiom,
% 13.77/7.74 ( ( ^ [Y6: list_real,Z4: list_real] : ( Y6 = Z4 ) )
% 13.77/7.74 = ( ^ [Xs2: list_real,Ys3: list_real] :
% 13.77/7.74 ( ( ( size_size_list_real @ Xs2 )
% 13.77/7.74 = ( size_size_list_real @ Ys3 ) )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 13.77/7.74 => ( ( nth_real @ Xs2 @ I3 )
% 13.77/7.74 = ( nth_real @ Ys3 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4472_list__eq__iff__nth__eq,axiom,
% 13.77/7.74 ( ( ^ [Y6: list_o,Z4: list_o] : ( Y6 = Z4 ) )
% 13.77/7.74 = ( ^ [Xs2: list_o,Ys3: list_o] :
% 13.77/7.74 ( ( ( size_size_list_o @ Xs2 )
% 13.77/7.74 = ( size_size_list_o @ Ys3 ) )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 13.77/7.74 => ( ( nth_o @ Xs2 @ I3 )
% 13.77/7.74 = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4473_list__eq__iff__nth__eq,axiom,
% 13.77/7.74 ( ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 ) )
% 13.77/7.74 = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 13.77/7.74 ( ( ( size_size_list_nat @ Xs2 )
% 13.77/7.74 = ( size_size_list_nat @ Ys3 ) )
% 13.77/7.74 & ! [I3: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 13.77/7.74 => ( ( nth_nat @ Xs2 @ I3 )
% 13.77/7.74 = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4474_obtain__list__from__elements,axiom,
% 13.77/7.74 ! [N: nat,P2: vEBT_VEBTi > nat > $o] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.74 => ? [Li: vEBT_VEBTi] : ( P2 @ Li @ I2 ) )
% 13.77/7.74 => ~ ! [L2: list_VEBT_VEBTi] :
% 13.77/7.74 ( ( ( size_s7982070591426661849_VEBTi @ L2 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ! [I4: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I4 @ N )
% 13.77/7.74 => ( P2 @ ( nth_VEBT_VEBTi @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4475_obtain__list__from__elements,axiom,
% 13.77/7.74 ! [N: nat,P2: int > nat > $o] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.74 => ? [Li: int] : ( P2 @ Li @ I2 ) )
% 13.77/7.74 => ~ ! [L2: list_int] :
% 13.77/7.74 ( ( ( size_size_list_int @ L2 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ! [I4: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I4 @ N )
% 13.77/7.74 => ( P2 @ ( nth_int @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4476_obtain__list__from__elements,axiom,
% 13.77/7.74 ! [N: nat,P2: vEBT_VEBT > nat > $o] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.74 => ? [Li: vEBT_VEBT] : ( P2 @ Li @ I2 ) )
% 13.77/7.74 => ~ ! [L2: list_VEBT_VEBT] :
% 13.77/7.74 ( ( ( size_s6755466524823107622T_VEBT @ L2 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ! [I4: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I4 @ N )
% 13.77/7.74 => ( P2 @ ( nth_VEBT_VEBT @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4477_obtain__list__from__elements,axiom,
% 13.77/7.74 ! [N: nat,P2: real > nat > $o] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.74 => ? [Li: real] : ( P2 @ Li @ I2 ) )
% 13.77/7.74 => ~ ! [L2: list_real] :
% 13.77/7.74 ( ( ( size_size_list_real @ L2 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ! [I4: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I4 @ N )
% 13.77/7.74 => ( P2 @ ( nth_real @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4478_obtain__list__from__elements,axiom,
% 13.77/7.74 ! [N: nat,P2: $o > nat > $o] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.74 => ? [Li: $o] : ( P2 @ Li @ I2 ) )
% 13.77/7.74 => ~ ! [L2: list_o] :
% 13.77/7.74 ( ( ( size_size_list_o @ L2 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ! [I4: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I4 @ N )
% 13.77/7.74 => ( P2 @ ( nth_o @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4479_obtain__list__from__elements,axiom,
% 13.77/7.74 ! [N: nat,P2: nat > nat > $o] :
% 13.77/7.74 ( ! [I2: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.74 => ? [Li: nat] : ( P2 @ Li @ I2 ) )
% 13.77/7.74 => ~ ! [L2: list_nat] :
% 13.77/7.74 ( ( ( size_size_list_nat @ L2 )
% 13.77/7.74 = N )
% 13.77/7.74 => ~ ! [I4: nat] :
% 13.77/7.74 ( ( ord_less_nat @ I4 @ N )
% 13.77/7.74 => ( P2 @ ( nth_nat @ L2 @ I4 ) @ I4 ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4480_slice__nth,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_VEBT_VEBTi,I: nat] :
% 13.77/7.74 ( ( ord_less_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.74 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 13.77/7.74 => ( ( nth_VEBT_VEBTi @ ( slice_VEBT_VEBTi @ From @ To @ Xs ) @ I )
% 13.77/7.74 = ( nth_VEBT_VEBTi @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4481_slice__nth,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_int,I: nat] :
% 13.77/7.74 ( ( ord_less_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 13.77/7.74 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 13.77/7.74 => ( ( nth_int @ ( slice_int @ From @ To @ Xs ) @ I )
% 13.77/7.74 = ( nth_int @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4482_slice__nth,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_VEBT_VEBT,I: nat] :
% 13.77/7.74 ( ( ord_less_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.74 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 13.77/7.74 => ( ( nth_VEBT_VEBT @ ( slice_VEBT_VEBT @ From @ To @ Xs ) @ I )
% 13.77/7.74 = ( nth_VEBT_VEBT @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4483_slice__nth,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_real,I: nat] :
% 13.77/7.74 ( ( ord_less_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_size_list_real @ Xs ) )
% 13.77/7.74 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 13.77/7.74 => ( ( nth_real @ ( slice_real @ From @ To @ Xs ) @ I )
% 13.77/7.74 = ( nth_real @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4484_slice__nth,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_o,I: nat] :
% 13.77/7.74 ( ( ord_less_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 13.77/7.74 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 13.77/7.74 => ( ( nth_o @ ( slice_o @ From @ To @ Xs ) @ I )
% 13.77/7.74 = ( nth_o @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 13.77/7.74
% 13.77/7.74 thf(fact_4485_slice__nth,axiom,
% 13.77/7.74 ! [From: nat,To: nat,Xs: list_nat,I: nat] :
% 13.77/7.74 ( ( ord_less_nat @ From @ To )
% 13.77/7.74 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 13.77/7.74 => ( ( ord_less_nat @ I @ ( minus_minus_nat @ To @ From ) )
% 13.77/7.74 => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs ) @ I )
% 13.77/7.74 = ( nth_nat @ Xs @ ( plus_plus_nat @ From @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4486_all__set__conv__nth,axiom,
% 13.77/7.75 ! [L: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o] :
% 13.77/7.75 ( ( ! [X4: vEBT_VEBTi] :
% 13.77/7.75 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ L ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBTi @ L @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4487_all__set__conv__nth,axiom,
% 13.77/7.75 ! [L: list_int,P2: int > $o] :
% 13.77/7.75 ( ( ! [X4: int] :
% 13.77/7.75 ( ( member_int @ X4 @ ( set_int2 @ L ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 13.77/7.75 => ( P2 @ ( nth_int @ L @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4488_all__set__conv__nth,axiom,
% 13.77/7.75 ! [L: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.75 ( ( ! [X4: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ L ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBT @ L @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4489_all__set__conv__nth,axiom,
% 13.77/7.75 ! [L: list_real,P2: real > $o] :
% 13.77/7.75 ( ( ! [X4: real] :
% 13.77/7.75 ( ( member_real @ X4 @ ( set_real2 @ L ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ L ) )
% 13.77/7.75 => ( P2 @ ( nth_real @ L @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4490_all__set__conv__nth,axiom,
% 13.77/7.75 ! [L: list_o,P2: $o > $o] :
% 13.77/7.75 ( ( ! [X4: $o] :
% 13.77/7.75 ( ( member_o @ X4 @ ( set_o2 @ L ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ L ) )
% 13.77/7.75 => ( P2 @ ( nth_o @ L @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4491_all__set__conv__nth,axiom,
% 13.77/7.75 ! [L: list_nat,P2: nat > $o] :
% 13.77/7.75 ( ( ! [X4: nat] :
% 13.77/7.75 ( ( member_nat @ X4 @ ( set_nat2 @ L ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ L ) )
% 13.77/7.75 => ( P2 @ ( nth_nat @ L @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4492_nth__mem,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_VEBT_VEBTi] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.75 => ( member_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N ) @ ( set_VEBT_VEBTi2 @ Xs ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4493_nth__mem,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_int] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 13.77/7.75 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4494_nth__mem,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_set_nat] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.75 => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4495_nth__mem,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4496_nth__mem,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_real] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.75 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4497_nth__mem,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_o] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.75 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4498_nth__mem,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_nat] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.75 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4499_list__ball__nth,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBTi] :
% 13.77/7.75 ( ( member_VEBT_VEBTi @ X3 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X3 ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4500_list__ball__nth,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_int,P2: int > $o] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X3 ) )
% 13.77/7.75 => ( P2 @ ( nth_int @ Xs @ N ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4501_list__ball__nth,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X3 ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4502_list__ball__nth,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_real,P2: real > $o] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X3 ) )
% 13.77/7.75 => ( P2 @ ( nth_real @ Xs @ N ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4503_list__ball__nth,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_o,P2: $o > $o] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.75 => ( ! [X3: $o] :
% 13.77/7.75 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X3 ) )
% 13.77/7.75 => ( P2 @ ( nth_o @ Xs @ N ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4504_list__ball__nth,axiom,
% 13.77/7.75 ! [N: nat,Xs: list_nat,P2: nat > $o] :
% 13.77/7.75 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X3 ) )
% 13.77/7.75 => ( P2 @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4505_in__set__conv__nth,axiom,
% 13.77/7.75 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 13.77/7.75 ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.75 & ( ( nth_VEBT_VEBTi @ Xs @ I3 )
% 13.77/7.75 = X ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4506_in__set__conv__nth,axiom,
% 13.77/7.75 ! [X: int,Xs: list_int] :
% 13.77/7.75 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 13.77/7.75 & ( ( nth_int @ Xs @ I3 )
% 13.77/7.75 = X ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4507_in__set__conv__nth,axiom,
% 13.77/7.75 ! [X: set_nat,Xs: list_set_nat] :
% 13.77/7.75 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.75 & ( ( nth_set_nat @ Xs @ I3 )
% 13.77/7.75 = X ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4508_in__set__conv__nth,axiom,
% 13.77/7.75 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.75 & ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 13.77/7.75 = X ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4509_in__set__conv__nth,axiom,
% 13.77/7.75 ! [X: real,Xs: list_real] :
% 13.77/7.75 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 13.77/7.75 & ( ( nth_real @ Xs @ I3 )
% 13.77/7.75 = X ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4510_in__set__conv__nth,axiom,
% 13.77/7.75 ! [X: $o,Xs: list_o] :
% 13.77/7.75 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 13.77/7.75 & ( ( nth_o @ Xs @ I3 )
% 13.77/7.75 = X ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4511_in__set__conv__nth,axiom,
% 13.77/7.75 ! [X: nat,Xs: list_nat] :
% 13.77/7.75 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.75 & ( ( nth_nat @ Xs @ I3 )
% 13.77/7.75 = X ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4512_all__nth__imp__all__set,axiom,
% 13.77/7.75 ! [Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o,X: vEBT_VEBTi] :
% 13.77/7.75 ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) ) )
% 13.77/7.75 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4513_all__nth__imp__all__set,axiom,
% 13.77/7.75 ! [Xs: list_int,P2: int > $o,X: int] :
% 13.77/7.75 ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_int @ Xs @ I2 ) ) )
% 13.77/7.75 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4514_all__nth__imp__all__set,axiom,
% 13.77/7.75 ! [Xs: list_set_nat,P2: set_nat > $o,X: set_nat] :
% 13.77/7.75 ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_set_nat @ Xs @ I2 ) ) )
% 13.77/7.75 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4515_all__nth__imp__all__set,axiom,
% 13.77/7.75 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 13.77/7.75 ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4516_all__nth__imp__all__set,axiom,
% 13.77/7.75 ! [Xs: list_real,P2: real > $o,X: real] :
% 13.77/7.75 ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_real @ Xs @ I2 ) ) )
% 13.77/7.75 => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4517_all__nth__imp__all__set,axiom,
% 13.77/7.75 ! [Xs: list_o,P2: $o > $o,X: $o] :
% 13.77/7.75 ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_o @ Xs @ I2 ) ) )
% 13.77/7.75 => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4518_all__nth__imp__all__set,axiom,
% 13.77/7.75 ! [Xs: list_nat,P2: nat > $o,X: nat] :
% 13.77/7.75 ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_nat @ Xs @ I2 ) ) )
% 13.77/7.75 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4519_all__set__conv__all__nth,axiom,
% 13.77/7.75 ! [Xs: list_VEBT_VEBTi,P2: vEBT_VEBTi > $o] :
% 13.77/7.75 ( ( ! [X4: vEBT_VEBTi] :
% 13.77/7.75 ( ( member_VEBT_VEBTi @ X4 @ ( set_VEBT_VEBTi2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4520_all__set__conv__all__nth,axiom,
% 13.77/7.75 ! [Xs: list_int,P2: int > $o] :
% 13.77/7.75 ( ( ! [X4: int] :
% 13.77/7.75 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_int @ Xs @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4521_all__set__conv__all__nth,axiom,
% 13.77/7.75 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.75 ( ( ! [X4: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4522_all__set__conv__all__nth,axiom,
% 13.77/7.75 ! [Xs: list_real,P2: real > $o] :
% 13.77/7.75 ( ( ! [X4: real] :
% 13.77/7.75 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_real @ Xs @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4523_all__set__conv__all__nth,axiom,
% 13.77/7.75 ! [Xs: list_o,P2: $o > $o] :
% 13.77/7.75 ( ( ! [X4: $o] :
% 13.77/7.75 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_o @ Xs @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4524_all__set__conv__all__nth,axiom,
% 13.77/7.75 ! [Xs: list_nat,P2: nat > $o] :
% 13.77/7.75 ( ( ! [X4: nat] :
% 13.77/7.75 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 13.77/7.75 => ( P2 @ X4 ) ) )
% 13.77/7.75 = ( ! [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.75 => ( P2 @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4525_realpow__pos__nth2,axiom,
% 13.77/7.75 ! [A: real,N: nat] :
% 13.77/7.75 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.75 => ? [R4: real] :
% 13.77/7.75 ( ( ord_less_real @ zero_zero_real @ R4 )
% 13.77/7.75 & ( ( power_power_real @ R4 @ ( suc @ N ) )
% 13.77/7.75 = A ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4526_VEBT_Osize_I4_J,axiom,
% 13.77/7.75 ! [X21: $o,X22: $o] :
% 13.77/7.75 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 13.77/7.75 = zero_zero_nat ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4527_set__image__eq__pointwiseI,axiom,
% 13.77/7.75 ! [L: list_int,L3: list_int,F: int > nat] :
% 13.77/7.75 ( ( ( size_size_list_int @ L )
% 13.77/7.75 = ( size_size_list_int @ L3 ) )
% 13.77/7.75 => ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ L ) )
% 13.77/7.75 => ( ( F @ ( nth_int @ L @ I2 ) )
% 13.77/7.75 = ( F @ ( nth_int @ L3 @ I2 ) ) ) )
% 13.77/7.75 => ( ( image_int_nat @ F @ ( set_int2 @ L ) )
% 13.77/7.75 = ( image_int_nat @ F @ ( set_int2 @ L3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4528_set__image__eq__pointwiseI,axiom,
% 13.77/7.75 ! [L: list_int,L3: list_int,F: int > int] :
% 13.77/7.75 ( ( ( size_size_list_int @ L )
% 13.77/7.75 = ( size_size_list_int @ L3 ) )
% 13.77/7.75 => ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ L ) )
% 13.77/7.75 => ( ( F @ ( nth_int @ L @ I2 ) )
% 13.77/7.75 = ( F @ ( nth_int @ L3 @ I2 ) ) ) )
% 13.77/7.75 => ( ( image_int_int @ F @ ( set_int2 @ L ) )
% 13.77/7.75 = ( image_int_int @ F @ ( set_int2 @ L3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4529_set__image__eq__pointwiseI,axiom,
% 13.77/7.75 ! [L: list_nat,L3: list_nat,F: nat > set_nat] :
% 13.77/7.75 ( ( ( size_size_list_nat @ L )
% 13.77/7.75 = ( size_size_list_nat @ L3 ) )
% 13.77/7.75 => ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ L ) )
% 13.77/7.75 => ( ( F @ ( nth_nat @ L @ I2 ) )
% 13.77/7.75 = ( F @ ( nth_nat @ L3 @ I2 ) ) ) )
% 13.77/7.75 => ( ( image_nat_set_nat @ F @ ( set_nat2 @ L ) )
% 13.77/7.75 = ( image_nat_set_nat @ F @ ( set_nat2 @ L3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4530_set__image__eq__pointwiseI,axiom,
% 13.77/7.75 ! [L: list_nat,L3: list_nat,F: nat > nat] :
% 13.77/7.75 ( ( ( size_size_list_nat @ L )
% 13.77/7.75 = ( size_size_list_nat @ L3 ) )
% 13.77/7.75 => ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ L ) )
% 13.77/7.75 => ( ( F @ ( nth_nat @ L @ I2 ) )
% 13.77/7.75 = ( F @ ( nth_nat @ L3 @ I2 ) ) ) )
% 13.77/7.75 => ( ( image_nat_nat @ F @ ( set_nat2 @ L ) )
% 13.77/7.75 = ( image_nat_nat @ F @ ( set_nat2 @ L3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4531_set__image__eq__pointwiseI,axiom,
% 13.77/7.75 ! [L: list_nat,L3: list_nat,F: nat > int] :
% 13.77/7.75 ( ( ( size_size_list_nat @ L )
% 13.77/7.75 = ( size_size_list_nat @ L3 ) )
% 13.77/7.75 => ( ! [I2: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ L ) )
% 13.77/7.75 => ( ( F @ ( nth_nat @ L @ I2 ) )
% 13.77/7.75 = ( F @ ( nth_nat @ L3 @ I2 ) ) ) )
% 13.77/7.75 => ( ( image_nat_int @ F @ ( set_nat2 @ L ) )
% 13.77/7.75 = ( image_nat_int @ F @ ( set_nat2 @ L3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4532_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: vEBT_VEBTi > nat,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 13.77/7.75 ( ( member_nat @ ( F @ X ) @ ( image_VEBT_VEBTi_nat @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4533_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: int > nat,X: int,L: list_int] :
% 13.77/7.75 ( ( member_nat @ ( F @ X ) @ ( image_int_nat @ F @ ( set_int2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_int @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4534_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: vEBT_VEBTi > vEBT_VEBT,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ ( F @ X ) @ ( image_7547481670047419768T_VEBT @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4535_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: int > vEBT_VEBT,X: int,L: list_int] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ ( F @ X ) @ ( image_int_VEBT_VEBT @ F @ ( set_int2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_int @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4536_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: vEBT_VEBTi > real,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 13.77/7.75 ( ( member_real @ ( F @ X ) @ ( image_6202559892754154600i_real @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4537_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: int > real,X: int,L: list_int] :
% 13.77/7.75 ( ( member_real @ ( F @ X ) @ ( image_int_real @ F @ ( set_int2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_int @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4538_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: vEBT_VEBTi > int,X: vEBT_VEBTi,L: list_VEBT_VEBTi] :
% 13.77/7.75 ( ( member_int @ ( F @ X ) @ ( image_VEBT_VEBTi_int @ F @ ( set_VEBT_VEBTi2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_VEBT_VEBTi @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4539_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: int > int,X: int,L: list_int] :
% 13.77/7.75 ( ( member_int @ ( F @ X ) @ ( image_int_int @ F @ ( set_int2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_int @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4540_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: vEBT_VEBT > nat,X: vEBT_VEBT,L: list_VEBT_VEBT] :
% 13.77/7.75 ( ( member_nat @ ( F @ X ) @ ( image_VEBT_VEBT_nat @ F @ ( set_VEBT_VEBT2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_VEBT_VEBT @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4541_in__set__image__conv__nth,axiom,
% 13.77/7.75 ! [F: vEBT_VEBT > vEBT_VEBT,X: vEBT_VEBT,L: list_VEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ ( F @ X ) @ ( image_3375948659692109573T_VEBT @ F @ ( set_VEBT_VEBT2 @ L ) ) )
% 13.77/7.75 = ( ? [I3: nat] :
% 13.77/7.75 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.75 & ( ( F @ ( nth_VEBT_VEBT @ L @ I3 ) )
% 13.77/7.75 = ( F @ X ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4542_sum__count__set,axiom,
% 13.77/7.75 ! [Xs: list_complex,X6: set_complex] :
% 13.77/7.75 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ X6 )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ X6 )
% 13.77/7.75 => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs ) @ X6 )
% 13.77/7.75 = ( size_s3451745648224563538omplex @ Xs ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4543_sum__count__set,axiom,
% 13.77/7.75 ! [Xs: list_Code_integer,X6: set_Code_integer] :
% 13.77/7.75 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs ) @ X6 )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ X6 )
% 13.77/7.75 => ( ( groups7237345082560585321er_nat @ ( count_3970941599679287265nteger @ Xs ) @ X6 )
% 13.77/7.75 = ( size_s3445333598471063425nteger @ Xs ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4544_sum__count__set,axiom,
% 13.77/7.75 ! [Xs: list_VEBT_VEBT,X6: set_VEBT_VEBT] :
% 13.77/7.75 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ X6 )
% 13.77/7.75 => ( ( finite5795047828879050333T_VEBT @ X6 )
% 13.77/7.75 => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs ) @ X6 )
% 13.77/7.75 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4545_sum__count__set,axiom,
% 13.77/7.75 ! [Xs: list_real,X6: set_real] :
% 13.77/7.75 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ X6 )
% 13.77/7.75 => ( ( finite_finite_real @ X6 )
% 13.77/7.75 => ( ( groups1935376822645274424al_nat @ ( count_list_real @ Xs ) @ X6 )
% 13.77/7.75 = ( size_size_list_real @ Xs ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4546_sum__count__set,axiom,
% 13.77/7.75 ! [Xs: list_o,X6: set_o] :
% 13.77/7.75 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ X6 )
% 13.77/7.75 => ( ( finite_finite_o @ X6 )
% 13.77/7.75 => ( ( groups8507830703676809646_o_nat @ ( count_list_o @ Xs ) @ X6 )
% 13.77/7.75 = ( size_size_list_o @ Xs ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4547_sum__count__set,axiom,
% 13.77/7.75 ! [Xs: list_int,X6: set_int] :
% 13.77/7.75 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ X6 )
% 13.77/7.75 => ( ( finite_finite_int @ X6 )
% 13.77/7.75 => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs ) @ X6 )
% 13.77/7.75 = ( size_size_list_int @ Xs ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4548_sum__count__set,axiom,
% 13.77/7.75 ! [Xs: list_nat,X6: set_nat] :
% 13.77/7.75 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ X6 )
% 13.77/7.75 => ( ( finite_finite_nat @ X6 )
% 13.77/7.75 => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs ) @ X6 )
% 13.77/7.75 = ( size_size_list_nat @ Xs ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4549_sum__le__card__Max,axiom,
% 13.77/7.75 ! [A4: set_literal,F: literal > nat] :
% 13.77/7.75 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups8652099787943017962al_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_literal @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_literal_nat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4550_sum__le__card__Max,axiom,
% 13.77/7.75 ! [A4: set_list_nat,F: list_nat > nat] :
% 13.77/7.75 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups4396056296759096172at_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_list_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_list_nat_nat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4551_sum__le__card__Max,axiom,
% 13.77/7.75 ! [A4: set_set_nat,F: set_nat > nat] :
% 13.77/7.75 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_set_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_set_nat_nat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4552_sum__le__card__Max,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > nat] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_int @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_int_nat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4553_sum__le__card__Max,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > nat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_complex @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_complex_nat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4554_sum__le__card__Max,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > nat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( times_times_nat @ ( finite4902975817058060853nteger @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_951025933927791156er_nat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4555_sum__le__card__Max,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > nat] :
% 13.77/7.75 ( ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( times_times_nat @ ( finite_card_nat @ A4 ) @ ( lattic8265883725875713057ax_nat @ ( image_nat_nat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4556_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_o,X: $o,G: $o > real] :
% 13.77/7.75 ( ( finite_finite_o @ A4 )
% 13.77/7.75 => ( ~ ( member_o @ X @ A4 )
% 13.77/7.75 => ( ( groups8691415230153176458o_real @ G @ ( insert_o @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups8691415230153176458o_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4557_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4558_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_real,X: real,G: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ~ ( member_real @ X @ A4 )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4559_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_int,X: int,G: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ~ ( member_int @ X @ A4 )
% 13.77/7.75 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4560_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_complex,X: complex,G: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ~ ( member_complex @ X @ A4 )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4561_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,X: code_integer,G: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ~ ( member_Code_integer @ X @ A4 )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4562_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_o,X: $o,G: $o > rat] :
% 13.77/7.75 ( ( finite_finite_o @ A4 )
% 13.77/7.75 => ( ~ ( member_o @ X @ A4 )
% 13.77/7.75 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4563_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.75 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4564_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_real,X: real,G: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ~ ( member_real @ X @ A4 )
% 13.77/7.75 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4565_sum_Oinsert,axiom,
% 13.77/7.75 ! [A4: set_nat,X: nat,G: nat > rat] :
% 13.77/7.75 ( ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ~ ( member_nat @ X @ A4 )
% 13.77/7.75 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4566_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_nat,G: nat > uint32] :
% 13.77/7.75 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ( groups833757482993574392uint32 @ G @ A4 )
% 13.77/7.75 = zero_zero_uint32 ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4567_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_int,G: int > uint32] :
% 13.77/7.75 ( ~ ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( groups5712668689793887828uint32 @ G @ A4 )
% 13.77/7.75 = zero_zero_uint32 ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4568_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_complex,G: complex > uint32] :
% 13.77/7.75 ( ~ ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ G @ A4 )
% 13.77/7.75 = zero_zero_uint32 ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4569_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,G: code_integer > uint32] :
% 13.77/7.75 ( ~ ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ G @ A4 )
% 13.77/7.75 = zero_zero_uint32 ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4570_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_int,G: int > real] :
% 13.77/7.75 ( ~ ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( groups8778361861064173332t_real @ G @ A4 )
% 13.77/7.75 = zero_zero_real ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4571_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_complex,G: complex > real] :
% 13.77/7.75 ( ~ ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 13.77/7.75 = zero_zero_real ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4572_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,G: code_integer > real] :
% 13.77/7.75 ( ~ ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 13.77/7.75 = zero_zero_real ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4573_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_nat,G: nat > rat] :
% 13.77/7.75 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 13.77/7.75 = zero_zero_rat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4574_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_int,G: int > rat] :
% 13.77/7.75 ( ~ ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( groups3906332499630173760nt_rat @ G @ A4 )
% 13.77/7.75 = zero_zero_rat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4575_sum_Oinfinite,axiom,
% 13.77/7.75 ! [A4: set_complex,G: complex > rat] :
% 13.77/7.75 ( ~ ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 13.77/7.75 = zero_zero_rat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4576_sum__eq__0__iff,axiom,
% 13.77/7.75 ! [F2: set_int,F: int > nat] :
% 13.77/7.75 ( ( finite_finite_int @ F2 )
% 13.77/7.75 => ( ( ( groups4541462559716669496nt_nat @ F @ F2 )
% 13.77/7.75 = zero_zero_nat )
% 13.77/7.75 = ( ! [X4: int] :
% 13.77/7.75 ( ( member_int @ X4 @ F2 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4577_sum__eq__0__iff,axiom,
% 13.77/7.75 ! [F2: set_complex,F: complex > nat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ F2 )
% 13.77/7.75 => ( ( ( groups5693394587270226106ex_nat @ F @ F2 )
% 13.77/7.75 = zero_zero_nat )
% 13.77/7.75 = ( ! [X4: complex] :
% 13.77/7.75 ( ( member_complex @ X4 @ F2 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4578_sum__eq__0__iff,axiom,
% 13.77/7.75 ! [F2: set_Code_integer,F: code_integer > nat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ F2 )
% 13.77/7.75 => ( ( ( groups7237345082560585321er_nat @ F @ F2 )
% 13.77/7.75 = zero_zero_nat )
% 13.77/7.75 = ( ! [X4: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X4 @ F2 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4579_sum__eq__0__iff,axiom,
% 13.77/7.75 ! [F2: set_nat,F: nat > nat] :
% 13.77/7.75 ( ( finite_finite_nat @ F2 )
% 13.77/7.75 => ( ( ( groups3542108847815614940at_nat @ F @ F2 )
% 13.77/7.75 = zero_zero_nat )
% 13.77/7.75 = ( ! [X4: nat] :
% 13.77/7.75 ( ( member_nat @ X4 @ F2 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4580_sum_Oempty,axiom,
% 13.77/7.75 ! [G: nat > uint32] :
% 13.77/7.75 ( ( groups833757482993574392uint32 @ G @ bot_bot_set_nat )
% 13.77/7.75 = zero_zero_uint32 ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4581_sum_Oempty,axiom,
% 13.77/7.75 ! [G: nat > rat] :
% 13.77/7.75 ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 13.77/7.75 = zero_zero_rat ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4582_sum_Oempty,axiom,
% 13.77/7.75 ! [G: nat > int] :
% 13.77/7.75 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 13.77/7.75 = zero_zero_int ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4583_sum_Oempty,axiom,
% 13.77/7.75 ! [G: int > uint32] :
% 13.77/7.75 ( ( groups5712668689793887828uint32 @ G @ bot_bot_set_int )
% 13.77/7.75 = zero_zero_uint32 ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4584_sum_Oempty,axiom,
% 13.77/7.75 ! [G: int > real] :
% 13.77/7.75 ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 13.77/7.75 = zero_zero_real ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4585_sum_Oempty,axiom,
% 13.77/7.75 ! [G: int > rat] :
% 13.77/7.75 ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 13.77/7.75 = zero_zero_rat ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4586_sum_Oempty,axiom,
% 13.77/7.75 ! [G: int > nat] :
% 13.77/7.75 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 13.77/7.75 = zero_zero_nat ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4587_sum_Oempty,axiom,
% 13.77/7.75 ! [G: $o > uint32] :
% 13.77/7.75 ( ( groups7241207224191747786uint32 @ G @ bot_bot_set_o )
% 13.77/7.75 = zero_zero_uint32 ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4588_sum_Oempty,axiom,
% 13.77/7.75 ! [G: $o > real] :
% 13.77/7.75 ( ( groups8691415230153176458o_real @ G @ bot_bot_set_o )
% 13.77/7.75 = zero_zero_real ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4589_sum_Oempty,axiom,
% 13.77/7.75 ! [G: $o > rat] :
% 13.77/7.75 ( ( groups7872700643590313910_o_rat @ G @ bot_bot_set_o )
% 13.77/7.75 = zero_zero_rat ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4590_member__le__sum,axiom,
% 13.77/7.75 ! [I: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I @ A4 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ I ) @ ( groups2240296850493347238T_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4591_member__le__sum,axiom,
% 13.77/7.75 ! [I: real,A4: set_real,F: real > real] :
% 13.77/7.75 ( ( member_real @ I @ A4 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4592_member__le__sum,axiom,
% 13.77/7.75 ! [I: complex,A4: set_complex,F: complex > real] :
% 13.77/7.75 ( ( member_complex @ I @ A4 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4593_member__le__sum,axiom,
% 13.77/7.75 ! [I: code_integer,A4: set_Code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( member_Code_integer @ I @ A4 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ I @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ I ) @ ( groups1270011288395367621r_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4594_member__le__sum,axiom,
% 13.77/7.75 ! [I: int,A4: set_int,F: int > real] :
% 13.77/7.75 ( ( member_int @ I @ A4 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4595_member__le__sum,axiom,
% 13.77/7.75 ! [I: $o,A4: set_o,F: $o > real] :
% 13.77/7.75 ( ( member_o @ I @ A4 )
% 13.77/7.75 => ( ! [X3: $o] :
% 13.77/7.75 ( ( member_o @ X3 @ ( minus_minus_set_o @ A4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite_finite_o @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8691415230153176458o_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4596_member__le__sum,axiom,
% 13.77/7.75 ! [I: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I @ A4 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4597_member__le__sum,axiom,
% 13.77/7.75 ! [I: real,A4: set_real,F: real > rat] :
% 13.77/7.75 ( ( member_real @ I @ A4 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4598_member__le__sum,axiom,
% 13.77/7.75 ! [I: complex,A4: set_complex,F: complex > rat] :
% 13.77/7.75 ( ( member_complex @ I @ A4 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4599_member__le__sum,axiom,
% 13.77/7.75 ! [I: code_integer,A4: set_Code_integer,F: code_integer > rat] :
% 13.77/7.75 ( ( member_Code_integer @ I @ A4 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ I @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups6602215022474089585er_rat @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4600_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( groups2240296850493347238T_real @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4601_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_real,A4: set_real,B: real,F: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ B4 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 13.77/7.75 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4602_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_complex,A4: set_complex,B: complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.75 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4603_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_Code_integer,A4: set_Code_integer,B: code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.75 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4604_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ ( groups136491112297645522BT_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4605_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_real,A4: set_real,B: real,F: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ B4 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 13.77/7.75 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4606_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_complex,A4: set_complex,B: complex,F: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.75 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4607_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_Code_integer,A4: set_Code_integer,B: code_integer,F: code_integer > rat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.75 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4608_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_nat,A4: set_nat,B: nat,F: nat > rat] :
% 13.77/7.75 ( ( finite_finite_nat @ B4 )
% 13.77/7.75 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.75 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4609_sum__strict__mono2,axiom,
% 13.77/7.75 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,B: vEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ B @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 13.77/7.75 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 13.77/7.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( groups771621172384141258BT_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4610_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( ( member_VEBT_VEBT @ A @ A4 )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.75 = ( minus_minus_uint32 @ ( groups8325533452322294502uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4611_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_real,A: real,F: real > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ( ( member_real @ A @ A4 )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 13.77/7.75 = ( minus_minus_uint32 @ ( groups5944083974425963860uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_real @ A @ A4 )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4612_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_complex,A: complex,F: complex > uint32] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( ( member_complex @ A @ A4 )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 13.77/7.75 = ( minus_minus_uint32 @ ( groups8736914816313324502uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_complex @ A @ A4 )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4613_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,A: code_integer,F: code_integer > uint32] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( ( member_Code_integer @ A @ A4 )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.75 = ( minus_minus_uint32 @ ( groups8847630953604152069uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_Code_integer @ A @ A4 )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4614_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_int,A: int,F: int > uint32] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( ( member_int @ A @ A4 )
% 13.77/7.75 => ( ( groups5712668689793887828uint32 @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.77/7.75 = ( minus_minus_uint32 @ ( groups5712668689793887828uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_int @ A @ A4 )
% 13.77/7.75 => ( ( groups5712668689793887828uint32 @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.77/7.75 = ( groups5712668689793887828uint32 @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4615_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_o,A: $o,F: $o > uint32] :
% 13.77/7.75 ( ( finite_finite_o @ A4 )
% 13.77/7.75 => ( ( ( member_o @ A @ A4 )
% 13.77/7.75 => ( ( groups7241207224191747786uint32 @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.77/7.75 = ( minus_minus_uint32 @ ( groups7241207224191747786uint32 @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_o @ A @ A4 )
% 13.77/7.75 => ( ( groups7241207224191747786uint32 @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.77/7.75 = ( groups7241207224191747786uint32 @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4616_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,A: vEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( ( member_VEBT_VEBT @ A @ A4 )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.75 = ( minus_minus_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.75 = ( groups2240296850493347238T_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4617_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_real,A: real,F: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ( ( member_real @ A @ A4 )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 13.77/7.75 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_real @ A @ A4 )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 13.77/7.75 = ( groups8097168146408367636l_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4618_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_complex,A: complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( ( member_complex @ A @ A4 )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 13.77/7.75 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_complex @ A @ A4 )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 13.77/7.75 = ( groups5808333547571424918x_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4619_sum__diff1,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,A: code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( ( member_Code_integer @ A @ A4 )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.75 = ( minus_minus_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.75 & ( ~ ( member_Code_integer @ A @ A4 )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.75 = ( groups1270011288395367621r_real @ F @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4620_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > real,X: vEBT_VEBT] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4621_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_complex,G: complex > real,X: complex] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4622_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,G: code_integer > real,X: code_integer] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4623_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > rat,X: vEBT_VEBT] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4624_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_complex,G: complex > rat,X: complex] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4625_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,G: code_integer > rat,X: code_integer] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( groups6602215022474089585er_rat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4626_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > nat,X: vEBT_VEBT] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4627_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_complex,G: complex > nat,X: complex] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4628_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,G: code_integer > nat,X: code_integer] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( groups7237345082560585321er_nat @ G @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_nat @ ( G @ X ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4629_sum_Oinsert__remove,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > int,X: vEBT_VEBT] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_int @ ( G @ X ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4630_complete__real,axiom,
% 13.77/7.75 ! [S3: set_real] :
% 13.77/7.75 ( ? [X5: real] : ( member_real @ X5 @ S3 )
% 13.77/7.75 => ( ? [Z5: real] :
% 13.77/7.75 ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ S3 )
% 13.77/7.75 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 13.77/7.75 => ? [Y3: real] :
% 13.77/7.75 ( ! [X5: real] :
% 13.77/7.75 ( ( member_real @ X5 @ S3 )
% 13.77/7.75 => ( ord_less_eq_real @ X5 @ Y3 ) )
% 13.77/7.75 & ! [Z5: real] :
% 13.77/7.75 ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ S3 )
% 13.77/7.75 => ( ord_less_eq_real @ X3 @ Z5 ) )
% 13.77/7.75 => ( ord_less_eq_real @ Y3 @ Z5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4631_real__minus__mult__self__le,axiom,
% 13.77/7.75 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4632_sum__cong__Suc,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 13.77/7.75 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 13.77/7.75 => ( ( F @ ( suc @ X3 ) )
% 13.77/7.75 = ( G @ ( suc @ X3 ) ) ) )
% 13.77/7.75 => ( ( groups3542108847815614940at_nat @ F @ A4 )
% 13.77/7.75 = ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4633_sum__cong__Suc,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > real,G: nat > real] :
% 13.77/7.75 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 13.77/7.75 => ( ( F @ ( suc @ X3 ) )
% 13.77/7.75 = ( G @ ( suc @ X3 ) ) ) )
% 13.77/7.75 => ( ( groups6591440286371151544t_real @ F @ A4 )
% 13.77/7.75 = ( groups6591440286371151544t_real @ G @ A4 ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4634_sum_Oneutral,axiom,
% 13.77/7.75 ! [A4: set_nat,G: nat > nat] :
% 13.77/7.75 ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ A4 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_nat ) )
% 13.77/7.75 => ( ( groups3542108847815614940at_nat @ G @ A4 )
% 13.77/7.75 = zero_zero_nat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4635_sum_Oneutral,axiom,
% 13.77/7.75 ! [A4: set_complex,G: complex > complex] :
% 13.77/7.75 ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_complex ) )
% 13.77/7.75 => ( ( groups7754918857620584856omplex @ G @ A4 )
% 13.77/7.75 = zero_zero_complex ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4636_sum_Oneutral,axiom,
% 13.77/7.75 ! [A4: set_nat,G: nat > real] :
% 13.77/7.75 ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ A4 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( groups6591440286371151544t_real @ G @ A4 )
% 13.77/7.75 = zero_zero_real ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4637_sum_Oneutral,axiom,
% 13.77/7.75 ! [A4: set_int,G: int > int] :
% 13.77/7.75 ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_int ) )
% 13.77/7.75 => ( ( groups4538972089207619220nt_int @ G @ A4 )
% 13.77/7.75 = zero_zero_int ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4638_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: nat > uint32,A4: set_nat] :
% 13.77/7.75 ( ( ( groups833757482993574392uint32 @ G @ A4 )
% 13.77/7.75 != zero_zero_uint32 )
% 13.77/7.75 => ~ ! [A3: nat] :
% 13.77/7.75 ( ( member_nat @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4639_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: vEBT_VEBT > uint32,A4: set_VEBT_VEBT] :
% 13.77/7.75 ( ( ( groups8325533452322294502uint32 @ G @ A4 )
% 13.77/7.75 != zero_zero_uint32 )
% 13.77/7.75 => ~ ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4640_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: real > uint32,A4: set_real] :
% 13.77/7.75 ( ( ( groups5944083974425963860uint32 @ G @ A4 )
% 13.77/7.75 != zero_zero_uint32 )
% 13.77/7.75 => ~ ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4641_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: int > uint32,A4: set_int] :
% 13.77/7.75 ( ( ( groups5712668689793887828uint32 @ G @ A4 )
% 13.77/7.75 != zero_zero_uint32 )
% 13.77/7.75 => ~ ! [A3: int] :
% 13.77/7.75 ( ( member_int @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4642_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: vEBT_VEBT > real,A4: set_VEBT_VEBT] :
% 13.77/7.75 ( ( ( groups2240296850493347238T_real @ G @ A4 )
% 13.77/7.75 != zero_zero_real )
% 13.77/7.75 => ~ ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4643_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: real > real,A4: set_real] :
% 13.77/7.75 ( ( ( groups8097168146408367636l_real @ G @ A4 )
% 13.77/7.75 != zero_zero_real )
% 13.77/7.75 => ~ ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4644_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: int > real,A4: set_int] :
% 13.77/7.75 ( ( ( groups8778361861064173332t_real @ G @ A4 )
% 13.77/7.75 != zero_zero_real )
% 13.77/7.75 => ~ ! [A3: int] :
% 13.77/7.75 ( ( member_int @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4645_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: nat > rat,A4: set_nat] :
% 13.77/7.75 ( ( ( groups2906978787729119204at_rat @ G @ A4 )
% 13.77/7.75 != zero_zero_rat )
% 13.77/7.75 => ~ ! [A3: nat] :
% 13.77/7.75 ( ( member_nat @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_rat ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4646_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: vEBT_VEBT > rat,A4: set_VEBT_VEBT] :
% 13.77/7.75 ( ( ( groups136491112297645522BT_rat @ G @ A4 )
% 13.77/7.75 != zero_zero_rat )
% 13.77/7.75 => ~ ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_rat ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4647_sum_Onot__neutral__contains__not__neutral,axiom,
% 13.77/7.75 ! [G: real > rat,A4: set_real] :
% 13.77/7.75 ( ( ( groups1300246762558778688al_rat @ G @ A4 )
% 13.77/7.75 != zero_zero_rat )
% 13.77/7.75 => ~ ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ A4 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_rat ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4648_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ zero_zero_real ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4649_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > real] :
% 13.77/7.75 ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ zero_zero_real ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4650_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > real] :
% 13.77/7.75 ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ X3 ) @ zero_zero_real ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ zero_zero_real ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4651_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > rat] :
% 13.77/7.75 ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 13.77/7.75 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4652_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.75 ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 13.77/7.75 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4653_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > rat] :
% 13.77/7.75 ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 13.77/7.75 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4654_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > rat] :
% 13.77/7.75 ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 13.77/7.75 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4655_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.75 ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4656_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > nat] :
% 13.77/7.75 ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4657_sum__nonpos,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > nat] :
% 13.77/7.75 ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 13.77/7.75 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4658_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4659_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > real] :
% 13.77/7.75 ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4660_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > real] :
% 13.77/7.75 ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4661_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > rat] :
% 13.77/7.75 ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4662_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.75 ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4663_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > rat] :
% 13.77/7.75 ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4664_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > rat] :
% 13.77/7.75 ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4665_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.75 ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4666_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > nat] :
% 13.77/7.75 ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4667_sum__nonneg,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > nat] :
% 13.77/7.75 ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4668_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: vEBT_VEBT > rat,I5: set_VEBT_VEBT,G: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 13.77/7.75 ( ( ( groups136491112297645522BT_rat @ F @ I5 )
% 13.77/7.75 = ( groups136491112297645522BT_rat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ I @ I5 )
% 13.77/7.75 => ( ( finite5795047828879050333T_VEBT @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4669_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 13.77/7.75 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 13.77/7.75 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: real] :
% 13.77/7.75 ( ( member_real @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_real @ I @ I5 )
% 13.77/7.75 => ( ( finite_finite_real @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4670_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 13.77/7.75 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 13.77/7.75 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: nat] :
% 13.77/7.75 ( ( member_nat @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_nat @ I @ I5 )
% 13.77/7.75 => ( ( finite_finite_nat @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4671_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 13.77/7.75 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 13.77/7.75 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: int] :
% 13.77/7.75 ( ( member_int @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_int @ I @ I5 )
% 13.77/7.75 => ( ( finite_finite_int @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4672_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 13.77/7.75 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 13.77/7.75 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: complex] :
% 13.77/7.75 ( ( member_complex @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_complex @ I @ I5 )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4673_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: code_integer > rat,I5: set_Code_integer,G: code_integer > rat,I: code_integer] :
% 13.77/7.75 ( ( ( groups6602215022474089585er_rat @ F @ I5 )
% 13.77/7.75 = ( groups6602215022474089585er_rat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_Code_integer @ I @ I5 )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4674_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: vEBT_VEBT > nat,I5: set_VEBT_VEBT,G: vEBT_VEBT > nat,I: vEBT_VEBT] :
% 13.77/7.75 ( ( ( groups771621172384141258BT_nat @ F @ I5 )
% 13.77/7.75 = ( groups771621172384141258BT_nat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ I @ I5 )
% 13.77/7.75 => ( ( finite5795047828879050333T_VEBT @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4675_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 13.77/7.75 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 13.77/7.75 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: real] :
% 13.77/7.75 ( ( member_real @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_real @ I @ I5 )
% 13.77/7.75 => ( ( finite_finite_real @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4676_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 13.77/7.75 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 13.77/7.75 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: int] :
% 13.77/7.75 ( ( member_int @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_int @ I @ I5 )
% 13.77/7.75 => ( ( finite_finite_int @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4677_sum__mono__inv,axiom,
% 13.77/7.75 ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 13.77/7.75 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 13.77/7.75 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 13.77/7.75 => ( ! [I2: complex] :
% 13.77/7.75 ( ( member_complex @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.75 => ( ( member_complex @ I @ I5 )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ I5 )
% 13.77/7.75 => ( ( F @ I )
% 13.77/7.75 = ( G @ I ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4678_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups2240296850493347238T_real @ F @ A4 )
% 13.77/7.75 = zero_zero_real )
% 13.77/7.75 = ( ! [X4: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4679_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups8097168146408367636l_real @ F @ A4 )
% 13.77/7.75 = zero_zero_real )
% 13.77/7.75 = ( ! [X4: real] :
% 13.77/7.75 ( ( member_real @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4680_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups8778361861064173332t_real @ F @ A4 )
% 13.77/7.75 = zero_zero_real )
% 13.77/7.75 = ( ! [X4: int] :
% 13.77/7.75 ( ( member_int @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4681_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups5808333547571424918x_real @ F @ A4 )
% 13.77/7.75 = zero_zero_real )
% 13.77/7.75 = ( ! [X4: complex] :
% 13.77/7.75 ( ( member_complex @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4682_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups1270011288395367621r_real @ F @ A4 )
% 13.77/7.75 = zero_zero_real )
% 13.77/7.75 = ( ! [X4: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4683_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups136491112297645522BT_rat @ F @ A4 )
% 13.77/7.75 = zero_zero_rat )
% 13.77/7.75 = ( ! [X4: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_rat ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4684_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups1300246762558778688al_rat @ F @ A4 )
% 13.77/7.75 = zero_zero_rat )
% 13.77/7.75 = ( ! [X4: real] :
% 13.77/7.75 ( ( member_real @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_rat ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4685_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > rat] :
% 13.77/7.75 ( ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups2906978787729119204at_rat @ F @ A4 )
% 13.77/7.75 = zero_zero_rat )
% 13.77/7.75 = ( ! [X4: nat] :
% 13.77/7.75 ( ( member_nat @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_rat ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4686_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > rat] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups3906332499630173760nt_rat @ F @ A4 )
% 13.77/7.75 = zero_zero_rat )
% 13.77/7.75 = ( ! [X4: int] :
% 13.77/7.75 ( ( member_int @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_rat ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4687_sum__nonneg__eq__0__iff,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 13.77/7.75 => ( ( ( groups5058264527183730370ex_rat @ F @ A4 )
% 13.77/7.75 = zero_zero_rat )
% 13.77/7.75 = ( ! [X4: complex] :
% 13.77/7.75 ( ( member_complex @ X4 @ A4 )
% 13.77/7.75 => ( ( F @ X4 )
% 13.77/7.75 = zero_zero_rat ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4688_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ S )
% 13.77/7.75 => ( ( finite_finite_int @ T )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ S )
% 13.77/7.75 => ? [Xa: int] :
% 13.77/7.75 ( ( member_int @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4689_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ S )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ T )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ S )
% 13.77/7.75 => ? [Xa: complex] :
% 13.77/7.75 ( ( member_complex @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4690_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_int,T: set_Code_integer,G: code_integer > real,I: code_integer > int,F: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ S )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ T )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ S )
% 13.77/7.75 => ? [Xa: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4691_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ S )
% 13.77/7.75 => ( ( finite_finite_int @ T )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S )
% 13.77/7.75 => ? [Xa: int] :
% 13.77/7.75 ( ( member_int @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4692_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ S )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ T )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S )
% 13.77/7.75 => ? [Xa: complex] :
% 13.77/7.75 ( ( member_complex @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4693_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_complex,T: set_Code_integer,G: code_integer > real,I: code_integer > complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ S )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ T )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S )
% 13.77/7.75 => ? [Xa: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4694_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_Code_integer,T: set_int,G: int > real,I: int > code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ S )
% 13.77/7.75 => ( ( finite_finite_int @ T )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S )
% 13.77/7.75 => ? [Xa: int] :
% 13.77/7.75 ( ( member_int @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4695_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_Code_integer,T: set_complex,G: complex > real,I: complex > code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ S )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ T )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S )
% 13.77/7.75 => ? [Xa: complex] :
% 13.77/7.75 ( ( member_complex @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4696_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_Code_integer,T: set_Code_integer,G: code_integer > real,I: code_integer > code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ S )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ T )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S )
% 13.77/7.75 => ? [Xa: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ S ) @ ( groups1270011288395367621r_real @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4697_sum__le__included,axiom,
% 13.77/7.75 ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 13.77/7.75 ( ( finite_finite_nat @ S )
% 13.77/7.75 => ( ( finite_finite_nat @ T )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ T )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ S )
% 13.77/7.75 => ? [Xa: nat] :
% 13.77/7.75 ( ( member_nat @ Xa @ T )
% 13.77/7.75 & ( ( I @ Xa )
% 13.77/7.75 = X3 )
% 13.77/7.75 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa ) ) ) )
% 13.77/7.75 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4698_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > real,G: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: int] :
% 13.77/7.75 ( ( member_int @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4699_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > real,G: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: complex] :
% 13.77/7.75 ( ( member_complex @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4700_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_real @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4701_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 13.77/7.75 ( ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: nat] :
% 13.77/7.75 ( ( member_nat @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4702_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > rat,G: int > rat] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: int] :
% 13.77/7.75 ( ( member_int @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4703_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > rat,G: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: complex] :
% 13.77/7.75 ( ( member_complex @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4704_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_rat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4705_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > nat,G: int > nat] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: int] :
% 13.77/7.75 ( ( member_int @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4706_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > nat,G: complex > nat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: complex] :
% 13.77/7.75 ( ( member_complex @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4707_sum__strict__mono__ex1,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ? [X5: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X5 @ A4 )
% 13.77/7.75 & ( ord_less_nat @ ( F @ X5 ) @ ( G @ X5 ) ) )
% 13.77/7.75 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4708_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: uint32 > uint32 > $o,S3: set_nat,H2: nat > uint32,G: nat > uint32] :
% 13.77/7.75 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 13.77/7.75 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite_finite_nat @ S3 )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups833757482993574392uint32 @ H2 @ S3 ) @ ( groups833757482993574392uint32 @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4709_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: uint32 > uint32 > $o,S3: set_int,H2: int > uint32,G: int > uint32] :
% 13.77/7.75 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 13.77/7.75 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite_finite_int @ S3 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups5712668689793887828uint32 @ H2 @ S3 ) @ ( groups5712668689793887828uint32 @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4710_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: uint32 > uint32 > $o,S3: set_complex,H2: complex > uint32,G: complex > uint32] :
% 13.77/7.75 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 13.77/7.75 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups8736914816313324502uint32 @ H2 @ S3 ) @ ( groups8736914816313324502uint32 @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4711_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: uint32 > uint32 > $o,S3: set_Code_integer,H2: code_integer > uint32,G: code_integer > uint32] :
% 13.77/7.75 ( ( R2 @ zero_zero_uint32 @ zero_zero_uint32 )
% 13.77/7.75 => ( ! [X15: uint32,Y15: uint32,X23: uint32,Y23: uint32] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_uint32 @ X15 @ Y15 ) @ ( plus_plus_uint32 @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups8847630953604152069uint32 @ H2 @ S3 ) @ ( groups8847630953604152069uint32 @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4712_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 13.77/7.75 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 13.77/7.75 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite_finite_int @ S3 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups8778361861064173332t_real @ H2 @ S3 ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4713_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 13.77/7.75 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 13.77/7.75 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4714_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: real > real > $o,S3: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 13.77/7.75 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 13.77/7.75 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups1270011288395367621r_real @ H2 @ S3 ) @ ( groups1270011288395367621r_real @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4715_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 13.77/7.75 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 13.77/7.75 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite_finite_nat @ S3 )
% 13.77/7.75 => ( ! [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4716_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 13.77/7.75 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 13.77/7.75 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite_finite_int @ S3 )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups3906332499630173760nt_rat @ H2 @ S3 ) @ ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4717_sum_Orelated,axiom,
% 13.77/7.75 ! [R2: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 13.77/7.75 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 13.77/7.75 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 13.77/7.75 ( ( ( R2 @ X15 @ X23 )
% 13.77/7.75 & ( R2 @ Y15 @ Y23 ) )
% 13.77/7.75 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S3 )
% 13.77/7.75 => ( R2 @ ( H2 @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( R2 @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4718_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bo8194388402131092736T_VEBT )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4719_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > real,G: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bot_set_real )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4720_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > real,G: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bot_set_complex )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4721_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > real,G: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4722_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > real,G: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bot_set_int )
% 13.77/7.75 => ( ! [X3: int] :
% 13.77/7.75 ( ( member_int @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4723_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_o,F: $o > real,G: $o > real] :
% 13.77/7.75 ( ( finite_finite_o @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bot_set_o )
% 13.77/7.75 => ( ! [X3: $o] :
% 13.77/7.75 ( ( member_o @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_real @ ( groups8691415230153176458o_real @ F @ A4 ) @ ( groups8691415230153176458o_real @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4724_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bo8194388402131092736T_VEBT )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4725_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_real,F: real > rat,G: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bot_set_real )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4726_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > rat,G: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bot_set_complex )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4727_sum__strict__mono,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ A4 )
% 13.77/7.75 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 13.77/7.75 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4728_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_o,X: $o,G: $o > real] :
% 13.77/7.75 ( ( finite_finite_o @ A4 )
% 13.77/7.75 => ( ( ( member_o @ X @ A4 )
% 13.77/7.75 => ( ( groups8691415230153176458o_real @ G @ ( insert_o @ X @ A4 ) )
% 13.77/7.75 = ( groups8691415230153176458o_real @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_o @ X @ A4 )
% 13.77/7.75 => ( ( groups8691415230153176458o_real @ G @ ( insert_o @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups8691415230153176458o_real @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4729_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( groups2240296850493347238T_real @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4730_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_real,X: real,G: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ( ( member_real @ X @ A4 )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A4 ) )
% 13.77/7.75 = ( groups8097168146408367636l_real @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_real @ X @ A4 )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4731_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_int,X: int,G: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( ( member_int @ X @ A4 )
% 13.77/7.75 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A4 ) )
% 13.77/7.75 = ( groups8778361861064173332t_real @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_int @ X @ A4 )
% 13.77/7.75 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4732_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_complex,X: complex,G: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( ( member_complex @ X @ A4 )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 13.77/7.75 = ( groups5808333547571424918x_real @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_complex @ X @ A4 )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4733_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,X: code_integer,G: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( ( member_Code_integer @ X @ A4 )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.75 = ( groups1270011288395367621r_real @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_Code_integer @ X @ A4 )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4734_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_o,X: $o,G: $o > rat] :
% 13.77/7.75 ( ( finite_finite_o @ A4 )
% 13.77/7.75 => ( ( ( member_o @ X @ A4 )
% 13.77/7.75 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 13.77/7.75 = ( groups7872700643590313910_o_rat @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_o @ X @ A4 )
% 13.77/7.75 => ( ( groups7872700643590313910_o_rat @ G @ ( insert_o @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups7872700643590313910_o_rat @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4735_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.75 => ( ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.75 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( groups136491112297645522BT_rat @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.75 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4736_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_real,X: real,G: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ A4 )
% 13.77/7.75 => ( ( ( member_real @ X @ A4 )
% 13.77/7.75 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A4 ) )
% 13.77/7.75 = ( groups1300246762558778688al_rat @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_real @ X @ A4 )
% 13.77/7.75 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4737_sum_Oinsert__if,axiom,
% 13.77/7.75 ! [A4: set_nat,X: nat,G: nat > rat] :
% 13.77/7.75 ( ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ( ( member_nat @ X @ A4 )
% 13.77/7.75 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 13.77/7.75 = ( groups2906978787729119204at_rat @ G @ A4 ) ) )
% 13.77/7.75 & ( ~ ( member_nat @ X @ A4 )
% 13.77/7.75 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A4 ) )
% 13.77/7.75 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4738_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_VEBT_VEBT,T5: set_VEBT_VEBT,S3: set_VEBT_VEBT,I: vEBT_VEBT > vEBT_VEBT,J: vEBT_VEBT > vEBT_VEBT,T3: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ S7 )
% 13.77/7.75 => ( ( finite5795047828879050333T_VEBT @ T5 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4739_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_VEBT_VEBT,T5: set_real,S3: set_VEBT_VEBT,I: real > vEBT_VEBT,J: vEBT_VEBT > real,T3: set_real,G: vEBT_VEBT > uint32,H2: real > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ S7 )
% 13.77/7.75 => ( ( finite_finite_real @ T5 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4740_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_real,T5: set_VEBT_VEBT,S3: set_real,I: vEBT_VEBT > real,J: real > vEBT_VEBT,T3: set_VEBT_VEBT,G: real > uint32,H2: vEBT_VEBT > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ S7 )
% 13.77/7.75 => ( ( finite5795047828879050333T_VEBT @ T5 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( J @ A3 ) @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ T3 @ T5 ) )
% 13.77/7.75 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4741_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_real,T5: set_real,S3: set_real,I: real > real,J: real > real,T3: set_real,G: real > uint32,H2: real > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ S7 )
% 13.77/7.75 => ( ( finite_finite_real @ T5 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( member_real @ ( J @ A3 ) @ ( minus_minus_set_real @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ T3 @ T5 ) )
% 13.77/7.75 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4742_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_VEBT_VEBT,T5: set_int,S3: set_VEBT_VEBT,I: int > vEBT_VEBT,J: vEBT_VEBT > int,T3: set_int,G: vEBT_VEBT > uint32,H2: int > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ S7 )
% 13.77/7.75 => ( ( finite_finite_int @ T5 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: int] :
% 13.77/7.75 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: int] :
% 13.77/7.75 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: int] :
% 13.77/7.75 ( ( member_int @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups5712668689793887828uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4743_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_real,T5: set_int,S3: set_real,I: int > real,J: real > int,T3: set_int,G: real > uint32,H2: int > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ S7 )
% 13.77/7.75 => ( ( finite_finite_int @ T5 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( member_int @ ( J @ A3 ) @ ( minus_minus_set_int @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: int] :
% 13.77/7.75 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: int] :
% 13.77/7.75 ( ( member_int @ B3 @ ( minus_minus_set_int @ T3 @ T5 ) )
% 13.77/7.75 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: int] :
% 13.77/7.75 ( ( member_int @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 13.77/7.75 = ( groups5712668689793887828uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4744_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_VEBT_VEBT,T5: set_complex,S3: set_VEBT_VEBT,I: complex > vEBT_VEBT,J: vEBT_VEBT > complex,T3: set_complex,G: vEBT_VEBT > uint32,H2: complex > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ S7 )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ T5 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4745_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_real,T5: set_complex,S3: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > uint32,H2: complex > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ S7 )
% 13.77/7.75 => ( ( finite3207457112153483333omplex @ T5 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( member_complex @ ( J @ A3 ) @ ( minus_811609699411566653omplex @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T3 @ T5 ) )
% 13.77/7.75 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4746_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_VEBT_VEBT,T5: set_Code_integer,S3: set_VEBT_VEBT,I: code_integer > vEBT_VEBT,J: vEBT_VEBT > code_integer,T3: set_Code_integer,G: vEBT_VEBT > uint32,H2: code_integer > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ S7 )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ T5 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) )
% 13.77/7.75 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 13.77/7.75 => ( member_VEBT_VEBT @ ( I @ B3 ) @ ( minus_5127226145743854075T_VEBT @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4747_sum_Oreindex__bij__witness__not__neutral,axiom,
% 13.77/7.75 ! [S7: set_real,T5: set_Code_integer,S3: set_real,I: code_integer > real,J: real > code_integer,T3: set_Code_integer,G: real > uint32,H2: code_integer > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ S7 )
% 13.77/7.75 => ( ( finite6017078050557962740nteger @ T5 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( ( I @ ( J @ A3 ) )
% 13.77/7.75 = A3 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S7 ) )
% 13.77/7.75 => ( member_Code_integer @ ( J @ A3 ) @ ( minus_2355218937544613996nteger @ T3 @ T5 ) ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 13.77/7.75 => ( ( J @ ( I @ B3 ) )
% 13.77/7.75 = B3 ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ T3 @ T5 ) )
% 13.77/7.75 => ( member_real @ ( I @ B3 ) @ ( minus_minus_set_real @ S3 @ S7 ) ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S7 )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ T5 )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ S3 )
% 13.77/7.75 => ( ( H2 @ ( J @ A3 ) )
% 13.77/7.75 = ( G @ A3 ) ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4748_sum__SucD,axiom,
% 13.77/7.75 ! [F: nat > nat,A4: set_nat,N: nat] :
% 13.77/7.75 ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 13.77/7.75 = ( suc @ N ) )
% 13.77/7.75 => ? [X3: nat] :
% 13.77/7.75 ( ( member_nat @ X3 @ A4 )
% 13.77/7.75 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4749_sum__eq__Suc0__iff,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > nat] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 = ( ? [X4: int] :
% 13.77/7.75 ( ( member_int @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 & ! [Y4: int] :
% 13.77/7.75 ( ( member_int @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4750_sum__eq__Suc0__iff,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > nat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( ( groups5693394587270226106ex_nat @ F @ A4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 = ( ? [X4: complex] :
% 13.77/7.75 ( ( member_complex @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 & ! [Y4: complex] :
% 13.77/7.75 ( ( member_complex @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4751_sum__eq__Suc0__iff,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > nat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( ( groups7237345082560585321er_nat @ F @ A4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 = ( ? [X4: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 & ! [Y4: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4752_sum__eq__Suc0__iff,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > nat] :
% 13.77/7.75 ( ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 = ( ? [X4: nat] :
% 13.77/7.75 ( ( member_nat @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = ( suc @ zero_zero_nat ) )
% 13.77/7.75 & ! [Y4: nat] :
% 13.77/7.75 ( ( member_nat @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4753_sum__eq__1__iff,axiom,
% 13.77/7.75 ! [A4: set_int,F: int > nat] :
% 13.77/7.75 ( ( finite_finite_int @ A4 )
% 13.77/7.75 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 = ( ? [X4: int] :
% 13.77/7.75 ( ( member_int @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 & ! [Y4: int] :
% 13.77/7.75 ( ( member_int @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4754_sum__eq__1__iff,axiom,
% 13.77/7.75 ! [A4: set_complex,F: complex > nat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.75 => ( ( ( groups5693394587270226106ex_nat @ F @ A4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 = ( ? [X4: complex] :
% 13.77/7.75 ( ( member_complex @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 & ! [Y4: complex] :
% 13.77/7.75 ( ( member_complex @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4755_sum__eq__1__iff,axiom,
% 13.77/7.75 ! [A4: set_Code_integer,F: code_integer > nat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.75 => ( ( ( groups7237345082560585321er_nat @ F @ A4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 = ( ? [X4: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 & ! [Y4: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4756_sum__eq__1__iff,axiom,
% 13.77/7.75 ! [A4: set_nat,F: nat > nat] :
% 13.77/7.75 ( ( finite_finite_nat @ A4 )
% 13.77/7.75 => ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 = ( ? [X4: nat] :
% 13.77/7.75 ( ( member_nat @ X4 @ A4 )
% 13.77/7.75 & ( ( F @ X4 )
% 13.77/7.75 = one_one_nat )
% 13.77/7.75 & ! [Y4: nat] :
% 13.77/7.75 ( ( member_nat @ Y4 @ A4 )
% 13.77/7.75 => ( ( X4 != Y4 )
% 13.77/7.75 => ( ( F @ Y4 )
% 13.77/7.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4757_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ I5 )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4758_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_real,I: real,F: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ I5 )
% 13.77/7.75 => ( ( member_real @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: real] :
% 13.77/7.75 ( ( member_real @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4759_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_int,I: int,F: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ I5 )
% 13.77/7.75 => ( ( member_int @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: int] :
% 13.77/7.75 ( ( member_int @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4760_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_complex,I: complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ I5 )
% 13.77/7.75 => ( ( member_complex @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: complex] :
% 13.77/7.75 ( ( member_complex @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4761_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_Code_integer,I: code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ I5 )
% 13.77/7.75 => ( ( member_Code_integer @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups1270011288395367621r_real @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4762_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_VEBT_VEBT,I: vEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ I5 )
% 13.77/7.75 => ( ( member_VEBT_VEBT @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4763_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_real,I: real,F: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ I5 )
% 13.77/7.75 => ( ( member_real @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: real] :
% 13.77/7.75 ( ( member_real @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4764_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_nat,I: nat,F: nat > rat] :
% 13.77/7.75 ( ( finite_finite_nat @ I5 )
% 13.77/7.75 => ( ( member_nat @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: nat] :
% 13.77/7.75 ( ( member_nat @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4765_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_int,I: int,F: int > rat] :
% 13.77/7.75 ( ( finite_finite_int @ I5 )
% 13.77/7.75 => ( ( member_int @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: int] :
% 13.77/7.75 ( ( member_int @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4766_sum__pos2,axiom,
% 13.77/7.75 ! [I5: set_complex,I: complex,F: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ I5 )
% 13.77/7.75 => ( ( member_complex @ I @ I5 )
% 13.77/7.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 13.77/7.75 => ( ! [I2: complex] :
% 13.77/7.75 ( ( member_complex @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4767_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bo8194388402131092736T_VEBT )
% 13.77/7.75 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups2240296850493347238T_real @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4768_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_real,F: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bot_set_real )
% 13.77/7.75 => ( ! [I2: real] :
% 13.77/7.75 ( ( member_real @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4769_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_complex,F: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bot_set_complex )
% 13.77/7.75 => ( ! [I2: complex] :
% 13.77/7.75 ( ( member_complex @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4770_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_Code_integer,F: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bo3990330152332043303nteger )
% 13.77/7.75 => ( ! [I2: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups1270011288395367621r_real @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4771_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_int,F: int > real] :
% 13.77/7.75 ( ( finite_finite_int @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bot_set_int )
% 13.77/7.75 => ( ! [I2: int] :
% 13.77/7.75 ( ( member_int @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4772_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_o,F: $o > real] :
% 13.77/7.75 ( ( finite_finite_o @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bot_set_o )
% 13.77/7.75 => ( ! [I2: $o] :
% 13.77/7.75 ( ( member_o @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_real @ zero_zero_real @ ( groups8691415230153176458o_real @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4773_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bo8194388402131092736T_VEBT )
% 13.77/7.75 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups136491112297645522BT_rat @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4774_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_real,F: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bot_set_real )
% 13.77/7.75 => ( ! [I2: real] :
% 13.77/7.75 ( ( member_real @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4775_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_complex,F: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bot_set_complex )
% 13.77/7.75 => ( ! [I2: complex] :
% 13.77/7.75 ( ( member_complex @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4776_sum__pos,axiom,
% 13.77/7.75 ! [I5: set_Code_integer,F: code_integer > rat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ I5 )
% 13.77/7.75 => ( ( I5 != bot_bo3990330152332043303nteger )
% 13.77/7.75 => ( ! [I2: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ I2 @ I5 )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.75 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I5 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4777_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups8325533452322294502uint32 @ G @ A4 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups8325533452322294502uint32 @ G @ C3 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4778_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_real,A4: set_real,B4: set_real,G: real > uint32,H2: real > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups5944083974425963860uint32 @ G @ A4 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups5944083974425963860uint32 @ G @ C3 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4779_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > uint32,H2: complex > uint32] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: complex] :
% 13.77/7.75 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups8736914816313324502uint32 @ G @ A4 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups8736914816313324502uint32 @ G @ C3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4780_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > uint32,H2: code_integer > uint32] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups8847630953604152069uint32 @ G @ A4 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups8847630953604152069uint32 @ G @ C3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4781_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups2240296850493347238T_real @ G @ A4 )
% 13.77/7.75 = ( groups2240296850493347238T_real @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups2240296850493347238T_real @ G @ C3 )
% 13.77/7.75 = ( groups2240296850493347238T_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4782_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_real,A4: set_real,B4: set_real,G: real > real,H2: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups8097168146408367636l_real @ G @ A4 )
% 13.77/7.75 = ( groups8097168146408367636l_real @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups8097168146408367636l_real @ G @ C3 )
% 13.77/7.75 = ( groups8097168146408367636l_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4783_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: complex] :
% 13.77/7.75 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups5808333547571424918x_real @ G @ A4 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups5808333547571424918x_real @ G @ C3 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4784_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups1270011288395367621r_real @ G @ A4 )
% 13.77/7.75 = ( groups1270011288395367621r_real @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups1270011288395367621r_real @ G @ C3 )
% 13.77/7.75 = ( groups1270011288395367621r_real @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4785_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( ( groups136491112297645522BT_rat @ G @ A4 )
% 13.77/7.75 = ( groups136491112297645522BT_rat @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups136491112297645522BT_rat @ G @ C3 )
% 13.77/7.75 = ( groups136491112297645522BT_rat @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4786_sum_Osame__carrier,axiom,
% 13.77/7.75 ! [C3: set_real,A4: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( ( groups1300246762558778688al_rat @ G @ A4 )
% 13.77/7.75 = ( groups1300246762558778688al_rat @ H2 @ B4 ) )
% 13.77/7.75 = ( ( groups1300246762558778688al_rat @ G @ C3 )
% 13.77/7.75 = ( groups1300246762558778688al_rat @ H2 @ C3 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4787_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups8325533452322294502uint32 @ G @ C3 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ A4 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4788_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_real,A4: set_real,B4: set_real,G: real > uint32,H2: real > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups5944083974425963860uint32 @ G @ C3 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ A4 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4789_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > uint32,H2: complex > uint32] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: complex] :
% 13.77/7.75 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups8736914816313324502uint32 @ G @ C3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ G @ A4 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4790_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > uint32,H2: code_integer > uint32] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( ( groups8847630953604152069uint32 @ G @ C3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ G @ A4 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4791_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups2240296850493347238T_real @ G @ C3 )
% 13.77/7.75 = ( groups2240296850493347238T_real @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ G @ A4 )
% 13.77/7.75 = ( groups2240296850493347238T_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4792_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_real,A4: set_real,B4: set_real,G: real > real,H2: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups8097168146408367636l_real @ G @ C3 )
% 13.77/7.75 = ( groups8097168146408367636l_real @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ G @ A4 )
% 13.77/7.75 = ( groups8097168146408367636l_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4793_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_complex,A4: set_complex,B4: set_complex,G: complex > real,H2: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: complex] :
% 13.77/7.75 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: complex] :
% 13.77/7.75 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups5808333547571424918x_real @ G @ C3 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4794_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_Code_integer,A4: set_Code_integer,B4: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ A3 @ ( minus_2355218937544613996nteger @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [B3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( ( groups1270011288395367621r_real @ G @ C3 )
% 13.77/7.75 = ( groups1270011288395367621r_real @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 13.77/7.75 = ( groups1270011288395367621r_real @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4795_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_VEBT_VEBT,A4: set_VEBT_VEBT,B4: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ A3 @ ( minus_5127226145743854075T_VEBT @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( ( groups136491112297645522BT_rat @ G @ C3 )
% 13.77/7.75 = ( groups136491112297645522BT_rat @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups136491112297645522BT_rat @ G @ A4 )
% 13.77/7.75 = ( groups136491112297645522BT_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4796_sum_Osame__carrierI,axiom,
% 13.77/7.75 ! [C3: set_real,A4: set_real,B4: set_real,G: real > rat,H2: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ A4 @ C3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ B4 @ C3 )
% 13.77/7.75 => ( ! [A3: real] :
% 13.77/7.75 ( ( member_real @ A3 @ ( minus_minus_set_real @ C3 @ A4 ) )
% 13.77/7.75 => ( ( G @ A3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ! [B3: real] :
% 13.77/7.75 ( ( member_real @ B3 @ ( minus_minus_set_real @ C3 @ B4 ) )
% 13.77/7.75 => ( ( H2 @ B3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( ( groups1300246762558778688al_rat @ G @ C3 )
% 13.77/7.75 = ( groups1300246762558778688al_rat @ H2 @ C3 ) )
% 13.77/7.75 => ( ( groups1300246762558778688al_rat @ G @ A4 )
% 13.77/7.75 = ( groups1300246762558778688al_rat @ H2 @ B4 ) ) ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4797_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > uint32] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4798_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > uint32] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4799_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4800_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ S3 )
% 13.77/7.75 = ( groups1270011288395367621r_real @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4801_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( groups5058264527183730370ex_rat @ G @ S3 )
% 13.77/7.75 = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4802_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > rat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( groups6602215022474089585er_rat @ G @ S3 )
% 13.77/7.75 = ( groups6602215022474089585er_rat @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4803_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_nat ) )
% 13.77/7.75 => ( ( groups5693394587270226106ex_nat @ G @ S3 )
% 13.77/7.75 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4804_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > nat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_nat ) )
% 13.77/7.75 => ( ( groups7237345082560585321er_nat @ G @ S3 )
% 13.77/7.75 = ( groups7237345082560585321er_nat @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4805_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_int ) )
% 13.77/7.75 => ( ( groups5690904116761175830ex_int @ G @ S3 )
% 13.77/7.75 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4806_sum_Omono__neutral__left,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > int] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_int ) )
% 13.77/7.75 => ( ( groups7234854612051535045er_int @ G @ S3 )
% 13.77/7.75 = ( groups7234854612051535045er_int @ G @ T3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4807_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > uint32] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ G @ T3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4808_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > uint32] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ G @ T3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4809_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4810_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ T3 )
% 13.77/7.75 = ( groups1270011288395367621r_real @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4811_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > rat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 13.77/7.75 = ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4812_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > rat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ( groups6602215022474089585er_rat @ G @ T3 )
% 13.77/7.75 = ( groups6602215022474089585er_rat @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4813_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > nat] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_nat ) )
% 13.77/7.75 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 13.77/7.75 = ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4814_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > nat] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_nat ) )
% 13.77/7.75 => ( ( groups7237345082560585321er_nat @ G @ T3 )
% 13.77/7.75 = ( groups7237345082560585321er_nat @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4815_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > int] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_int ) )
% 13.77/7.75 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 13.77/7.75 = ( groups5690904116761175830ex_int @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4816_sum_Omono__neutral__right,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > int] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_int ) )
% 13.77/7.75 => ( ( groups7234854612051535045er_int @ G @ T3 )
% 13.77/7.75 = ( groups7234854612051535045er_int @ G @ S3 ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4817_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > uint32,G: vEBT_VEBT > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4818_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_real,S3: set_real,H2: real > uint32,G: real > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ T3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ S3 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4819_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,H2: complex > uint32,G: complex > uint32] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4820_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,H2: code_integer > uint32,G: code_integer > uint32] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ G @ S3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4821_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > real,G: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ G @ S3 )
% 13.77/7.75 = ( groups2240296850493347238T_real @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4822_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_real,S3: set_real,H2: real > real,G: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ T3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ G @ S3 )
% 13.77/7.75 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4823_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ S3 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4824_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,H2: code_integer > real,G: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups1270011288395367621r_real @ G @ S3 )
% 13.77/7.75 = ( groups1270011288395367621r_real @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4825_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,H2: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups136491112297645522BT_rat @ G @ S3 )
% 13.77/7.75 = ( groups136491112297645522BT_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4826_sum_Omono__neutral__cong__left,axiom,
% 13.77/7.75 ! [T3: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 13.77/7.75 ( ( finite_finite_real @ T3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 13.77/7.75 => ( ( H2 @ X3 )
% 13.77/7.75 = zero_zero_rat ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups1300246762558778688al_rat @ G @ S3 )
% 13.77/7.75 = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4827_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > uint32,H2: vEBT_VEBT > uint32] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8325533452322294502uint32 @ G @ T3 )
% 13.77/7.75 = ( groups8325533452322294502uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4828_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_real,S3: set_real,G: real > uint32,H2: real > uint32] :
% 13.77/7.75 ( ( finite_finite_real @ T3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups5944083974425963860uint32 @ G @ T3 )
% 13.77/7.75 = ( groups5944083974425963860uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4829_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > uint32,H2: complex > uint32] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8736914816313324502uint32 @ G @ T3 )
% 13.77/7.75 = ( groups8736914816313324502uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4830_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > uint32,H2: code_integer > uint32] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_uint32 ) )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8847630953604152069uint32 @ G @ T3 )
% 13.77/7.75 = ( groups8847630953604152069uint32 @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4831_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > real,H2: vEBT_VEBT > real] :
% 13.77/7.75 ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.75 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.75 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups2240296850493347238T_real @ G @ T3 )
% 13.77/7.75 = ( groups2240296850493347238T_real @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4832_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_real,S3: set_real,G: real > real,H2: real > real] :
% 13.77/7.75 ( ( finite_finite_real @ T3 )
% 13.77/7.75 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [X3: real] :
% 13.77/7.75 ( ( member_real @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 13.77/7.75 = ( groups8097168146408367636l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4833_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 13.77/7.75 ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.75 => ( ( ord_le211207098394363844omplex @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.75 => ( ! [X3: complex] :
% 13.77/7.75 ( ( member_complex @ X3 @ S3 )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = ( H2 @ X3 ) ) )
% 13.77/7.75 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 13.77/7.75 = ( groups5808333547571424918x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.75
% 13.77/7.75 thf(fact_4834_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.75 ! [T3: set_Code_integer,S3: set_Code_integer,G: code_integer > real,H2: code_integer > real] :
% 13.77/7.75 ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.75 => ( ( ord_le7084787975880047091nteger @ S3 @ T3 )
% 13.77/7.75 => ( ! [X3: code_integer] :
% 13.77/7.75 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T3 @ S3 ) )
% 13.77/7.75 => ( ( G @ X3 )
% 13.77/7.75 = zero_zero_real ) )
% 13.77/7.76 => ( ! [X3: code_integer] :
% 13.77/7.76 ( ( member_Code_integer @ X3 @ S3 )
% 13.77/7.76 => ( ( G @ X3 )
% 13.77/7.76 = ( H2 @ X3 ) ) )
% 13.77/7.76 => ( ( groups1270011288395367621r_real @ G @ T3 )
% 13.77/7.76 = ( groups1270011288395367621r_real @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4835_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.76 ! [T3: set_VEBT_VEBT,S3: set_VEBT_VEBT,G: vEBT_VEBT > rat,H2: vEBT_VEBT > rat] :
% 13.77/7.76 ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.76 => ( ( ord_le4337996190870823476T_VEBT @ S3 @ T3 )
% 13.77/7.76 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.76 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ T3 @ S3 ) )
% 13.77/7.76 => ( ( G @ X3 )
% 13.77/7.76 = zero_zero_rat ) )
% 13.77/7.76 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.76 ( ( member_VEBT_VEBT @ X3 @ S3 )
% 13.77/7.76 => ( ( G @ X3 )
% 13.77/7.76 = ( H2 @ X3 ) ) )
% 13.77/7.76 => ( ( groups136491112297645522BT_rat @ G @ T3 )
% 13.77/7.76 = ( groups136491112297645522BT_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4836_sum_Omono__neutral__cong__right,axiom,
% 13.77/7.76 ! [T3: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 13.77/7.76 ( ( finite_finite_real @ T3 )
% 13.77/7.76 => ( ( ord_less_eq_set_real @ S3 @ T3 )
% 13.77/7.76 => ( ! [X3: real] :
% 13.77/7.76 ( ( member_real @ X3 @ ( minus_minus_set_real @ T3 @ S3 ) )
% 13.77/7.76 => ( ( G @ X3 )
% 13.77/7.76 = zero_zero_rat ) )
% 13.77/7.76 => ( ! [X3: real] :
% 13.77/7.76 ( ( member_real @ X3 @ S3 )
% 13.77/7.76 => ( ( G @ X3 )
% 13.77/7.76 = ( H2 @ X3 ) ) )
% 13.77/7.76 => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 13.77/7.76 = ( groups1300246762558778688al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4837_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_complex,A4: set_complex,G: complex > real] :
% 13.77/7.76 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 13.77/7.76 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5808333547571424918x_real @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4838_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > real] :
% 13.77/7.76 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 13.77/7.76 = ( plus_plus_real @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups1270011288395367621r_real @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4839_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_complex,A4: set_complex,G: complex > rat] :
% 13.77/7.76 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5058264527183730370ex_rat @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4840_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > rat] :
% 13.77/7.76 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups6602215022474089585er_rat @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4841_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_complex,A4: set_complex,G: complex > nat] :
% 13.77/7.76 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( groups5693394587270226106ex_nat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5693394587270226106ex_nat @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4842_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > nat] :
% 13.77/7.76 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( groups7237345082560585321er_nat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups7237345082560585321er_nat @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4843_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_complex,A4: set_complex,G: complex > int] :
% 13.77/7.76 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( groups5690904116761175830ex_int @ G @ A4 )
% 13.77/7.76 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5690904116761175830ex_int @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4844_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_Code_integer,A4: set_Code_integer,G: code_integer > int] :
% 13.77/7.76 ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( groups7234854612051535045er_int @ G @ A4 )
% 13.77/7.76 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A4 @ B4 ) ) @ ( groups7234854612051535045er_int @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4845_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_nat,A4: set_nat,G: nat > rat] :
% 13.77/7.76 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.76 => ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups2906978787729119204at_rat @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4846_sum_Osubset__diff,axiom,
% 13.77/7.76 ! [B4: set_nat,A4: set_nat,G: nat > int] :
% 13.77/7.76 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.76 => ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( groups3539618377306564664at_int @ G @ A4 )
% 13.77/7.76 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups3539618377306564664at_int @ G @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4847_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_complex,B4: set_complex,F: complex > uint32] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( groups8736914816313324502uint32 @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_uint32 @ ( groups8736914816313324502uint32 @ F @ A4 ) @ ( groups8736914816313324502uint32 @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4848_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,B4: set_Code_integer,F: code_integer > uint32] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( groups8847630953604152069uint32 @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_uint32 @ ( groups8847630953604152069uint32 @ F @ A4 ) @ ( groups8847630953604152069uint32 @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4849_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_complex,B4: set_complex,F: complex > real] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4850_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,B4: set_Code_integer,F: code_integer > real] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( groups1270011288395367621r_real @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4851_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_complex,B4: set_complex,F: complex > int] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ ( groups5690904116761175830ex_int @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4852_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,B4: set_Code_integer,F: code_integer > int] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_int @ ( groups7234854612051535045er_int @ F @ A4 ) @ ( groups7234854612051535045er_int @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4853_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_nat,B4: set_nat,F: nat > uint32] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.76 => ( ( groups833757482993574392uint32 @ F @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_uint32 @ ( groups833757482993574392uint32 @ F @ A4 ) @ ( groups833757482993574392uint32 @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4854_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_nat,B4: set_nat,F: nat > int] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.76 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4855_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_int,B4: set_int,F: int > uint32] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.77/7.76 => ( ( groups5712668689793887828uint32 @ F @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_uint32 @ ( groups5712668689793887828uint32 @ F @ A4 ) @ ( groups5712668689793887828uint32 @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4856_sum__diff,axiom,
% 13.77/7.76 ! [A4: set_int,B4: set_int,F: int > real] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.77/7.76 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4857_sum__diff__nat,axiom,
% 13.77/7.76 ! [B4: set_complex,A4: set_complex,F: complex > nat] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.76 => ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.76 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4858_sum__diff__nat,axiom,
% 13.77/7.76 ! [B4: set_Code_integer,A4: set_Code_integer,F: code_integer > nat] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.76 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups7237345082560585321er_nat @ F @ A4 ) @ ( groups7237345082560585321er_nat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4859_sum__diff__nat,axiom,
% 13.77/7.76 ! [B4: set_int,A4: set_int,F: int > nat] :
% 13.77/7.76 ( ( finite_finite_int @ B4 )
% 13.77/7.76 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.77/7.76 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4860_sum__diff__nat,axiom,
% 13.77/7.76 ! [B4: set_nat,A4: set_nat,F: nat > nat] :
% 13.77/7.76 ( ( finite_finite_nat @ B4 )
% 13.77/7.76 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.76 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ B4 ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4861_sum__diff1__nat,axiom,
% 13.77/7.76 ! [A: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.76 ( ( ( member_VEBT_VEBT @ A @ A4 )
% 13.77/7.76 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.76 & ( ~ ( member_VEBT_VEBT @ A @ A4 )
% 13.77/7.76 => ( ( groups771621172384141258BT_nat @ F @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.76 = ( groups771621172384141258BT_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4862_sum__diff1__nat,axiom,
% 13.77/7.76 ! [A: real,A4: set_real,F: real > nat] :
% 13.77/7.76 ( ( ( member_real @ A @ A4 )
% 13.77/7.76 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.76 & ( ~ ( member_real @ A @ A4 )
% 13.77/7.76 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 13.77/7.76 = ( groups1935376822645274424al_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4863_sum__diff1__nat,axiom,
% 13.77/7.76 ! [A: set_nat,A4: set_set_nat,F: set_nat > nat] :
% 13.77/7.76 ( ( ( member_set_nat @ A @ A4 )
% 13.77/7.76 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.76 & ( ~ ( member_set_nat @ A @ A4 )
% 13.77/7.76 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 13.77/7.76 = ( groups8294997508430121362at_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4864_sum__diff1__nat,axiom,
% 13.77/7.76 ! [A: int,A4: set_int,F: int > nat] :
% 13.77/7.76 ( ( ( member_int @ A @ A4 )
% 13.77/7.76 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.76 & ( ~ ( member_int @ A @ A4 )
% 13.77/7.76 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.77/7.76 = ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4865_sum__diff1__nat,axiom,
% 13.77/7.76 ! [A: $o,A4: set_o,F: $o > nat] :
% 13.77/7.76 ( ( ( member_o @ A @ A4 )
% 13.77/7.76 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.76 & ( ~ ( member_o @ A @ A4 )
% 13.77/7.76 => ( ( groups8507830703676809646_o_nat @ F @ ( minus_minus_set_o @ A4 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.77/7.76 = ( groups8507830703676809646_o_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4866_sum__diff1__nat,axiom,
% 13.77/7.76 ! [A: nat,A4: set_nat,F: nat > nat] :
% 13.77/7.76 ( ( ( member_nat @ A @ A4 )
% 13.77/7.76 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 13.77/7.76 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( F @ A ) ) ) )
% 13.77/7.76 & ( ~ ( member_nat @ A @ A4 )
% 13.77/7.76 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 13.77/7.76 = ( groups3542108847815614940at_nat @ F @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4867_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > real] :
% 13.77/7.76 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.76 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.76 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( groups2240296850493347238T_real @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4868_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_real,A4: set_real,F: real > real] :
% 13.77/7.76 ( ( finite_finite_real @ B4 )
% 13.77/7.76 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: real] :
% 13.77/7.76 ( ( member_real @ B3 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4869_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_complex,A4: set_complex,F: complex > real] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.76 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: complex] :
% 13.77/7.76 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4870_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_Code_integer,A4: set_Code_integer,F: code_integer > real] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.76 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: code_integer] :
% 13.77/7.76 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( groups1270011288395367621r_real @ F @ A4 ) @ ( groups1270011288395367621r_real @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4871_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 13.77/7.76 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.76 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.76 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ A4 ) @ ( groups136491112297645522BT_rat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4872_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_real,A4: set_real,F: real > rat] :
% 13.77/7.76 ( ( finite_finite_real @ B4 )
% 13.77/7.76 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: real] :
% 13.77/7.76 ( ( member_real @ B3 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4873_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_complex,A4: set_complex,F: complex > rat] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.76 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: complex] :
% 13.77/7.76 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4874_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_Code_integer,A4: set_Code_integer,F: code_integer > rat] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.76 => ( ( ord_le7084787975880047091nteger @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: code_integer] :
% 13.77/7.76 ( ( member_Code_integer @ B3 @ ( minus_2355218937544613996nteger @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( groups6602215022474089585er_rat @ F @ A4 ) @ ( groups6602215022474089585er_rat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4875_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_nat,A4: set_nat,F: nat > rat] :
% 13.77/7.76 ( ( finite_finite_nat @ B4 )
% 13.77/7.76 => ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: nat] :
% 13.77/7.76 ( ( member_nat @ B3 @ ( minus_minus_set_nat @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4876_sum__mono2,axiom,
% 13.77/7.76 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.76 ( ( finite5795047828879050333T_VEBT @ B4 )
% 13.77/7.76 => ( ( ord_le4337996190870823476T_VEBT @ A4 @ B4 )
% 13.77/7.76 => ( ! [B3: vEBT_VEBT] :
% 13.77/7.76 ( ( member_VEBT_VEBT @ B3 @ ( minus_5127226145743854075T_VEBT @ B4 @ A4 ) )
% 13.77/7.76 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B3 ) ) )
% 13.77/7.76 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( groups771621172384141258BT_nat @ F @ B4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4877_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > real] :
% 13.77/7.76 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.76 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.76 => ( ( groups2240296850493347238T_real @ G @ A4 )
% 13.77/7.76 = ( plus_plus_real @ ( G @ X ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4878_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_real,X: real,G: real > real] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ( ( member_real @ X @ A4 )
% 13.77/7.76 => ( ( groups8097168146408367636l_real @ G @ A4 )
% 13.77/7.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4879_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_complex,X: complex,G: complex > real] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( member_complex @ X @ A4 )
% 13.77/7.76 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 13.77/7.76 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4880_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,X: code_integer,G: code_integer > real] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.76 => ( ( groups1270011288395367621r_real @ G @ A4 )
% 13.77/7.76 = ( plus_plus_real @ ( G @ X ) @ ( groups1270011288395367621r_real @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4881_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 13.77/7.76 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.76 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.76 => ( ( groups136491112297645522BT_rat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4882_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_real,X: real,G: real > rat] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ( ( member_real @ X @ A4 )
% 13.77/7.76 => ( ( groups1300246762558778688al_rat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4883_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_complex,X: complex,G: complex > rat] :
% 13.77/7.76 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.76 => ( ( member_complex @ X @ A4 )
% 13.77/7.76 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4884_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,X: code_integer,G: code_integer > rat] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.76 => ( ( groups6602215022474089585er_rat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4885_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_VEBT_VEBT,X: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 13.77/7.76 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.76 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.76 => ( ( groups771621172384141258BT_nat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4886_sum_Oremove,axiom,
% 13.77/7.76 ! [A4: set_real,X: real,G: real > nat] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ( ( member_real @ X @ A4 )
% 13.77/7.76 => ( ( groups1935376822645274424al_nat @ G @ A4 )
% 13.77/7.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4887_max__idx__list,axiom,
% 13.77/7.76 ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 13.77/7.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 13.77/7.76 => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4888_cnt__non__neg,axiom,
% 13.77/7.76 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ zero_zero_real @ ( vEBT_VEBT_cnt @ T ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4889_height__i__max,axiom,
% 13.77/7.76 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 13.77/7.76 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4890_Bolzano,axiom,
% 13.77/7.76 ! [A: real,B: real,P2: real > real > $o] :
% 13.77/7.76 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.76 => ( ! [A3: real,B3: real,C: real] :
% 13.77/7.76 ( ( P2 @ A3 @ B3 )
% 13.77/7.76 => ( ( P2 @ B3 @ C )
% 13.77/7.76 => ( ( ord_less_eq_real @ A3 @ B3 )
% 13.77/7.76 => ( ( ord_less_eq_real @ B3 @ C )
% 13.77/7.76 => ( P2 @ A3 @ C ) ) ) ) )
% 13.77/7.76 => ( ! [X3: real] :
% 13.77/7.76 ( ( ord_less_eq_real @ A @ X3 )
% 13.77/7.76 => ( ( ord_less_eq_real @ X3 @ B )
% 13.77/7.76 => ? [D3: real] :
% 13.77/7.76 ( ( ord_less_real @ zero_zero_real @ D3 )
% 13.77/7.76 & ! [A3: real,B3: real] :
% 13.77/7.76 ( ( ( ord_less_eq_real @ A3 @ X3 )
% 13.77/7.76 & ( ord_less_eq_real @ X3 @ B3 )
% 13.77/7.76 & ( ord_less_real @ ( minus_minus_real @ B3 @ A3 ) @ D3 ) )
% 13.77/7.76 => ( P2 @ A3 @ B3 ) ) ) ) )
% 13.77/7.76 => ( P2 @ A @ B ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4891_option_Osize_I3_J,axiom,
% 13.77/7.76 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 13.77/7.76 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4892_option_Osize_I3_J,axiom,
% 13.77/7.76 ( ( size_size_option_nat @ none_nat )
% 13.77/7.76 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4893_option_Osize_I4_J,axiom,
% 13.77/7.76 ! [X2: product_prod_nat_nat] :
% 13.77/7.76 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 13.77/7.76 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4894_option_Osize_I4_J,axiom,
% 13.77/7.76 ! [X2: nat] :
% 13.77/7.76 ( ( size_size_option_nat @ ( some_nat @ X2 ) )
% 13.77/7.76 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4895_max__bot,axiom,
% 13.77/7.76 ! [X: set_nat] :
% 13.77/7.76 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4896_max__bot,axiom,
% 13.77/7.76 ! [X: assn] :
% 13.77/7.76 ( ( ord_max_assn @ bot_bot_assn @ X )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4897_max__bot,axiom,
% 13.77/7.76 ! [X: set_int] :
% 13.77/7.76 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4898_max__bot,axiom,
% 13.77/7.76 ! [X: set_o] :
% 13.77/7.76 ( ( ord_max_set_o @ bot_bot_set_o @ X )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4899_max__bot,axiom,
% 13.77/7.76 ! [X: nat] :
% 13.77/7.76 ( ( ord_max_nat @ bot_bot_nat @ X )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4900_max__bot2,axiom,
% 13.77/7.76 ! [X: set_nat] :
% 13.77/7.76 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4901_max__bot2,axiom,
% 13.77/7.76 ! [X: assn] :
% 13.77/7.76 ( ( ord_max_assn @ X @ bot_bot_assn )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4902_max__bot2,axiom,
% 13.77/7.76 ! [X: set_int] :
% 13.77/7.76 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4903_max__bot2,axiom,
% 13.77/7.76 ! [X: set_o] :
% 13.77/7.76 ( ( ord_max_set_o @ X @ bot_bot_set_o )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4904_max__bot2,axiom,
% 13.77/7.76 ! [X: nat] :
% 13.77/7.76 ( ( ord_max_nat @ X @ bot_bot_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4905_max__Suc__Suc,axiom,
% 13.77/7.76 ! [M: nat,N: nat] :
% 13.77/7.76 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 13.77/7.76 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4906_max__nat_Oeq__neutr__iff,axiom,
% 13.77/7.76 ! [A: nat,B: nat] :
% 13.77/7.76 ( ( ( ord_max_nat @ A @ B )
% 13.77/7.76 = zero_zero_nat )
% 13.77/7.76 = ( ( A = zero_zero_nat )
% 13.77/7.76 & ( B = zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4907_max__nat_Oleft__neutral,axiom,
% 13.77/7.76 ! [A: nat] :
% 13.77/7.76 ( ( ord_max_nat @ zero_zero_nat @ A )
% 13.77/7.76 = A ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4908_max__nat_Oneutr__eq__iff,axiom,
% 13.77/7.76 ! [A: nat,B: nat] :
% 13.77/7.76 ( ( zero_zero_nat
% 13.77/7.76 = ( ord_max_nat @ A @ B ) )
% 13.77/7.76 = ( ( A = zero_zero_nat )
% 13.77/7.76 & ( B = zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4909_max__nat_Oright__neutral,axiom,
% 13.77/7.76 ! [A: nat] :
% 13.77/7.76 ( ( ord_max_nat @ A @ zero_zero_nat )
% 13.77/7.76 = A ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4910_max__0L,axiom,
% 13.77/7.76 ! [N: nat] :
% 13.77/7.76 ( ( ord_max_nat @ zero_zero_nat @ N )
% 13.77/7.76 = N ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4911_max__0R,axiom,
% 13.77/7.76 ! [N: nat] :
% 13.77/7.76 ( ( ord_max_nat @ N @ zero_zero_nat )
% 13.77/7.76 = N ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4912_max__0__1_I2_J,axiom,
% 13.77/7.76 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 13.77/7.76 = one_one_real ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4913_max__0__1_I2_J,axiom,
% 13.77/7.76 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 13.77/7.76 = one_one_rat ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4914_max__0__1_I2_J,axiom,
% 13.77/7.76 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 13.77/7.76 = one_one_nat ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4915_max__0__1_I2_J,axiom,
% 13.77/7.76 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 13.77/7.76 = one_one_Code_integer ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4916_max__0__1_I2_J,axiom,
% 13.77/7.76 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 13.77/7.76 = one_one_int ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4917_max__0__1_I1_J,axiom,
% 13.77/7.76 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 13.77/7.76 = one_one_real ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4918_max__0__1_I1_J,axiom,
% 13.77/7.76 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 13.77/7.76 = one_one_rat ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4919_max__0__1_I1_J,axiom,
% 13.77/7.76 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 13.77/7.76 = one_one_nat ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4920_max__0__1_I1_J,axiom,
% 13.77/7.76 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 13.77/7.76 = one_one_Code_integer ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4921_max__0__1_I1_J,axiom,
% 13.77/7.76 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 13.77/7.76 = one_one_int ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4922_Max__insert,axiom,
% 13.77/7.76 ! [A4: set_o,X: $o] :
% 13.77/7.76 ( ( finite_finite_o @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_o )
% 13.77/7.76 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4923_Max__insert,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4924_Max__insert,axiom,
% 13.77/7.76 ! [A4: set_int,X: int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_int )
% 13.77/7.76 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4925_Max__insert,axiom,
% 13.77/7.76 ! [A4: set_nat,X: nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.76 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4926_max__def,axiom,
% 13.77/7.76 ( ord_max_Code_integer
% 13.77/7.76 = ( ^ [A7: code_integer,B7: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4927_max__def,axiom,
% 13.77/7.76 ( ord_max_set_int
% 13.77/7.76 = ( ^ [A7: set_int,B7: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4928_max__def,axiom,
% 13.77/7.76 ( ord_max_rat
% 13.77/7.76 = ( ^ [A7: rat,B7: rat] : ( if_rat @ ( ord_less_eq_rat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4929_max__def,axiom,
% 13.77/7.76 ( ord_max_num
% 13.77/7.76 = ( ^ [A7: num,B7: num] : ( if_num @ ( ord_less_eq_num @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4930_max__def,axiom,
% 13.77/7.76 ( ord_max_nat
% 13.77/7.76 = ( ^ [A7: nat,B7: nat] : ( if_nat @ ( ord_less_eq_nat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4931_max__def,axiom,
% 13.77/7.76 ( ord_max_int
% 13.77/7.76 = ( ^ [A7: int,B7: int] : ( if_int @ ( ord_less_eq_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4932_max__absorb1,axiom,
% 13.77/7.76 ! [Y: code_integer,X: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ Y @ X )
% 13.77/7.76 => ( ( ord_max_Code_integer @ X @ Y )
% 13.77/7.76 = X ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4933_max__absorb1,axiom,
% 13.77/7.76 ! [Y: set_int,X: set_int] :
% 13.77/7.76 ( ( ord_less_eq_set_int @ Y @ X )
% 13.77/7.76 => ( ( ord_max_set_int @ X @ Y )
% 13.77/7.76 = X ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4934_max__absorb1,axiom,
% 13.77/7.76 ! [Y: rat,X: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ Y @ X )
% 13.77/7.76 => ( ( ord_max_rat @ X @ Y )
% 13.77/7.76 = X ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4935_max__absorb1,axiom,
% 13.77/7.76 ! [Y: num,X: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ Y @ X )
% 13.77/7.76 => ( ( ord_max_num @ X @ Y )
% 13.77/7.76 = X ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4936_max__absorb1,axiom,
% 13.77/7.76 ! [Y: nat,X: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ Y @ X )
% 13.77/7.76 => ( ( ord_max_nat @ X @ Y )
% 13.77/7.76 = X ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4937_max__absorb1,axiom,
% 13.77/7.76 ! [Y: int,X: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ Y @ X )
% 13.77/7.76 => ( ( ord_max_int @ X @ Y )
% 13.77/7.76 = X ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4938_max__absorb2,axiom,
% 13.77/7.76 ! [X: code_integer,Y: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 13.77/7.76 => ( ( ord_max_Code_integer @ X @ Y )
% 13.77/7.76 = Y ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4939_max__absorb2,axiom,
% 13.77/7.76 ! [X: set_int,Y: set_int] :
% 13.77/7.76 ( ( ord_less_eq_set_int @ X @ Y )
% 13.77/7.76 => ( ( ord_max_set_int @ X @ Y )
% 13.77/7.76 = Y ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4940_max__absorb2,axiom,
% 13.77/7.76 ! [X: rat,Y: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ X @ Y )
% 13.77/7.76 => ( ( ord_max_rat @ X @ Y )
% 13.77/7.76 = Y ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4941_max__absorb2,axiom,
% 13.77/7.76 ! [X: num,Y: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ X @ Y )
% 13.77/7.76 => ( ( ord_max_num @ X @ Y )
% 13.77/7.76 = Y ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4942_max__absorb2,axiom,
% 13.77/7.76 ! [X: nat,Y: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ X @ Y )
% 13.77/7.76 => ( ( ord_max_nat @ X @ Y )
% 13.77/7.76 = Y ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4943_max__absorb2,axiom,
% 13.77/7.76 ! [X: int,Y: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ X @ Y )
% 13.77/7.76 => ( ( ord_max_int @ X @ Y )
% 13.77/7.76 = Y ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4944_max__add__distrib__right,axiom,
% 13.77/7.76 ! [X: real,Y: real,Z: real] :
% 13.77/7.76 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 13.77/7.76 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4945_max__add__distrib__right,axiom,
% 13.77/7.76 ! [X: rat,Y: rat,Z: rat] :
% 13.77/7.76 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 13.77/7.76 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4946_max__add__distrib__right,axiom,
% 13.77/7.76 ! [X: nat,Y: nat,Z: nat] :
% 13.77/7.76 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 13.77/7.76 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4947_max__add__distrib__right,axiom,
% 13.77/7.76 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 13.77/7.76 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 13.77/7.76 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4948_max__add__distrib__right,axiom,
% 13.77/7.76 ! [X: int,Y: int,Z: int] :
% 13.77/7.76 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 13.77/7.76 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4949_max__add__distrib__left,axiom,
% 13.77/7.76 ! [X: real,Y: real,Z: real] :
% 13.77/7.76 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4950_max__add__distrib__left,axiom,
% 13.77/7.76 ! [X: rat,Y: rat,Z: rat] :
% 13.77/7.76 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4951_max__add__distrib__left,axiom,
% 13.77/7.76 ! [X: nat,Y: nat,Z: nat] :
% 13.77/7.76 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4952_max__add__distrib__left,axiom,
% 13.77/7.76 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 13.77/7.76 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4953_max__add__distrib__left,axiom,
% 13.77/7.76 ! [X: int,Y: int,Z: int] :
% 13.77/7.76 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4954_max__diff__distrib__left,axiom,
% 13.77/7.76 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 13.77/7.76 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4955_max__diff__distrib__left,axiom,
% 13.77/7.76 ! [X: real,Y: real,Z: real] :
% 13.77/7.76 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4956_max__diff__distrib__left,axiom,
% 13.77/7.76 ! [X: int,Y: int,Z: int] :
% 13.77/7.76 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 13.77/7.76 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4957_nat__add__max__right,axiom,
% 13.77/7.76 ! [M: nat,N: nat,Q3: nat] :
% 13.77/7.76 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 13.77/7.76 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4958_nat__add__max__left,axiom,
% 13.77/7.76 ! [M: nat,N: nat,Q3: nat] :
% 13.77/7.76 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 13.77/7.76 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4959_nat__mult__max__right,axiom,
% 13.77/7.76 ! [M: nat,N: nat,Q3: nat] :
% 13.77/7.76 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 13.77/7.76 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4960_nat__mult__max__left,axiom,
% 13.77/7.76 ! [M: nat,N: nat,Q3: nat] :
% 13.77/7.76 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 13.77/7.76 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4961_nat__minus__add__max,axiom,
% 13.77/7.76 ! [N: nat,M: nat] :
% 13.77/7.76 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 13.77/7.76 = ( ord_max_nat @ N @ M ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4962_Max_Oin__idem,axiom,
% 13.77/7.76 ! [A4: set_real,X: real] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ( ( member_real @ X @ A4 )
% 13.77/7.76 => ( ( ord_max_real @ X @ ( lattic4275903605611617917x_real @ A4 ) )
% 13.77/7.76 = ( lattic4275903605611617917x_real @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4963_Max_Oin__idem,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.76 => ( ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A4 ) )
% 13.77/7.76 = ( lattic4901227151466704046nteger @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4964_Max_Oin__idem,axiom,
% 13.77/7.76 ! [A4: set_int,X: int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( member_int @ X @ A4 )
% 13.77/7.76 => ( ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) )
% 13.77/7.76 = ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4965_Max_Oin__idem,axiom,
% 13.77/7.76 ! [A4: set_nat,X: nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( member_nat @ X @ A4 )
% 13.77/7.76 => ( ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 13.77/7.76 = ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4966_VEBT__internal_Ocnt_Osimps_I1_J,axiom,
% 13.77/7.76 ! [A: $o,B: $o] :
% 13.77/7.76 ( ( vEBT_VEBT_cnt @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.76 = one_one_real ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4967_hom__Max__commute,axiom,
% 13.77/7.76 ! [H2: $o > $o,N8: set_o] :
% 13.77/7.76 ( ! [X3: $o,Y3: $o] :
% 13.77/7.76 ( ( H2 @ ( ord_max_o @ X3 @ Y3 ) )
% 13.77/7.76 = ( ord_max_o @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 13.77/7.76 => ( ( finite_finite_o @ N8 )
% 13.77/7.76 => ( ( N8 != bot_bot_set_o )
% 13.77/7.76 => ( ( H2 @ ( lattic1921953407002678535_Max_o @ N8 ) )
% 13.77/7.76 = ( lattic1921953407002678535_Max_o @ ( image_o_o @ H2 @ N8 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4968_hom__Max__commute,axiom,
% 13.77/7.76 ! [H2: code_integer > code_integer,N8: set_Code_integer] :
% 13.77/7.76 ( ! [X3: code_integer,Y3: code_integer] :
% 13.77/7.76 ( ( H2 @ ( ord_max_Code_integer @ X3 @ Y3 ) )
% 13.77/7.76 = ( ord_max_Code_integer @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 13.77/7.76 => ( ( finite6017078050557962740nteger @ N8 )
% 13.77/7.76 => ( ( N8 != bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( H2 @ ( lattic4901227151466704046nteger @ N8 ) )
% 13.77/7.76 = ( lattic4901227151466704046nteger @ ( image_4470545334726330049nteger @ H2 @ N8 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4969_hom__Max__commute,axiom,
% 13.77/7.76 ! [H2: int > int,N8: set_int] :
% 13.77/7.76 ( ! [X3: int,Y3: int] :
% 13.77/7.76 ( ( H2 @ ( ord_max_int @ X3 @ Y3 ) )
% 13.77/7.76 = ( ord_max_int @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 13.77/7.76 => ( ( finite_finite_int @ N8 )
% 13.77/7.76 => ( ( N8 != bot_bot_set_int )
% 13.77/7.76 => ( ( H2 @ ( lattic8263393255366662781ax_int @ N8 ) )
% 13.77/7.76 = ( lattic8263393255366662781ax_int @ ( image_int_int @ H2 @ N8 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4970_hom__Max__commute,axiom,
% 13.77/7.76 ! [H2: nat > nat,N8: set_nat] :
% 13.77/7.76 ( ! [X3: nat,Y3: nat] :
% 13.77/7.76 ( ( H2 @ ( ord_max_nat @ X3 @ Y3 ) )
% 13.77/7.76 = ( ord_max_nat @ ( H2 @ X3 ) @ ( H2 @ Y3 ) ) )
% 13.77/7.76 => ( ( finite_finite_nat @ N8 )
% 13.77/7.76 => ( ( N8 != bot_bot_set_nat )
% 13.77/7.76 => ( ( H2 @ ( lattic8265883725875713057ax_nat @ N8 ) )
% 13.77/7.76 = ( lattic8265883725875713057ax_nat @ ( image_nat_nat @ H2 @ N8 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4971_Max_Osubset,axiom,
% 13.77/7.76 ! [A4: set_o,B4: set_o] :
% 13.77/7.76 ( ( finite_finite_o @ A4 )
% 13.77/7.76 => ( ( B4 != bot_bot_set_o )
% 13.77/7.76 => ( ( ord_less_eq_set_o @ B4 @ A4 )
% 13.77/7.76 => ( ( ord_max_o @ ( lattic1921953407002678535_Max_o @ B4 ) @ ( lattic1921953407002678535_Max_o @ A4 ) )
% 13.77/7.76 = ( lattic1921953407002678535_Max_o @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4972_Max_Osubset,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( B4 != bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( ord_le7084787975880047091nteger @ B4 @ A4 )
% 13.77/7.76 => ( ( ord_max_Code_integer @ ( lattic4901227151466704046nteger @ B4 ) @ ( lattic4901227151466704046nteger @ A4 ) )
% 13.77/7.76 = ( lattic4901227151466704046nteger @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4973_Max_Osubset,axiom,
% 13.77/7.76 ! [A4: set_int,B4: set_int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( B4 != bot_bot_set_int )
% 13.77/7.76 => ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.77/7.76 => ( ( ord_max_int @ ( lattic8263393255366662781ax_int @ B4 ) @ ( lattic8263393255366662781ax_int @ A4 ) )
% 13.77/7.76 = ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4974_Max_Osubset,axiom,
% 13.77/7.76 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( B4 != bot_bot_set_nat )
% 13.77/7.76 => ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.76 => ( ( ord_max_nat @ ( lattic8265883725875713057ax_nat @ B4 ) @ ( lattic8265883725875713057ax_nat @ A4 ) )
% 13.77/7.76 = ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4975_Max_Oclosed,axiom,
% 13.77/7.76 ! [A4: set_real] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_real )
% 13.77/7.76 => ( ! [X3: real,Y3: real] : ( member_real @ ( ord_max_real @ X3 @ Y3 ) @ ( insert_real @ X3 @ ( insert_real @ Y3 @ bot_bot_set_real ) ) )
% 13.77/7.76 => ( member_real @ ( lattic4275903605611617917x_real @ A4 ) @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4976_Max_Oclosed,axiom,
% 13.77/7.76 ! [A4: set_o] :
% 13.77/7.76 ( ( finite_finite_o @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_o )
% 13.77/7.76 => ( ! [X3: $o,Y3: $o] : ( member_o @ ( ord_max_o @ X3 @ Y3 ) @ ( insert_o @ X3 @ ( insert_o @ Y3 @ bot_bot_set_o ) ) )
% 13.77/7.76 => ( member_o @ ( lattic1921953407002678535_Max_o @ A4 ) @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4977_Max_Oclosed,axiom,
% 13.77/7.76 ! [A4: set_Code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ! [X3: code_integer,Y3: code_integer] : ( member_Code_integer @ ( ord_max_Code_integer @ X3 @ Y3 ) @ ( insert_Code_integer @ X3 @ ( insert_Code_integer @ Y3 @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.76 => ( member_Code_integer @ ( lattic4901227151466704046nteger @ A4 ) @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4978_Max_Oclosed,axiom,
% 13.77/7.76 ! [A4: set_int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_int )
% 13.77/7.76 => ( ! [X3: int,Y3: int] : ( member_int @ ( ord_max_int @ X3 @ Y3 ) @ ( insert_int @ X3 @ ( insert_int @ Y3 @ bot_bot_set_int ) ) )
% 13.77/7.76 => ( member_int @ ( lattic8263393255366662781ax_int @ A4 ) @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4979_Max_Oclosed,axiom,
% 13.77/7.76 ! [A4: set_nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.76 => ( ! [X3: nat,Y3: nat] : ( member_nat @ ( ord_max_nat @ X3 @ Y3 ) @ ( insert_nat @ X3 @ ( insert_nat @ Y3 @ bot_bot_set_nat ) ) )
% 13.77/7.76 => ( member_nat @ ( lattic8265883725875713057ax_nat @ A4 ) @ A4 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4980_Max_Oinsert__not__elem,axiom,
% 13.77/7.76 ! [A4: set_real,X: real] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ( ~ ( member_real @ X @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_real )
% 13.77/7.76 => ( ( lattic4275903605611617917x_real @ ( insert_real @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_real @ X @ ( lattic4275903605611617917x_real @ A4 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4981_Max_Oinsert__not__elem,axiom,
% 13.77/7.76 ! [A4: set_o,X: $o] :
% 13.77/7.76 ( ( finite_finite_o @ A4 )
% 13.77/7.76 => ( ~ ( member_o @ X @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_o )
% 13.77/7.76 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ A4 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4982_Max_Oinsert__not__elem,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ~ ( member_Code_integer @ X @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ A4 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4983_Max_Oinsert__not__elem,axiom,
% 13.77/7.76 ! [A4: set_int,X: int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ~ ( member_int @ X @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_int )
% 13.77/7.76 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ A4 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4984_Max_Oinsert__not__elem,axiom,
% 13.77/7.76 ! [A4: set_nat,X: nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ~ ( member_nat @ X @ A4 )
% 13.77/7.76 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.76 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ A4 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4985_Max_Oinsert__remove,axiom,
% 13.77/7.76 ! [A4: set_o,X: $o] :
% 13.77/7.76 ( ( finite_finite_o @ A4 )
% 13.77/7.76 => ( ( lattic1921953407002678535_Max_o @ ( insert_o @ X @ A4 ) )
% 13.77/7.76 = ( ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.76 = bot_bot_set_o )
% 13.77/7.76 => X )
% 13.77/7.76 & ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.76 != bot_bot_set_o )
% 13.77/7.76 => ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4986_Max_Oinsert__remove,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 13.77/7.76 = bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 13.77/7.76 != bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( lattic4901227151466704046nteger @ ( insert_Code_integer @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4987_Max_Oinsert__remove,axiom,
% 13.77/7.76 ! [A4: set_int,X: int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.76 = bot_bot_set_int )
% 13.77/7.76 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.76 != bot_bot_set_int )
% 13.77/7.76 => ( ( lattic8263393255366662781ax_int @ ( insert_int @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4988_Max_Oinsert__remove,axiom,
% 13.77/7.76 ! [A4: set_nat,X: nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.76 = bot_bot_set_nat )
% 13.77/7.76 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.76 != bot_bot_set_nat )
% 13.77/7.76 => ( ( lattic8265883725875713057ax_nat @ ( insert_nat @ X @ A4 ) )
% 13.77/7.76 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4989_Max_Oremove,axiom,
% 13.77/7.76 ! [A4: set_real,X: real] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ( ( member_real @ X @ A4 )
% 13.77/7.76 => ( ( ( ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) )
% 13.77/7.76 = bot_bot_set_real )
% 13.77/7.76 => ( ( lattic4275903605611617917x_real @ A4 )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) )
% 13.77/7.76 != bot_bot_set_real )
% 13.77/7.76 => ( ( lattic4275903605611617917x_real @ A4 )
% 13.77/7.76 = ( ord_max_real @ X @ ( lattic4275903605611617917x_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4990_Max_Oremove,axiom,
% 13.77/7.76 ! [A4: set_o,X: $o] :
% 13.77/7.76 ( ( finite_finite_o @ A4 )
% 13.77/7.76 => ( ( member_o @ X @ A4 )
% 13.77/7.76 => ( ( lattic1921953407002678535_Max_o @ A4 )
% 13.77/7.76 = ( ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.76 = bot_bot_set_o )
% 13.77/7.76 => X )
% 13.77/7.76 & ( ( ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) )
% 13.77/7.76 != bot_bot_set_o )
% 13.77/7.76 => ( ord_max_o @ X @ ( lattic1921953407002678535_Max_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4991_Max_Oremove,axiom,
% 13.77/7.76 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ( ( member_Code_integer @ X @ A4 )
% 13.77/7.76 => ( ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 13.77/7.76 = bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( lattic4901227151466704046nteger @ A4 )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) )
% 13.77/7.76 != bot_bo3990330152332043303nteger )
% 13.77/7.76 => ( ( lattic4901227151466704046nteger @ A4 )
% 13.77/7.76 = ( ord_max_Code_integer @ X @ ( lattic4901227151466704046nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4992_Max_Oremove,axiom,
% 13.77/7.76 ! [A4: set_int,X: int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ( ( member_int @ X @ A4 )
% 13.77/7.76 => ( ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.76 = bot_bot_set_int )
% 13.77/7.76 => ( ( lattic8263393255366662781ax_int @ A4 )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) )
% 13.77/7.76 != bot_bot_set_int )
% 13.77/7.76 => ( ( lattic8263393255366662781ax_int @ A4 )
% 13.77/7.76 = ( ord_max_int @ X @ ( lattic8263393255366662781ax_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4993_Max_Oremove,axiom,
% 13.77/7.76 ! [A4: set_nat,X: nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ( ( member_nat @ X @ A4 )
% 13.77/7.76 => ( ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.76 = bot_bot_set_nat )
% 13.77/7.76 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.76 != bot_bot_set_nat )
% 13.77/7.76 => ( ( lattic8265883725875713057ax_nat @ A4 )
% 13.77/7.76 = ( ord_max_nat @ X @ ( lattic8265883725875713057ax_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4994_max_Oabsorb3,axiom,
% 13.77/7.76 ! [B: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le6747313008572928689nteger @ B @ A )
% 13.77/7.76 => ( ( ord_max_Code_integer @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4995_max_Oabsorb3,axiom,
% 13.77/7.76 ! [B: real,A: real] :
% 13.77/7.76 ( ( ord_less_real @ B @ A )
% 13.77/7.76 => ( ( ord_max_real @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4996_max_Oabsorb3,axiom,
% 13.77/7.76 ! [B: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_rat @ B @ A )
% 13.77/7.76 => ( ( ord_max_rat @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4997_max_Oabsorb3,axiom,
% 13.77/7.76 ! [B: num,A: num] :
% 13.77/7.76 ( ( ord_less_num @ B @ A )
% 13.77/7.76 => ( ( ord_max_num @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4998_max_Oabsorb3,axiom,
% 13.77/7.76 ! [B: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_nat @ B @ A )
% 13.77/7.76 => ( ( ord_max_nat @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_4999_max_Oabsorb3,axiom,
% 13.77/7.76 ! [B: int,A: int] :
% 13.77/7.76 ( ( ord_less_int @ B @ A )
% 13.77/7.76 => ( ( ord_max_int @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5000_max_Oabsorb4,axiom,
% 13.77/7.76 ! [A: code_integer,B: code_integer] :
% 13.77/7.76 ( ( ord_le6747313008572928689nteger @ A @ B )
% 13.77/7.76 => ( ( ord_max_Code_integer @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5001_max_Oabsorb4,axiom,
% 13.77/7.76 ! [A: real,B: real] :
% 13.77/7.76 ( ( ord_less_real @ A @ B )
% 13.77/7.76 => ( ( ord_max_real @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5002_max_Oabsorb4,axiom,
% 13.77/7.76 ! [A: rat,B: rat] :
% 13.77/7.76 ( ( ord_less_rat @ A @ B )
% 13.77/7.76 => ( ( ord_max_rat @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5003_max_Oabsorb4,axiom,
% 13.77/7.76 ! [A: num,B: num] :
% 13.77/7.76 ( ( ord_less_num @ A @ B )
% 13.77/7.76 => ( ( ord_max_num @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5004_max_Oabsorb4,axiom,
% 13.77/7.76 ! [A: nat,B: nat] :
% 13.77/7.76 ( ( ord_less_nat @ A @ B )
% 13.77/7.76 => ( ( ord_max_nat @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5005_max_Oabsorb4,axiom,
% 13.77/7.76 ! [A: int,B: int] :
% 13.77/7.76 ( ( ord_less_int @ A @ B )
% 13.77/7.76 => ( ( ord_max_int @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5006_max__less__iff__conj,axiom,
% 13.77/7.76 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 13.77/7.76 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 13.77/7.76 = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 13.77/7.76 & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5007_max__less__iff__conj,axiom,
% 13.77/7.76 ! [X: real,Y: real,Z: real] :
% 13.77/7.76 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 13.77/7.76 = ( ( ord_less_real @ X @ Z )
% 13.77/7.76 & ( ord_less_real @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5008_max__less__iff__conj,axiom,
% 13.77/7.76 ! [X: rat,Y: rat,Z: rat] :
% 13.77/7.76 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 13.77/7.76 = ( ( ord_less_rat @ X @ Z )
% 13.77/7.76 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5009_max__less__iff__conj,axiom,
% 13.77/7.76 ! [X: num,Y: num,Z: num] :
% 13.77/7.76 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 13.77/7.76 = ( ( ord_less_num @ X @ Z )
% 13.77/7.76 & ( ord_less_num @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5010_max__less__iff__conj,axiom,
% 13.77/7.76 ! [X: nat,Y: nat,Z: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 13.77/7.76 = ( ( ord_less_nat @ X @ Z )
% 13.77/7.76 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5011_max__less__iff__conj,axiom,
% 13.77/7.76 ! [X: int,Y: int,Z: int] :
% 13.77/7.76 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 13.77/7.76 = ( ( ord_less_int @ X @ Z )
% 13.77/7.76 & ( ord_less_int @ Y @ Z ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5012_max_Obounded__iff,axiom,
% 13.77/7.76 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A )
% 13.77/7.76 = ( ( ord_le3102999989581377725nteger @ B @ A )
% 13.77/7.76 & ( ord_le3102999989581377725nteger @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5013_max_Obounded__iff,axiom,
% 13.77/7.76 ! [B: rat,C2: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 13.77/7.76 = ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.76 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5014_max_Obounded__iff,axiom,
% 13.77/7.76 ! [B: num,C2: num,A: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 13.77/7.76 = ( ( ord_less_eq_num @ B @ A )
% 13.77/7.76 & ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5015_max_Obounded__iff,axiom,
% 13.77/7.76 ! [B: nat,C2: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 13.77/7.76 = ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.76 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5016_max_Obounded__iff,axiom,
% 13.77/7.76 ! [B: int,C2: int,A: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 13.77/7.76 = ( ( ord_less_eq_int @ B @ A )
% 13.77/7.76 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5017_max_Oabsorb2,axiom,
% 13.77/7.76 ! [A: code_integer,B: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ A @ B )
% 13.77/7.76 => ( ( ord_max_Code_integer @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5018_max_Oabsorb2,axiom,
% 13.77/7.76 ! [A: rat,B: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ A @ B )
% 13.77/7.76 => ( ( ord_max_rat @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5019_max_Oabsorb2,axiom,
% 13.77/7.76 ! [A: num,B: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ A @ B )
% 13.77/7.76 => ( ( ord_max_num @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5020_max_Oabsorb2,axiom,
% 13.77/7.76 ! [A: nat,B: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.76 => ( ( ord_max_nat @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5021_max_Oabsorb2,axiom,
% 13.77/7.76 ! [A: int,B: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ A @ B )
% 13.77/7.76 => ( ( ord_max_int @ A @ B )
% 13.77/7.76 = B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5022_max_Oabsorb1,axiom,
% 13.77/7.76 ! [B: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ B @ A )
% 13.77/7.76 => ( ( ord_max_Code_integer @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5023_max_Oabsorb1,axiom,
% 13.77/7.76 ! [B: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.76 => ( ( ord_max_rat @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5024_max_Oabsorb1,axiom,
% 13.77/7.76 ! [B: num,A: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ B @ A )
% 13.77/7.76 => ( ( ord_max_num @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5025_max_Oabsorb1,axiom,
% 13.77/7.76 ! [B: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.76 => ( ( ord_max_nat @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5026_max_Oabsorb1,axiom,
% 13.77/7.76 ! [B: int,A: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.76 => ( ( ord_max_int @ A @ B )
% 13.77/7.76 = A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5027_option_Osize__gen_I2_J,axiom,
% 13.77/7.76 ! [X: product_prod_nat_nat > nat,X2: product_prod_nat_nat] :
% 13.77/7.76 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X2 ) )
% 13.77/7.76 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5028_option_Osize__gen_I2_J,axiom,
% 13.77/7.76 ! [X: nat > nat,X2: nat] :
% 13.77/7.76 ( ( size_option_nat @ X @ ( some_nat @ X2 ) )
% 13.77/7.76 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5029_option_Osize__gen_I1_J,axiom,
% 13.77/7.76 ! [X: product_prod_nat_nat > nat] :
% 13.77/7.76 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 13.77/7.76 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5030_option_Osize__gen_I1_J,axiom,
% 13.77/7.76 ! [X: nat > nat] :
% 13.77/7.76 ( ( size_option_nat @ X @ none_nat )
% 13.77/7.76 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5031_max_Omono,axiom,
% 13.77/7.76 ! [C2: code_integer,A: code_integer,D: code_integer,B: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 13.77/7.76 => ( ( ord_le3102999989581377725nteger @ D @ B )
% 13.77/7.76 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C2 @ D ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5032_max_Omono,axiom,
% 13.77/7.76 ! [C2: rat,A: rat,D: rat,B: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ C2 @ A )
% 13.77/7.76 => ( ( ord_less_eq_rat @ D @ B )
% 13.77/7.76 => ( ord_less_eq_rat @ ( ord_max_rat @ C2 @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5033_max_Omono,axiom,
% 13.77/7.76 ! [C2: num,A: num,D: num,B: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ C2 @ A )
% 13.77/7.76 => ( ( ord_less_eq_num @ D @ B )
% 13.77/7.76 => ( ord_less_eq_num @ ( ord_max_num @ C2 @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5034_max_Omono,axiom,
% 13.77/7.76 ! [C2: nat,A: nat,D: nat,B: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ C2 @ A )
% 13.77/7.76 => ( ( ord_less_eq_nat @ D @ B )
% 13.77/7.76 => ( ord_less_eq_nat @ ( ord_max_nat @ C2 @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5035_max_Omono,axiom,
% 13.77/7.76 ! [C2: int,A: int,D: int,B: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ C2 @ A )
% 13.77/7.76 => ( ( ord_less_eq_int @ D @ B )
% 13.77/7.76 => ( ord_less_eq_int @ ( ord_max_int @ C2 @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5036_max_OorderE,axiom,
% 13.77/7.76 ! [B: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ B @ A )
% 13.77/7.76 => ( A
% 13.77/7.76 = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5037_max_OorderE,axiom,
% 13.77/7.76 ! [B: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.76 => ( A
% 13.77/7.76 = ( ord_max_rat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5038_max_OorderE,axiom,
% 13.77/7.76 ! [B: num,A: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ B @ A )
% 13.77/7.76 => ( A
% 13.77/7.76 = ( ord_max_num @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5039_max_OorderE,axiom,
% 13.77/7.76 ! [B: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.76 => ( A
% 13.77/7.76 = ( ord_max_nat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5040_max_OorderE,axiom,
% 13.77/7.76 ! [B: int,A: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.76 => ( A
% 13.77/7.76 = ( ord_max_int @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5041_max_OorderI,axiom,
% 13.77/7.76 ! [A: code_integer,B: code_integer] :
% 13.77/7.76 ( ( A
% 13.77/7.76 = ( ord_max_Code_integer @ A @ B ) )
% 13.77/7.76 => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5042_max_OorderI,axiom,
% 13.77/7.76 ! [A: rat,B: rat] :
% 13.77/7.76 ( ( A
% 13.77/7.76 = ( ord_max_rat @ A @ B ) )
% 13.77/7.76 => ( ord_less_eq_rat @ B @ A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5043_max_OorderI,axiom,
% 13.77/7.76 ! [A: num,B: num] :
% 13.77/7.76 ( ( A
% 13.77/7.76 = ( ord_max_num @ A @ B ) )
% 13.77/7.76 => ( ord_less_eq_num @ B @ A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5044_max_OorderI,axiom,
% 13.77/7.76 ! [A: nat,B: nat] :
% 13.77/7.76 ( ( A
% 13.77/7.76 = ( ord_max_nat @ A @ B ) )
% 13.77/7.76 => ( ord_less_eq_nat @ B @ A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5045_max_OorderI,axiom,
% 13.77/7.76 ! [A: int,B: int] :
% 13.77/7.76 ( ( A
% 13.77/7.76 = ( ord_max_int @ A @ B ) )
% 13.77/7.76 => ( ord_less_eq_int @ B @ A ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5046_max_OboundedE,axiom,
% 13.77/7.76 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 13.77/7.76 => ~ ( ord_le3102999989581377725nteger @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5047_max_OboundedE,axiom,
% 13.77/7.76 ! [B: rat,C2: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.76 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5048_max_OboundedE,axiom,
% 13.77/7.76 ! [B: num,C2: num,A: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_eq_num @ B @ A )
% 13.77/7.76 => ~ ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5049_max_OboundedE,axiom,
% 13.77/7.76 ! [B: nat,C2: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.76 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5050_max_OboundedE,axiom,
% 13.77/7.76 ! [B: int,C2: int,A: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_eq_int @ B @ A )
% 13.77/7.76 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5051_max_OboundedI,axiom,
% 13.77/7.76 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ B @ A )
% 13.77/7.76 => ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 13.77/7.76 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5052_max_OboundedI,axiom,
% 13.77/7.76 ! [B: rat,A: rat,C2: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.76 => ( ( ord_less_eq_rat @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5053_max_OboundedI,axiom,
% 13.77/7.76 ! [B: num,A: num,C2: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ B @ A )
% 13.77/7.76 => ( ( ord_less_eq_num @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5054_max_OboundedI,axiom,
% 13.77/7.76 ! [B: nat,A: nat,C2: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.76 => ( ( ord_less_eq_nat @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5055_max_OboundedI,axiom,
% 13.77/7.76 ! [B: int,A: int,C2: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.76 => ( ( ord_less_eq_int @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5056_max_Oorder__iff,axiom,
% 13.77/7.76 ( ord_le3102999989581377725nteger
% 13.77/7.76 = ( ^ [B7: code_integer,A7: code_integer] :
% 13.77/7.76 ( A7
% 13.77/7.76 = ( ord_max_Code_integer @ A7 @ B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5057_max_Oorder__iff,axiom,
% 13.77/7.76 ( ord_less_eq_rat
% 13.77/7.76 = ( ^ [B7: rat,A7: rat] :
% 13.77/7.76 ( A7
% 13.77/7.76 = ( ord_max_rat @ A7 @ B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5058_max_Oorder__iff,axiom,
% 13.77/7.76 ( ord_less_eq_num
% 13.77/7.76 = ( ^ [B7: num,A7: num] :
% 13.77/7.76 ( A7
% 13.77/7.76 = ( ord_max_num @ A7 @ B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5059_max_Oorder__iff,axiom,
% 13.77/7.76 ( ord_less_eq_nat
% 13.77/7.76 = ( ^ [B7: nat,A7: nat] :
% 13.77/7.76 ( A7
% 13.77/7.76 = ( ord_max_nat @ A7 @ B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5060_max_Oorder__iff,axiom,
% 13.77/7.76 ( ord_less_eq_int
% 13.77/7.76 = ( ^ [B7: int,A7: int] :
% 13.77/7.76 ( A7
% 13.77/7.76 = ( ord_max_int @ A7 @ B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5061_max_Ocobounded1,axiom,
% 13.77/7.76 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5062_max_Ocobounded1,axiom,
% 13.77/7.76 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5063_max_Ocobounded1,axiom,
% 13.77/7.76 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5064_max_Ocobounded1,axiom,
% 13.77/7.76 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5065_max_Ocobounded1,axiom,
% 13.77/7.76 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5066_max_Ocobounded2,axiom,
% 13.77/7.76 ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5067_max_Ocobounded2,axiom,
% 13.77/7.76 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5068_max_Ocobounded2,axiom,
% 13.77/7.76 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5069_max_Ocobounded2,axiom,
% 13.77/7.76 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5070_max_Ocobounded2,axiom,
% 13.77/7.76 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5071_le__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 13.77/7.76 = ( ( ord_le3102999989581377725nteger @ Z @ X )
% 13.77/7.76 | ( ord_le3102999989581377725nteger @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5072_le__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: rat,X: rat,Y: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_eq_rat @ Z @ X )
% 13.77/7.76 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5073_le__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: num,X: num,Y: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_eq_num @ Z @ X )
% 13.77/7.76 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5074_le__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: nat,X: nat,Y: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_eq_nat @ Z @ X )
% 13.77/7.76 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5075_le__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: int,X: int,Y: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_eq_int @ Z @ X )
% 13.77/7.76 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5076_max_Oabsorb__iff1,axiom,
% 13.77/7.76 ( ord_le3102999989581377725nteger
% 13.77/7.76 = ( ^ [B7: code_integer,A7: code_integer] :
% 13.77/7.76 ( ( ord_max_Code_integer @ A7 @ B7 )
% 13.77/7.76 = A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5077_max_Oabsorb__iff1,axiom,
% 13.77/7.76 ( ord_less_eq_rat
% 13.77/7.76 = ( ^ [B7: rat,A7: rat] :
% 13.77/7.76 ( ( ord_max_rat @ A7 @ B7 )
% 13.77/7.76 = A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5078_max_Oabsorb__iff1,axiom,
% 13.77/7.76 ( ord_less_eq_num
% 13.77/7.76 = ( ^ [B7: num,A7: num] :
% 13.77/7.76 ( ( ord_max_num @ A7 @ B7 )
% 13.77/7.76 = A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5079_max_Oabsorb__iff1,axiom,
% 13.77/7.76 ( ord_less_eq_nat
% 13.77/7.76 = ( ^ [B7: nat,A7: nat] :
% 13.77/7.76 ( ( ord_max_nat @ A7 @ B7 )
% 13.77/7.76 = A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5080_max_Oabsorb__iff1,axiom,
% 13.77/7.76 ( ord_less_eq_int
% 13.77/7.76 = ( ^ [B7: int,A7: int] :
% 13.77/7.76 ( ( ord_max_int @ A7 @ B7 )
% 13.77/7.76 = A7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5081_max_Oabsorb__iff2,axiom,
% 13.77/7.76 ( ord_le3102999989581377725nteger
% 13.77/7.76 = ( ^ [A7: code_integer,B7: code_integer] :
% 13.77/7.76 ( ( ord_max_Code_integer @ A7 @ B7 )
% 13.77/7.76 = B7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5082_max_Oabsorb__iff2,axiom,
% 13.77/7.76 ( ord_less_eq_rat
% 13.77/7.76 = ( ^ [A7: rat,B7: rat] :
% 13.77/7.76 ( ( ord_max_rat @ A7 @ B7 )
% 13.77/7.76 = B7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5083_max_Oabsorb__iff2,axiom,
% 13.77/7.76 ( ord_less_eq_num
% 13.77/7.76 = ( ^ [A7: num,B7: num] :
% 13.77/7.76 ( ( ord_max_num @ A7 @ B7 )
% 13.77/7.76 = B7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5084_max_Oabsorb__iff2,axiom,
% 13.77/7.76 ( ord_less_eq_nat
% 13.77/7.76 = ( ^ [A7: nat,B7: nat] :
% 13.77/7.76 ( ( ord_max_nat @ A7 @ B7 )
% 13.77/7.76 = B7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5085_max_Oabsorb__iff2,axiom,
% 13.77/7.76 ( ord_less_eq_int
% 13.77/7.76 = ( ^ [A7: int,B7: int] :
% 13.77/7.76 ( ( ord_max_int @ A7 @ B7 )
% 13.77/7.76 = B7 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5086_max_OcoboundedI1,axiom,
% 13.77/7.76 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 13.77/7.76 => ( ord_le3102999989581377725nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5087_max_OcoboundedI1,axiom,
% 13.77/7.76 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5088_max_OcoboundedI1,axiom,
% 13.77/7.76 ! [C2: num,A: num,B: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5089_max_OcoboundedI1,axiom,
% 13.77/7.76 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5090_max_OcoboundedI1,axiom,
% 13.77/7.76 ! [C2: int,A: int,B: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ C2 @ A )
% 13.77/7.76 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5091_max_OcoboundedI2,axiom,
% 13.77/7.76 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le3102999989581377725nteger @ C2 @ B )
% 13.77/7.76 => ( ord_le3102999989581377725nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5092_max_OcoboundedI2,axiom,
% 13.77/7.76 ! [C2: rat,B: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_eq_rat @ C2 @ B )
% 13.77/7.76 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5093_max_OcoboundedI2,axiom,
% 13.77/7.76 ! [C2: num,B: num,A: num] :
% 13.77/7.76 ( ( ord_less_eq_num @ C2 @ B )
% 13.77/7.76 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5094_max_OcoboundedI2,axiom,
% 13.77/7.76 ! [C2: nat,B: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ C2 @ B )
% 13.77/7.76 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5095_max_OcoboundedI2,axiom,
% 13.77/7.76 ! [C2: int,B: int,A: int] :
% 13.77/7.76 ( ( ord_less_eq_int @ C2 @ B )
% 13.77/7.76 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5096_max_Ostrict__coboundedI2,axiom,
% 13.77/7.76 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le6747313008572928689nteger @ C2 @ B )
% 13.77/7.76 => ( ord_le6747313008572928689nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5097_max_Ostrict__coboundedI2,axiom,
% 13.77/7.76 ! [C2: real,B: real,A: real] :
% 13.77/7.76 ( ( ord_less_real @ C2 @ B )
% 13.77/7.76 => ( ord_less_real @ C2 @ ( ord_max_real @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5098_max_Ostrict__coboundedI2,axiom,
% 13.77/7.76 ! [C2: rat,B: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_rat @ C2 @ B )
% 13.77/7.76 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5099_max_Ostrict__coboundedI2,axiom,
% 13.77/7.76 ! [C2: num,B: num,A: num] :
% 13.77/7.76 ( ( ord_less_num @ C2 @ B )
% 13.77/7.76 => ( ord_less_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5100_max_Ostrict__coboundedI2,axiom,
% 13.77/7.76 ! [C2: nat,B: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_nat @ C2 @ B )
% 13.77/7.76 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5101_max_Ostrict__coboundedI2,axiom,
% 13.77/7.76 ! [C2: int,B: int,A: int] :
% 13.77/7.76 ( ( ord_less_int @ C2 @ B )
% 13.77/7.76 => ( ord_less_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5102_max_Ostrict__coboundedI1,axiom,
% 13.77/7.76 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 13.77/7.76 ( ( ord_le6747313008572928689nteger @ C2 @ A )
% 13.77/7.76 => ( ord_le6747313008572928689nteger @ C2 @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5103_max_Ostrict__coboundedI1,axiom,
% 13.77/7.76 ! [C2: real,A: real,B: real] :
% 13.77/7.76 ( ( ord_less_real @ C2 @ A )
% 13.77/7.76 => ( ord_less_real @ C2 @ ( ord_max_real @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5104_max_Ostrict__coboundedI1,axiom,
% 13.77/7.76 ! [C2: rat,A: rat,B: rat] :
% 13.77/7.76 ( ( ord_less_rat @ C2 @ A )
% 13.77/7.76 => ( ord_less_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5105_max_Ostrict__coboundedI1,axiom,
% 13.77/7.76 ! [C2: num,A: num,B: num] :
% 13.77/7.76 ( ( ord_less_num @ C2 @ A )
% 13.77/7.76 => ( ord_less_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5106_max_Ostrict__coboundedI1,axiom,
% 13.77/7.76 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.76 ( ( ord_less_nat @ C2 @ A )
% 13.77/7.76 => ( ord_less_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5107_max_Ostrict__coboundedI1,axiom,
% 13.77/7.76 ! [C2: int,A: int,B: int] :
% 13.77/7.76 ( ( ord_less_int @ C2 @ A )
% 13.77/7.76 => ( ord_less_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5108_max_Ostrict__order__iff,axiom,
% 13.77/7.76 ( ord_le6747313008572928689nteger
% 13.77/7.76 = ( ^ [B7: code_integer,A7: code_integer] :
% 13.77/7.76 ( ( A7
% 13.77/7.76 = ( ord_max_Code_integer @ A7 @ B7 ) )
% 13.77/7.76 & ( A7 != B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5109_max_Ostrict__order__iff,axiom,
% 13.77/7.76 ( ord_less_real
% 13.77/7.76 = ( ^ [B7: real,A7: real] :
% 13.77/7.76 ( ( A7
% 13.77/7.76 = ( ord_max_real @ A7 @ B7 ) )
% 13.77/7.76 & ( A7 != B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5110_max_Ostrict__order__iff,axiom,
% 13.77/7.76 ( ord_less_rat
% 13.77/7.76 = ( ^ [B7: rat,A7: rat] :
% 13.77/7.76 ( ( A7
% 13.77/7.76 = ( ord_max_rat @ A7 @ B7 ) )
% 13.77/7.76 & ( A7 != B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5111_max_Ostrict__order__iff,axiom,
% 13.77/7.76 ( ord_less_num
% 13.77/7.76 = ( ^ [B7: num,A7: num] :
% 13.77/7.76 ( ( A7
% 13.77/7.76 = ( ord_max_num @ A7 @ B7 ) )
% 13.77/7.76 & ( A7 != B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5112_max_Ostrict__order__iff,axiom,
% 13.77/7.76 ( ord_less_nat
% 13.77/7.76 = ( ^ [B7: nat,A7: nat] :
% 13.77/7.76 ( ( A7
% 13.77/7.76 = ( ord_max_nat @ A7 @ B7 ) )
% 13.77/7.76 & ( A7 != B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5113_max_Ostrict__order__iff,axiom,
% 13.77/7.76 ( ord_less_int
% 13.77/7.76 = ( ^ [B7: int,A7: int] :
% 13.77/7.76 ( ( A7
% 13.77/7.76 = ( ord_max_int @ A7 @ B7 ) )
% 13.77/7.76 & ( A7 != B7 ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5114_max_Ostrict__boundedE,axiom,
% 13.77/7.76 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 13.77/7.76 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 13.77/7.76 => ~ ( ord_le6747313008572928689nteger @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5115_max_Ostrict__boundedE,axiom,
% 13.77/7.76 ! [B: real,C2: real,A: real] :
% 13.77/7.76 ( ( ord_less_real @ ( ord_max_real @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_real @ B @ A )
% 13.77/7.76 => ~ ( ord_less_real @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5116_max_Ostrict__boundedE,axiom,
% 13.77/7.76 ! [B: rat,C2: rat,A: rat] :
% 13.77/7.76 ( ( ord_less_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_rat @ B @ A )
% 13.77/7.76 => ~ ( ord_less_rat @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5117_max_Ostrict__boundedE,axiom,
% 13.77/7.76 ! [B: num,C2: num,A: num] :
% 13.77/7.76 ( ( ord_less_num @ ( ord_max_num @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_num @ B @ A )
% 13.77/7.76 => ~ ( ord_less_num @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5118_max_Ostrict__boundedE,axiom,
% 13.77/7.76 ! [B: nat,C2: nat,A: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_nat @ B @ A )
% 13.77/7.76 => ~ ( ord_less_nat @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5119_max_Ostrict__boundedE,axiom,
% 13.77/7.76 ! [B: int,C2: int,A: int] :
% 13.77/7.76 ( ( ord_less_int @ ( ord_max_int @ B @ C2 ) @ A )
% 13.77/7.76 => ~ ( ( ord_less_int @ B @ A )
% 13.77/7.76 => ~ ( ord_less_int @ C2 @ A ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5120_less__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 13.77/7.76 ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 13.77/7.76 = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 13.77/7.76 | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5121_less__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: real,X: real,Y: real] :
% 13.77/7.76 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_real @ Z @ X )
% 13.77/7.76 | ( ord_less_real @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5122_less__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: rat,X: rat,Y: rat] :
% 13.77/7.76 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_rat @ Z @ X )
% 13.77/7.76 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5123_less__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: num,X: num,Y: num] :
% 13.77/7.76 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_num @ Z @ X )
% 13.77/7.76 | ( ord_less_num @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5124_less__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: nat,X: nat,Y: nat] :
% 13.77/7.76 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_nat @ Z @ X )
% 13.77/7.76 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5125_less__max__iff__disj,axiom,
% 13.77/7.76 ! [Z: int,X: int,Y: int] :
% 13.77/7.76 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 13.77/7.76 = ( ( ord_less_int @ Z @ X )
% 13.77/7.76 | ( ord_less_int @ Z @ Y ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5126_sorted__in__between,axiom,
% 13.77/7.76 ! [I: nat,J: nat,L: list_o,X: $o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 13.77/7.76 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 13.77/7.76 => ( ( ord_less_eq_o @ ( nth_o @ L @ I ) @ X )
% 13.77/7.76 => ( ( ord_less_o @ X @ ( nth_o @ L @ J ) )
% 13.77/7.76 => ~ ! [K2: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I @ K2 )
% 13.77/7.76 => ( ( ord_less_nat @ K2 @ J )
% 13.77/7.76 => ( ( ord_less_eq_o @ ( nth_o @ L @ K2 ) @ X )
% 13.77/7.76 => ~ ( ord_less_o @ X @ ( nth_o @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5127_sorted__in__between,axiom,
% 13.77/7.76 ! [I: nat,J: nat,L: list_real,X: real] :
% 13.77/7.76 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 13.77/7.76 => ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 13.77/7.76 => ( ( ord_less_eq_real @ ( nth_real @ L @ I ) @ X )
% 13.77/7.76 => ( ( ord_less_real @ X @ ( nth_real @ L @ J ) )
% 13.77/7.76 => ~ ! [K2: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I @ K2 )
% 13.77/7.76 => ( ( ord_less_nat @ K2 @ J )
% 13.77/7.76 => ( ( ord_less_eq_real @ ( nth_real @ L @ K2 ) @ X )
% 13.77/7.76 => ~ ( ord_less_real @ X @ ( nth_real @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5128_sorted__in__between,axiom,
% 13.77/7.76 ! [I: nat,J: nat,L: list_rat,X: rat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 13.77/7.76 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 13.77/7.76 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I ) @ X )
% 13.77/7.76 => ( ( ord_less_rat @ X @ ( nth_rat @ L @ J ) )
% 13.77/7.76 => ~ ! [K2: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I @ K2 )
% 13.77/7.76 => ( ( ord_less_nat @ K2 @ J )
% 13.77/7.76 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ K2 ) @ X )
% 13.77/7.76 => ~ ( ord_less_rat @ X @ ( nth_rat @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5129_sorted__in__between,axiom,
% 13.77/7.76 ! [I: nat,J: nat,L: list_num,X: num] :
% 13.77/7.76 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 13.77/7.76 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 13.77/7.76 => ( ( ord_less_eq_num @ ( nth_num @ L @ I ) @ X )
% 13.77/7.76 => ( ( ord_less_num @ X @ ( nth_num @ L @ J ) )
% 13.77/7.76 => ~ ! [K2: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I @ K2 )
% 13.77/7.76 => ( ( ord_less_nat @ K2 @ J )
% 13.77/7.76 => ( ( ord_less_eq_num @ ( nth_num @ L @ K2 ) @ X )
% 13.77/7.76 => ~ ( ord_less_num @ X @ ( nth_num @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5130_sorted__in__between,axiom,
% 13.77/7.76 ! [I: nat,J: nat,L: list_nat,X: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 13.77/7.76 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 13.77/7.76 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ X )
% 13.77/7.76 => ( ( ord_less_nat @ X @ ( nth_nat @ L @ J ) )
% 13.77/7.76 => ~ ! [K2: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I @ K2 )
% 13.77/7.76 => ( ( ord_less_nat @ K2 @ J )
% 13.77/7.76 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ K2 ) @ X )
% 13.77/7.76 => ~ ( ord_less_nat @ X @ ( nth_nat @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5131_sorted__in__between,axiom,
% 13.77/7.76 ! [I: nat,J: nat,L: list_int,X: int] :
% 13.77/7.76 ( ( ord_less_eq_nat @ zero_zero_nat @ I )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 13.77/7.76 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 13.77/7.76 => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ X )
% 13.77/7.76 => ( ( ord_less_int @ X @ ( nth_int @ L @ J ) )
% 13.77/7.76 => ~ ! [K2: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I @ K2 )
% 13.77/7.76 => ( ( ord_less_nat @ K2 @ J )
% 13.77/7.76 => ( ( ord_less_eq_int @ ( nth_int @ L @ K2 ) @ X )
% 13.77/7.76 => ~ ( ord_less_int @ X @ ( nth_int @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5132_nth__enumerate__eq,axiom,
% 13.77/7.76 ! [M: nat,Xs: list_VEBT_VEBTi,N: nat] :
% 13.77/7.76 ( ( ord_less_nat @ M @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( nth_Pr3244165891152107629_VEBTi @ ( enumerate_VEBT_VEBTi @ N @ Xs ) @ M )
% 13.77/7.76 = ( produc2649746096677893406_VEBTi @ ( plus_plus_nat @ N @ M ) @ ( nth_VEBT_VEBTi @ Xs @ M ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5133_nth__enumerate__eq,axiom,
% 13.77/7.76 ! [M: nat,Xs: list_int,N: nat] :
% 13.77/7.76 ( ( ord_less_nat @ M @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs ) @ M )
% 13.77/7.76 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M ) @ ( nth_int @ Xs @ M ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5134_nth__enumerate__eq,axiom,
% 13.77/7.76 ! [M: nat,Xs: list_VEBT_VEBT,N: nat] :
% 13.77/7.76 ( ( ord_less_nat @ M @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs ) @ M )
% 13.77/7.76 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N @ M ) @ ( nth_VEBT_VEBT @ Xs @ M ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5135_nth__enumerate__eq,axiom,
% 13.77/7.76 ! [M: nat,Xs: list_real,N: nat] :
% 13.77/7.76 ( ( ord_less_nat @ M @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( ( nth_Pr7767817059697521252t_real @ ( enumerate_real @ N @ Xs ) @ M )
% 13.77/7.76 = ( produc7837566107596912789t_real @ ( plus_plus_nat @ N @ M ) @ ( nth_real @ Xs @ M ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5136_nth__enumerate__eq,axiom,
% 13.77/7.76 ! [M: nat,Xs: list_o,N: nat] :
% 13.77/7.76 ( ( ord_less_nat @ M @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N @ Xs ) @ M )
% 13.77/7.76 = ( product_Pair_nat_o @ ( plus_plus_nat @ N @ M ) @ ( nth_o @ Xs @ M ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5137_nth__enumerate__eq,axiom,
% 13.77/7.76 ! [M: nat,Xs: list_nat,N: nat] :
% 13.77/7.76 ( ( ord_less_nat @ M @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs ) @ M )
% 13.77/7.76 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M ) @ ( nth_nat @ Xs @ M ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5138_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5139_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > nat > assn,Xsi: list_nat] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5140_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5141_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > int > assn,Xsi: list_int] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5142_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5143_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > nat > assn,Xsi: list_nat] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5144_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5145_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > int > assn,Xsi: list_int] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5146_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5147_listI__assn__extract,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > nat > assn,Xsi: list_nat] :
% 13.77/7.76 ( ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5148_nth__step__trancl,axiom,
% 13.77/7.76 ! [Xs: list_VEBT_VEBTi,R2: set_Pr2227491710730465451_VEBTi,N: nat,M: nat] :
% 13.77/7.76 ( ! [N2: nat] :
% 13.77/7.76 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) @ one_one_nat ) )
% 13.77/7.76 => ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ ( suc @ N2 ) ) @ ( nth_VEBT_VEBTi @ Xs @ N2 ) ) @ R2 ) )
% 13.77/7.76 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ord_less_nat @ M @ N )
% 13.77/7.76 => ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N ) @ ( nth_VEBT_VEBTi @ Xs @ M ) ) @ ( transi2803566869205510612_VEBTi @ R2 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5149_nth__step__trancl,axiom,
% 13.77/7.76 ! [Xs: list_uint32,R2: set_Pr1773385645901665561uint32,N: nat,M: nat] :
% 13.77/7.76 ( ! [N2: nat] :
% 13.77/7.76 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_s4844771616002835472uint32 @ Xs ) @ one_one_nat ) )
% 13.77/7.76 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ ( suc @ N2 ) ) @ ( nth_uint32 @ Xs @ N2 ) ) @ R2 ) )
% 13.77/7.76 => ( ( ord_less_nat @ N @ ( size_s4844771616002835472uint32 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_nat @ M @ N )
% 13.77/7.76 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ N ) @ ( nth_uint32 @ Xs @ M ) ) @ ( transi3114468042090999947uint32 @ R2 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5150_nth__step__trancl,axiom,
% 13.77/7.76 ! [Xs: list_int,R2: set_Pr958786334691620121nt_int,N: nat,M: nat] :
% 13.77/7.76 ( ! [N2: nat] :
% 13.77/7.76 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_int @ Xs ) @ one_one_nat ) )
% 13.77/7.76 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ ( suc @ N2 ) ) @ ( nth_int @ Xs @ N2 ) ) @ R2 ) )
% 13.77/7.76 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ord_less_nat @ M @ N )
% 13.77/7.76 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N ) @ ( nth_int @ Xs @ M ) ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5151_nth__step__trancl,axiom,
% 13.77/7.76 ! [Xs: list_VEBT_VEBT,R2: set_Pr6192946355708809607T_VEBT,N: nat,M: nat] :
% 13.77/7.76 ( ! [N2: nat] :
% 13.77/7.76 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat ) )
% 13.77/7.76 => ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( suc @ N2 ) ) @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) @ R2 ) )
% 13.77/7.76 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( ( ord_less_nat @ M @ N )
% 13.77/7.76 => ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( nth_VEBT_VEBT @ Xs @ M ) ) @ ( transi8906537157094044885T_VEBT @ R2 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5152_nth__step__trancl,axiom,
% 13.77/7.76 ! [Xs: list_real,R2: set_Pr6218003697084177305l_real,N: nat,M: nat] :
% 13.77/7.76 ( ! [N2: nat] :
% 13.77/7.76 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_real @ Xs ) @ one_one_nat ) )
% 13.77/7.76 => ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ ( suc @ N2 ) ) @ ( nth_real @ Xs @ N2 ) ) @ R2 ) )
% 13.77/7.76 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( ( ord_less_nat @ M @ N )
% 13.77/7.76 => ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ N ) @ ( nth_real @ Xs @ M ) ) @ ( transi1789104906590519371l_real @ R2 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5153_nth__step__trancl,axiom,
% 13.77/7.76 ! [Xs: list_o,R2: set_Product_prod_o_o,N: nat,M: nat] :
% 13.77/7.76 ( ! [N2: nat] :
% 13.77/7.76 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_o @ Xs ) @ one_one_nat ) )
% 13.77/7.76 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ ( suc @ N2 ) ) @ ( nth_o @ Xs @ N2 ) ) @ R2 ) )
% 13.77/7.76 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( ( ord_less_nat @ M @ N )
% 13.77/7.76 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ N ) @ ( nth_o @ Xs @ M ) ) @ ( transitive_trancl_o @ R2 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5154_nth__step__trancl,axiom,
% 13.77/7.76 ! [Xs: list_nat,R2: set_Pr1261947904930325089at_nat,N: nat,M: nat] :
% 13.77/7.76 ( ! [N2: nat] :
% 13.77/7.76 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat ) )
% 13.77/7.76 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( suc @ N2 ) ) @ ( nth_nat @ Xs @ N2 ) ) @ R2 ) )
% 13.77/7.76 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( ( ord_less_nat @ M @ N )
% 13.77/7.76 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N ) @ ( nth_nat @ Xs @ M ) ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5155_nth__Cons__pos,axiom,
% 13.77/7.76 ! [N: nat,X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.76 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5156_nth__Cons__pos,axiom,
% 13.77/7.76 ! [N: nat,X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.76 => ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5157_nth__Cons__pos,axiom,
% 13.77/7.76 ! [N: nat,X: int,Xs: list_int] :
% 13.77/7.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.76 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5158_nth__Cons__pos,axiom,
% 13.77/7.76 ! [N: nat,X: nat,Xs: list_nat] :
% 13.77/7.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.76 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5159_nth__Cons__pos,axiom,
% 13.77/7.76 ! [N: nat,X: $o,Xs: list_o] :
% 13.77/7.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.76 => ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_o @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5160_length__nth__simps_I4_J,axiom,
% 13.77/7.76 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 13.77/7.76 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5161_length__nth__simps_I4_J,axiom,
% 13.77/7.76 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 13.77/7.76 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5162_length__nth__simps_I4_J,axiom,
% 13.77/7.76 ! [X: int,Xs: list_int,N: nat] :
% 13.77/7.76 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_int @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5163_length__nth__simps_I4_J,axiom,
% 13.77/7.76 ! [X: nat,Xs: list_nat,N: nat] :
% 13.77/7.76 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_nat @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5164_length__nth__simps_I4_J,axiom,
% 13.77/7.76 ! [X: $o,Xs: list_o,N: nat] :
% 13.77/7.76 ( ( nth_o @ ( cons_o @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_o @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5165_nth__Cons__Suc,axiom,
% 13.77/7.76 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 13.77/7.76 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5166_nth__Cons__Suc,axiom,
% 13.77/7.76 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 13.77/7.76 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5167_nth__Cons__Suc,axiom,
% 13.77/7.76 ! [X: int,Xs: list_int,N: nat] :
% 13.77/7.76 ( ( nth_int @ ( cons_int @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_int @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5168_nth__Cons__Suc,axiom,
% 13.77/7.76 ! [X: nat,Xs: list_nat,N: nat] :
% 13.77/7.76 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_nat @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5169_nth__Cons__Suc,axiom,
% 13.77/7.76 ! [X: $o,Xs: list_o,N: nat] :
% 13.77/7.76 ( ( nth_o @ ( cons_o @ X @ Xs ) @ ( suc @ N ) )
% 13.77/7.76 = ( nth_o @ Xs @ N ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5170_length__nth__simps_I3_J,axiom,
% 13.77/7.76 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.76 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5171_length__nth__simps_I3_J,axiom,
% 13.77/7.76 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5172_length__nth__simps_I3_J,axiom,
% 13.77/7.76 ! [X: int,Xs: list_int] :
% 13.77/7.76 ( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5173_length__nth__simps_I3_J,axiom,
% 13.77/7.76 ! [X: nat,Xs: list_nat] :
% 13.77/7.76 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5174_length__nth__simps_I3_J,axiom,
% 13.77/7.76 ! [X: $o,Xs: list_o] :
% 13.77/7.76 ( ( nth_o @ ( cons_o @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5175_nth__Cons__0,axiom,
% 13.77/7.76 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.76 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5176_nth__Cons__0,axiom,
% 13.77/7.76 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5177_nth__Cons__0,axiom,
% 13.77/7.76 ! [X: int,Xs: list_int] :
% 13.77/7.76 ( ( nth_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5178_nth__Cons__0,axiom,
% 13.77/7.76 ! [X: nat,Xs: list_nat] :
% 13.77/7.76 ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5179_nth__Cons__0,axiom,
% 13.77/7.76 ! [X: $o,Xs: list_o] :
% 13.77/7.76 ( ( nth_o @ ( cons_o @ X @ Xs ) @ zero_zero_nat )
% 13.77/7.76 = X ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5180_trancl__single,axiom,
% 13.77/7.76 ! [A: uint32,B: uint32] :
% 13.77/7.76 ( ( transi3114468042090999947uint32 @ ( insert4454361187789264009uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ bot_bo8438649754162204037uint32 ) )
% 13.77/7.76 = ( insert4454361187789264009uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ bot_bo8438649754162204037uint32 ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5181_trancl__single,axiom,
% 13.77/7.76 ! [A: nat,B: nat] :
% 13.77/7.76 ( ( transi6264000038957366511cl_nat @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ bot_bo2099793752762293965at_nat ) )
% 13.77/7.76 = ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ A @ B ) @ bot_bo2099793752762293965at_nat ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5182_trancl__single,axiom,
% 13.77/7.76 ! [A: int,B: int] :
% 13.77/7.76 ( ( transi6261509568448316235cl_int @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ bot_bo1796632182523588997nt_int ) )
% 13.77/7.76 = ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ A @ B ) @ bot_bo1796632182523588997nt_int ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5183_listI__assn__finite,axiom,
% 13.77/7.76 ! [I5: set_nat,A4: vEBT_VEBT > vEBT_VEBTi > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi] :
% 13.77/7.76 ( ~ ( finite_finite_nat @ I5 )
% 13.77/7.76 => ( ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = bot_bot_assn ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5184_enumerate__simps_I2_J,axiom,
% 13.77/7.76 ! [N: nat,X: int,Xs: list_int] :
% 13.77/7.76 ( ( enumerate_int @ N @ ( cons_int @ X @ Xs ) )
% 13.77/7.76 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ N @ X ) @ ( enumerate_int @ ( suc @ N ) @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5185_enumerate__simps_I2_J,axiom,
% 13.77/7.76 ! [N: nat,X: $o,Xs: list_o] :
% 13.77/7.76 ( ( enumerate_o @ N @ ( cons_o @ X @ Xs ) )
% 13.77/7.76 = ( cons_P9142372351690779143_nat_o @ ( product_Pair_nat_o @ N @ X ) @ ( enumerate_o @ ( suc @ N ) @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5186_enumerate__simps_I2_J,axiom,
% 13.77/7.76 ! [N: nat,X: nat,Xs: list_nat] :
% 13.77/7.76 ( ( enumerate_nat @ N @ ( cons_nat @ X @ Xs ) )
% 13.77/7.76 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ N @ X ) @ ( enumerate_nat @ ( suc @ N ) @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5187_list__tail__coinc,axiom,
% 13.77/7.76 ! [N1: int,R1: list_int,N22: int,R22: list_int] :
% 13.77/7.76 ( ( ( cons_int @ N1 @ R1 )
% 13.77/7.76 = ( cons_int @ N22 @ R22 ) )
% 13.77/7.76 => ( ( N1 = N22 )
% 13.77/7.76 & ( R1 = R22 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5188_list__tail__coinc,axiom,
% 13.77/7.76 ! [N1: nat,R1: list_nat,N22: nat,R22: list_nat] :
% 13.77/7.76 ( ( ( cons_nat @ N1 @ R1 )
% 13.77/7.76 = ( cons_nat @ N22 @ R22 ) )
% 13.77/7.76 => ( ( N1 = N22 )
% 13.77/7.76 & ( R1 = R22 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5189_list__tail__coinc,axiom,
% 13.77/7.76 ! [N1: $o,R1: list_o,N22: $o,R22: list_o] :
% 13.77/7.76 ( ( ( cons_o @ N1 @ R1 )
% 13.77/7.76 = ( cons_o @ N22 @ R22 ) )
% 13.77/7.76 => ( ( N1 = N22 )
% 13.77/7.76 & ( R1 = R22 ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5190_sorted2,axiom,
% 13.77/7.76 ! [X: $o,Y: $o,Zs: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_eq_o @ ( cons_o @ X @ ( cons_o @ Y @ Zs ) ) )
% 13.77/7.76 = ( ( ord_less_eq_o @ X @ Y )
% 13.77/7.76 & ( sorted_wrt_o @ ord_less_eq_o @ ( cons_o @ Y @ Zs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5191_sorted2,axiom,
% 13.77/7.76 ! [X: rat,Y: rat,Zs: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X @ ( cons_rat @ Y @ Zs ) ) )
% 13.77/7.76 = ( ( ord_less_eq_rat @ X @ Y )
% 13.77/7.76 & ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ Y @ Zs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5192_sorted2,axiom,
% 13.77/7.76 ! [X: num,Y: num,Zs: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X @ ( cons_num @ Y @ Zs ) ) )
% 13.77/7.76 = ( ( ord_less_eq_num @ X @ Y )
% 13.77/7.76 & ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ Y @ Zs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5193_sorted2,axiom,
% 13.77/7.76 ! [X: nat,Y: nat,Zs: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X @ ( cons_nat @ Y @ Zs ) ) )
% 13.77/7.76 = ( ( ord_less_eq_nat @ X @ Y )
% 13.77/7.76 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ Y @ Zs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5194_sorted2,axiom,
% 13.77/7.76 ! [X: int,Y: int,Zs: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X @ ( cons_int @ Y @ Zs ) ) )
% 13.77/7.76 = ( ( ord_less_eq_int @ X @ Y )
% 13.77/7.76 & ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ Y @ Zs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5195_sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: real,Ys: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_eq_real @ ( cons_real @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: real] :
% 13.77/7.76 ( ( member_real @ X4 @ ( set_real2 @ Ys ) )
% 13.77/7.76 => ( ord_less_eq_real @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_real @ ord_less_eq_real @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5196_sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: $o,Ys: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_eq_o @ ( cons_o @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: $o] :
% 13.77/7.76 ( ( member_o @ X4 @ ( set_o2 @ Ys ) )
% 13.77/7.76 => ( ord_less_eq_o @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_o @ ord_less_eq_o @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5197_sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: rat,Ys: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_eq_rat @ ( cons_rat @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: rat] :
% 13.77/7.76 ( ( member_rat @ X4 @ ( set_rat2 @ Ys ) )
% 13.77/7.76 => ( ord_less_eq_rat @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_rat @ ord_less_eq_rat @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5198_sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: num,Ys: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_eq_num @ ( cons_num @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: num] :
% 13.77/7.76 ( ( member_num @ X4 @ ( set_num2 @ Ys ) )
% 13.77/7.76 => ( ord_less_eq_num @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_num @ ord_less_eq_num @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5199_sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: nat,Ys: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_eq_nat @ ( cons_nat @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: nat] :
% 13.77/7.76 ( ( member_nat @ X4 @ ( set_nat2 @ Ys ) )
% 13.77/7.76 => ( ord_less_eq_nat @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_nat @ ord_less_eq_nat @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5200_sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: int,Ys: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_eq_int @ ( cons_int @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: int] :
% 13.77/7.76 ( ( member_int @ X4 @ ( set_int2 @ Ys ) )
% 13.77/7.76 => ( ord_less_eq_int @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_int @ ord_less_eq_int @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5201_strict__sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: $o,Ys: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_o @ ( cons_o @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: $o] :
% 13.77/7.76 ( ( member_o @ X4 @ ( set_o2 @ Ys ) )
% 13.77/7.76 => ( ord_less_o @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_o @ ord_less_o @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5202_strict__sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: real,Ys: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_real @ ( cons_real @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: real] :
% 13.77/7.76 ( ( member_real @ X4 @ ( set_real2 @ Ys ) )
% 13.77/7.76 => ( ord_less_real @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_real @ ord_less_real @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5203_strict__sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: rat,Ys: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_rat @ ( cons_rat @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: rat] :
% 13.77/7.76 ( ( member_rat @ X4 @ ( set_rat2 @ Ys ) )
% 13.77/7.76 => ( ord_less_rat @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_rat @ ord_less_rat @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5204_strict__sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: num,Ys: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_num @ ( cons_num @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: num] :
% 13.77/7.76 ( ( member_num @ X4 @ ( set_num2 @ Ys ) )
% 13.77/7.76 => ( ord_less_num @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_num @ ord_less_num @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5205_strict__sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: nat,Ys: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_nat @ ( cons_nat @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: nat] :
% 13.77/7.76 ( ( member_nat @ X4 @ ( set_nat2 @ Ys ) )
% 13.77/7.76 => ( ord_less_nat @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_nat @ ord_less_nat @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5206_strict__sorted__simps_I2_J,axiom,
% 13.77/7.76 ! [X: int,Ys: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_int @ ( cons_int @ X @ Ys ) )
% 13.77/7.76 = ( ! [X4: int] :
% 13.77/7.76 ( ( member_int @ X4 @ ( set_int2 @ Ys ) )
% 13.77/7.76 => ( ord_less_int @ X @ X4 ) )
% 13.77/7.76 & ( sorted_wrt_int @ ord_less_int @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5207_strict__sorted__imp__sorted,axiom,
% 13.77/7.76 ! [Xs: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_real @ Xs )
% 13.77/7.76 => ( sorted_wrt_real @ ord_less_eq_real @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5208_strict__sorted__imp__sorted,axiom,
% 13.77/7.76 ! [Xs: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 13.77/7.76 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5209_strict__sorted__imp__sorted,axiom,
% 13.77/7.76 ! [Xs: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 13.77/7.76 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5210_strict__sorted__imp__sorted,axiom,
% 13.77/7.76 ! [Xs: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 13.77/7.76 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5211_strict__sorted__imp__sorted,axiom,
% 13.77/7.76 ! [Xs: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 13.77/7.76 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5212_strict__sorted__equal,axiom,
% 13.77/7.76 ! [Xs: list_o,Ys: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_o @ Xs )
% 13.77/7.76 => ( ( sorted_wrt_o @ ord_less_o @ Ys )
% 13.77/7.76 => ( ( ( set_o2 @ Ys )
% 13.77/7.76 = ( set_o2 @ Xs ) )
% 13.77/7.76 => ( Ys = Xs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5213_strict__sorted__equal,axiom,
% 13.77/7.76 ! [Xs: list_real,Ys: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_real @ Xs )
% 13.77/7.76 => ( ( sorted_wrt_real @ ord_less_real @ Ys )
% 13.77/7.76 => ( ( ( set_real2 @ Ys )
% 13.77/7.76 = ( set_real2 @ Xs ) )
% 13.77/7.76 => ( Ys = Xs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5214_strict__sorted__equal,axiom,
% 13.77/7.76 ! [Xs: list_rat,Ys: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 13.77/7.76 => ( ( sorted_wrt_rat @ ord_less_rat @ Ys )
% 13.77/7.76 => ( ( ( set_rat2 @ Ys )
% 13.77/7.76 = ( set_rat2 @ Xs ) )
% 13.77/7.76 => ( Ys = Xs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5215_strict__sorted__equal,axiom,
% 13.77/7.76 ! [Xs: list_num,Ys: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 13.77/7.76 => ( ( sorted_wrt_num @ ord_less_num @ Ys )
% 13.77/7.76 => ( ( ( set_num2 @ Ys )
% 13.77/7.76 = ( set_num2 @ Xs ) )
% 13.77/7.76 => ( Ys = Xs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5216_strict__sorted__equal,axiom,
% 13.77/7.76 ! [Xs: list_nat,Ys: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 13.77/7.76 => ( ( sorted_wrt_nat @ ord_less_nat @ Ys )
% 13.77/7.76 => ( ( ( set_nat2 @ Ys )
% 13.77/7.76 = ( set_nat2 @ Xs ) )
% 13.77/7.76 => ( Ys = Xs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5217_strict__sorted__equal,axiom,
% 13.77/7.76 ! [Xs: list_int,Ys: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 13.77/7.76 => ( ( sorted_wrt_int @ ord_less_int @ Ys )
% 13.77/7.76 => ( ( ( set_int2 @ Ys )
% 13.77/7.76 = ( set_int2 @ Xs ) )
% 13.77/7.76 => ( Ys = Xs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5218_length__nth__simps_I2_J,axiom,
% 13.77/7.76 ! [X: int,Xs: list_int] :
% 13.77/7.76 ( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
% 13.77/7.76 = ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5219_length__nth__simps_I2_J,axiom,
% 13.77/7.76 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.76 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) )
% 13.77/7.76 = ( suc @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5220_length__nth__simps_I2_J,axiom,
% 13.77/7.76 ! [X: real,Xs: list_real] :
% 13.77/7.76 ( ( size_size_list_real @ ( cons_real @ X @ Xs ) )
% 13.77/7.76 = ( suc @ ( size_size_list_real @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5221_length__nth__simps_I2_J,axiom,
% 13.77/7.76 ! [X: $o,Xs: list_o] :
% 13.77/7.76 ( ( size_size_list_o @ ( cons_o @ X @ Xs ) )
% 13.77/7.76 = ( suc @ ( size_size_list_o @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5222_length__nth__simps_I2_J,axiom,
% 13.77/7.76 ! [X: nat,Xs: list_nat] :
% 13.77/7.76 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs ) )
% 13.77/7.76 = ( suc @ ( size_size_list_nat @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5223_length__Suc__conv,axiom,
% 13.77/7.76 ! [Xs: list_int,N: nat] :
% 13.77/7.76 ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( suc @ N ) )
% 13.77/7.76 = ( ? [Y4: int,Ys3: list_int] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_int @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_int @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5224_length__Suc__conv,axiom,
% 13.77/7.76 ! [Xs: list_VEBT_VEBT,N: nat] :
% 13.77/7.76 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.76 = ( suc @ N ) )
% 13.77/7.76 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5225_length__Suc__conv,axiom,
% 13.77/7.76 ! [Xs: list_real,N: nat] :
% 13.77/7.76 ( ( ( size_size_list_real @ Xs )
% 13.77/7.76 = ( suc @ N ) )
% 13.77/7.76 = ( ? [Y4: real,Ys3: list_real] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_real @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_real @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5226_length__Suc__conv,axiom,
% 13.77/7.76 ! [Xs: list_o,N: nat] :
% 13.77/7.76 ( ( ( size_size_list_o @ Xs )
% 13.77/7.76 = ( suc @ N ) )
% 13.77/7.76 = ( ? [Y4: $o,Ys3: list_o] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_o @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_o @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5227_length__Suc__conv,axiom,
% 13.77/7.76 ! [Xs: list_nat,N: nat] :
% 13.77/7.76 ( ( ( size_size_list_nat @ Xs )
% 13.77/7.76 = ( suc @ N ) )
% 13.77/7.76 = ( ? [Y4: nat,Ys3: list_nat] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_nat @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_nat @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5228_Suc__length__conv,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_int] :
% 13.77/7.76 ( ( ( suc @ N )
% 13.77/7.76 = ( size_size_list_int @ Xs ) )
% 13.77/7.76 = ( ? [Y4: int,Ys3: list_int] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_int @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_int @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5229_Suc__length__conv,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.76 ( ( ( suc @ N )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5230_Suc__length__conv,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_real] :
% 13.77/7.76 ( ( ( suc @ N )
% 13.77/7.76 = ( size_size_list_real @ Xs ) )
% 13.77/7.76 = ( ? [Y4: real,Ys3: list_real] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_real @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_real @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5231_Suc__length__conv,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_o] :
% 13.77/7.76 ( ( ( suc @ N )
% 13.77/7.76 = ( size_size_list_o @ Xs ) )
% 13.77/7.76 = ( ? [Y4: $o,Ys3: list_o] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_o @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_o @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5232_Suc__length__conv,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_nat] :
% 13.77/7.76 ( ( ( suc @ N )
% 13.77/7.76 = ( size_size_list_nat @ Xs ) )
% 13.77/7.76 = ( ? [Y4: nat,Ys3: list_nat] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_nat @ Y4 @ Ys3 ) )
% 13.77/7.76 & ( ( size_size_list_nat @ Ys3 )
% 13.77/7.76 = N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5233_impossible__Cons,axiom,
% 13.77/7.76 ! [Xs: list_int,Ys: list_int,X: int] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys ) )
% 13.77/7.76 => ( Xs
% 13.77/7.76 != ( cons_int @ X @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5234_impossible__Cons,axiom,
% 13.77/7.76 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.76 => ( Xs
% 13.77/7.76 != ( cons_VEBT_VEBT @ X @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5235_impossible__Cons,axiom,
% 13.77/7.76 ! [Xs: list_real,Ys: list_real,X: real] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ ( size_size_list_real @ Ys ) )
% 13.77/7.76 => ( Xs
% 13.77/7.76 != ( cons_real @ X @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5236_impossible__Cons,axiom,
% 13.77/7.76 ! [Xs: list_o,Ys: list_o,X: $o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) )
% 13.77/7.76 => ( Xs
% 13.77/7.76 != ( cons_o @ X @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5237_impossible__Cons,axiom,
% 13.77/7.76 ! [Xs: list_nat,Ys: list_nat,X: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys ) )
% 13.77/7.76 => ( Xs
% 13.77/7.76 != ( cons_nat @ X @ Ys ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5238_set__subset__Cons,axiom,
% 13.77/7.76 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( set_VEBT_VEBT2 @ ( cons_VEBT_VEBT @ X @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5239_set__subset__Cons,axiom,
% 13.77/7.76 ! [Xs: list_real,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ ( set_real2 @ ( cons_real @ X @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5240_set__subset__Cons,axiom,
% 13.77/7.76 ! [Xs: list_nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ ( set_nat2 @ ( cons_nat @ X @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5241_set__subset__Cons,axiom,
% 13.77/7.76 ! [Xs: list_o,X: $o] : ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ ( set_o2 @ ( cons_o @ X @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5242_set__subset__Cons,axiom,
% 13.77/7.76 ! [Xs: list_int,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ ( set_int2 @ ( cons_int @ X @ Xs ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5243_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,A9: vEBT_VEBTi > vEBT_VEBTi > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L886525131989349516_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5244_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_int,Xsi2: list_int,A4: vEBT_VEBTi > int > assn,A9: vEBT_VEBTi > int > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xsi )
% 13.77/7.76 = ( size_size_list_int @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_int @ Xsi @ I2 )
% 13.77/7.76 = ( nth_int @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_int @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_int @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L2806540629473551875Ti_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5245_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi,A4: int > vEBT_VEBTi > assn,A9: int > vEBT_VEBTi > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L114188773329725699_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5246_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_int,Xsi2: list_int,A4: int > int > assn,A9: int > int > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xsi )
% 13.77/7.76 = ( size_size_list_int @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_int @ Xsi @ I2 )
% 13.77/7.76 = ( nth_int @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_int @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L8888932350013902202nt_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5247_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A4: vEBT_VEBTi > vEBT_VEBT > assn,A9: vEBT_VEBTi > vEBT_VEBT > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L2497118539674116125T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5248_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT,A4: int > vEBT_VEBT > assn,A9: int > vEBT_VEBT > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L2018189785592951398T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5249_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_real,Xsi2: list_real,A4: vEBT_VEBTi > real > assn,A9: vEBT_VEBTi > real > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_real @ Xsi )
% 13.77/7.76 = ( size_size_list_real @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_size_list_real @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_real @ Xsi @ I2 )
% 13.77/7.76 = ( nth_real @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_real @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_real @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L7728200936804140803i_real @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L7728200936804140803i_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5250_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_real,Xsi2: list_real,A4: int > real > assn,A9: int > real > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_real @ Xsi )
% 13.77/7.76 = ( size_size_list_real @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_real @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_real @ Xsi @ I2 )
% 13.77/7.76 = ( nth_real @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_real @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_real @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L7077748017936769786t_real @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L7077748017936769786t_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5251_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_o,Xsi2: list_o,A4: vEBT_VEBTi > $o > assn,A9: vEBT_VEBTi > $o > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_o @ Xsi )
% 13.77/7.76 = ( size_size_list_o @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_size_list_o @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_o @ Xsi @ I2 )
% 13.77/7.76 = ( nth_o @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_o @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_VEBT_VEBTi @ Xs4 @ I2 ) @ ( nth_o @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L3328983362619735041EBTi_o @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L3328983362619735041EBTi_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5252_listI__assn__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,Xs: list_int,Xs4: list_int,Xsi: list_o,Xsi2: list_o,A4: int > $o > assn,A9: int > $o > assn] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_o @ Xsi )
% 13.77/7.76 = ( size_size_list_o @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_o @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_o @ Xsi @ I2 )
% 13.77/7.76 = ( nth_o @ Xsi2 @ I2 ) )
% 13.77/7.76 & ( ( A4 @ ( nth_int @ Xs @ I2 ) @ ( nth_o @ Xsi @ I2 ) )
% 13.77/7.76 = ( A9 @ ( nth_int @ Xs4 @ I2 ) @ ( nth_o @ Xsi2 @ I2 ) ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L3563379889750563018_int_o @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L3563379889750563018_int_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5253_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > vEBT_VEBTi > assn,A9: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L886525131989349516_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5254_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > int > assn,A9: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_int,Xsi2: list_int] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xsi )
% 13.77/7.76 = ( size_size_list_int @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_int @ Xsi @ I2 )
% 13.77/7.76 = ( nth_int @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L2806540629473551875Ti_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5255_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: int > vEBT_VEBTi > assn,A9: int > vEBT_VEBTi > assn,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBTi,Xsi2: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xsi )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBTi @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L114188773329725699_VEBTi @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5256_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: int > int > assn,A9: int > int > assn,Xs: list_int,Xs4: list_int,Xsi: list_int,Xsi2: list_int] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xsi )
% 13.77/7.76 = ( size_size_list_int @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_int @ Xsi @ I2 )
% 13.77/7.76 = ( nth_int @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L8888932350013902202nt_int @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5257_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > vEBT_VEBT > assn,A9: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L2497118539674116125T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5258_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: int > vEBT_VEBT > assn,A9: int > vEBT_VEBT > assn,Xs: list_int,Xs4: list_int,Xsi: list_VEBT_VEBT,Xsi2: list_VEBT_VEBT] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_s6755466524823107622T_VEBT @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_VEBT_VEBT @ Xsi @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L2018189785592951398T_VEBT @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5259_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > real > assn,A9: vEBT_VEBTi > real > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_real,Xsi2: list_real] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_real @ Xsi )
% 13.77/7.76 = ( size_size_list_real @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_size_list_real @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_real @ Xsi @ I2 )
% 13.77/7.76 = ( nth_real @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L7728200936804140803i_real @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L7728200936804140803i_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5260_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: int > real > assn,A9: int > real > assn,Xs: list_int,Xs4: list_int,Xsi: list_real,Xsi2: list_real] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_real @ Xsi )
% 13.77/7.76 = ( size_size_list_real @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_real @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_real @ Xsi @ I2 )
% 13.77/7.76 = ( nth_real @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L7077748017936769786t_real @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L7077748017936769786t_real @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5261_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: vEBT_VEBTi > $o > assn,A9: vEBT_VEBTi > $o > assn,Xs: list_VEBT_VEBTi,Xs4: list_VEBT_VEBTi,Xsi: list_o,Xsi2: list_o] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_s7982070591426661849_VEBTi @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_o @ Xsi )
% 13.77/7.76 = ( size_size_list_o @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( size_s7982070591426661849_VEBTi @ Xs )
% 13.77/7.76 = ( size_size_list_o @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_o @ Xsi @ I2 )
% 13.77/7.76 = ( nth_o @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L3328983362619735041EBTi_o @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L3328983362619735041EBTi_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5262_listI__assn__weak__cong,axiom,
% 13.77/7.76 ! [I5: set_nat,I6: set_nat,A4: int > $o > assn,A9: int > $o > assn,Xs: list_int,Xs4: list_int,Xsi: list_o,Xsi2: list_o] :
% 13.77/7.76 ( ( I5 = I6 )
% 13.77/7.76 => ( ( A4 = A9 )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_int @ Xs4 ) )
% 13.77/7.76 => ( ( ( size_size_list_o @ Xsi )
% 13.77/7.76 = ( size_size_list_o @ Xsi2 ) )
% 13.77/7.76 => ( ! [I2: nat] :
% 13.77/7.76 ( ( member_nat @ I2 @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( size_size_list_int @ Xs )
% 13.77/7.76 = ( size_size_list_o @ Xsi ) )
% 13.77/7.76 => ( ( ( nth_int @ Xs @ I2 )
% 13.77/7.76 = ( nth_int @ Xs4 @ I2 ) )
% 13.77/7.76 & ( ( nth_o @ Xsi @ I2 )
% 13.77/7.76 = ( nth_o @ Xsi2 @ I2 ) ) ) ) ) )
% 13.77/7.76 => ( ( vEBT_L3563379889750563018_int_o @ I5 @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( vEBT_L3563379889750563018_int_o @ I6 @ A9 @ Xs4 @ Xsi2 ) ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5263_sorted__wrt01,axiom,
% 13.77/7.76 ! [Xs: list_int,P2: int > int > $o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_int @ P2 @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5264_sorted__wrt01,axiom,
% 13.77/7.76 ! [Xs: list_VEBT_VEBT,P2: vEBT_VEBT > vEBT_VEBT > $o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_VEBT_VEBT @ P2 @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5265_sorted__wrt01,axiom,
% 13.77/7.76 ! [Xs: list_real,P2: real > real > $o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_real @ P2 @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5266_sorted__wrt01,axiom,
% 13.77/7.76 ! [Xs: list_o,P2: $o > $o > $o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_o @ P2 @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5267_sorted__wrt01,axiom,
% 13.77/7.76 ! [Xs: list_nat,P2: nat > nat > $o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_nat @ P2 @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5268_sorted__wrt__iff__nth__less,axiom,
% 13.77/7.76 ( sorted9206477368072086664_VEBTi
% 13.77/7.76 = ( ^ [P5: vEBT_VEBTi > vEBT_VEBTi > $o,Xs2: list_VEBT_VEBTi] :
% 13.77/7.76 ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 13.77/7.76 => ( P5 @ ( nth_VEBT_VEBTi @ Xs2 @ I3 ) @ ( nth_VEBT_VEBTi @ Xs2 @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5269_sorted__wrt__iff__nth__less,axiom,
% 13.77/7.76 ( sorted_wrt_int
% 13.77/7.76 = ( ^ [P5: int > int > $o,Xs2: list_int] :
% 13.77/7.76 ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs2 ) )
% 13.77/7.76 => ( P5 @ ( nth_int @ Xs2 @ I3 ) @ ( nth_int @ Xs2 @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5270_sorted__wrt__iff__nth__less,axiom,
% 13.77/7.76 ( sorted_wrt_VEBT_VEBT
% 13.77/7.76 = ( ^ [P5: vEBT_VEBT > vEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 13.77/7.76 ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 13.77/7.76 => ( P5 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) @ ( nth_VEBT_VEBT @ Xs2 @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5271_sorted__wrt__iff__nth__less,axiom,
% 13.77/7.76 ( sorted_wrt_real
% 13.77/7.76 = ( ^ [P5: real > real > $o,Xs2: list_real] :
% 13.77/7.76 ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs2 ) )
% 13.77/7.76 => ( P5 @ ( nth_real @ Xs2 @ I3 ) @ ( nth_real @ Xs2 @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5272_sorted__wrt__iff__nth__less,axiom,
% 13.77/7.76 ( sorted_wrt_o
% 13.77/7.76 = ( ^ [P5: $o > $o > $o,Xs2: list_o] :
% 13.77/7.76 ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs2 ) )
% 13.77/7.76 => ( P5 @ ( nth_o @ Xs2 @ I3 ) @ ( nth_o @ Xs2 @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5273_sorted__wrt__iff__nth__less,axiom,
% 13.77/7.76 ( sorted_wrt_nat
% 13.77/7.76 = ( ^ [P5: nat > nat > $o,Xs2: list_nat] :
% 13.77/7.76 ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs2 ) )
% 13.77/7.76 => ( P5 @ ( nth_nat @ Xs2 @ I3 ) @ ( nth_nat @ Xs2 @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5274_sorted__wrt__nth__less,axiom,
% 13.77/7.76 ! [P2: vEBT_VEBTi > vEBT_VEBTi > $o,Xs: list_VEBT_VEBTi,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted9206477368072086664_VEBTi @ P2 @ Xs )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( P2 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5275_sorted__wrt__nth__less,axiom,
% 13.77/7.76 ! [P2: int > int > $o,Xs: list_int,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_int @ P2 @ Xs )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( P2 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5276_sorted__wrt__nth__less,axiom,
% 13.77/7.76 ! [P2: vEBT_VEBT > vEBT_VEBT > $o,Xs: list_VEBT_VEBT,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_VEBT_VEBT @ P2 @ Xs )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( P2 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5277_sorted__wrt__nth__less,axiom,
% 13.77/7.76 ! [P2: real > real > $o,Xs: list_real,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_real @ P2 @ Xs )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( P2 @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5278_sorted__wrt__nth__less,axiom,
% 13.77/7.76 ! [P2: $o > $o > $o,Xs: list_o,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_o @ P2 @ Xs )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( P2 @ ( nth_o @ Xs @ I ) @ ( nth_o @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5279_sorted__wrt__nth__less,axiom,
% 13.77/7.76 ! [P2: nat > nat > $o,Xs: list_nat,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ P2 @ Xs )
% 13.77/7.76 => ( ( ord_less_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( P2 @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5280_sorted__wrt__less__idx,axiom,
% 13.77/7.76 ! [Ns: list_nat,I: nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 13.77/7.76 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5281_Suc__le__length__iff,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_int] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 = ( ? [X4: int,Ys3: list_int] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_int @ X4 @ Ys3 ) )
% 13.77/7.76 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5282_Suc__le__length__iff,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 = ( ? [X4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_VEBT_VEBT @ X4 @ Ys3 ) )
% 13.77/7.76 & ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys3 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5283_Suc__le__length__iff,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_real] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 = ( ? [X4: real,Ys3: list_real] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_real @ X4 @ Ys3 ) )
% 13.77/7.76 & ( ord_less_eq_nat @ N @ ( size_size_list_real @ Ys3 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5284_Suc__le__length__iff,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 = ( ? [X4: $o,Ys3: list_o] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_o @ X4 @ Ys3 ) )
% 13.77/7.76 & ( ord_less_eq_nat @ N @ ( size_size_list_o @ Ys3 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5285_Suc__le__length__iff,axiom,
% 13.77/7.76 ! [N: nat,Xs: list_nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 = ( ? [X4: nat,Ys3: list_nat] :
% 13.77/7.76 ( ( Xs
% 13.77/7.76 = ( cons_nat @ X4 @ Ys3 ) )
% 13.77/7.76 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5286_sorted01,axiom,
% 13.77/7.76 ! [Xs: list_real] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_real @ ord_less_eq_real @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5287_sorted01,axiom,
% 13.77/7.76 ! [Xs: list_o] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_o @ ord_less_eq_o @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5288_sorted01,axiom,
% 13.77/7.76 ! [Xs: list_rat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_rat @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5289_sorted01,axiom,
% 13.77/7.76 ! [Xs: list_num] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_num @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5290_sorted01,axiom,
% 13.77/7.76 ! [Xs: list_nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5291_sorted01,axiom,
% 13.77/7.76 ! [Xs: list_int] :
% 13.77/7.76 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 13.77/7.76 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5292_sorted__iff__nth__mono__less,axiom,
% 13.77/7.76 ! [Xs: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( nth_real @ Xs @ I3 ) @ ( nth_real @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5293_sorted__iff__nth__mono__less,axiom,
% 13.77/7.76 ! [Xs: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_o @ ( nth_o @ Xs @ I3 ) @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5294_sorted__iff__nth__mono__less,axiom,
% 13.77/7.76 ! [Xs: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_rat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I3 ) @ ( nth_rat @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5295_sorted__iff__nth__mono__less,axiom,
% 13.77/7.76 ! [Xs: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_num @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_num @ ( nth_num @ Xs @ I3 ) @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5296_sorted__iff__nth__mono__less,axiom,
% 13.77/7.76 ! [Xs: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5297_sorted__iff__nth__mono__less,axiom,
% 13.77/7.76 ! [Xs: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_int @ ( nth_int @ Xs @ I3 ) @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5298_list_Osize_I4_J,axiom,
% 13.77/7.76 ! [X21: int,X22: list_int] :
% 13.77/7.76 ( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
% 13.77/7.76 = ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5299_list_Osize_I4_J,axiom,
% 13.77/7.76 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 13.77/7.76 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X21 @ X22 ) )
% 13.77/7.76 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5300_list_Osize_I4_J,axiom,
% 13.77/7.76 ! [X21: real,X22: list_real] :
% 13.77/7.76 ( ( size_size_list_real @ ( cons_real @ X21 @ X22 ) )
% 13.77/7.76 = ( plus_plus_nat @ ( size_size_list_real @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5301_list_Osize_I4_J,axiom,
% 13.77/7.76 ! [X21: $o,X22: list_o] :
% 13.77/7.76 ( ( size_size_list_o @ ( cons_o @ X21 @ X22 ) )
% 13.77/7.76 = ( plus_plus_nat @ ( size_size_list_o @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5302_list_Osize_I4_J,axiom,
% 13.77/7.76 ! [X21: nat,X22: list_nat] :
% 13.77/7.76 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X22 ) )
% 13.77/7.76 = ( plus_plus_nat @ ( size_size_list_nat @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5303_nth__Cons_H,axiom,
% 13.77/7.76 ! [N: nat,X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.76 ( ( ( N = zero_zero_nat )
% 13.77/7.76 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( N != zero_zero_nat )
% 13.77/7.76 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5304_nth__Cons_H,axiom,
% 13.77/7.76 ! [N: nat,X: vEBT_VEBTi,Xs: list_VEBT_VEBTi] :
% 13.77/7.76 ( ( ( N = zero_zero_nat )
% 13.77/7.76 => ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( N != zero_zero_nat )
% 13.77/7.76 => ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_VEBT_VEBTi @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5305_nth__Cons_H,axiom,
% 13.77/7.76 ! [N: nat,X: int,Xs: list_int] :
% 13.77/7.76 ( ( ( N = zero_zero_nat )
% 13.77/7.76 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( N != zero_zero_nat )
% 13.77/7.76 => ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5306_nth__Cons_H,axiom,
% 13.77/7.76 ! [N: nat,X: nat,Xs: list_nat] :
% 13.77/7.76 ( ( ( N = zero_zero_nat )
% 13.77/7.76 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 13.77/7.76 = X ) )
% 13.77/7.76 & ( ( N != zero_zero_nat )
% 13.77/7.76 => ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 13.77/7.76 = ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5307_nth__Cons_H,axiom,
% 13.77/7.76 ! [X: $o,Xs: list_o,N: nat] :
% 13.77/7.76 ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 13.77/7.76 = ( ( ( N = zero_zero_nat )
% 13.77/7.76 => X )
% 13.77/7.76 & ( ( N != zero_zero_nat )
% 13.77/7.76 => ( nth_o @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5308_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2497118539674116125T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5309_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > nat > assn,Xsi: list_nat] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2809031099982602151Ti_nat @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5310_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L886525131989349516_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5311_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > int > assn,Xsi: list_int] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2806540629473551875Ti_int @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5312_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L2018189785592951398T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5313_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > nat > assn,Xsi: list_nat] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L8891422820522952478nt_nat @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5314_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L114188773329725699_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5315_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_int,A4: int > int > assn,Xsi: list_int] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L8888932350013902202nt_int @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5316_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,Xsi: list_VEBT_VEBT] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L3204528365124325536T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5317_listI__assn__insert,axiom,
% 13.77/7.76 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > nat > assn,Xsi: list_nat] :
% 13.77/7.76 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.76 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( ( vEBT_L8650695023172932196BT_nat @ ( insert_nat @ I @ I5 ) @ A4 @ Xs @ Xsi )
% 13.77/7.76 = ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5318_sorted__iff__nth__Suc,axiom,
% 13.77/7.76 ! [Xs: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 13.77/7.76 = ( ! [I3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( nth_real @ Xs @ I3 ) @ ( nth_real @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5319_sorted__iff__nth__Suc,axiom,
% 13.77/7.76 ! [Xs: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 13.77/7.76 = ( ! [I3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_o @ ( nth_o @ Xs @ I3 ) @ ( nth_o @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5320_sorted__iff__nth__Suc,axiom,
% 13.77/7.76 ! [Xs: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.76 = ( ! [I3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_rat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I3 ) @ ( nth_rat @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5321_sorted__iff__nth__Suc,axiom,
% 13.77/7.76 ! [Xs: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.76 = ( ! [I3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_num @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_num @ ( nth_num @ Xs @ I3 ) @ ( nth_num @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5322_sorted__iff__nth__Suc,axiom,
% 13.77/7.76 ! [Xs: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.76 = ( ! [I3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5323_sorted__iff__nth__Suc,axiom,
% 13.77/7.76 ! [Xs: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.76 = ( ! [I3: nat] :
% 13.77/7.76 ( ( ord_less_nat @ ( suc @ I3 ) @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_int @ ( nth_int @ Xs @ I3 ) @ ( nth_int @ Xs @ ( suc @ I3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5324_sorted__iff__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( nth_real @ Xs @ I3 ) @ ( nth_real @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5325_sorted__iff__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_o @ ( nth_o @ Xs @ I3 ) @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5326_sorted__iff__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_rat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I3 ) @ ( nth_rat @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5327_sorted__iff__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_num @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_num @ ( nth_num @ Xs @ I3 ) @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5328_sorted__iff__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I3 ) @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5329_sorted__iff__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.76 = ( ! [I3: nat,J3: nat] :
% 13.77/7.76 ( ( ord_less_eq_nat @ I3 @ J3 )
% 13.77/7.76 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_int @ ( nth_int @ Xs @ I3 ) @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5330_sorted__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_real,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 13.77/7.76 => ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_real @ ( nth_real @ Xs @ I ) @ ( nth_real @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5331_sorted__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_o,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 13.77/7.76 => ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_o @ ( nth_o @ Xs @ I ) @ ( nth_o @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5332_sorted__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_rat,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.76 => ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I ) @ ( nth_rat @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5333_sorted__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_num,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.76 => ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_num @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_num @ ( nth_num @ Xs @ I ) @ ( nth_num @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5334_sorted__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_nat,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.76 => ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5335_sorted__nth__mono,axiom,
% 13.77/7.76 ! [Xs: list_int,I: nat,J: nat] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.76 => ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.76 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ord_less_eq_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5336_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_literal] :
% 13.77/7.76 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.76 => ~ ! [L2: list_literal] :
% 13.77/7.76 ( ( sorted_wrt_literal @ ord_less_literal @ L2 )
% 13.77/7.76 => ( ( ( set_literal2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_s2501651207091587910iteral @ L2 )
% 13.77/7.76 != ( finite_card_literal @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5337_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_Code_integer] :
% 13.77/7.76 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.76 => ~ ! [L2: list_Code_integer] :
% 13.77/7.76 ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ L2 )
% 13.77/7.76 => ( ( ( set_Code_integer2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_s3445333598471063425nteger @ L2 )
% 13.77/7.76 != ( finite4902975817058060853nteger @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5338_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_o] :
% 13.77/7.76 ( ( finite_finite_o @ A4 )
% 13.77/7.76 => ~ ! [L2: list_o] :
% 13.77/7.76 ( ( sorted_wrt_o @ ord_less_o @ L2 )
% 13.77/7.76 => ( ( ( set_o2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_size_list_o @ L2 )
% 13.77/7.76 != ( finite_card_o @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5339_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_real] :
% 13.77/7.76 ( ( finite_finite_real @ A4 )
% 13.77/7.76 => ~ ! [L2: list_real] :
% 13.77/7.76 ( ( sorted_wrt_real @ ord_less_real @ L2 )
% 13.77/7.76 => ( ( ( set_real2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_size_list_real @ L2 )
% 13.77/7.76 != ( finite_card_real @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5340_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_rat] :
% 13.77/7.76 ( ( finite_finite_rat @ A4 )
% 13.77/7.76 => ~ ! [L2: list_rat] :
% 13.77/7.76 ( ( sorted_wrt_rat @ ord_less_rat @ L2 )
% 13.77/7.76 => ( ( ( set_rat2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_size_list_rat @ L2 )
% 13.77/7.76 != ( finite_card_rat @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5341_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_num] :
% 13.77/7.76 ( ( finite_finite_num @ A4 )
% 13.77/7.76 => ~ ! [L2: list_num] :
% 13.77/7.76 ( ( sorted_wrt_num @ ord_less_num @ L2 )
% 13.77/7.76 => ( ( ( set_num2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_size_list_num @ L2 )
% 13.77/7.76 != ( finite_card_num @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5342_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_nat] :
% 13.77/7.76 ( ( finite_finite_nat @ A4 )
% 13.77/7.76 => ~ ! [L2: list_nat] :
% 13.77/7.76 ( ( sorted_wrt_nat @ ord_less_nat @ L2 )
% 13.77/7.76 => ( ( ( set_nat2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_size_list_nat @ L2 )
% 13.77/7.76 != ( finite_card_nat @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5343_sorted__list__of__set_Ofinite__set__strict__sorted,axiom,
% 13.77/7.76 ! [A4: set_int] :
% 13.77/7.76 ( ( finite_finite_int @ A4 )
% 13.77/7.76 => ~ ! [L2: list_int] :
% 13.77/7.76 ( ( sorted_wrt_int @ ord_less_int @ L2 )
% 13.77/7.76 => ( ( ( set_int2 @ L2 )
% 13.77/7.76 = A4 )
% 13.77/7.76 => ( ( size_size_list_int @ L2 )
% 13.77/7.76 != ( finite_card_int @ A4 ) ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5344_nth__non__equal__first__eq,axiom,
% 13.77/7.76 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 13.77/7.76 ( ( X != Y )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 13.77/7.76 = Y )
% 13.77/7.76 = ( ( ( nth_VEBT_VEBT @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.76 = Y )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5345_nth__non__equal__first__eq,axiom,
% 13.77/7.76 ! [X: vEBT_VEBTi,Y: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 13.77/7.76 ( ( X != Y )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 13.77/7.76 = Y )
% 13.77/7.76 = ( ( ( nth_VEBT_VEBTi @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.76 = Y )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5346_nth__non__equal__first__eq,axiom,
% 13.77/7.76 ! [X: int,Y: int,Xs: list_int,N: nat] :
% 13.77/7.76 ( ( X != Y )
% 13.77/7.76 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 13.77/7.76 = Y )
% 13.77/7.76 = ( ( ( nth_int @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.76 = Y )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5347_nth__non__equal__first__eq,axiom,
% 13.77/7.76 ! [X: nat,Y: nat,Xs: list_nat,N: nat] :
% 13.77/7.76 ( ( X != Y )
% 13.77/7.76 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 13.77/7.76 = Y )
% 13.77/7.76 = ( ( ( nth_nat @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.76 = Y )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5348_nth__non__equal__first__eq,axiom,
% 13.77/7.76 ! [X: $o,Y: $o,Xs: list_o,N: nat] :
% 13.77/7.76 ( ( X != Y )
% 13.77/7.76 => ( ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 13.77/7.76 = Y )
% 13.77/7.76 = ( ( ( nth_o @ Xs @ ( minus_minus_nat @ N @ one_one_nat ) )
% 13.77/7.76 = Y )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5349_nth__equal__first__eq,axiom,
% 13.77/7.76 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,N: nat] :
% 13.77/7.76 ( ~ ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_eq_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ N )
% 13.77/7.76 = X )
% 13.77/7.76 = ( N = zero_zero_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5350_nth__equal__first__eq,axiom,
% 13.77/7.76 ! [X: set_nat,Xs: list_set_nat,N: nat] :
% 13.77/7.76 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_eq_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.76 => ( ( ( nth_set_nat @ ( cons_set_nat @ X @ Xs ) @ N )
% 13.77/7.76 = X )
% 13.77/7.76 = ( N = zero_zero_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5351_nth__equal__first__eq,axiom,
% 13.77/7.76 ! [X: int,Xs: list_int,N: nat] :
% 13.77/7.76 ( ~ ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs ) )
% 13.77/7.76 => ( ( ( nth_int @ ( cons_int @ X @ Xs ) @ N )
% 13.77/7.76 = X )
% 13.77/7.76 = ( N = zero_zero_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5352_nth__equal__first__eq,axiom,
% 13.77/7.76 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,N: nat] :
% 13.77/7.76 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.76 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ N )
% 13.77/7.76 = X )
% 13.77/7.76 = ( N = zero_zero_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5353_nth__equal__first__eq,axiom,
% 13.77/7.76 ! [X: real,Xs: list_real,N: nat] :
% 13.77/7.76 ( ~ ( member_real @ X @ ( set_real2 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.76 => ( ( ( nth_real @ ( cons_real @ X @ Xs ) @ N )
% 13.77/7.76 = X )
% 13.77/7.76 = ( N = zero_zero_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5354_nth__equal__first__eq,axiom,
% 13.77/7.76 ! [X: $o,Xs: list_o,N: nat] :
% 13.77/7.76 ( ~ ( member_o @ X @ ( set_o2 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.76 => ( ( ( nth_o @ ( cons_o @ X @ Xs ) @ N )
% 13.77/7.76 = X )
% 13.77/7.76 = ( N = zero_zero_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5355_nth__equal__first__eq,axiom,
% 13.77/7.76 ! [X: nat,Xs: list_nat,N: nat] :
% 13.77/7.76 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.76 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.76 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs ) @ N )
% 13.77/7.76 = X )
% 13.77/7.76 = ( N = zero_zero_nat ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5356_slice__Cons,axiom,
% 13.77/7.76 ! [Begin: nat,End: nat,X: int,Xs: list_int] :
% 13.77/7.76 ( ( ( ( Begin = zero_zero_nat )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 13.77/7.76 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 13.77/7.76 = ( cons_int @ X @ ( slice_int @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 13.77/7.76 & ( ~ ( ( Begin = zero_zero_nat )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 13.77/7.76 => ( ( slice_int @ Begin @ End @ ( cons_int @ X @ Xs ) )
% 13.77/7.76 = ( slice_int @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 13.77/7.76
% 13.77/7.76 thf(fact_5357_slice__Cons,axiom,
% 13.77/7.76 ! [Begin: nat,End: nat,X: nat,Xs: list_nat] :
% 13.77/7.76 ( ( ( ( Begin = zero_zero_nat )
% 13.77/7.76 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 13.77/7.76 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 13.77/7.76 = ( cons_nat @ X @ ( slice_nat @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 13.77/7.76 & ( ~ ( ( Begin = zero_zero_nat )
% 13.77/7.77 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 13.77/7.77 => ( ( slice_nat @ Begin @ End @ ( cons_nat @ X @ Xs ) )
% 13.77/7.77 = ( slice_nat @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5358_slice__Cons,axiom,
% 13.77/7.77 ! [Begin: nat,End: nat,X: $o,Xs: list_o] :
% 13.77/7.77 ( ( ( ( Begin = zero_zero_nat )
% 13.77/7.77 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 13.77/7.77 => ( ( slice_o @ Begin @ End @ ( cons_o @ X @ Xs ) )
% 13.77/7.77 = ( cons_o @ X @ ( slice_o @ Begin @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) )
% 13.77/7.77 & ( ~ ( ( Begin = zero_zero_nat )
% 13.77/7.77 & ( ord_less_nat @ zero_zero_nat @ End ) )
% 13.77/7.77 => ( ( slice_o @ Begin @ End @ ( cons_o @ X @ Xs ) )
% 13.77/7.77 = ( slice_o @ ( minus_minus_nat @ Begin @ one_one_nat ) @ ( minus_minus_nat @ End @ one_one_nat ) @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5359_length__Cons,axiom,
% 13.77/7.77 ! [X: int,Xs: list_int] :
% 13.77/7.77 ( ( size_size_list_int @ ( cons_int @ X @ Xs ) )
% 13.77/7.77 = ( suc @ ( size_size_list_int @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5360_length__Cons,axiom,
% 13.77/7.77 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.77 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) )
% 13.77/7.77 = ( suc @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5361_length__Cons,axiom,
% 13.77/7.77 ! [X: real,Xs: list_real] :
% 13.77/7.77 ( ( size_size_list_real @ ( cons_real @ X @ Xs ) )
% 13.77/7.77 = ( suc @ ( size_size_list_real @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5362_length__Cons,axiom,
% 13.77/7.77 ! [X: $o,Xs: list_o] :
% 13.77/7.77 ( ( size_size_list_o @ ( cons_o @ X @ Xs ) )
% 13.77/7.77 = ( suc @ ( size_size_list_o @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5363_length__Cons,axiom,
% 13.77/7.77 ! [X: nat,Xs: list_nat] :
% 13.77/7.77 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs ) )
% 13.77/7.77 = ( suc @ ( size_size_list_nat @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5364_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5365_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > nat > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5366_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5367_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_int,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5368_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > vEBT_VEBT > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5369_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > nat > assn,Xs: list_int,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5370_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > vEBT_VEBTi > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5371_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > int > assn,Xs: list_int,I: nat,Xsi: list_int,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5372_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5373_listI__assn__reinsert,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5374_sorted__list__of__set__nonempty,axiom,
% 13.77/7.77 ! [A4: set_Code_integer] :
% 13.77/7.77 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.77 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.77 => ( ( linord2324613341767563021nteger @ A4 )
% 13.77/7.77 = ( cons_Code_integer @ ( lattic1063845414844153500nteger @ A4 ) @ ( linord2324613341767563021nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ ( lattic1063845414844153500nteger @ A4 ) @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5375_sorted__list__of__set__nonempty,axiom,
% 13.77/7.77 ! [A4: set_int] :
% 13.77/7.77 ( ( finite_finite_int @ A4 )
% 13.77/7.77 => ( ( A4 != bot_bot_set_int )
% 13.77/7.77 => ( ( linord2612477271533052124et_int @ A4 )
% 13.77/7.77 = ( cons_int @ ( lattic8718645017227715691in_int @ A4 ) @ ( linord2612477271533052124et_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ ( lattic8718645017227715691in_int @ A4 ) @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5376_sorted__list__of__set__nonempty,axiom,
% 13.77/7.77 ! [A4: set_o] :
% 13.77/7.77 ( ( finite_finite_o @ A4 )
% 13.77/7.77 => ( ( A4 != bot_bot_set_o )
% 13.77/7.77 => ( ( linord3142498349692569832_set_o @ A4 )
% 13.77/7.77 = ( cons_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ ( linord3142498349692569832_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ ( lattic1973801136483472281_Min_o @ A4 ) @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5377_sorted__list__of__set__nonempty,axiom,
% 13.77/7.77 ! [A4: set_nat] :
% 13.77/7.77 ( ( finite_finite_nat @ A4 )
% 13.77/7.77 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.77 => ( ( linord2614967742042102400et_nat @ A4 )
% 13.77/7.77 = ( cons_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ ( linord2614967742042102400et_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ ( lattic8721135487736765967in_nat @ A4 ) @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5378_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_literal,L: list_literal] :
% 13.77/7.77 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.77 => ( ( ( sorted_wrt_literal @ ord_less_literal @ L )
% 13.77/7.77 & ( ( set_literal2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_s2501651207091587910iteral @ L )
% 13.77/7.77 = ( finite_card_literal @ A4 ) ) )
% 13.77/7.77 = ( ( linord2913955441264437540iteral @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5379_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_Code_integer,L: list_Code_integer] :
% 13.77/7.77 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.77 => ( ( ( sorted710888440204495920nteger @ ord_le6747313008572928689nteger @ L )
% 13.77/7.77 & ( ( set_Code_integer2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_s3445333598471063425nteger @ L )
% 13.77/7.77 = ( finite4902975817058060853nteger @ A4 ) ) )
% 13.77/7.77 = ( ( linord2324613341767563021nteger @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5380_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_o,L: list_o] :
% 13.77/7.77 ( ( finite_finite_o @ A4 )
% 13.77/7.77 => ( ( ( sorted_wrt_o @ ord_less_o @ L )
% 13.77/7.77 & ( ( set_o2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_size_list_o @ L )
% 13.77/7.77 = ( finite_card_o @ A4 ) ) )
% 13.77/7.77 = ( ( linord3142498349692569832_set_o @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5381_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_real,L: list_real] :
% 13.77/7.77 ( ( finite_finite_real @ A4 )
% 13.77/7.77 => ( ( ( sorted_wrt_real @ ord_less_real @ L )
% 13.77/7.77 & ( ( set_real2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_size_list_real @ L )
% 13.77/7.77 = ( finite_card_real @ A4 ) ) )
% 13.77/7.77 = ( ( linord4252657396651189596t_real @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5382_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_rat,L: list_rat] :
% 13.77/7.77 ( ( finite_finite_rat @ A4 )
% 13.77/7.77 => ( ( ( sorted_wrt_rat @ ord_less_rat @ L )
% 13.77/7.77 & ( ( set_rat2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_size_list_rat @ L )
% 13.77/7.77 = ( finite_card_rat @ A4 ) ) )
% 13.77/7.77 = ( ( linord1979837681955606664et_rat @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5383_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_num,L: list_num] :
% 13.77/7.77 ( ( finite_finite_num @ A4 )
% 13.77/7.77 => ( ( ( sorted_wrt_num @ ord_less_num @ L )
% 13.77/7.77 & ( ( set_num2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_size_list_num @ L )
% 13.77/7.77 = ( finite_card_num @ A4 ) ) )
% 13.77/7.77 = ( ( linord8395671565052656842et_num @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5384_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_int,L: list_int] :
% 13.77/7.77 ( ( finite_finite_int @ A4 )
% 13.77/7.77 => ( ( ( sorted_wrt_int @ ord_less_int @ L )
% 13.77/7.77 & ( ( set_int2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_size_list_int @ L )
% 13.77/7.77 = ( finite_card_int @ A4 ) ) )
% 13.77/7.77 = ( ( linord2612477271533052124et_int @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5385_sorted__list__of__set_Osorted__key__list__of__set__unique,axiom,
% 13.77/7.77 ! [A4: set_nat,L: list_nat] :
% 13.77/7.77 ( ( finite_finite_nat @ A4 )
% 13.77/7.77 => ( ( ( sorted_wrt_nat @ ord_less_nat @ L )
% 13.77/7.77 & ( ( set_nat2 @ L )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( ( size_size_list_nat @ L )
% 13.77/7.77 = ( finite_card_nat @ A4 ) ) )
% 13.77/7.77 = ( ( linord2614967742042102400et_nat @ A4 )
% 13.77/7.77 = L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5386_converse__trancl__induct,axiom,
% 13.77/7.77 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,P2: uint32 > $o] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ! [Y3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ B ) @ R )
% 13.77/7.77 => ( P2 @ Y3 ) )
% 13.77/7.77 => ( ! [Y3: uint32,Z3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z3 ) @ R )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Z3 @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ( P2 @ Z3 )
% 13.77/7.77 => ( P2 @ Y3 ) ) ) )
% 13.77/7.77 => ( P2 @ A ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5387_converse__trancl__induct,axiom,
% 13.77/7.77 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,P2: nat > $o] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ! [Y3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ B ) @ R )
% 13.77/7.77 => ( P2 @ Y3 ) )
% 13.77/7.77 => ( ! [Y3: nat,Z3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ R )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Z3 @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ( P2 @ Z3 )
% 13.77/7.77 => ( P2 @ Y3 ) ) ) )
% 13.77/7.77 => ( P2 @ A ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5388_converse__trancl__induct,axiom,
% 13.77/7.77 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,P2: int > $o] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ! [Y3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ B ) @ R )
% 13.77/7.77 => ( P2 @ Y3 ) )
% 13.77/7.77 => ( ! [Y3: int,Z3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z3 ) @ R )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Z3 @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ( P2 @ Z3 )
% 13.77/7.77 => ( P2 @ Y3 ) ) ) )
% 13.77/7.77 => ( P2 @ A ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5389_trancl__trans__induct,axiom,
% 13.77/7.77 ! [X: uint32,Y: uint32,R: set_Pr1773385645901665561uint32,P2: uint32 > uint32 > $o] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ! [X3: uint32,Y3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ R )
% 13.77/7.77 => ( P2 @ X3 @ Y3 ) )
% 13.77/7.77 => ( ! [X3: uint32,Y3: uint32,Z3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ( P2 @ X3 @ Y3 )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ( P2 @ Y3 @ Z3 )
% 13.77/7.77 => ( P2 @ X3 @ Z3 ) ) ) ) )
% 13.77/7.77 => ( P2 @ X @ Y ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5390_trancl__trans__induct,axiom,
% 13.77/7.77 ! [X: nat,Y: nat,R: set_Pr1261947904930325089at_nat,P2: nat > nat > $o] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ! [X3: nat,Y3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 13.77/7.77 => ( P2 @ X3 @ Y3 ) )
% 13.77/7.77 => ( ! [X3: nat,Y3: nat,Z3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ( P2 @ X3 @ Y3 )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ( P2 @ Y3 @ Z3 )
% 13.77/7.77 => ( P2 @ X3 @ Z3 ) ) ) ) )
% 13.77/7.77 => ( P2 @ X @ Y ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5391_trancl__trans__induct,axiom,
% 13.77/7.77 ! [X: int,Y: int,R: set_Pr958786334691620121nt_int,P2: int > int > $o] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ! [X3: int,Y3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R )
% 13.77/7.77 => ( P2 @ X3 @ Y3 ) )
% 13.77/7.77 => ( ! [X3: int,Y3: int,Z3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ( P2 @ X3 @ Y3 )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ( P2 @ Y3 @ Z3 )
% 13.77/7.77 => ( P2 @ X3 @ Z3 ) ) ) ) )
% 13.77/7.77 => ( P2 @ X @ Y ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5392_groupy,axiom,
% 13.77/7.77 ! [A4: assn,B4: assn,C3: assn,D4: assn,X6: assn] :
% 13.77/7.77 ( ( entails @ ( times_times_assn @ ( times_times_assn @ A4 @ B4 ) @ ( times_times_assn @ C3 @ D4 ) ) @ X6 )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ A4 @ B4 ) @ C3 ) @ D4 ) @ X6 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5393_midextr,axiom,
% 13.77/7.77 ! [P2: assn,Q2: assn,Q4: assn,R2: assn,X6: assn] :
% 13.77/7.77 ( ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ P2 @ Q2 ) @ Q4 ) @ R2 ) @ X6 )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ P2 @ R2 ) @ Q2 ) @ Q4 ) @ X6 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5394_swappa,axiom,
% 13.77/7.77 ! [B4: assn,A4: assn,C3: assn,X6: assn] :
% 13.77/7.77 ( ( entails @ ( times_times_assn @ ( times_times_assn @ B4 @ A4 ) @ C3 ) @ X6 )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ A4 @ B4 ) @ C3 ) @ X6 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5395_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_real] :
% 13.77/7.77 ( ( finite_finite_real @ A4 )
% 13.77/7.77 => ( ( set_real2 @ ( linord4252657396651189596t_real @ A4 ) )
% 13.77/7.77 = A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5396_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_o] :
% 13.77/7.77 ( ( finite_finite_o @ A4 )
% 13.77/7.77 => ( ( set_o2 @ ( linord3142498349692569832_set_o @ A4 ) )
% 13.77/7.77 = A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5397_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_int] :
% 13.77/7.77 ( ( finite_finite_int @ A4 )
% 13.77/7.77 => ( ( set_int2 @ ( linord2612477271533052124et_int @ A4 ) )
% 13.77/7.77 = A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5398_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_Code_integer] :
% 13.77/7.77 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.77 => ( ( set_Code_integer2 @ ( linord2324613341767563021nteger @ A4 ) )
% 13.77/7.77 = A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5399_sorted__list__of__set_Oset__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_nat] :
% 13.77/7.77 ( ( finite_finite_nat @ A4 )
% 13.77/7.77 => ( ( set_nat2 @ ( linord2614967742042102400et_nat @ A4 ) )
% 13.77/7.77 = A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5400_ent__false__iff,axiom,
% 13.77/7.77 ! [P2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ bot_bot_assn )
% 13.77/7.77 = ( ! [H4: produc3658429121746597890et_nat] :
% 13.77/7.77 ~ ( rep_assn @ P2 @ H4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5401_ent__trans,axiom,
% 13.77/7.77 ! [P2: assn,Q2: assn,R2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ Q2 )
% 13.77/7.77 => ( ( entails @ Q2 @ R2 )
% 13.77/7.77 => ( entails @ P2 @ R2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5402_ent__refl,axiom,
% 13.77/7.77 ! [P2: assn] : ( entails @ P2 @ P2 ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5403_ent__iffI,axiom,
% 13.77/7.77 ! [A4: assn,B4: assn] :
% 13.77/7.77 ( ( entails @ A4 @ B4 )
% 13.77/7.77 => ( ( entails @ B4 @ A4 )
% 13.77/7.77 => ( A4 = B4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5404_ent__star__mono,axiom,
% 13.77/7.77 ! [P2: assn,P6: assn,Q2: assn,Q4: assn] :
% 13.77/7.77 ( ( entails @ P2 @ P6 )
% 13.77/7.77 => ( ( entails @ Q2 @ Q4 )
% 13.77/7.77 => ( entails @ ( times_times_assn @ P2 @ Q2 ) @ ( times_times_assn @ P6 @ Q4 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5405_entails__def,axiom,
% 13.77/7.77 ( entails
% 13.77/7.77 = ( ^ [P5: assn,Q6: assn] :
% 13.77/7.77 ! [H4: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P5 @ H4 )
% 13.77/7.77 => ( rep_assn @ Q6 @ H4 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5406_entailsI,axiom,
% 13.77/7.77 ! [P2: assn,Q2: assn] :
% 13.77/7.77 ( ! [H: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H )
% 13.77/7.77 => ( rep_assn @ Q2 @ H ) )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5407_entailsD,axiom,
% 13.77/7.77 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( entails @ P2 @ Q2 )
% 13.77/7.77 => ( ( rep_assn @ P2 @ H2 )
% 13.77/7.77 => ( rep_assn @ Q2 @ H2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5408_ent__fwd,axiom,
% 13.77/7.77 ! [P2: assn,H2: produc3658429121746597890et_nat,Q2: assn] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H2 )
% 13.77/7.77 => ( ( entails @ P2 @ Q2 )
% 13.77/7.77 => ( rep_assn @ Q2 @ H2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5409_ent__false,axiom,
% 13.77/7.77 ! [P2: assn] : ( entails @ bot_bot_assn @ P2 ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5410_sorted__list__of__set_Osorted__key__list__of__set__inject,axiom,
% 13.77/7.77 ! [A4: set_int,B4: set_int] :
% 13.77/7.77 ( ( ( linord2612477271533052124et_int @ A4 )
% 13.77/7.77 = ( linord2612477271533052124et_int @ B4 ) )
% 13.77/7.77 => ( ( finite_finite_int @ A4 )
% 13.77/7.77 => ( ( finite_finite_int @ B4 )
% 13.77/7.77 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5411_sorted__list__of__set_Osorted__key__list__of__set__inject,axiom,
% 13.77/7.77 ! [A4: set_Code_integer,B4: set_Code_integer] :
% 13.77/7.77 ( ( ( linord2324613341767563021nteger @ A4 )
% 13.77/7.77 = ( linord2324613341767563021nteger @ B4 ) )
% 13.77/7.77 => ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.77 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.77 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5412_sorted__list__of__set_Osorted__key__list__of__set__inject,axiom,
% 13.77/7.77 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.77 ( ( ( linord2614967742042102400et_nat @ A4 )
% 13.77/7.77 = ( linord2614967742042102400et_nat @ B4 ) )
% 13.77/7.77 => ( ( finite_finite_nat @ A4 )
% 13.77/7.77 => ( ( finite_finite_nat @ B4 )
% 13.77/7.77 => ( A4 = B4 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5413_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_rat] : ( sorted_wrt_rat @ ord_less_eq_rat @ ( linord1979837681955606664et_rat @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5414_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_num] : ( sorted_wrt_num @ ord_less_eq_num @ ( linord8395671565052656842et_num @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5415_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_int] : ( sorted_wrt_int @ ord_less_eq_int @ ( linord2612477271533052124et_int @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5416_sorted__list__of__set_Osorted__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( linord2614967742042102400et_nat @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5417_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_real] : ( sorted_wrt_real @ ord_less_real @ ( linord4252657396651189596t_real @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5418_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_rat] : ( sorted_wrt_rat @ ord_less_rat @ ( linord1979837681955606664et_rat @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5419_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_num] : ( sorted_wrt_num @ ord_less_num @ ( linord8395671565052656842et_num @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5420_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_int] : ( sorted_wrt_int @ ord_less_int @ ( linord2612477271533052124et_int @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5421_sorted__list__of__set_Ostrict__sorted__key__list__of__set,axiom,
% 13.77/7.77 ! [A4: set_nat] : ( sorted_wrt_nat @ ord_less_nat @ ( linord2614967742042102400et_nat @ A4 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5422_trancl__induct2,axiom,
% 13.77/7.77 ! [Ax: uint32,Ay: uint32,Bx: uint32,By: uint32,R: set_Pr3773659940955823943uint32,P2: uint32 > uint32 > $o] :
% 13.77/7.77 ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ Ax @ Ay ) @ ( produc1400373151660368625uint32 @ Bx @ By ) ) @ ( transi5456044692924788698uint32 @ R ) )
% 13.77/7.77 => ( ! [A3: uint32,B3: uint32] :
% 13.77/7.77 ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ Ax @ Ay ) @ ( produc1400373151660368625uint32 @ A3 @ B3 ) ) @ R )
% 13.77/7.77 => ( P2 @ A3 @ B3 ) )
% 13.77/7.77 => ( ! [A3: uint32,B3: uint32,Aa: uint32,Ba: uint32] :
% 13.77/7.77 ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ Ax @ Ay ) @ ( produc1400373151660368625uint32 @ A3 @ B3 ) ) @ ( transi5456044692924788698uint32 @ R ) )
% 13.77/7.77 => ( ( member4724532482705224080uint32 @ ( produc6884863695460953815uint32 @ ( produc1400373151660368625uint32 @ A3 @ B3 ) @ ( produc1400373151660368625uint32 @ Aa @ Ba ) ) @ R )
% 13.77/7.77 => ( ( P2 @ A3 @ B3 )
% 13.77/7.77 => ( P2 @ Aa @ Ba ) ) ) )
% 13.77/7.77 => ( P2 @ Bx @ By ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5423_trancl__induct2,axiom,
% 13.77/7.77 ! [Ax: nat,Ay: nat,Bx: nat,By: nat,R: set_Pr8693737435421807431at_nat,P2: nat > nat > $o] :
% 13.77/7.77 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ Bx @ By ) ) @ ( transi243908449541399842at_nat @ R ) )
% 13.77/7.77 => ( ! [A3: nat,B3: nat] :
% 13.77/7.77 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ A3 @ B3 ) ) @ R )
% 13.77/7.77 => ( P2 @ A3 @ B3 ) )
% 13.77/7.77 => ( ! [A3: nat,B3: nat,Aa: nat,Ba: nat] :
% 13.77/7.77 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ Ax @ Ay ) @ ( product_Pair_nat_nat @ A3 @ B3 ) ) @ ( transi243908449541399842at_nat @ R ) )
% 13.77/7.77 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A3 @ B3 ) @ ( product_Pair_nat_nat @ Aa @ Ba ) ) @ R )
% 13.77/7.77 => ( ( P2 @ A3 @ B3 )
% 13.77/7.77 => ( P2 @ Aa @ Ba ) ) ) )
% 13.77/7.77 => ( P2 @ Bx @ By ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5424_trancl__induct2,axiom,
% 13.77/7.77 ! [Ax: int,Ay: int,Bx: int,By: int,R: set_Pr2560585780119916871nt_int,P2: int > int > $o] :
% 13.77/7.77 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ Bx @ By ) ) @ ( transi6288783178788033498nt_int @ R ) )
% 13.77/7.77 => ( ! [A3: int,B3: int] :
% 13.77/7.77 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A3 @ B3 ) ) @ R )
% 13.77/7.77 => ( P2 @ A3 @ B3 ) )
% 13.77/7.77 => ( ! [A3: int,B3: int,Aa: int,Ba: int] :
% 13.77/7.77 ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ Ax @ Ay ) @ ( product_Pair_int_int @ A3 @ B3 ) ) @ ( transi6288783178788033498nt_int @ R ) )
% 13.77/7.77 => ( ( member8566619992076573584nt_int @ ( produc3646306378393792727nt_int @ ( product_Pair_int_int @ A3 @ B3 ) @ ( product_Pair_int_int @ Aa @ Ba ) ) @ R )
% 13.77/7.77 => ( ( P2 @ A3 @ B3 )
% 13.77/7.77 => ( P2 @ Aa @ Ba ) ) ) )
% 13.77/7.77 => ( P2 @ Bx @ By ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5425_trancl__induct2,axiom,
% 13.77/7.77 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3658429121746597890et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3658429121746597890et_nat,R: set_Pr7928877670098842301et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 13.77/7.77 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ Bx @ By ) ) @ ( transi3145040225084697757et_nat @ R ) )
% 13.77/7.77 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A3 @ B3 ) ) @ R )
% 13.77/7.77 => ( P2 @ A3 @ B3 ) )
% 13.77/7.77 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3658429121746597890et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ Ax @ Ay ) @ ( produc5001842942810119800et_nat @ A3 @ B3 ) ) @ ( transi3145040225084697757et_nat @ R ) )
% 13.77/7.77 => ( ( member4763271486408492550et_nat @ ( produc8599840265553166229et_nat @ ( produc5001842942810119800et_nat @ A3 @ B3 ) @ ( produc5001842942810119800et_nat @ Aa @ Ba ) ) @ R )
% 13.77/7.77 => ( ( P2 @ A3 @ B3 )
% 13.77/7.77 => ( P2 @ Aa @ Ba ) ) ) )
% 13.77/7.77 => ( P2 @ Bx @ By ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5426_trancl__induct2,axiom,
% 13.77/7.77 ! [Ax: produc3658429121746597890et_nat > $o,Ay: produc3925858234332021118et_nat,Bx: produc3658429121746597890et_nat > $o,By: produc3925858234332021118et_nat,R: set_Pr3444600963470892981et_nat,P2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 13.77/7.77 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ Bx @ By ) ) @ ( transi5221092739591632921et_nat @ R ) )
% 13.77/7.77 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat] :
% 13.77/7.77 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A3 @ B3 ) ) @ R )
% 13.77/7.77 => ( P2 @ A3 @ B3 ) )
% 13.77/7.77 => ( ! [A3: produc3658429121746597890et_nat > $o,B3: produc3925858234332021118et_nat,Aa: produc3658429121746597890et_nat > $o,Ba: produc3925858234332021118et_nat] :
% 13.77/7.77 ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ Ax @ Ay ) @ ( produc2245416461498447860et_nat @ A3 @ B3 ) ) @ ( transi5221092739591632921et_nat @ R ) )
% 13.77/7.77 => ( ( member6341495586645257982et_nat @ ( produc1940133919992309389et_nat @ ( produc2245416461498447860et_nat @ A3 @ B3 ) @ ( produc2245416461498447860et_nat @ Aa @ Ba ) ) @ R )
% 13.77/7.77 => ( ( P2 @ A3 @ B3 )
% 13.77/7.77 => ( P2 @ Aa @ Ba ) ) ) )
% 13.77/7.77 => ( P2 @ Bx @ By ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5427_trancl_Ocases,axiom,
% 13.77/7.77 ! [A12: uint32,A23: uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ A23 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ A23 ) @ R )
% 13.77/7.77 => ~ ! [B3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ B3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B3 @ A23 ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5428_trancl_Ocases,axiom,
% 13.77/7.77 ! [A12: nat,A23: nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ A23 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ A23 ) @ R )
% 13.77/7.77 => ~ ! [B3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ B3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B3 @ A23 ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5429_trancl_Ocases,axiom,
% 13.77/7.77 ! [A12: int,A23: int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ A23 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ A23 ) @ R )
% 13.77/7.77 => ~ ! [B3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ B3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B3 @ A23 ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5430_trancl_Osimps,axiom,
% 13.77/7.77 ! [A12: uint32,A23: uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A12 @ A23 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 = ( ? [A7: uint32,B7: uint32] :
% 13.77/7.77 ( ( A12 = A7 )
% 13.77/7.77 & ( A23 = B7 )
% 13.77/7.77 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A7 @ B7 ) @ R ) )
% 13.77/7.77 | ? [A7: uint32,B7: uint32,C6: uint32] :
% 13.77/7.77 ( ( A12 = A7 )
% 13.77/7.77 & ( A23 = C6 )
% 13.77/7.77 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A7 @ B7 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B7 @ C6 ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5431_trancl_Osimps,axiom,
% 13.77/7.77 ! [A12: nat,A23: nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A12 @ A23 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 = ( ? [A7: nat,B7: nat] :
% 13.77/7.77 ( ( A12 = A7 )
% 13.77/7.77 & ( A23 = B7 )
% 13.77/7.77 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A7 @ B7 ) @ R ) )
% 13.77/7.77 | ? [A7: nat,B7: nat,C6: nat] :
% 13.77/7.77 ( ( A12 = A7 )
% 13.77/7.77 & ( A23 = C6 )
% 13.77/7.77 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A7 @ B7 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B7 @ C6 ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5432_trancl_Osimps,axiom,
% 13.77/7.77 ! [A12: int,A23: int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A12 @ A23 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 = ( ? [A7: int,B7: int] :
% 13.77/7.77 ( ( A12 = A7 )
% 13.77/7.77 & ( A23 = B7 )
% 13.77/7.77 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A7 @ B7 ) @ R ) )
% 13.77/7.77 | ? [A7: int,B7: int,C6: int] :
% 13.77/7.77 ( ( A12 = A7 )
% 13.77/7.77 & ( A23 = C6 )
% 13.77/7.77 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A7 @ B7 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B7 @ C6 ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5433_trancl_Or__into__trancl,axiom,
% 13.77/7.77 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R )
% 13.77/7.77 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5434_trancl_Or__into__trancl,axiom,
% 13.77/7.77 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 13.77/7.77 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5435_trancl_Or__into__trancl,axiom,
% 13.77/7.77 ! [A: int,B: int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 13.77/7.77 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5436_tranclE,axiom,
% 13.77/7.77 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R )
% 13.77/7.77 => ~ ! [C: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ C @ B ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5437_tranclE,axiom,
% 13.77/7.77 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 13.77/7.77 => ~ ! [C: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ C @ B ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5438_tranclE,axiom,
% 13.77/7.77 ! [A: int,B: int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 13.77/7.77 => ~ ! [C: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ C @ B ) @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5439_trancl__trans,axiom,
% 13.77/7.77 ! [X: uint32,Y: uint32,R: set_Pr1773385645901665561uint32,Z: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y @ Z ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Z ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5440_trancl__trans,axiom,
% 13.77/7.77 ! [X: nat,Y: nat,R: set_Pr1261947904930325089at_nat,Z: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Z ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5441_trancl__trans,axiom,
% 13.77/7.77 ! [X: int,Y: int,R: set_Pr958786334691620121nt_int,Z: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Z ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5442_trancl__induct,axiom,
% 13.77/7.77 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,P2: uint32 > $o] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ! [Y3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ Y3 ) @ R )
% 13.77/7.77 => ( P2 @ Y3 ) )
% 13.77/7.77 => ( ! [Y3: uint32,Z3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ Y3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z3 ) @ R )
% 13.77/7.77 => ( ( P2 @ Y3 )
% 13.77/7.77 => ( P2 @ Z3 ) ) ) )
% 13.77/7.77 => ( P2 @ B ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5443_trancl__induct,axiom,
% 13.77/7.77 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,P2: nat > $o] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ! [Y3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ R )
% 13.77/7.77 => ( P2 @ Y3 ) )
% 13.77/7.77 => ( ! [Y3: nat,Z3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ Y3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z3 ) @ R )
% 13.77/7.77 => ( ( P2 @ Y3 )
% 13.77/7.77 => ( P2 @ Z3 ) ) ) )
% 13.77/7.77 => ( P2 @ B ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5444_trancl__induct,axiom,
% 13.77/7.77 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,P2: int > $o] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ! [Y3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ Y3 ) @ R )
% 13.77/7.77 => ( P2 @ Y3 ) )
% 13.77/7.77 => ( ! [Y3: int,Z3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ Y3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z3 ) @ R )
% 13.77/7.77 => ( ( P2 @ Y3 )
% 13.77/7.77 => ( P2 @ Z3 ) ) ) )
% 13.77/7.77 => ( P2 @ B ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5445_r__r__into__trancl,axiom,
% 13.77/7.77 ! [A: uint32,B: uint32,R2: set_Pr1773385645901665561uint32,C2: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R2 )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B @ C2 ) @ R2 )
% 13.77/7.77 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C2 ) @ ( transi3114468042090999947uint32 @ R2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5446_r__r__into__trancl,axiom,
% 13.77/7.77 ! [A: nat,B: nat,R2: set_Pr1261947904930325089at_nat,C2: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R2 )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ R2 )
% 13.77/7.77 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5447_r__r__into__trancl,axiom,
% 13.77/7.77 ! [A: int,B: int,R2: set_Pr958786334691620121nt_int,C2: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R2 )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ R2 )
% 13.77/7.77 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5448_converse__tranclE,axiom,
% 13.77/7.77 ! [X: uint32,Z: uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Z ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Z ) @ R )
% 13.77/7.77 => ~ ! [Y3: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y3 ) @ R )
% 13.77/7.77 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ Z ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5449_converse__tranclE,axiom,
% 13.77/7.77 ! [X: nat,Z: nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R )
% 13.77/7.77 => ~ ! [Y3: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) @ R )
% 13.77/7.77 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ Z ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5450_converse__tranclE,axiom,
% 13.77/7.77 ! [X: int,Z: int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Z ) @ R )
% 13.77/7.77 => ~ ! [Y3: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y3 ) @ R )
% 13.77/7.77 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ Z ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5451_irrefl__trancl__rD,axiom,
% 13.77/7.77 ! [R: set_Pr1773385645901665561uint32,X: uint32,Y: uint32] :
% 13.77/7.77 ( ! [X3: uint32] :
% 13.77/7.77 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ X3 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 13.77/7.77 => ( X != Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5452_irrefl__trancl__rD,axiom,
% 13.77/7.77 ! [R: set_Pr1261947904930325089at_nat,X: nat,Y: nat] :
% 13.77/7.77 ( ! [X3: nat] :
% 13.77/7.77 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 13.77/7.77 => ( X != Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5453_irrefl__trancl__rD,axiom,
% 13.77/7.77 ! [R: set_Pr958786334691620121nt_int,X: int,Y: int] :
% 13.77/7.77 ( ! [X3: int] :
% 13.77/7.77 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 13.77/7.77 => ( X != Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5454_Transitive__Closure_Otrancl__into__trancl,axiom,
% 13.77/7.77 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,C2: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B @ C2 ) @ R )
% 13.77/7.77 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C2 ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5455_Transitive__Closure_Otrancl__into__trancl,axiom,
% 13.77/7.77 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,C2: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ R )
% 13.77/7.77 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5456_Transitive__Closure_Otrancl__into__trancl,axiom,
% 13.77/7.77 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,C2: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ R )
% 13.77/7.77 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5457_trancl__into__trancl2,axiom,
% 13.77/7.77 ! [A: uint32,B: uint32,R: set_Pr1773385645901665561uint32,C2: uint32] :
% 13.77/7.77 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ R )
% 13.77/7.77 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ B @ C2 ) @ ( transi3114468042090999947uint32 @ R ) )
% 13.77/7.77 => ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ C2 ) @ ( transi3114468042090999947uint32 @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5458_trancl__into__trancl2,axiom,
% 13.77/7.77 ! [A: nat,B: nat,R: set_Pr1261947904930325089at_nat,C2: nat] :
% 13.77/7.77 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 13.77/7.77 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ B @ C2 ) @ ( transi6264000038957366511cl_nat @ R ) )
% 13.77/7.77 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ C2 ) @ ( transi6264000038957366511cl_nat @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5459_trancl__into__trancl2,axiom,
% 13.77/7.77 ! [A: int,B: int,R: set_Pr958786334691620121nt_int,C2: int] :
% 13.77/7.77 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ R )
% 13.77/7.77 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ B @ C2 ) @ ( transi6261509568448316235cl_int @ R ) )
% 13.77/7.77 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ C2 ) @ ( transi6261509568448316235cl_int @ R ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5460_local_Oext,axiom,
% 13.77/7.77 ! [Y: nat,TreeList: list_VEBT_VEBT,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ Y @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5461_mod__frame__fwd,axiom,
% 13.77/7.77 ! [Ps: assn,H2: produc3658429121746597890et_nat,P2: assn,R2: assn,F2: assn] :
% 13.77/7.77 ( ( rep_assn @ Ps @ H2 )
% 13.77/7.77 => ( ( entails @ P2 @ R2 )
% 13.77/7.77 => ( ( entails @ Ps @ ( times_times_assn @ P2 @ F2 ) )
% 13.77/7.77 => ( rep_assn @ ( times_times_assn @ R2 @ F2 ) @ H2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5462_assnle,axiom,
% 13.77/7.77 ! [TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] : ( entails @ ( times_times_assn @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5463_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5464_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > nat > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2809031099982602151Ti_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5465_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5466_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,I: nat,Xsi: list_int,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2806540629473551875Ti_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5467_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > vEBT_VEBT > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2018189785592951398T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5468_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > nat > assn,Xs: list_int,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8891422820522952478nt_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5469_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > vEBT_VEBTi > assn,Xs: list_int,I: nat,Xsi: list_VEBT_VEBTi,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L114188773329725699_VEBTi @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5470_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: int > int > assn,Xs: list_int,I: nat,Xsi: list_int,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8888932350013902202nt_int @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5471_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_VEBT_VEBT,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5472_listI__assn__reinsert_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,I: nat,Xsi: list_nat,I5: set_nat,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8650695023172932196BT_nat @ I5 @ A4 @ Xs @ Xsi ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5473_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X: vEBT_VEBTi,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5474_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,X: vEBT_VEBTi,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5475_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,X: vEBT_VEBT,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5476_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: real > vEBT_VEBTi > assn,X: real,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5477_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: real > vEBT_VEBT > assn,X: real,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5478_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: $o > vEBT_VEBTi > assn,X: $o,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L6286945158656146733_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5479_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: $o > vEBT_VEBT > assn,X: $o,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5480_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: nat > vEBT_VEBTi > assn,X: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7489483478785760935_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5481_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: nat > vEBT_VEBT > assn,X: nat,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBT,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L8511957252848910786T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5482_listI__assn__reinsert__upd,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBTi > assn,X: vEBT_VEBT,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,Q2: assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( entails @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ Q2 )
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5483_recomp,axiom,
% 13.77/7.77 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ I ) @ ( nth_VEBT_VEBTi @ Tree_is @ I ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5484_repack,axiom,
% 13.77/7.77 ! [I: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,Rest: assn,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ I ) @ ( nth_VEBT_VEBTi @ Tree_is @ I ) ) @ Rest ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ Rest @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5485_finite__atLeastLessThan,axiom,
% 13.77/7.77 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5486_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: set_nat,L: set_nat,U: set_nat] :
% 13.77/7.77 ( ( member_set_nat @ I @ ( set_or3540276404033026485et_nat @ L @ U ) )
% 13.77/7.77 = ( ( ord_less_eq_set_nat @ L @ I )
% 13.77/7.77 & ( ord_less_set_nat @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5487_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: real,L: real,U: real] :
% 13.77/7.77 ( ( member_real @ I @ ( set_or66887138388493659n_real @ L @ U ) )
% 13.77/7.77 = ( ( ord_less_eq_real @ L @ I )
% 13.77/7.77 & ( ord_less_real @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5488_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: set_int,L: set_int,U: set_int] :
% 13.77/7.77 ( ( member_set_int @ I @ ( set_or8585797421378605585et_int @ L @ U ) )
% 13.77/7.77 = ( ( ord_less_eq_set_int @ L @ I )
% 13.77/7.77 & ( ord_less_set_int @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5489_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: rat,L: rat,U: rat] :
% 13.77/7.77 ( ( member_rat @ I @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 13.77/7.77 = ( ( ord_less_eq_rat @ L @ I )
% 13.77/7.77 & ( ord_less_rat @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5490_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: num,L: num,U: num] :
% 13.77/7.77 ( ( member_num @ I @ ( set_or1222409239386451017an_num @ L @ U ) )
% 13.77/7.77 = ( ( ord_less_eq_num @ L @ I )
% 13.77/7.77 & ( ord_less_num @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5491_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: nat,L: nat,U: nat] :
% 13.77/7.77 ( ( member_nat @ I @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 13.77/7.77 = ( ( ord_less_eq_nat @ L @ I )
% 13.77/7.77 & ( ord_less_nat @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5492_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: int,L: int,U: int] :
% 13.77/7.77 ( ( member_int @ I @ ( set_or4662586982721622107an_int @ L @ U ) )
% 13.77/7.77 = ( ( ord_less_eq_int @ L @ I )
% 13.77/7.77 & ( ord_less_int @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5493_atLeastLessThan__iff,axiom,
% 13.77/7.77 ! [I: code_integer,L: code_integer,U: code_integer] :
% 13.77/7.77 ( ( member_Code_integer @ I @ ( set_or8404916559141939852nteger @ L @ U ) )
% 13.77/7.77 = ( ( ord_le3102999989581377725nteger @ L @ I )
% 13.77/7.77 & ( ord_le6747313008572928689nteger @ I @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5494_atLeastLessThan__empty,axiom,
% 13.77/7.77 ! [B: $o,A: $o] :
% 13.77/7.77 ( ( ord_less_eq_o @ B @ A )
% 13.77/7.77 => ( ( set_or7139685690850216873Than_o @ A @ B )
% 13.77/7.77 = bot_bot_set_o ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5495_atLeastLessThan__empty,axiom,
% 13.77/7.77 ! [B: set_int,A: set_int] :
% 13.77/7.77 ( ( ord_less_eq_set_int @ B @ A )
% 13.77/7.77 => ( ( set_or8585797421378605585et_int @ A @ B )
% 13.77/7.77 = bot_bot_set_set_int ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5496_atLeastLessThan__empty,axiom,
% 13.77/7.77 ! [B: rat,A: rat] :
% 13.77/7.77 ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.77 => ( ( set_or4029947393144176647an_rat @ A @ B )
% 13.77/7.77 = bot_bot_set_rat ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5497_atLeastLessThan__empty,axiom,
% 13.77/7.77 ! [B: num,A: num] :
% 13.77/7.77 ( ( ord_less_eq_num @ B @ A )
% 13.77/7.77 => ( ( set_or1222409239386451017an_num @ A @ B )
% 13.77/7.77 = bot_bot_set_num ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5498_atLeastLessThan__empty,axiom,
% 13.77/7.77 ! [B: nat,A: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.77 => ( ( set_or4665077453230672383an_nat @ A @ B )
% 13.77/7.77 = bot_bot_set_nat ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5499_atLeastLessThan__empty,axiom,
% 13.77/7.77 ! [B: int,A: int] :
% 13.77/7.77 ( ( ord_less_eq_int @ B @ A )
% 13.77/7.77 => ( ( set_or4662586982721622107an_int @ A @ B )
% 13.77/7.77 = bot_bot_set_int ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5500_atLeastLessThan__empty,axiom,
% 13.77/7.77 ! [B: code_integer,A: code_integer] :
% 13.77/7.77 ( ( ord_le3102999989581377725nteger @ B @ A )
% 13.77/7.77 => ( ( set_or8404916559141939852nteger @ A @ B )
% 13.77/7.77 = bot_bo3990330152332043303nteger ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5501_atLeastLessThan__empty__iff2,axiom,
% 13.77/7.77 ! [A: $o,B: $o] :
% 13.77/7.77 ( ( bot_bot_set_o
% 13.77/7.77 = ( set_or7139685690850216873Than_o @ A @ B ) )
% 13.77/7.77 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5502_atLeastLessThan__empty__iff2,axiom,
% 13.77/7.77 ! [A: real,B: real] :
% 13.77/7.77 ( ( bot_bot_set_real
% 13.77/7.77 = ( set_or66887138388493659n_real @ A @ B ) )
% 13.77/7.77 = ( ~ ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5503_atLeastLessThan__empty__iff2,axiom,
% 13.77/7.77 ! [A: rat,B: rat] :
% 13.77/7.77 ( ( bot_bot_set_rat
% 13.77/7.77 = ( set_or4029947393144176647an_rat @ A @ B ) )
% 13.77/7.77 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5504_atLeastLessThan__empty__iff2,axiom,
% 13.77/7.77 ! [A: num,B: num] :
% 13.77/7.77 ( ( bot_bot_set_num
% 13.77/7.77 = ( set_or1222409239386451017an_num @ A @ B ) )
% 13.77/7.77 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5505_atLeastLessThan__empty__iff2,axiom,
% 13.77/7.77 ! [A: nat,B: nat] :
% 13.77/7.77 ( ( bot_bot_set_nat
% 13.77/7.77 = ( set_or4665077453230672383an_nat @ A @ B ) )
% 13.77/7.77 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5506_atLeastLessThan__empty__iff2,axiom,
% 13.77/7.77 ! [A: int,B: int] :
% 13.77/7.77 ( ( bot_bot_set_int
% 13.77/7.77 = ( set_or4662586982721622107an_int @ A @ B ) )
% 13.77/7.77 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5507_atLeastLessThan__empty__iff2,axiom,
% 13.77/7.77 ! [A: code_integer,B: code_integer] :
% 13.77/7.77 ( ( bot_bo3990330152332043303nteger
% 13.77/7.77 = ( set_or8404916559141939852nteger @ A @ B ) )
% 13.77/7.77 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5508_atLeastLessThan__empty__iff,axiom,
% 13.77/7.77 ! [A: $o,B: $o] :
% 13.77/7.77 ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 13.77/7.77 = bot_bot_set_o )
% 13.77/7.77 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5509_atLeastLessThan__empty__iff,axiom,
% 13.77/7.77 ! [A: real,B: real] :
% 13.77/7.77 ( ( ( set_or66887138388493659n_real @ A @ B )
% 13.77/7.77 = bot_bot_set_real )
% 13.77/7.77 = ( ~ ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5510_atLeastLessThan__empty__iff,axiom,
% 13.77/7.77 ! [A: rat,B: rat] :
% 13.77/7.77 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 13.77/7.77 = bot_bot_set_rat )
% 13.77/7.77 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5511_atLeastLessThan__empty__iff,axiom,
% 13.77/7.77 ! [A: num,B: num] :
% 13.77/7.77 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 13.77/7.77 = bot_bot_set_num )
% 13.77/7.77 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5512_atLeastLessThan__empty__iff,axiom,
% 13.77/7.77 ! [A: nat,B: nat] :
% 13.77/7.77 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 13.77/7.77 = bot_bot_set_nat )
% 13.77/7.77 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5513_atLeastLessThan__empty__iff,axiom,
% 13.77/7.77 ! [A: int,B: int] :
% 13.77/7.77 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 13.77/7.77 = bot_bot_set_int )
% 13.77/7.77 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5514_atLeastLessThan__empty__iff,axiom,
% 13.77/7.77 ! [A: code_integer,B: code_integer] :
% 13.77/7.77 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 13.77/7.77 = bot_bo3990330152332043303nteger )
% 13.77/7.77 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5515_infinite__Ico__iff,axiom,
% 13.77/7.77 ! [A: real,B: real] :
% 13.77/7.77 ( ( ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A @ B ) ) )
% 13.77/7.77 = ( ord_less_real @ A @ B ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5516_infinite__Ico__iff,axiom,
% 13.77/7.77 ! [A: rat,B: rat] :
% 13.77/7.77 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) )
% 13.77/7.77 = ( ord_less_rat @ A @ B ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5517_ivl__subset,axiom,
% 13.77/7.77 ! [I: rat,J: rat,M: rat,N: rat] :
% 13.77/7.77 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ I @ J ) @ ( set_or4029947393144176647an_rat @ M @ N ) )
% 13.77/7.77 = ( ( ord_less_eq_rat @ J @ I )
% 13.77/7.77 | ( ( ord_less_eq_rat @ M @ I )
% 13.77/7.77 & ( ord_less_eq_rat @ J @ N ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5518_ivl__subset,axiom,
% 13.77/7.77 ! [I: num,J: num,M: num,N: num] :
% 13.77/7.77 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I @ J ) @ ( set_or1222409239386451017an_num @ M @ N ) )
% 13.77/7.77 = ( ( ord_less_eq_num @ J @ I )
% 13.77/7.77 | ( ( ord_less_eq_num @ M @ I )
% 13.77/7.77 & ( ord_less_eq_num @ J @ N ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5519_ivl__subset,axiom,
% 13.77/7.77 ! [I: nat,J: nat,M: nat,N: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.77 = ( ( ord_less_eq_nat @ J @ I )
% 13.77/7.77 | ( ( ord_less_eq_nat @ M @ I )
% 13.77/7.77 & ( ord_less_eq_nat @ J @ N ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5520_ivl__subset,axiom,
% 13.77/7.77 ! [I: int,J: int,M: int,N: int] :
% 13.77/7.77 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I @ J ) @ ( set_or4662586982721622107an_int @ M @ N ) )
% 13.77/7.77 = ( ( ord_less_eq_int @ J @ I )
% 13.77/7.77 | ( ( ord_less_eq_int @ M @ I )
% 13.77/7.77 & ( ord_less_eq_int @ J @ N ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5521_ivl__subset,axiom,
% 13.77/7.77 ! [I: code_integer,J: code_integer,M: code_integer,N: code_integer] :
% 13.77/7.77 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ I @ J ) @ ( set_or8404916559141939852nteger @ M @ N ) )
% 13.77/7.77 = ( ( ord_le3102999989581377725nteger @ J @ I )
% 13.77/7.77 | ( ( ord_le3102999989581377725nteger @ M @ I )
% 13.77/7.77 & ( ord_le3102999989581377725nteger @ J @ N ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5522_ivl__diff,axiom,
% 13.77/7.77 ! [I: rat,N: rat,M: rat] :
% 13.77/7.77 ( ( ord_less_eq_rat @ I @ N )
% 13.77/7.77 => ( ( minus_minus_set_rat @ ( set_or4029947393144176647an_rat @ I @ M ) @ ( set_or4029947393144176647an_rat @ I @ N ) )
% 13.77/7.77 = ( set_or4029947393144176647an_rat @ N @ M ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5523_ivl__diff,axiom,
% 13.77/7.77 ! [I: num,N: num,M: num] :
% 13.77/7.77 ( ( ord_less_eq_num @ I @ N )
% 13.77/7.77 => ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I @ M ) @ ( set_or1222409239386451017an_num @ I @ N ) )
% 13.77/7.77 = ( set_or1222409239386451017an_num @ N @ M ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5524_ivl__diff,axiom,
% 13.77/7.77 ! [I: nat,N: nat,M: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ I @ N )
% 13.77/7.77 => ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I @ M ) @ ( set_or4665077453230672383an_nat @ I @ N ) )
% 13.77/7.77 = ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5525_ivl__diff,axiom,
% 13.77/7.77 ! [I: int,N: int,M: int] :
% 13.77/7.77 ( ( ord_less_eq_int @ I @ N )
% 13.77/7.77 => ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I @ M ) @ ( set_or4662586982721622107an_int @ I @ N ) )
% 13.77/7.77 = ( set_or4662586982721622107an_int @ N @ M ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5526_ivl__diff,axiom,
% 13.77/7.77 ! [I: code_integer,N: code_integer,M: code_integer] :
% 13.77/7.77 ( ( ord_le3102999989581377725nteger @ I @ N )
% 13.77/7.77 => ( ( minus_2355218937544613996nteger @ ( set_or8404916559141939852nteger @ I @ M ) @ ( set_or8404916559141939852nteger @ I @ N ) )
% 13.77/7.77 = ( set_or8404916559141939852nteger @ N @ M ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5527_list__update__beyond,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) @ I )
% 13.77/7.77 => ( ( list_u6098035379799741383_VEBTi @ Xs @ I @ X )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5528_list__update__beyond,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 13.77/7.77 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5529_list__update__beyond,axiom,
% 13.77/7.77 ! [Xs: list_real,I: nat,X: real] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ I )
% 13.77/7.77 => ( ( list_update_real @ Xs @ I @ X )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5530_list__update__beyond,axiom,
% 13.77/7.77 ! [Xs: list_o,I: nat,X: $o] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 13.77/7.77 => ( ( list_update_o @ Xs @ I @ X )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5531_list__update__beyond,axiom,
% 13.77/7.77 ! [Xs: list_nat,I: nat,X: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 13.77/7.77 => ( ( list_update_nat @ Xs @ I @ X )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5532_image__Suc__atLeastLessThan,axiom,
% 13.77/7.77 ! [I: nat,J: nat] :
% 13.77/7.77 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 13.77/7.77 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5533_tcd,axiom,
% 13.77/7.77 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_VEBT_VEBT,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.77 = ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5534_tcd,axiom,
% 13.77/7.77 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_real,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.77 = ( size_size_list_real @ TreeList3 ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5535_tcd,axiom,
% 13.77/7.77 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_o,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.77 = ( size_size_list_o @ TreeList3 ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5536_tcd,axiom,
% 13.77/7.77 ! [I: nat,TreeList: list_VEBT_VEBT,TreeList3: list_nat,Y: vEBT_VEBT,X: vEBT_VEBTi,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.77 = ( size_size_list_nat @ TreeList3 ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Y @ X ) @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ I @ Y ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ I @ X ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5537_nth__update__invalid,axiom,
% 13.77/7.77 ! [I: nat,L: list_int,J: nat,X: int] :
% 13.77/7.77 ( ~ ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 13.77/7.77 => ( ( nth_int @ ( list_update_int @ L @ J @ X ) @ I )
% 13.77/7.77 = ( nth_int @ L @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5538_nth__update__invalid,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBTi,J: nat,X: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ J @ X ) @ I )
% 13.77/7.77 = ( nth_VEBT_VEBTi @ L @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5539_nth__update__invalid,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ J @ X ) @ I )
% 13.77/7.77 = ( nth_VEBT_VEBT @ L @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5540_nth__update__invalid,axiom,
% 13.77/7.77 ! [I: nat,L: list_real,J: nat,X: real] :
% 13.77/7.77 ( ~ ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 13.77/7.77 => ( ( nth_real @ ( list_update_real @ L @ J @ X ) @ I )
% 13.77/7.77 = ( nth_real @ L @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5541_nth__update__invalid,axiom,
% 13.77/7.77 ! [I: nat,L: list_o,J: nat,X: $o] :
% 13.77/7.77 ( ~ ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 13.77/7.77 => ( ( nth_o @ ( list_update_o @ L @ J @ X ) @ I )
% 13.77/7.77 = ( nth_o @ L @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5542_nth__update__invalid,axiom,
% 13.77/7.77 ! [I: nat,L: list_nat,J: nat,X: nat] :
% 13.77/7.77 ( ~ ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 13.77/7.77 => ( ( nth_nat @ ( list_update_nat @ L @ J @ X ) @ I )
% 13.77/7.77 = ( nth_nat @ L @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5543_nth__list__update__eq,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_int,X: int] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 13.77/7.77 = X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5544_nth__list__update__eq,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ I )
% 13.77/7.77 = X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5545_nth__list__update__eq,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I )
% 13.77/7.77 = X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5546_nth__list__update__eq,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_real,X: real] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X ) @ I )
% 13.77/7.77 = X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5547_nth__list__update__eq,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_o,X: $o] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ I )
% 13.77/7.77 = X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5548_nth__list__update__eq,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_nat,X: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 13.77/7.77 = X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5549_atLeastLessThan__singleton,axiom,
% 13.77/7.77 ! [M: nat] :
% 13.77/7.77 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 13.77/7.77 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5550_txe,axiom,
% 13.77/7.77 ! [Y: nat,TreeList: list_VEBT_VEBT,Tree_is: list_VEBT_VEBTi,X13: array_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ Y @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( entails @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( nth_VEBT_VEBT @ TreeList @ Y ) @ ( nth_VEBT_VEBTi @ Tree_is @ Y ) ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ Y @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) @ ( snga_assn_VEBT_VEBTi @ X13 @ Tree_is ) ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5551_set__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_int,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 13.77/7.77 = ( set_int2 @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5552_set__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ ( nth_VEBT_VEBTi @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBTi @ Xs @ I ) ) )
% 13.77/7.77 = ( set_VEBT_VEBTi2 @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5553_set__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 13.77/7.77 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5554_set__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_real,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( set_real2 @ ( list_update_real @ ( list_update_real @ Xs @ I @ ( nth_real @ Xs @ J ) ) @ J @ ( nth_real @ Xs @ I ) ) )
% 13.77/7.77 = ( set_real2 @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5555_set__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_o,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 13.77/7.77 = ( set_o2 @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5556_set__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_nat,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 13.77/7.77 = ( set_nat2 @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5557_sum_Oop__ivl__Suc,axiom,
% 13.77/7.77 ! [N: nat,M: nat,G: nat > uint32] :
% 13.77/7.77 ( ( ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups833757482993574392uint32 @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = zero_zero_uint32 ) )
% 13.77/7.77 & ( ~ ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups833757482993574392uint32 @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_uint32 @ ( groups833757482993574392uint32 @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5558_sum_Oop__ivl__Suc,axiom,
% 13.77/7.77 ! [N: nat,M: nat,G: nat > rat] :
% 13.77/7.77 ( ( ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = zero_zero_rat ) )
% 13.77/7.77 & ( ~ ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5559_sum_Oop__ivl__Suc,axiom,
% 13.77/7.77 ! [N: nat,M: nat,G: nat > int] :
% 13.77/7.77 ( ( ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = zero_zero_int ) )
% 13.77/7.77 & ( ~ ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5560_sum_Oop__ivl__Suc,axiom,
% 13.77/7.77 ! [N: nat,M: nat,G: nat > nat] :
% 13.77/7.77 ( ( ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = zero_zero_nat ) )
% 13.77/7.77 & ( ~ ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5561_sum_Oop__ivl__Suc,axiom,
% 13.77/7.77 ! [N: nat,M: nat,G: nat > real] :
% 13.77/7.77 ( ( ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = zero_zero_real ) )
% 13.77/7.77 & ( ~ ( ord_less_nat @ N @ M )
% 13.77/7.77 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5562_nth__image__indices,axiom,
% 13.77/7.77 ! [L: list_VEBT_VEBTi] :
% 13.77/7.77 ( ( image_nat_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 13.77/7.77 = ( set_VEBT_VEBTi2 @ L ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5563_nth__image__indices,axiom,
% 13.77/7.77 ! [L: list_set_nat] :
% 13.77/7.77 ( ( image_nat_set_nat @ ( nth_set_nat @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ L ) ) )
% 13.77/7.77 = ( set_set_nat2 @ L ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5564_nth__image__indices,axiom,
% 13.77/7.77 ! [L: list_int] :
% 13.77/7.77 ( ( image_nat_int @ ( nth_int @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ L ) ) )
% 13.77/7.77 = ( set_int2 @ L ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5565_nth__image__indices,axiom,
% 13.77/7.77 ! [L: list_VEBT_VEBT] :
% 13.77/7.77 ( ( image_nat_VEBT_VEBT @ ( nth_VEBT_VEBT @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 13.77/7.77 = ( set_VEBT_VEBT2 @ L ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5566_nth__image__indices,axiom,
% 13.77/7.77 ! [L: list_real] :
% 13.77/7.77 ( ( image_nat_real @ ( nth_real @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_real @ L ) ) )
% 13.77/7.77 = ( set_real2 @ L ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5567_nth__image__indices,axiom,
% 13.77/7.77 ! [L: list_o] :
% 13.77/7.77 ( ( image_nat_o @ ( nth_o @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ L ) ) )
% 13.77/7.77 = ( set_o2 @ L ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5568_nth__image__indices,axiom,
% 13.77/7.77 ! [L: list_nat] :
% 13.77/7.77 ( ( image_nat_nat @ ( nth_nat @ L ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ L ) ) )
% 13.77/7.77 = ( set_nat2 @ L ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5569_deleti_H__rf__abstr,axiom,
% 13.77/7.77 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.77 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V1365221501068881998eletei @ T @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ T @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5570_atLeastLessThan__eq__iff,axiom,
% 13.77/7.77 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.77 ( ( ord_less_real @ A @ B )
% 13.77/7.77 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.77 => ( ( ( set_or66887138388493659n_real @ A @ B )
% 13.77/7.77 = ( set_or66887138388493659n_real @ C2 @ D ) )
% 13.77/7.77 = ( ( A = C2 )
% 13.77/7.77 & ( B = D ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5571_atLeastLessThan__eq__iff,axiom,
% 13.77/7.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.77 ( ( ord_less_rat @ A @ B )
% 13.77/7.77 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.77 => ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 13.77/7.77 = ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 13.77/7.77 = ( ( A = C2 )
% 13.77/7.77 & ( B = D ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5572_atLeastLessThan__eq__iff,axiom,
% 13.77/7.77 ! [A: num,B: num,C2: num,D: num] :
% 13.77/7.77 ( ( ord_less_num @ A @ B )
% 13.77/7.77 => ( ( ord_less_num @ C2 @ D )
% 13.77/7.77 => ( ( ( set_or1222409239386451017an_num @ A @ B )
% 13.77/7.77 = ( set_or1222409239386451017an_num @ C2 @ D ) )
% 13.77/7.77 = ( ( A = C2 )
% 13.77/7.77 & ( B = D ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5573_atLeastLessThan__eq__iff,axiom,
% 13.77/7.77 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.77 ( ( ord_less_nat @ A @ B )
% 13.77/7.77 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.77 => ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 13.77/7.77 = ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 13.77/7.77 = ( ( A = C2 )
% 13.77/7.77 & ( B = D ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5574_atLeastLessThan__eq__iff,axiom,
% 13.77/7.77 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.77 ( ( ord_less_int @ A @ B )
% 13.77/7.77 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.77 => ( ( ( set_or4662586982721622107an_int @ A @ B )
% 13.77/7.77 = ( set_or4662586982721622107an_int @ C2 @ D ) )
% 13.77/7.77 = ( ( A = C2 )
% 13.77/7.77 & ( B = D ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5575_atLeastLessThan__eq__iff,axiom,
% 13.77/7.77 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 13.77/7.77 ( ( ord_le6747313008572928689nteger @ A @ B )
% 13.77/7.77 => ( ( ord_le6747313008572928689nteger @ C2 @ D )
% 13.77/7.77 => ( ( ( set_or8404916559141939852nteger @ A @ B )
% 13.77/7.77 = ( set_or8404916559141939852nteger @ C2 @ D ) )
% 13.77/7.77 = ( ( A = C2 )
% 13.77/7.77 & ( B = D ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5576_atLeastLessThan__inj_I1_J,axiom,
% 13.77/7.77 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.77 ( ( ( set_or66887138388493659n_real @ A @ B )
% 13.77/7.77 = ( set_or66887138388493659n_real @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_real @ A @ B )
% 13.77/7.77 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.77 => ( A = C2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5577_atLeastLessThan__inj_I1_J,axiom,
% 13.77/7.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.77 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 13.77/7.77 = ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_rat @ A @ B )
% 13.77/7.77 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.77 => ( A = C2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5578_atLeastLessThan__inj_I1_J,axiom,
% 13.77/7.77 ! [A: num,B: num,C2: num,D: num] :
% 13.77/7.77 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 13.77/7.77 = ( set_or1222409239386451017an_num @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_num @ A @ B )
% 13.77/7.77 => ( ( ord_less_num @ C2 @ D )
% 13.77/7.77 => ( A = C2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5579_atLeastLessThan__inj_I1_J,axiom,
% 13.77/7.77 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.77 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 13.77/7.77 = ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_nat @ A @ B )
% 13.77/7.77 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.77 => ( A = C2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5580_atLeastLessThan__inj_I1_J,axiom,
% 13.77/7.77 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.77 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 13.77/7.77 = ( set_or4662586982721622107an_int @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_int @ A @ B )
% 13.77/7.77 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.77 => ( A = C2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5581_atLeastLessThan__inj_I1_J,axiom,
% 13.77/7.77 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 13.77/7.77 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 13.77/7.77 = ( set_or8404916559141939852nteger @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 13.77/7.77 => ( ( ord_le6747313008572928689nteger @ C2 @ D )
% 13.77/7.77 => ( A = C2 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5582_atLeastLessThan__inj_I2_J,axiom,
% 13.77/7.77 ! [A: real,B: real,C2: real,D: real] :
% 13.77/7.77 ( ( ( set_or66887138388493659n_real @ A @ B )
% 13.77/7.77 = ( set_or66887138388493659n_real @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_real @ A @ B )
% 13.77/7.77 => ( ( ord_less_real @ C2 @ D )
% 13.77/7.77 => ( B = D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5583_atLeastLessThan__inj_I2_J,axiom,
% 13.77/7.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.77 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 13.77/7.77 = ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_rat @ A @ B )
% 13.77/7.77 => ( ( ord_less_rat @ C2 @ D )
% 13.77/7.77 => ( B = D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5584_atLeastLessThan__inj_I2_J,axiom,
% 13.77/7.77 ! [A: num,B: num,C2: num,D: num] :
% 13.77/7.77 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 13.77/7.77 = ( set_or1222409239386451017an_num @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_num @ A @ B )
% 13.77/7.77 => ( ( ord_less_num @ C2 @ D )
% 13.77/7.77 => ( B = D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5585_atLeastLessThan__inj_I2_J,axiom,
% 13.77/7.77 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.77 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 13.77/7.77 = ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_nat @ A @ B )
% 13.77/7.77 => ( ( ord_less_nat @ C2 @ D )
% 13.77/7.77 => ( B = D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5586_atLeastLessThan__inj_I2_J,axiom,
% 13.77/7.77 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.77 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 13.77/7.77 = ( set_or4662586982721622107an_int @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_int @ A @ B )
% 13.77/7.77 => ( ( ord_less_int @ C2 @ D )
% 13.77/7.77 => ( B = D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5587_atLeastLessThan__inj_I2_J,axiom,
% 13.77/7.77 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 13.77/7.77 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 13.77/7.77 = ( set_or8404916559141939852nteger @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 13.77/7.77 => ( ( ord_le6747313008572928689nteger @ C2 @ D )
% 13.77/7.77 => ( B = D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5588_listI__assn__conv,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi] :
% 13.77/7.77 ( ( N
% 13.77/7.77 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A4 @ Xs @ Xsi )
% 13.77/7.77 = ( vEBT_L6296928887356842470_VEBTi @ A4 @ Xs @ Xsi ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5589_list__assn__conv__idx,axiom,
% 13.77/7.77 ( vEBT_L6296928887356842470_VEBTi
% 13.77/7.77 = ( ^ [A6: vEBT_VEBT > vEBT_VEBTi > assn,Xs2: list_VEBT_VEBT] : ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) @ A6 @ Xs2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5590_list__update__code_I3_J,axiom,
% 13.77/7.77 ! [X: int,Xs: list_int,I: nat,Y: int] :
% 13.77/7.77 ( ( list_update_int @ ( cons_int @ X @ Xs ) @ ( suc @ I ) @ Y )
% 13.77/7.77 = ( cons_int @ X @ ( list_update_int @ Xs @ I @ Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5591_list__update__code_I3_J,axiom,
% 13.77/7.77 ! [X: nat,Xs: list_nat,I: nat,Y: nat] :
% 13.77/7.77 ( ( list_update_nat @ ( cons_nat @ X @ Xs ) @ ( suc @ I ) @ Y )
% 13.77/7.77 = ( cons_nat @ X @ ( list_update_nat @ Xs @ I @ Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5592_list__update__code_I3_J,axiom,
% 13.77/7.77 ! [X: $o,Xs: list_o,I: nat,Y: $o] :
% 13.77/7.77 ( ( list_update_o @ ( cons_o @ X @ Xs ) @ ( suc @ I ) @ Y )
% 13.77/7.77 = ( cons_o @ X @ ( list_update_o @ Xs @ I @ Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5593_list__update__code_I3_J,axiom,
% 13.77/7.77 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,I: nat,Y: vEBT_VEBTi] :
% 13.77/7.77 ( ( list_u6098035379799741383_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ ( suc @ I ) @ Y )
% 13.77/7.77 = ( cons_VEBT_VEBTi @ X @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5594_list__update__code_I3_J,axiom,
% 13.77/7.77 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,I: nat,Y: vEBT_VEBT] :
% 13.77/7.77 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( suc @ I ) @ Y )
% 13.77/7.77 = ( cons_VEBT_VEBT @ X @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5595_list__update__code_I2_J,axiom,
% 13.77/7.77 ! [X: int,Xs: list_int,Y: int] :
% 13.77/7.77 ( ( list_update_int @ ( cons_int @ X @ Xs ) @ zero_zero_nat @ Y )
% 13.77/7.77 = ( cons_int @ Y @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5596_list__update__code_I2_J,axiom,
% 13.77/7.77 ! [X: nat,Xs: list_nat,Y: nat] :
% 13.77/7.77 ( ( list_update_nat @ ( cons_nat @ X @ Xs ) @ zero_zero_nat @ Y )
% 13.77/7.77 = ( cons_nat @ Y @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5597_list__update__code_I2_J,axiom,
% 13.77/7.77 ! [X: $o,Xs: list_o,Y: $o] :
% 13.77/7.77 ( ( list_update_o @ ( cons_o @ X @ Xs ) @ zero_zero_nat @ Y )
% 13.77/7.77 = ( cons_o @ Y @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5598_list__update__code_I2_J,axiom,
% 13.77/7.77 ! [X: vEBT_VEBTi,Xs: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 13.77/7.77 ( ( list_u6098035379799741383_VEBTi @ ( cons_VEBT_VEBTi @ X @ Xs ) @ zero_zero_nat @ Y )
% 13.77/7.77 = ( cons_VEBT_VEBTi @ Y @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5599_list__update__code_I2_J,axiom,
% 13.77/7.77 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.77 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ zero_zero_nat @ Y )
% 13.77/7.77 = ( cons_VEBT_VEBT @ Y @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5600_set__update__subsetI,axiom,
% 13.77/7.77 ! [Xs: list_set_nat,A4: set_set_nat,X: set_nat,I: nat] :
% 13.77/7.77 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 13.77/7.77 => ( ( member_set_nat @ X @ A4 )
% 13.77/7.77 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5601_set__update__subsetI,axiom,
% 13.77/7.77 ! [Xs: list_nat,A4: set_nat,X: nat,I: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 13.77/7.77 => ( ( member_nat @ X @ A4 )
% 13.77/7.77 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5602_set__update__subsetI,axiom,
% 13.77/7.77 ! [Xs: list_real,A4: set_real,X: real,I: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A4 )
% 13.77/7.77 => ( ( member_real @ X @ A4 )
% 13.77/7.77 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5603_set__update__subsetI,axiom,
% 13.77/7.77 ! [Xs: list_o,A4: set_o,X: $o,I: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 13.77/7.77 => ( ( member_o @ X @ A4 )
% 13.77/7.77 => ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5604_set__update__subsetI,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBTi,A4: set_VEBT_VEBTi,X: vEBT_VEBTi,I: nat] :
% 13.77/7.77 ( ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ Xs ) @ A4 )
% 13.77/7.77 => ( ( member_VEBT_VEBTi @ X @ A4 )
% 13.77/7.77 => ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5605_set__update__subsetI,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBT,A4: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 13.77/7.77 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 13.77/7.77 => ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.77 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5606_set__update__subsetI,axiom,
% 13.77/7.77 ! [Xs: list_int,A4: set_int,X: int,I: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 13.77/7.77 => ( ( member_int @ X @ A4 )
% 13.77/7.77 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5607_infinite__Ico,axiom,
% 13.77/7.77 ! [A: real,B: real] :
% 13.77/7.77 ( ( ord_less_real @ A @ B )
% 13.77/7.77 => ~ ( finite_finite_real @ ( set_or66887138388493659n_real @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5608_infinite__Ico,axiom,
% 13.77/7.77 ! [A: rat,B: rat] :
% 13.77/7.77 ( ( ord_less_rat @ A @ B )
% 13.77/7.77 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5609_atLeastLessThan__subset__iff,axiom,
% 13.77/7.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 13.77/7.77 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_eq_rat @ B @ A )
% 13.77/7.77 | ( ( ord_less_eq_rat @ C2 @ A )
% 13.77/7.77 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5610_atLeastLessThan__subset__iff,axiom,
% 13.77/7.77 ! [A: num,B: num,C2: num,D: num] :
% 13.77/7.77 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_eq_num @ B @ A )
% 13.77/7.77 | ( ( ord_less_eq_num @ C2 @ A )
% 13.77/7.77 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5611_atLeastLessThan__subset__iff,axiom,
% 13.77/7.77 ! [A: nat,B: nat,C2: nat,D: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.77 | ( ( ord_less_eq_nat @ C2 @ A )
% 13.77/7.77 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5612_atLeastLessThan__subset__iff,axiom,
% 13.77/7.77 ! [A: int,B: int,C2: int,D: int] :
% 13.77/7.77 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_less_eq_int @ B @ A )
% 13.77/7.77 | ( ( ord_less_eq_int @ C2 @ A )
% 13.77/7.77 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5613_atLeastLessThan__subset__iff,axiom,
% 13.77/7.77 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] :
% 13.77/7.77 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C2 @ D ) )
% 13.77/7.77 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 13.77/7.77 | ( ( ord_le3102999989581377725nteger @ C2 @ A )
% 13.77/7.77 & ( ord_le3102999989581377725nteger @ B @ D ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5614_ex__nat__less__eq,axiom,
% 13.77/7.77 ! [N: nat,P2: nat > $o] :
% 13.77/7.77 ( ( ? [M5: nat] :
% 13.77/7.77 ( ( ord_less_nat @ M5 @ N )
% 13.77/7.77 & ( P2 @ M5 ) ) )
% 13.77/7.77 = ( ? [X4: nat] :
% 13.77/7.77 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 13.77/7.77 & ( P2 @ X4 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5615_all__nat__less__eq,axiom,
% 13.77/7.77 ! [N: nat,P2: nat > $o] :
% 13.77/7.77 ( ( ! [M5: nat] :
% 13.77/7.77 ( ( ord_less_nat @ M5 @ N )
% 13.77/7.77 => ( P2 @ M5 ) ) )
% 13.77/7.77 = ( ! [X4: nat] :
% 13.77/7.77 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 13.77/7.77 => ( P2 @ X4 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5616_atLeastLessThan0,axiom,
% 13.77/7.77 ! [M: nat] :
% 13.77/7.77 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 13.77/7.77 = bot_bot_set_nat ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5617_listI__assn__conv_H,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,Xsi: list_VEBT_VEBTi,F2: assn] :
% 13.77/7.77 ( ( N
% 13.77/7.77 = ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) @ A4 @ Xs @ Xsi ) @ F2 )
% 13.77/7.77 = ( times_times_assn @ ( vEBT_L6296928887356842470_VEBTi @ A4 @ Xs @ Xsi ) @ F2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5618_subset__eq__atLeast0__lessThan__finite,axiom,
% 13.77/7.77 ! [N8: set_nat,N: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_nat @ N8 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 13.77/7.77 => ( finite_finite_nat @ N8 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5619_subset__card__intvl__is__intvl,axiom,
% 13.77/7.77 ! [A4: set_nat,K: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) )
% 13.77/7.77 => ( A4
% 13.77/7.77 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5620_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L1279224858307276611T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.77 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5621_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: real > vEBT_VEBT > assn,Xs: list_real,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L4595930785310033027T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.77 = ( size_size_list_real @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5622_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: $o > vEBT_VEBT > assn,Xs: list_o,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L1750719106661372127T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.77 = ( size_size_list_o @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5623_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: nat > vEBT_VEBT > assn,Xs: list_nat,Xsi: list_VEBT_VEBT,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L8158188754432654943T_VEBT @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_s6755466524823107622T_VEBT @ Xsi )
% 13.77/7.77 = ( size_size_list_nat @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5624_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: vEBT_VEBT > real > assn,Xs: list_VEBT_VEBT,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L5781919052683127133T_real @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_size_list_real @ Xsi )
% 13.77/7.77 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5625_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: real > real > assn,Xs: list_real,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L1930518968523514909l_real @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_size_list_real @ Xsi )
% 13.77/7.77 = ( size_size_list_real @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5626_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: $o > real > assn,Xs: list_o,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L4725278957065240257o_real @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_size_list_real @ Xsi )
% 13.77/7.77 = ( size_size_list_o @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5627_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: nat > real > assn,Xs: list_nat,Xsi: list_real,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L6102073776069194049t_real @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_size_list_real @ Xsi )
% 13.77/7.77 = ( size_size_list_nat @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5628_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: vEBT_VEBT > $o > assn,Xs: list_VEBT_VEBT,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L7489408758114837031VEBT_o @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_size_list_o @ Xsi )
% 13.77/7.77 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5629_extract__pre__list__assn__lengthD,axiom,
% 13.77/7.77 ! [A4: real > $o > assn,Xs: list_real,Xsi: list_o,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( vEBT_L6234343332106409831real_o @ A4 @ Xs @ Xsi ) @ H2 )
% 13.77/7.77 => ( ( size_size_list_o @ Xsi )
% 13.77/7.77 = ( size_size_list_real @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5630_set__update__memI,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_int,X: int] :
% 13.77/7.77 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5631_set__update__memI,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_set_nat,X: set_nat] :
% 13.77/7.77 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.77 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5632_set__update__memI,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ N @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5633_set__update__memI,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5634_set__update__memI,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_real,X: real] :
% 13.77/7.77 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs @ N @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5635_set__update__memI,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_o,X: $o] :
% 13.77/7.77 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs @ N @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5636_set__update__memI,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_nat,X: nat] :
% 13.77/7.77 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5637_in__set__upd__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_int,X: int,Y: int] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 13.77/7.77 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ( ( member_int @ X @ ( set_int2 @ L ) )
% 13.77/7.77 & ! [Y4: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5638_in__set__upd__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_set_nat,X: set_nat,Y: set_nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ L ) )
% 13.77/7.77 => ( ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ( ( member_set_nat @ X @ ( set_set_nat2 @ L ) )
% 13.77/7.77 & ! [Y4: set_nat] : ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5639_in__set__upd__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi,Y: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.77 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) )
% 13.77/7.77 & ! [Y4: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5640_in__set__upd__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.77 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) )
% 13.77/7.77 & ! [Y4: vEBT_VEBT] : ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5641_in__set__upd__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_real,X: real,Y: real] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 13.77/7.77 => ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ( ( member_real @ X @ ( set_real2 @ L ) )
% 13.77/7.77 & ! [Y4: real] : ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5642_in__set__upd__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_o,X: $o,Y: $o] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 13.77/7.77 => ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ( ( member_o @ X @ ( set_o2 @ L ) )
% 13.77/7.77 & ! [Y4: $o] : ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5643_in__set__upd__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 13.77/7.77 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ( ( member_nat @ X @ ( set_nat2 @ L ) )
% 13.77/7.77 & ! [Y4: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y4 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5644_in__set__upd__cases,axiom,
% 13.77/7.77 ! [X: int,L: list_int,I: nat,Y: int] :
% 13.77/7.77 ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 13.77/7.77 => ( ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 13.77/7.77 => ( X != Y ) )
% 13.77/7.77 => ( member_int @ X @ ( set_int2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5645_in__set__upd__cases,axiom,
% 13.77/7.77 ! [X: set_nat,L: list_set_nat,I: nat,Y: set_nat] :
% 13.77/7.77 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y ) ) )
% 13.77/7.77 => ( ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ L ) )
% 13.77/7.77 => ( X != Y ) )
% 13.77/7.77 => ( member_set_nat @ X @ ( set_set_nat2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5646_in__set__upd__cases,axiom,
% 13.77/7.77 ! [X: vEBT_VEBTi,L: list_VEBT_VEBTi,I: nat,Y: vEBT_VEBTi] :
% 13.77/7.77 ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 13.77/7.77 => ( ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.77 => ( X != Y ) )
% 13.77/7.77 => ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5647_in__set__upd__cases,axiom,
% 13.77/7.77 ! [X: vEBT_VEBT,L: list_VEBT_VEBT,I: nat,Y: vEBT_VEBT] :
% 13.77/7.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 13.77/7.77 => ( ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.77 => ( X != Y ) )
% 13.77/7.77 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5648_in__set__upd__cases,axiom,
% 13.77/7.77 ! [X: real,L: list_real,I: nat,Y: real] :
% 13.77/7.77 ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 13.77/7.77 => ( ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 13.77/7.77 => ( X != Y ) )
% 13.77/7.77 => ( member_real @ X @ ( set_real2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5649_in__set__upd__cases,axiom,
% 13.77/7.77 ! [X: $o,L: list_o,I: nat,Y: $o] :
% 13.77/7.77 ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 13.77/7.77 => ( ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 13.77/7.77 => ( X = ~ Y ) )
% 13.77/7.77 => ( member_o @ X @ ( set_o2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5650_in__set__upd__cases,axiom,
% 13.77/7.77 ! [X: nat,L: list_nat,I: nat,Y: nat] :
% 13.77/7.77 ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 13.77/7.77 => ( ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 13.77/7.77 => ( X != Y ) )
% 13.77/7.77 => ( member_nat @ X @ ( set_nat2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5651_in__set__upd__eq__aux,axiom,
% 13.77/7.77 ! [I: nat,L: list_int,X: int,Y: int] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 13.77/7.77 => ( ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ! [Y4: int] : ( member_int @ X @ ( set_int2 @ ( list_update_int @ L @ I @ Y4 ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5652_in__set__upd__eq__aux,axiom,
% 13.77/7.77 ! [I: nat,L: list_set_nat,X: set_nat,Y: set_nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ L ) )
% 13.77/7.77 => ( ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ! [Y4: set_nat] : ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ L @ I @ Y4 ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5653_in__set__upd__eq__aux,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi,Y: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.77 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ! [Y4: vEBT_VEBTi] : ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ Y4 ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5654_in__set__upd__eq__aux,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.77 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ! [Y4: vEBT_VEBT] : ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ Y4 ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5655_in__set__upd__eq__aux,axiom,
% 13.77/7.77 ! [I: nat,L: list_real,X: real,Y: real] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 13.77/7.77 => ( ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ! [Y4: real] : ( member_real @ X @ ( set_real2 @ ( list_update_real @ L @ I @ Y4 ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5656_in__set__upd__eq__aux,axiom,
% 13.77/7.77 ! [I: nat,L: list_o,X: $o,Y: $o] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 13.77/7.77 => ( ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ! [Y4: $o] : ( member_o @ X @ ( set_o2 @ ( list_update_o @ L @ I @ Y4 ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5657_in__set__upd__eq__aux,axiom,
% 13.77/7.77 ! [I: nat,L: list_nat,X: nat,Y: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 13.77/7.77 => ( ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y ) ) )
% 13.77/7.77 = ( ( X = Y )
% 13.77/7.77 | ! [Y4: nat] : ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ L @ I @ Y4 ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5658_nth__list__update_H,axiom,
% 13.77/7.77 ! [I: nat,J: nat,L: list_int,X: int] :
% 13.77/7.77 ( ( ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 13.77/7.77 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ~ ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_int @ L ) ) )
% 13.77/7.77 => ( ( nth_int @ ( list_update_int @ L @ I @ X ) @ J )
% 13.77/7.77 = ( nth_int @ L @ J ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5659_nth__list__update_H,axiom,
% 13.77/7.77 ! [I: nat,J: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ~ ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) @ J )
% 13.77/7.77 = ( nth_VEBT_VEBTi @ L @ J ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5660_nth__list__update_H,axiom,
% 13.77/7.77 ! [I: nat,J: nat,L: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.77 ( ( ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ~ ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) ) )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) @ J )
% 13.77/7.77 = ( nth_VEBT_VEBT @ L @ J ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5661_nth__list__update_H,axiom,
% 13.77/7.77 ! [I: nat,J: nat,L: list_real,X: real] :
% 13.77/7.77 ( ( ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 13.77/7.77 => ( ( nth_real @ ( list_update_real @ L @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ~ ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_real @ L ) ) )
% 13.77/7.77 => ( ( nth_real @ ( list_update_real @ L @ I @ X ) @ J )
% 13.77/7.77 = ( nth_real @ L @ J ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5662_nth__list__update_H,axiom,
% 13.77/7.77 ! [L: list_o,I: nat,X: $o,J: nat] :
% 13.77/7.77 ( ( nth_o @ ( list_update_o @ L @ I @ X ) @ J )
% 13.77/7.77 = ( ( ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 13.77/7.77 => X )
% 13.77/7.77 & ( ~ ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_o @ L ) ) )
% 13.77/7.77 => ( nth_o @ L @ J ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5663_nth__list__update_H,axiom,
% 13.77/7.77 ! [I: nat,J: nat,L: list_nat,X: nat] :
% 13.77/7.77 ( ( ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 13.77/7.77 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ~ ( ( I = J )
% 13.77/7.77 & ( ord_less_nat @ I @ ( size_size_list_nat @ L ) ) )
% 13.77/7.77 => ( ( nth_nat @ ( list_update_nat @ L @ I @ X ) @ J )
% 13.77/7.77 = ( nth_nat @ L @ J ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5664_list__update__same__conv,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_int,X: int] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( ( list_update_int @ Xs @ I @ X )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ( nth_int @ Xs @ I )
% 13.77/7.77 = X ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5665_list__update__same__conv,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( ( list_u6098035379799741383_VEBTi @ Xs @ I @ X )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ( nth_VEBT_VEBTi @ Xs @ I )
% 13.77/7.77 = X ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5666_list__update__same__conv,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ( nth_VEBT_VEBT @ Xs @ I )
% 13.77/7.77 = X ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5667_list__update__same__conv,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_real,X: real] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( ( list_update_real @ Xs @ I @ X )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ( nth_real @ Xs @ I )
% 13.77/7.77 = X ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5668_list__update__same__conv,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_o,X: $o] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( ( list_update_o @ Xs @ I @ X )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ( nth_o @ Xs @ I )
% 13.77/7.77 = X ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5669_list__update__same__conv,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_nat,X: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( ( list_update_nat @ Xs @ I @ X )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ( nth_nat @ Xs @ I )
% 13.77/7.77 = X ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5670_nth__list__update,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_int,J: nat,X: int] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( ( I = J )
% 13.77/7.77 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ( I != J )
% 13.77/7.77 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 13.77/7.77 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5671_nth__list__update,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( ( I = J )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ( I != J )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ J )
% 13.77/7.77 = ( nth_VEBT_VEBTi @ Xs @ J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5672_nth__list__update,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( ( I = J )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ( I != J )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 13.77/7.77 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5673_nth__list__update,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_real,J: nat,X: real] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( ( I = J )
% 13.77/7.77 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ( I != J )
% 13.77/7.77 => ( ( nth_real @ ( list_update_real @ Xs @ I @ X ) @ J )
% 13.77/7.77 = ( nth_real @ Xs @ J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5674_nth__list__update,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_o,X: $o,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ J )
% 13.77/7.77 = ( ( ( I = J )
% 13.77/7.77 => X )
% 13.77/7.77 & ( ( I != J )
% 13.77/7.77 => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5675_nth__list__update,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( ( I = J )
% 13.77/7.77 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 13.77/7.77 = X ) )
% 13.77/7.77 & ( ( I != J )
% 13.77/7.77 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 13.77/7.77 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5676_set__update__subset__insert,axiom,
% 13.77/7.77 ! [Xs: list_nat,I: nat,X: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ ( insert_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5677_set__update__subset__insert,axiom,
% 13.77/7.77 ! [Xs: list_real,I: nat,X: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ ( insert_real @ X @ ( set_real2 @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5678_set__update__subset__insert,axiom,
% 13.77/7.77 ! [Xs: list_o,I: nat,X: $o] : ( ord_less_eq_set_o @ ( set_o2 @ ( list_update_o @ Xs @ I @ X ) ) @ ( insert_o @ X @ ( set_o2 @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5679_set__update__subset__insert,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] : ( ord_le6592769550269828683_VEBTi @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5680_set__update__subset__insert,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5681_set__update__subset__insert,axiom,
% 13.77/7.77 ! [Xs: list_int,I: nat,X: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ ( insert_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5682_sum_Oivl__cong,axiom,
% 13.77/7.77 ! [A: nat,C2: nat,B: nat,D: nat,G: nat > nat,H2: nat > nat] :
% 13.77/7.77 ( ( A = C2 )
% 13.77/7.77 => ( ( B = D )
% 13.77/7.77 => ( ! [X3: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ C2 @ X3 )
% 13.77/7.77 => ( ( ord_less_nat @ X3 @ D )
% 13.77/7.77 => ( ( G @ X3 )
% 13.77/7.77 = ( H2 @ X3 ) ) ) )
% 13.77/7.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 13.77/7.77 = ( groups3542108847815614940at_nat @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5683_sum_Oivl__cong,axiom,
% 13.77/7.77 ! [A: nat,C2: nat,B: nat,D: nat,G: nat > real,H2: nat > real] :
% 13.77/7.77 ( ( A = C2 )
% 13.77/7.77 => ( ( B = D )
% 13.77/7.77 => ( ! [X3: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ C2 @ X3 )
% 13.77/7.77 => ( ( ord_less_nat @ X3 @ D )
% 13.77/7.77 => ( ( G @ X3 )
% 13.77/7.77 = ( H2 @ X3 ) ) ) )
% 13.77/7.77 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 13.77/7.77 = ( groups6591440286371151544t_real @ H2 @ ( set_or4665077453230672383an_nat @ C2 @ D ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5684_sum_Oivl__cong,axiom,
% 13.77/7.77 ! [A: int,C2: int,B: int,D: int,G: int > int,H2: int > int] :
% 13.77/7.77 ( ( A = C2 )
% 13.77/7.77 => ( ( B = D )
% 13.77/7.77 => ( ! [X3: int] :
% 13.77/7.77 ( ( ord_less_eq_int @ C2 @ X3 )
% 13.77/7.77 => ( ( ord_less_int @ X3 @ D )
% 13.77/7.77 => ( ( G @ X3 )
% 13.77/7.77 = ( H2 @ X3 ) ) ) )
% 13.77/7.77 => ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 13.77/7.77 = ( groups4538972089207619220nt_int @ H2 @ ( set_or4662586982721622107an_int @ C2 @ D ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5685_sum_OatLeastLessThan__concat,axiom,
% 13.77/7.77 ! [M: nat,N: nat,P3: nat,G: nat > rat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( ord_less_eq_nat @ N @ P3 )
% 13.77/7.77 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 13.77/7.77 = ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5686_sum_OatLeastLessThan__concat,axiom,
% 13.77/7.77 ! [M: nat,N: nat,P3: nat,G: nat > int] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( ord_less_eq_nat @ N @ P3 )
% 13.77/7.77 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 13.77/7.77 = ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5687_sum_OatLeastLessThan__concat,axiom,
% 13.77/7.77 ! [M: nat,N: nat,P3: nat,G: nat > nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( ord_less_eq_nat @ N @ P3 )
% 13.77/7.77 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 13.77/7.77 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5688_sum_OatLeastLessThan__concat,axiom,
% 13.77/7.77 ! [M: nat,N: nat,P3: nat,G: nat > real] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( ord_less_eq_nat @ N @ P3 )
% 13.77/7.77 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) )
% 13.77/7.77 = ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5689_sum__diff__nat__ivl,axiom,
% 13.77/7.77 ! [M: nat,N: nat,P3: nat,F: nat > uint32] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( ord_less_eq_nat @ N @ P3 )
% 13.77/7.77 => ( ( minus_minus_uint32 @ ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 13.77/7.77 = ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5690_sum__diff__nat__ivl,axiom,
% 13.77/7.77 ! [M: nat,N: nat,P3: nat,F: nat > int] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( ord_less_eq_nat @ N @ P3 )
% 13.77/7.77 => ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 13.77/7.77 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5691_sum__diff__nat__ivl,axiom,
% 13.77/7.77 ! [M: nat,N: nat,P3: nat,F: nat > real] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( ord_less_eq_nat @ N @ P3 )
% 13.77/7.77 => ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ M @ N ) ) )
% 13.77/7.77 = ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ N @ P3 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5692_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5693_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5694_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5695_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBTi > assn,X1: real,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5696_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBT > assn,X1: real,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5697_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBTi > assn,X1: $o,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5698_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBT > assn,X1: $o,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5699_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBTi > assn,X1: nat,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5700_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBT > assn,X1: nat,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5701_subst__not__in,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5702_atLeast0__lessThan__Suc,axiom,
% 13.77/7.77 ! [N: nat] :
% 13.77/7.77 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 13.77/7.77 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5703_subset__eq__atLeast0__lessThan__card,axiom,
% 13.77/7.77 ! [N8: set_nat,N: nat] :
% 13.77/7.77 ( ( ord_less_eq_set_nat @ N8 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 13.77/7.77 => ( ord_less_eq_nat @ ( finite_card_nat @ N8 ) @ N ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5704_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X: vEBT_VEBTi,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5705_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,X: vEBT_VEBTi,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5706_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,X: vEBT_VEBT,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5707_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: real > vEBT_VEBTi > assn,X: real,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7851252805511451907_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5708_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: real > vEBT_VEBT > assn,X: real,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_real,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L3095048238742455910T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ ( list_update_real @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5709_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: $o > vEBT_VEBTi > assn,X: $o,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L6286945158656146733_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5710_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: $o > vEBT_VEBT > assn,X: $o,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_o,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L1319876754960170684T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ ( list_update_o @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5711_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: nat > vEBT_VEBTi > assn,X: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L7489483478785760935_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5712_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: nat > vEBT_VEBT > assn,X: nat,Xi: vEBT_VEBT,I5: set_nat,I: nat,Xs: list_nat,Xsi: list_VEBT_VEBT,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L8511957252848910786T_VEBT @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ ( list_update_nat @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5713_listI__assn__reinsert__upd_H,axiom,
% 13.77/7.77 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X: vEBT_VEBTi,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_Time_Heap_o,Q2: $o > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( A4 @ X @ Xi ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_hoare_triple_o @ ( times_times_assn @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5714_sum__shift__lb__Suc0__0__upt,axiom,
% 13.77/7.77 ! [F: nat > uint32,K: nat] :
% 13.77/7.77 ( ( ( F @ zero_zero_nat )
% 13.77/7.77 = zero_zero_uint32 )
% 13.77/7.77 => ( ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 13.77/7.77 = ( groups833757482993574392uint32 @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5715_sum__shift__lb__Suc0__0__upt,axiom,
% 13.77/7.77 ! [F: nat > rat,K: nat] :
% 13.77/7.77 ( ( ( F @ zero_zero_nat )
% 13.77/7.77 = zero_zero_rat )
% 13.77/7.77 => ( ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 13.77/7.77 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5716_sum__shift__lb__Suc0__0__upt,axiom,
% 13.77/7.77 ! [F: nat > int,K: nat] :
% 13.77/7.77 ( ( ( F @ zero_zero_nat )
% 13.77/7.77 = zero_zero_int )
% 13.77/7.77 => ( ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 13.77/7.77 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5717_sum__shift__lb__Suc0__0__upt,axiom,
% 13.77/7.77 ! [F: nat > nat,K: nat] :
% 13.77/7.77 ( ( ( F @ zero_zero_nat )
% 13.77/7.77 = zero_zero_nat )
% 13.77/7.77 => ( ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 13.77/7.77 = ( groups3542108847815614940at_nat @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5718_sum__shift__lb__Suc0__0__upt,axiom,
% 13.77/7.77 ! [F: nat > real,K: nat] :
% 13.77/7.77 ( ( ( F @ zero_zero_nat )
% 13.77/7.77 = zero_zero_real )
% 13.77/7.77 => ( ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 13.77/7.77 = ( groups6591440286371151544t_real @ F @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5719_sum_OatLeast0__lessThan__Suc,axiom,
% 13.77/7.77 ! [G: nat > rat,N: nat] :
% 13.77/7.77 ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5720_sum_OatLeast0__lessThan__Suc,axiom,
% 13.77/7.77 ! [G: nat > int,N: nat] :
% 13.77/7.77 ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5721_sum_OatLeast0__lessThan__Suc,axiom,
% 13.77/7.77 ! [G: nat > nat,N: nat] :
% 13.77/7.77 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5722_sum_OatLeast0__lessThan__Suc,axiom,
% 13.77/7.77 ! [G: nat > real,N: nat] :
% 13.77/7.77 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 13.77/7.77 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5723_sum_OatLeast__Suc__lessThan,axiom,
% 13.77/7.77 ! [M: nat,N: nat,G: nat > rat] :
% 13.77/7.77 ( ( ord_less_nat @ M @ N )
% 13.77/7.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.77 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5724_sum_OatLeast__Suc__lessThan,axiom,
% 13.77/7.77 ! [M: nat,N: nat,G: nat > int] :
% 13.77/7.77 ( ( ord_less_nat @ M @ N )
% 13.77/7.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.77 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5725_sum_OatLeast__Suc__lessThan,axiom,
% 13.77/7.77 ! [M: nat,N: nat,G: nat > nat] :
% 13.77/7.77 ( ( ord_less_nat @ M @ N )
% 13.77/7.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.77 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5726_sum_OatLeast__Suc__lessThan,axiom,
% 13.77/7.77 ! [M: nat,N: nat,G: nat > real] :
% 13.77/7.77 ( ( ord_less_nat @ M @ N )
% 13.77/7.77 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.77 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5727_sum_OatLeastLessThan__Suc,axiom,
% 13.77/7.77 ! [A: nat,B: nat,G: nat > rat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 13.77/7.77 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5728_sum_OatLeastLessThan__Suc,axiom,
% 13.77/7.77 ! [A: nat,B: nat,G: nat > int] :
% 13.77/7.77 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 13.77/7.77 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5729_sum_OatLeastLessThan__Suc,axiom,
% 13.77/7.77 ! [A: nat,B: nat,G: nat > nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 13.77/7.77 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5730_sum_OatLeastLessThan__Suc,axiom,
% 13.77/7.77 ! [A: nat,B: nat,G: nat > real] :
% 13.77/7.77 ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.77 => ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 13.77/7.77 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5731_atLeastLessThanSuc,axiom,
% 13.77/7.77 ! [M: nat,N: nat] :
% 13.77/7.77 ( ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 13.77/7.77 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 13.77/7.77 & ( ~ ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 13.77/7.77 = bot_bot_set_nat ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5732_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 13.77/7.77 ! [N: nat] :
% 13.77/7.77 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 13.77/7.77 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5733_insert__swap__set__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_int,X: int] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 13.77/7.77 => ( ( insert_int @ ( nth_int @ L @ I ) @ ( set_int2 @ ( list_update_int @ L @ I @ X ) ) )
% 13.77/7.77 = ( insert_int @ X @ ( set_int2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5734_insert__swap__set__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.77 => ( ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ L @ I ) @ ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) ) )
% 13.77/7.77 = ( insert_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5735_insert__swap__set__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.77 => ( ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ L @ I ) @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) ) )
% 13.77/7.77 = ( insert_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5736_insert__swap__set__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_real,X: real] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 13.77/7.77 => ( ( insert_real @ ( nth_real @ L @ I ) @ ( set_real2 @ ( list_update_real @ L @ I @ X ) ) )
% 13.77/7.77 = ( insert_real @ X @ ( set_real2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5737_insert__swap__set__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_o,X: $o] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 13.77/7.77 => ( ( insert_o @ ( nth_o @ L @ I ) @ ( set_o2 @ ( list_update_o @ L @ I @ X ) ) )
% 13.77/7.77 = ( insert_o @ X @ ( set_o2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5738_insert__swap__set__eq,axiom,
% 13.77/7.77 ! [I: nat,L: list_nat,X: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 13.77/7.77 => ( ( insert_nat @ ( nth_nat @ L @ I ) @ ( set_nat2 @ ( list_update_nat @ L @ I @ X ) ) )
% 13.77/7.77 = ( insert_nat @ X @ ( set_nat2 @ L ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5739_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBTi > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L886525131989349516_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L886525131989349516_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5740_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBTi,A4: vEBT_VEBTi > vEBT_VEBT > assn,X1: vEBT_VEBTi,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L2497118539674116125T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L2497118539674116125T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5741_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBT > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L3204528365124325536T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L3204528365124325536T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5742_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBTi > assn,X1: real,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L7851252805511451907_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L7851252805511451907_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5743_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_real,A4: real > vEBT_VEBT > assn,X1: real,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L3095048238742455910T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_real @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L3095048238742455910T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5744_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBTi > assn,X1: $o,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L6286945158656146733_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L6286945158656146733_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5745_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_o,A4: $o > vEBT_VEBT > assn,X1: $o,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L1319876754960170684T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_o @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L1319876754960170684T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5746_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBTi > assn,X1: nat,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L7489483478785760935_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L7489483478785760935_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5747_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_nat,A4: nat > vEBT_VEBT > assn,X1: nat,Xsi: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L8511957252848910786T_VEBT @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_update_nat @ Xs @ I @ X1 ) @ ( list_u1324408373059187874T_VEBT @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L8511957252848910786T_VEBT @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5748_listI__assn__subst,axiom,
% 13.77/7.77 ! [I: nat,I5: set_nat,Xs: list_VEBT_VEBT,A4: vEBT_VEBT > vEBT_VEBTi > assn,X1: vEBT_VEBT,Xsi: list_VEBT_VEBTi,X2: vEBT_VEBTi] :
% 13.77/7.77 ( ~ ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( vEBT_L1528199826722428489_VEBTi @ ( insert_nat @ I @ I5 ) @ A4 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X1 ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ X2 ) )
% 13.77/7.77 = ( times_times_assn @ ( A4 @ X1 @ X2 ) @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ A4 @ Xs @ Xsi ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5749_big__assn__simp_H,axiom,
% 13.77/7.77 ! [H2: nat,TreeList: list_VEBT_VEBT,Xaa: vEBT_VEBT,L: nat,X: vEBT_VEBTi,Xb: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( ( Xaa
% 13.77/7.77 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.77 => ( entails
% 13.77/7.77 @ ( times_times_assn
% 13.77/7.77 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ Xaa @ X )
% 13.77/7.77 @ ( pure_assn
% 13.77/7.77 @ ( Xb
% 13.77/7.77 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 13.77/7.77 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ H2 @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) )
% 13.77/7.77 @ ( times_times_assn
% 13.77/7.77 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 13.77/7.77 @ ( pure_assn
% 13.77/7.77 @ ( Xb
% 13.77/7.77 = ( vEBT_vebt_mint @ Xaa ) ) ) )
% 13.77/7.77 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Xaa ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5750_big__assn__simp,axiom,
% 13.77/7.77 ! [H2: nat,TreeList: list_VEBT_VEBT,L: nat,X: vEBT_VEBTi,Xaa: option_nat,X13: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,Summary: vEBT_VEBT,X14: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ H2 @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.77 => ( entails
% 13.77/7.77 @ ( times_times_assn
% 13.77/7.77 @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) @ X )
% 13.77/7.77 @ ( pure_assn
% 13.77/7.77 @ ( Xaa
% 13.77/7.77 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 13.77/7.77 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( insert_nat @ H2 @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) )
% 13.77/7.77 @ ( times_times_assn
% 13.77/7.77 @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ X13 @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) @ ( vEBT_vebt_assn_raw @ Summary @ X14 ) )
% 13.77/7.77 @ ( pure_assn
% 13.77/7.77 @ ( Xaa
% 13.77/7.77 = ( vEBT_vebt_mint @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) ) ) )
% 13.77/7.77 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( list_u6098035379799741383_VEBTi @ Tree_is @ H2 @ X ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5751_listI__assn__wrap__insert,axiom,
% 13.77/7.77 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5752_listI__assn__wrap__insert,axiom,
% 13.77/7.77 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_Time_Heap_o,Q2: $o > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_hoare_triple_o @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5753_listI__assn__wrap__insert,axiom,
% 13.77/7.77 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_T2636463487746394924on_nat,Q2: option_nat > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_7629718768684598413on_nat @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_7629718768684598413on_nat @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5754_listI__assn__wrap__insert,axiom,
% 13.77/7.77 ! [P2: assn,Uu2: vEBT_VEBT,Uua: nat,Xi: vEBT_VEBTi,I5: set_nat,I: nat,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBTi,F2: assn,C2: heap_Time_Heap_nat,Q2: nat > assn] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ ( times_times_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ Uu2 @ Uua ) @ Xi ) @ ( vEBT_L1528199826722428489_VEBTi @ ( minus_minus_set_nat @ I5 @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ vEBT_vebt_assn_raw @ Xs @ Xsi ) ) @ F2 ) )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( member_nat @ I @ I5 )
% 13.77/7.77 => ( ( hoare_3067605981109127869le_nat @ ( times_times_assn @ ( vEBT_L1528199826722428489_VEBTi @ I5 @ vEBT_vebt_assn_raw @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( vEBT_vebt_insert @ Uu2 @ Uua ) ) @ ( list_u6098035379799741383_VEBTi @ Xsi @ I @ Xi ) ) @ F2 ) @ C2 @ Q2 )
% 13.77/7.77 => ( hoare_3067605981109127869le_nat @ P2 @ C2 @ Q2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5755_set__update__distinct,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBTi,N: nat,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( distinct_VEBT_VEBTi @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( set_VEBT_VEBTi2 @ ( list_u6098035379799741383_VEBTi @ Xs @ N @ X ) )
% 13.77/7.77 = ( insert_VEBT_VEBTi @ X @ ( minus_3697805406911847364_VEBTi @ ( set_VEBT_VEBTi2 @ Xs ) @ ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N ) @ bot_bo8982466882572371071_VEBTi ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5756_set__update__distinct,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 13.77/7.77 ( ( distinct_VEBT_VEBT @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) )
% 13.77/7.77 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5757_set__update__distinct,axiom,
% 13.77/7.77 ! [Xs: list_real,N: nat,X: real] :
% 13.77/7.77 ( ( distinct_real @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( set_real2 @ ( list_update_real @ Xs @ N @ X ) )
% 13.77/7.77 = ( insert_real @ X @ ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ ( nth_real @ Xs @ N ) @ bot_bot_set_real ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5758_set__update__distinct,axiom,
% 13.77/7.77 ! [Xs: list_int,N: nat,X: int] :
% 13.77/7.77 ( ( distinct_int @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( set_int2 @ ( list_update_int @ Xs @ N @ X ) )
% 13.77/7.77 = ( insert_int @ X @ ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ ( nth_int @ Xs @ N ) @ bot_bot_set_int ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5759_set__update__distinct,axiom,
% 13.77/7.77 ! [Xs: list_o,N: nat,X: $o] :
% 13.77/7.77 ( ( distinct_o @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( set_o2 @ ( list_update_o @ Xs @ N @ X ) )
% 13.77/7.77 = ( insert_o @ X @ ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ ( nth_o @ Xs @ N ) @ bot_bot_set_o ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5760_set__update__distinct,axiom,
% 13.77/7.77 ! [Xs: list_nat,N: nat,X: nat] :
% 13.77/7.77 ( ( distinct_nat @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) )
% 13.77/7.77 = ( insert_nat @ X @ ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ ( nth_nat @ Xs @ N ) @ bot_bot_set_nat ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5761_hoare__triple__preI,axiom,
% 13.77/7.77 ! [P2: assn,C2: heap_T8145700208782473153_VEBTi,Q2: vEBT_VEBTi > assn] :
% 13.77/7.77 ( ! [H: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) )
% 13.77/7.77 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2 @ Q2 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5762_hoare__triple__preI,axiom,
% 13.77/7.77 ! [P2: assn,C2: heap_Time_Heap_o,Q2: $o > assn] :
% 13.77/7.77 ( ! [H: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H )
% 13.77/7.77 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) )
% 13.77/7.77 => ( hoare_hoare_triple_o @ P2 @ C2 @ Q2 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5763_hoare__triple__preI,axiom,
% 13.77/7.77 ! [P2: assn,C2: heap_T2636463487746394924on_nat,Q2: option_nat > assn] :
% 13.77/7.77 ( ! [H: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H )
% 13.77/7.77 => ( hoare_7629718768684598413on_nat @ P2 @ C2 @ Q2 ) )
% 13.77/7.77 => ( hoare_7629718768684598413on_nat @ P2 @ C2 @ Q2 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5764_hoare__triple__preI,axiom,
% 13.77/7.77 ! [P2: assn,C2: heap_Time_Heap_nat,Q2: nat > assn] :
% 13.77/7.77 ( ! [H: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H )
% 13.77/7.77 => ( hoare_3067605981109127869le_nat @ P2 @ C2 @ Q2 ) )
% 13.77/7.77 => ( hoare_3067605981109127869le_nat @ P2 @ C2 @ Q2 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5765_nth__image,axiom,
% 13.77/7.77 ! [L: nat,Xs: list_VEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_eq_nat @ L @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( image_nat_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 13.77/7.77 = ( set_VEBT_VEBTi2 @ ( take_VEBT_VEBTi @ L @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5766_nth__image,axiom,
% 13.77/7.77 ! [L: nat,Xs: list_set_nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ L @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.77 => ( ( image_nat_set_nat @ ( nth_set_nat @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 13.77/7.77 = ( set_set_nat2 @ ( take_set_nat @ L @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5767_nth__image,axiom,
% 13.77/7.77 ! [L: nat,Xs: list_int] :
% 13.77/7.77 ( ( ord_less_eq_nat @ L @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( image_nat_int @ ( nth_int @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 13.77/7.77 = ( set_int2 @ ( take_int @ L @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5768_nth__image,axiom,
% 13.77/7.77 ! [L: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_eq_nat @ L @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( image_nat_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 13.77/7.77 = ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ L @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5769_nth__image,axiom,
% 13.77/7.77 ! [L: nat,Xs: list_real] :
% 13.77/7.77 ( ( ord_less_eq_nat @ L @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( image_nat_real @ ( nth_real @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 13.77/7.77 = ( set_real2 @ ( take_real @ L @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5770_nth__image,axiom,
% 13.77/7.77 ! [L: nat,Xs: list_o] :
% 13.77/7.77 ( ( ord_less_eq_nat @ L @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( image_nat_o @ ( nth_o @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 13.77/7.77 = ( set_o2 @ ( take_o @ L @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5771_nth__image,axiom,
% 13.77/7.77 ! [L: nat,Xs: list_nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ L @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( image_nat_nat @ ( nth_nat @ Xs ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ L ) )
% 13.77/7.77 = ( set_nat2 @ ( take_nat @ L @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5772_pure__assn__eq__conv,axiom,
% 13.77/7.77 ! [P2: $o,Q2: $o] :
% 13.77/7.77 ( ( ( pure_assn @ P2 )
% 13.77/7.77 = ( pure_assn @ Q2 ) )
% 13.77/7.77 = ( P2 = Q2 ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5773_merge__pure__star,axiom,
% 13.77/7.77 ! [A: $o,B: $o] :
% 13.77/7.77 ( ( times_times_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 13.77/7.77 = ( pure_assn
% 13.77/7.77 @ ( A
% 13.77/7.77 & B ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5774_take__update,axiom,
% 13.77/7.77 ! [N: nat,L: list_nat,I: nat,X: nat] :
% 13.77/7.77 ( ( take_nat @ N @ ( list_update_nat @ L @ I @ X ) )
% 13.77/7.77 = ( list_update_nat @ ( take_nat @ N @ L ) @ I @ X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5775_take__update,axiom,
% 13.77/7.77 ! [N: nat,L: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 13.77/7.77 ( ( take_VEBT_VEBTi @ N @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) )
% 13.77/7.77 = ( list_u6098035379799741383_VEBTi @ ( take_VEBT_VEBTi @ N @ L ) @ I @ X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5776_take__update,axiom,
% 13.77/7.77 ! [N: nat,L: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 13.77/7.77 ( ( take_VEBT_VEBT @ N @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) )
% 13.77/7.77 = ( list_u1324408373059187874T_VEBT @ ( take_VEBT_VEBT @ N @ L ) @ I @ X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5777_pure__assn__eq__emp__iff,axiom,
% 13.77/7.77 ! [P2: $o] :
% 13.77/7.77 ( ( ( pure_assn @ P2 )
% 13.77/7.77 = one_one_assn )
% 13.77/7.77 = P2 ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5778_pure__true,axiom,
% 13.77/7.77 ( ( pure_assn @ $true )
% 13.77/7.77 = one_one_assn ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5779_pure__false,axiom,
% 13.77/7.77 ( ( pure_assn @ $false )
% 13.77/7.77 = bot_bot_assn ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5780_pure__assn__eq__false__iff,axiom,
% 13.77/7.77 ! [P2: $o] :
% 13.77/7.77 ( ( ( pure_assn @ P2 )
% 13.77/7.77 = bot_bot_assn )
% 13.77/7.77 = ~ P2 ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5781_take__Suc__Cons,axiom,
% 13.77/7.77 ! [N: nat,X: int,Xs: list_int] :
% 13.77/7.77 ( ( take_int @ ( suc @ N ) @ ( cons_int @ X @ Xs ) )
% 13.77/7.77 = ( cons_int @ X @ ( take_int @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5782_take__Suc__Cons,axiom,
% 13.77/7.77 ! [N: nat,X: nat,Xs: list_nat] :
% 13.77/7.77 ( ( take_nat @ ( suc @ N ) @ ( cons_nat @ X @ Xs ) )
% 13.77/7.77 = ( cons_nat @ X @ ( take_nat @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5783_take__Suc__Cons,axiom,
% 13.77/7.77 ! [N: nat,X: $o,Xs: list_o] :
% 13.77/7.77 ( ( take_o @ ( suc @ N ) @ ( cons_o @ X @ Xs ) )
% 13.77/7.77 = ( cons_o @ X @ ( take_o @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5784_take__all,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBT,N: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N )
% 13.77/7.77 => ( ( take_VEBT_VEBT @ N @ Xs )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5785_take__all,axiom,
% 13.77/7.77 ! [Xs: list_real,N: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N )
% 13.77/7.77 => ( ( take_real @ N @ Xs )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5786_take__all,axiom,
% 13.77/7.77 ! [Xs: list_o,N: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N )
% 13.77/7.77 => ( ( take_o @ N @ Xs )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5787_take__all,axiom,
% 13.77/7.77 ! [Xs: list_nat,N: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N )
% 13.77/7.77 => ( ( take_nat @ N @ Xs )
% 13.77/7.77 = Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5788_take__all__iff,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.77 ( ( ( take_VEBT_VEBT @ N @ Xs )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5789_take__all__iff,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_real] :
% 13.77/7.77 ( ( ( take_real @ N @ Xs )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ord_less_eq_nat @ ( size_size_list_real @ Xs ) @ N ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5790_take__all__iff,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_o] :
% 13.77/7.77 ( ( ( take_o @ N @ Xs )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5791_take__all__iff,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_nat] :
% 13.77/7.77 ( ( ( take_nat @ N @ Xs )
% 13.77/7.77 = Xs )
% 13.77/7.77 = ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5792_nth__take,axiom,
% 13.77/7.77 ! [I: nat,N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_nat @ I @ N )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ Xs ) @ I )
% 13.77/7.77 = ( nth_VEBT_VEBT @ Xs @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5793_nth__take,axiom,
% 13.77/7.77 ! [I: nat,N: nat,Xs: list_VEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_nat @ I @ N )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ ( take_VEBT_VEBTi @ N @ Xs ) @ I )
% 13.77/7.77 = ( nth_VEBT_VEBTi @ Xs @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5794_nth__take,axiom,
% 13.77/7.77 ! [I: nat,N: nat,Xs: list_int] :
% 13.77/7.77 ( ( ord_less_nat @ I @ N )
% 13.77/7.77 => ( ( nth_int @ ( take_int @ N @ Xs ) @ I )
% 13.77/7.77 = ( nth_int @ Xs @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5795_nth__take,axiom,
% 13.77/7.77 ! [I: nat,N: nat,Xs: list_nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ N )
% 13.77/7.77 => ( ( nth_nat @ ( take_nat @ N @ Xs ) @ I )
% 13.77/7.77 = ( nth_nat @ Xs @ I ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5796_take__update__cancel,axiom,
% 13.77/7.77 ! [N: nat,M: nat,Xs: list_nat,Y: nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.77 => ( ( take_nat @ N @ ( list_update_nat @ Xs @ M @ Y ) )
% 13.77/7.77 = ( take_nat @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5797_take__update__cancel,axiom,
% 13.77/7.77 ! [N: nat,M: nat,Xs: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.77 => ( ( take_VEBT_VEBTi @ N @ ( list_u6098035379799741383_VEBTi @ Xs @ M @ Y ) )
% 13.77/7.77 = ( take_VEBT_VEBTi @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5798_take__update__cancel,axiom,
% 13.77/7.77 ! [N: nat,M: nat,Xs: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.77 => ( ( take_VEBT_VEBT @ N @ ( list_u1324408373059187874T_VEBT @ Xs @ M @ Y ) )
% 13.77/7.77 = ( take_VEBT_VEBT @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5799_ent__pure__pre__iff,axiom,
% 13.77/7.77 ! [P2: assn,B: $o,Q2: assn] :
% 13.77/7.77 ( ( entails @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ Q2 )
% 13.77/7.77 = ( B
% 13.77/7.77 => ( entails @ P2 @ Q2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5800_mod__pure__star__dist,axiom,
% 13.77/7.77 ! [P2: assn,B: $o,H2: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ ( times_times_assn @ P2 @ ( pure_assn @ B ) ) @ H2 )
% 13.77/7.77 = ( ( rep_assn @ P2 @ H2 )
% 13.77/7.77 & B ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5801_ent__pure__pre__iff__sng,axiom,
% 13.77/7.77 ! [B: $o,Q2: assn] :
% 13.77/7.77 ( ( entails @ ( pure_assn @ B ) @ Q2 )
% 13.77/7.77 = ( B
% 13.77/7.77 => ( entails @ one_one_assn @ Q2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5802_ent__pure__post__iff,axiom,
% 13.77/7.77 ! [P2: assn,Q2: assn,B: $o] :
% 13.77/7.77 ( ( entails @ P2 @ ( times_times_assn @ Q2 @ ( pure_assn @ B ) ) )
% 13.77/7.77 = ( ! [H4: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H4 )
% 13.77/7.77 => B )
% 13.77/7.77 & ( entails @ P2 @ Q2 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5803_mod__h__bot__iff_I1_J,axiom,
% 13.77/7.77 ! [B: $o,H2: heap_e7401611519738050253t_unit] :
% 13.77/7.77 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.77/7.77 = B ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5804_ent__pure__post__iff__sng,axiom,
% 13.77/7.77 ! [P2: assn,B: $o] :
% 13.77/7.77 ( ( entails @ P2 @ ( pure_assn @ B ) )
% 13.77/7.77 = ( ! [H4: produc3658429121746597890et_nat] :
% 13.77/7.77 ( ( rep_assn @ P2 @ H4 )
% 13.77/7.77 => B )
% 13.77/7.77 & ( entails @ P2 @ one_one_assn ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5805_distinct__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_int,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( distinct_int @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 13.77/7.77 = ( distinct_int @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5806_distinct__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBTi,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( distinct_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ ( nth_VEBT_VEBTi @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBTi @ Xs @ I ) ) )
% 13.77/7.77 = ( distinct_VEBT_VEBTi @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5807_distinct__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 13.77/7.77 = ( distinct_VEBT_VEBT @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5808_distinct__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_real,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( distinct_real @ ( list_update_real @ ( list_update_real @ Xs @ I @ ( nth_real @ Xs @ J ) ) @ J @ ( nth_real @ Xs @ I ) ) )
% 13.77/7.77 = ( distinct_real @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5809_distinct__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_o,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( distinct_o @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 13.77/7.77 = ( distinct_o @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5810_distinct__swap,axiom,
% 13.77/7.77 ! [I: nat,Xs: list_nat,J: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 13.77/7.77 = ( distinct_nat @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5811_VEBT__internal_OperInsTrans_Ointros_I2_J,axiom,
% 13.77/7.77 ! [T: vEBT_VEBT,S: vEBT_VEBT,X: nat,U: vEBT_VEBT] :
% 13.77/7.77 ( ( T
% 13.77/7.77 = ( vEBT_vebt_insert @ S @ X ) )
% 13.77/7.77 => ( ( vEBT_V6289311342943941716sTrans @ T @ U )
% 13.77/7.77 => ( vEBT_V6289311342943941716sTrans @ S @ U ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5812_VEBT__internal_OperInsTrans_Ocases,axiom,
% 13.77/7.77 ! [A12: vEBT_VEBT,A23: vEBT_VEBT] :
% 13.77/7.77 ( ( vEBT_V6289311342943941716sTrans @ A12 @ A23 )
% 13.77/7.77 => ( ( A23 != A12 )
% 13.77/7.77 => ~ ! [T6: vEBT_VEBT] :
% 13.77/7.77 ( ? [X3: nat] :
% 13.77/7.77 ( T6
% 13.77/7.77 = ( vEBT_vebt_insert @ A12 @ X3 ) )
% 13.77/7.77 => ~ ( vEBT_V6289311342943941716sTrans @ T6 @ A23 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5813_VEBT__internal_OperInsTrans_Osimps,axiom,
% 13.77/7.77 ( vEBT_V6289311342943941716sTrans
% 13.77/7.77 = ( ^ [A13: vEBT_VEBT,A24: vEBT_VEBT] :
% 13.77/7.77 ( ? [T2: vEBT_VEBT] :
% 13.77/7.77 ( ( A13 = T2 )
% 13.77/7.77 & ( A24 = T2 ) )
% 13.77/7.77 | ? [T2: vEBT_VEBT,S8: vEBT_VEBT,X4: nat,U2: vEBT_VEBT] :
% 13.77/7.77 ( ( A13 = S8 )
% 13.77/7.77 & ( A24 = U2 )
% 13.77/7.77 & ( T2
% 13.77/7.77 = ( vEBT_vebt_insert @ S8 @ X4 ) )
% 13.77/7.77 & ( vEBT_V6289311342943941716sTrans @ T2 @ U2 ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5814_set__take__subset,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_VEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ N @ Xs ) ) @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5815_set__take__subset,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( take_nat @ N @ Xs ) ) @ ( set_nat2 @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5816_set__take__subset,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_real] : ( ord_less_eq_set_real @ ( set_real2 @ ( take_real @ N @ Xs ) ) @ ( set_real2 @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5817_set__take__subset,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_o] : ( ord_less_eq_set_o @ ( set_o2 @ ( take_o @ N @ Xs ) ) @ ( set_o2 @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5818_set__take__subset,axiom,
% 13.77/7.77 ! [N: nat,Xs: list_int] : ( ord_less_eq_set_int @ ( set_int2 @ ( take_int @ N @ Xs ) ) @ ( set_int2 @ Xs ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5819_sorted__take,axiom,
% 13.77/7.77 ! [Xs: list_rat,N: nat] :
% 13.77/7.77 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.77 => ( sorted_wrt_rat @ ord_less_eq_rat @ ( take_rat @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5820_sorted__take,axiom,
% 13.77/7.77 ! [Xs: list_num,N: nat] :
% 13.77/7.77 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.77 => ( sorted_wrt_num @ ord_less_eq_num @ ( take_num @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5821_sorted__take,axiom,
% 13.77/7.77 ! [Xs: list_nat,N: nat] :
% 13.77/7.77 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.77 => ( sorted_wrt_nat @ ord_less_eq_nat @ ( take_nat @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5822_sorted__take,axiom,
% 13.77/7.77 ! [Xs: list_int,N: nat] :
% 13.77/7.77 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.77 => ( sorted_wrt_int @ ord_less_eq_int @ ( take_int @ N @ Xs ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5823_finite__distinct__list,axiom,
% 13.77/7.77 ! [A4: set_VEBT_VEBT] :
% 13.77/7.77 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.77 => ? [Xs3: list_VEBT_VEBT] :
% 13.77/7.77 ( ( ( set_VEBT_VEBT2 @ Xs3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( distinct_VEBT_VEBT @ Xs3 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5824_finite__distinct__list,axiom,
% 13.77/7.77 ! [A4: set_real] :
% 13.77/7.77 ( ( finite_finite_real @ A4 )
% 13.77/7.77 => ? [Xs3: list_real] :
% 13.77/7.77 ( ( ( set_real2 @ Xs3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( distinct_real @ Xs3 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5825_finite__distinct__list,axiom,
% 13.77/7.77 ! [A4: set_o] :
% 13.77/7.77 ( ( finite_finite_o @ A4 )
% 13.77/7.77 => ? [Xs3: list_o] :
% 13.77/7.77 ( ( ( set_o2 @ Xs3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( distinct_o @ Xs3 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5826_finite__distinct__list,axiom,
% 13.77/7.77 ! [A4: set_nat] :
% 13.77/7.77 ( ( finite_finite_nat @ A4 )
% 13.77/7.77 => ? [Xs3: list_nat] :
% 13.77/7.77 ( ( ( set_nat2 @ Xs3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( distinct_nat @ Xs3 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5827_finite__distinct__list,axiom,
% 13.77/7.77 ! [A4: set_int] :
% 13.77/7.77 ( ( finite_finite_int @ A4 )
% 13.77/7.77 => ? [Xs3: list_int] :
% 13.77/7.77 ( ( ( set_int2 @ Xs3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( distinct_int @ Xs3 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5828_finite__distinct__list,axiom,
% 13.77/7.77 ! [A4: set_complex] :
% 13.77/7.77 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.77 => ? [Xs3: list_complex] :
% 13.77/7.77 ( ( ( set_complex2 @ Xs3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( distinct_complex @ Xs3 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5829_finite__distinct__list,axiom,
% 13.77/7.77 ! [A4: set_Code_integer] :
% 13.77/7.77 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.77 => ? [Xs3: list_Code_integer] :
% 13.77/7.77 ( ( ( set_Code_integer2 @ Xs3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( distin1543349897113766820nteger @ Xs3 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5830_finite__set__image,axiom,
% 13.77/7.77 ! [A4: set_list_VEBT_VEBT] :
% 13.77/7.77 ( ( finite9070685783930458813T_VEBT @ ( image_6463372868993444447T_VEBT @ set_VEBT_VEBT2 @ A4 ) )
% 13.77/7.77 => ( ! [Xs3: list_VEBT_VEBT] :
% 13.77/7.77 ( ( member2936631157270082147T_VEBT @ Xs3 @ A4 )
% 13.77/7.77 => ( distinct_VEBT_VEBT @ Xs3 ) )
% 13.77/7.77 => ( finite3004134309566078307T_VEBT @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5831_finite__set__image,axiom,
% 13.77/7.77 ! [A4: set_list_nat] :
% 13.77/7.77 ( ( finite1152437895449049373et_nat @ ( image_1775855109352712557et_nat @ set_nat2 @ A4 ) )
% 13.77/7.77 => ( ! [Xs3: list_nat] :
% 13.77/7.77 ( ( member_list_nat @ Xs3 @ A4 )
% 13.77/7.77 => ( distinct_nat @ Xs3 ) )
% 13.77/7.77 => ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5832_finite__set__image,axiom,
% 13.77/7.77 ! [A4: set_list_real] :
% 13.77/7.77 ( ( finite9007344921179782393t_real @ ( image_6239767680843085477t_real @ set_real2 @ A4 ) )
% 13.77/7.77 => ( ! [Xs3: list_real] :
% 13.77/7.77 ( ( member_list_real @ Xs3 @ A4 )
% 13.77/7.77 => ( distinct_real @ Xs3 ) )
% 13.77/7.77 => ( finite306553202115118035t_real @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5833_finite__set__image,axiom,
% 13.77/7.77 ! [A4: set_list_o] :
% 13.77/7.77 ( ( finite_finite_set_o @ ( image_list_o_set_o @ set_o2 @ A4 ) )
% 13.77/7.77 => ( ! [Xs3: list_o] :
% 13.77/7.77 ( ( member_list_o @ Xs3 @ A4 )
% 13.77/7.77 => ( distinct_o @ Xs3 ) )
% 13.77/7.77 => ( finite_finite_list_o @ A4 ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5834_set__take__subset__set__take,axiom,
% 13.77/7.77 ! [M: nat,N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ M @ Xs ) ) @ ( set_VEBT_VEBT2 @ ( take_VEBT_VEBT @ N @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5835_set__take__subset__set__take,axiom,
% 13.77/7.77 ! [M: nat,N: nat,Xs: list_nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( take_nat @ M @ Xs ) ) @ ( set_nat2 @ ( take_nat @ N @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5836_set__take__subset__set__take,axiom,
% 13.77/7.77 ! [M: nat,N: nat,Xs: list_real] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ord_less_eq_set_real @ ( set_real2 @ ( take_real @ M @ Xs ) ) @ ( set_real2 @ ( take_real @ N @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5837_set__take__subset__set__take,axiom,
% 13.77/7.77 ! [M: nat,N: nat,Xs: list_o] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ord_less_eq_set_o @ ( set_o2 @ ( take_o @ M @ Xs ) ) @ ( set_o2 @ ( take_o @ N @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5838_set__take__subset__set__take,axiom,
% 13.77/7.77 ! [M: nat,N: nat,Xs: list_int] :
% 13.77/7.77 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.77 => ( ord_less_eq_set_int @ ( set_int2 @ ( take_int @ M @ Xs ) ) @ ( set_int2 @ ( take_int @ N @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5839_strict__sorted__iff,axiom,
% 13.77/7.77 ! [L: list_real] :
% 13.77/7.77 ( ( sorted_wrt_real @ ord_less_real @ L )
% 13.77/7.77 = ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 13.77/7.77 & ( distinct_real @ L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5840_strict__sorted__iff,axiom,
% 13.77/7.77 ! [L: list_rat] :
% 13.77/7.77 ( ( sorted_wrt_rat @ ord_less_rat @ L )
% 13.77/7.77 = ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 13.77/7.77 & ( distinct_rat @ L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5841_strict__sorted__iff,axiom,
% 13.77/7.77 ! [L: list_num] :
% 13.77/7.77 ( ( sorted_wrt_num @ ord_less_num @ L )
% 13.77/7.77 = ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 13.77/7.77 & ( distinct_num @ L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5842_strict__sorted__iff,axiom,
% 13.77/7.77 ! [L: list_nat] :
% 13.77/7.77 ( ( sorted_wrt_nat @ ord_less_nat @ L )
% 13.77/7.77 = ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 13.77/7.77 & ( distinct_nat @ L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5843_strict__sorted__iff,axiom,
% 13.77/7.77 ! [L: list_int] :
% 13.77/7.77 ( ( sorted_wrt_int @ ord_less_int @ L )
% 13.77/7.77 = ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 13.77/7.77 & ( distinct_int @ L ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5844_distinct__conv__nth,axiom,
% 13.77/7.77 ( distinct_VEBT_VEBTi
% 13.77/7.77 = ( ^ [Xs2: list_VEBT_VEBTi] :
% 13.77/7.77 ! [I3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 13.77/7.77 => ! [J3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ J3 @ ( size_s7982070591426661849_VEBTi @ Xs2 ) )
% 13.77/7.77 => ( ( I3 != J3 )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ Xs2 @ I3 )
% 13.77/7.77 != ( nth_VEBT_VEBTi @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5845_distinct__conv__nth,axiom,
% 13.77/7.77 ( distinct_int
% 13.77/7.77 = ( ^ [Xs2: list_int] :
% 13.77/7.77 ! [I3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 13.77/7.77 => ! [J3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs2 ) )
% 13.77/7.77 => ( ( I3 != J3 )
% 13.77/7.77 => ( ( nth_int @ Xs2 @ I3 )
% 13.77/7.77 != ( nth_int @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5846_distinct__conv__nth,axiom,
% 13.77/7.77 ( distinct_VEBT_VEBT
% 13.77/7.77 = ( ^ [Xs2: list_VEBT_VEBT] :
% 13.77/7.77 ! [I3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 13.77/7.77 => ! [J3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ J3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 13.77/7.77 => ( ( I3 != J3 )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 13.77/7.77 != ( nth_VEBT_VEBT @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5847_distinct__conv__nth,axiom,
% 13.77/7.77 ( distinct_real
% 13.77/7.77 = ( ^ [Xs2: list_real] :
% 13.77/7.77 ! [I3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 13.77/7.77 => ! [J3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ J3 @ ( size_size_list_real @ Xs2 ) )
% 13.77/7.77 => ( ( I3 != J3 )
% 13.77/7.77 => ( ( nth_real @ Xs2 @ I3 )
% 13.77/7.77 != ( nth_real @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5848_distinct__conv__nth,axiom,
% 13.77/7.77 ( distinct_o
% 13.77/7.77 = ( ^ [Xs2: list_o] :
% 13.77/7.77 ! [I3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 13.77/7.77 => ! [J3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs2 ) )
% 13.77/7.77 => ( ( I3 != J3 )
% 13.77/7.77 => ( ( nth_o @ Xs2 @ I3 )
% 13.77/7.77 != ( nth_o @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5849_distinct__conv__nth,axiom,
% 13.77/7.77 ( distinct_nat
% 13.77/7.77 = ( ^ [Xs2: list_nat] :
% 13.77/7.77 ! [I3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 13.77/7.77 => ! [J3: nat] :
% 13.77/7.77 ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs2 ) )
% 13.77/7.77 => ( ( I3 != J3 )
% 13.77/7.77 => ( ( nth_nat @ Xs2 @ I3 )
% 13.77/7.77 != ( nth_nat @ Xs2 @ J3 ) ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5850_nth__eq__iff__index__eq,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBTi,I: nat,J: nat] :
% 13.77/7.77 ( ( distinct_VEBT_VEBTi @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( ( nth_VEBT_VEBTi @ Xs @ I )
% 13.77/7.77 = ( nth_VEBT_VEBTi @ Xs @ J ) )
% 13.77/7.77 = ( I = J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5851_nth__eq__iff__index__eq,axiom,
% 13.77/7.77 ! [Xs: list_int,I: nat,J: nat] :
% 13.77/7.77 ( ( distinct_int @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( ( nth_int @ Xs @ I )
% 13.77/7.77 = ( nth_int @ Xs @ J ) )
% 13.77/7.77 = ( I = J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5852_nth__eq__iff__index__eq,axiom,
% 13.77/7.77 ! [Xs: list_VEBT_VEBT,I: nat,J: nat] :
% 13.77/7.77 ( ( distinct_VEBT_VEBT @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( ( nth_VEBT_VEBT @ Xs @ I )
% 13.77/7.77 = ( nth_VEBT_VEBT @ Xs @ J ) )
% 13.77/7.77 = ( I = J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5853_nth__eq__iff__index__eq,axiom,
% 13.77/7.77 ! [Xs: list_real,I: nat,J: nat] :
% 13.77/7.77 ( ( distinct_real @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( ( nth_real @ Xs @ I )
% 13.77/7.77 = ( nth_real @ Xs @ J ) )
% 13.77/7.77 = ( I = J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5854_nth__eq__iff__index__eq,axiom,
% 13.77/7.77 ! [Xs: list_o,I: nat,J: nat] :
% 13.77/7.77 ( ( distinct_o @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( ( nth_o @ Xs @ I )
% 13.77/7.77 = ( nth_o @ Xs @ J ) )
% 13.77/7.77 = ( I = J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5855_nth__eq__iff__index__eq,axiom,
% 13.77/7.77 ! [Xs: list_nat,I: nat,J: nat] :
% 13.77/7.77 ( ( distinct_nat @ Xs )
% 13.77/7.77 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( ( nth_nat @ Xs @ I )
% 13.77/7.77 = ( nth_nat @ Xs @ J ) )
% 13.77/7.77 = ( I = J ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5856_distinct__length__le,axiom,
% 13.77/7.77 ! [Ys: list_VEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.77 ( ( distinct_VEBT_VEBT @ Ys )
% 13.77/7.77 => ( ( ( set_VEBT_VEBT2 @ Ys )
% 13.77/7.77 = ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.77 => ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Ys ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5857_distinct__length__le,axiom,
% 13.77/7.77 ! [Ys: list_real,Xs: list_real] :
% 13.77/7.77 ( ( distinct_real @ Ys )
% 13.77/7.77 => ( ( ( set_real2 @ Ys )
% 13.77/7.77 = ( set_real2 @ Xs ) )
% 13.77/7.77 => ( ord_less_eq_nat @ ( size_size_list_real @ Ys ) @ ( size_size_list_real @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5858_distinct__length__le,axiom,
% 13.77/7.77 ! [Ys: list_o,Xs: list_o] :
% 13.77/7.77 ( ( distinct_o @ Ys )
% 13.77/7.77 => ( ( ( set_o2 @ Ys )
% 13.77/7.77 = ( set_o2 @ Xs ) )
% 13.77/7.77 => ( ord_less_eq_nat @ ( size_size_list_o @ Ys ) @ ( size_size_list_o @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5859_distinct__length__le,axiom,
% 13.77/7.77 ! [Ys: list_nat,Xs: list_nat] :
% 13.77/7.77 ( ( distinct_nat @ Ys )
% 13.77/7.77 => ( ( ( set_nat2 @ Ys )
% 13.77/7.77 = ( set_nat2 @ Xs ) )
% 13.77/7.77 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5860_sorted__distinct__set__unique,axiom,
% 13.77/7.77 ! [Xs: list_real,Ys: list_real] :
% 13.77/7.77 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 13.77/7.77 => ( ( distinct_real @ Xs )
% 13.77/7.77 => ( ( sorted_wrt_real @ ord_less_eq_real @ Ys )
% 13.77/7.77 => ( ( distinct_real @ Ys )
% 13.77/7.77 => ( ( ( set_real2 @ Xs )
% 13.77/7.77 = ( set_real2 @ Ys ) )
% 13.77/7.77 => ( Xs = Ys ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5861_sorted__distinct__set__unique,axiom,
% 13.77/7.77 ! [Xs: list_o,Ys: list_o] :
% 13.77/7.77 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 13.77/7.77 => ( ( distinct_o @ Xs )
% 13.77/7.77 => ( ( sorted_wrt_o @ ord_less_eq_o @ Ys )
% 13.77/7.77 => ( ( distinct_o @ Ys )
% 13.77/7.77 => ( ( ( set_o2 @ Xs )
% 13.77/7.77 = ( set_o2 @ Ys ) )
% 13.77/7.77 => ( Xs = Ys ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5862_sorted__distinct__set__unique,axiom,
% 13.77/7.77 ! [Xs: list_rat,Ys: list_rat] :
% 13.77/7.77 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.77 => ( ( distinct_rat @ Xs )
% 13.77/7.77 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ Ys )
% 13.77/7.77 => ( ( distinct_rat @ Ys )
% 13.77/7.77 => ( ( ( set_rat2 @ Xs )
% 13.77/7.77 = ( set_rat2 @ Ys ) )
% 13.77/7.77 => ( Xs = Ys ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5863_sorted__distinct__set__unique,axiom,
% 13.77/7.77 ! [Xs: list_num,Ys: list_num] :
% 13.77/7.77 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.77 => ( ( distinct_num @ Xs )
% 13.77/7.77 => ( ( sorted_wrt_num @ ord_less_eq_num @ Ys )
% 13.77/7.77 => ( ( distinct_num @ Ys )
% 13.77/7.77 => ( ( ( set_num2 @ Xs )
% 13.77/7.77 = ( set_num2 @ Ys ) )
% 13.77/7.77 => ( Xs = Ys ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5864_sorted__distinct__set__unique,axiom,
% 13.77/7.77 ! [Xs: list_nat,Ys: list_nat] :
% 13.77/7.77 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.77 => ( ( distinct_nat @ Xs )
% 13.77/7.77 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ Ys )
% 13.77/7.77 => ( ( distinct_nat @ Ys )
% 13.77/7.77 => ( ( ( set_nat2 @ Xs )
% 13.77/7.77 = ( set_nat2 @ Ys ) )
% 13.77/7.77 => ( Xs = Ys ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5865_sorted__distinct__set__unique,axiom,
% 13.77/7.77 ! [Xs: list_int,Ys: list_int] :
% 13.77/7.77 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.77 => ( ( distinct_int @ Xs )
% 13.77/7.77 => ( ( sorted_wrt_int @ ord_less_eq_int @ Ys )
% 13.77/7.77 => ( ( distinct_int @ Ys )
% 13.77/7.77 => ( ( ( set_int2 @ Xs )
% 13.77/7.77 = ( set_int2 @ Ys ) )
% 13.77/7.77 => ( Xs = Ys ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5866_VEBT__internal_Oinsert_H_Osimps_I1_J,axiom,
% 13.77/7.77 ! [A: $o,B: $o,X: nat] :
% 13.77/7.77 ( ( vEBT_VEBT_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.77 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5867_vebt__insert__code_I1_J,axiom,
% 13.77/7.77 ! [X: nat,A: $o,B: $o] :
% 13.77/7.77 ( ( ( X = zero_zero_nat )
% 13.77/7.77 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.77 = ( vEBT_Leaf @ $true @ B ) ) )
% 13.77/7.77 & ( ( X != zero_zero_nat )
% 13.77/7.77 => ( ( ( X = one_one_nat )
% 13.77/7.77 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.77 = ( vEBT_Leaf @ A @ $true ) ) )
% 13.77/7.77 & ( ( X != one_one_nat )
% 13.77/7.77 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.77 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5868_nth__take__lemma,axiom,
% 13.77/7.77 ! [K: nat,Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 13.77/7.77 ( ( ord_less_eq_nat @ K @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.77 => ( ( ord_less_eq_nat @ K @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 13.77/7.77 => ( ! [I2: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I2 @ K )
% 13.77/7.77 => ( ( nth_VEBT_VEBTi @ Xs @ I2 )
% 13.77/7.77 = ( nth_VEBT_VEBTi @ Ys @ I2 ) ) )
% 13.77/7.77 => ( ( take_VEBT_VEBTi @ K @ Xs )
% 13.77/7.77 = ( take_VEBT_VEBTi @ K @ Ys ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5869_nth__take__lemma,axiom,
% 13.77/7.77 ! [K: nat,Xs: list_int,Ys: list_int] :
% 13.77/7.77 ( ( ord_less_eq_nat @ K @ ( size_size_list_int @ Xs ) )
% 13.77/7.77 => ( ( ord_less_eq_nat @ K @ ( size_size_list_int @ Ys ) )
% 13.77/7.77 => ( ! [I2: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I2 @ K )
% 13.77/7.77 => ( ( nth_int @ Xs @ I2 )
% 13.77/7.77 = ( nth_int @ Ys @ I2 ) ) )
% 13.77/7.77 => ( ( take_int @ K @ Xs )
% 13.77/7.77 = ( take_int @ K @ Ys ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5870_nth__take__lemma,axiom,
% 13.77/7.77 ! [K: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 13.77/7.77 ( ( ord_less_eq_nat @ K @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.77 => ( ( ord_less_eq_nat @ K @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.77 => ( ! [I2: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I2 @ K )
% 13.77/7.77 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 13.77/7.77 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 13.77/7.77 => ( ( take_VEBT_VEBT @ K @ Xs )
% 13.77/7.77 = ( take_VEBT_VEBT @ K @ Ys ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5871_nth__take__lemma,axiom,
% 13.77/7.77 ! [K: nat,Xs: list_real,Ys: list_real] :
% 13.77/7.77 ( ( ord_less_eq_nat @ K @ ( size_size_list_real @ Xs ) )
% 13.77/7.77 => ( ( ord_less_eq_nat @ K @ ( size_size_list_real @ Ys ) )
% 13.77/7.77 => ( ! [I2: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I2 @ K )
% 13.77/7.77 => ( ( nth_real @ Xs @ I2 )
% 13.77/7.77 = ( nth_real @ Ys @ I2 ) ) )
% 13.77/7.77 => ( ( take_real @ K @ Xs )
% 13.77/7.77 = ( take_real @ K @ Ys ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5872_nth__take__lemma,axiom,
% 13.77/7.77 ! [K: nat,Xs: list_o,Ys: list_o] :
% 13.77/7.77 ( ( ord_less_eq_nat @ K @ ( size_size_list_o @ Xs ) )
% 13.77/7.77 => ( ( ord_less_eq_nat @ K @ ( size_size_list_o @ Ys ) )
% 13.77/7.77 => ( ! [I2: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I2 @ K )
% 13.77/7.77 => ( ( nth_o @ Xs @ I2 )
% 13.77/7.77 = ( nth_o @ Ys @ I2 ) ) )
% 13.77/7.77 => ( ( take_o @ K @ Xs )
% 13.77/7.77 = ( take_o @ K @ Ys ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5873_nth__take__lemma,axiom,
% 13.77/7.77 ! [K: nat,Xs: list_nat,Ys: list_nat] :
% 13.77/7.77 ( ( ord_less_eq_nat @ K @ ( size_size_list_nat @ Xs ) )
% 13.77/7.77 => ( ( ord_less_eq_nat @ K @ ( size_size_list_nat @ Ys ) )
% 13.77/7.77 => ( ! [I2: nat] :
% 13.77/7.77 ( ( ord_less_nat @ I2 @ K )
% 13.77/7.77 => ( ( nth_nat @ Xs @ I2 )
% 13.77/7.77 = ( nth_nat @ Ys @ I2 ) ) )
% 13.77/7.77 => ( ( take_nat @ K @ Xs )
% 13.77/7.77 = ( take_nat @ K @ Ys ) ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5874_finite__sorted__distinct__unique,axiom,
% 13.77/7.77 ! [A4: set_real] :
% 13.77/7.77 ( ( finite_finite_real @ A4 )
% 13.77/7.77 => ? [X3: list_real] :
% 13.77/7.77 ( ( ( set_real2 @ X3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted_wrt_real @ ord_less_eq_real @ X3 )
% 13.77/7.77 & ( distinct_real @ X3 )
% 13.77/7.77 & ! [Y5: list_real] :
% 13.77/7.77 ( ( ( ( set_real2 @ Y5 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted_wrt_real @ ord_less_eq_real @ Y5 )
% 13.77/7.77 & ( distinct_real @ Y5 ) )
% 13.77/7.77 => ( Y5 = X3 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5875_finite__sorted__distinct__unique,axiom,
% 13.77/7.77 ! [A4: set_o] :
% 13.77/7.77 ( ( finite_finite_o @ A4 )
% 13.77/7.77 => ? [X3: list_o] :
% 13.77/7.77 ( ( ( set_o2 @ X3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted_wrt_o @ ord_less_eq_o @ X3 )
% 13.77/7.77 & ( distinct_o @ X3 )
% 13.77/7.77 & ! [Y5: list_o] :
% 13.77/7.77 ( ( ( ( set_o2 @ Y5 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted_wrt_o @ ord_less_eq_o @ Y5 )
% 13.77/7.77 & ( distinct_o @ Y5 ) )
% 13.77/7.77 => ( Y5 = X3 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5876_finite__sorted__distinct__unique,axiom,
% 13.77/7.77 ! [A4: set_Code_integer] :
% 13.77/7.77 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.77 => ? [X3: list_Code_integer] :
% 13.77/7.77 ( ( ( set_Code_integer2 @ X3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ X3 )
% 13.77/7.77 & ( distin1543349897113766820nteger @ X3 )
% 13.77/7.77 & ! [Y5: list_Code_integer] :
% 13.77/7.77 ( ( ( ( set_Code_integer2 @ Y5 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted710888440204495920nteger @ ord_le3102999989581377725nteger @ Y5 )
% 13.77/7.77 & ( distin1543349897113766820nteger @ Y5 ) )
% 13.77/7.77 => ( Y5 = X3 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5877_finite__sorted__distinct__unique,axiom,
% 13.77/7.77 ! [A4: set_rat] :
% 13.77/7.77 ( ( finite_finite_rat @ A4 )
% 13.77/7.77 => ? [X3: list_rat] :
% 13.77/7.77 ( ( ( set_rat2 @ X3 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted_wrt_rat @ ord_less_eq_rat @ X3 )
% 13.77/7.77 & ( distinct_rat @ X3 )
% 13.77/7.77 & ! [Y5: list_rat] :
% 13.77/7.77 ( ( ( ( set_rat2 @ Y5 )
% 13.77/7.77 = A4 )
% 13.77/7.77 & ( sorted_wrt_rat @ ord_less_eq_rat @ Y5 )
% 13.77/7.77 & ( distinct_rat @ Y5 ) )
% 13.77/7.77 => ( Y5 = X3 ) ) ) ) ).
% 13.77/7.77
% 13.77/7.77 thf(fact_5878_finite__sorted__distinct__unique,axiom,
% 13.77/7.77 ! [A4: set_num] :
% 13.77/7.77 ( ( finite_finite_num @ A4 )
% 13.77/7.78 => ? [X3: list_num] :
% 13.77/7.78 ( ( ( set_num2 @ X3 )
% 13.77/7.78 = A4 )
% 13.77/7.78 & ( sorted_wrt_num @ ord_less_eq_num @ X3 )
% 13.77/7.78 & ( distinct_num @ X3 )
% 13.77/7.78 & ! [Y5: list_num] :
% 13.77/7.78 ( ( ( ( set_num2 @ Y5 )
% 13.77/7.78 = A4 )
% 13.77/7.78 & ( sorted_wrt_num @ ord_less_eq_num @ Y5 )
% 13.77/7.78 & ( distinct_num @ Y5 ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5879_finite__sorted__distinct__unique,axiom,
% 13.77/7.78 ! [A4: set_nat] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ? [X3: list_nat] :
% 13.77/7.78 ( ( ( set_nat2 @ X3 )
% 13.77/7.78 = A4 )
% 13.77/7.78 & ( sorted_wrt_nat @ ord_less_eq_nat @ X3 )
% 13.77/7.78 & ( distinct_nat @ X3 )
% 13.77/7.78 & ! [Y5: list_nat] :
% 13.77/7.78 ( ( ( ( set_nat2 @ Y5 )
% 13.77/7.78 = A4 )
% 13.77/7.78 & ( sorted_wrt_nat @ ord_less_eq_nat @ Y5 )
% 13.77/7.78 & ( distinct_nat @ Y5 ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5880_finite__sorted__distinct__unique,axiom,
% 13.77/7.78 ! [A4: set_int] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ? [X3: list_int] :
% 13.77/7.78 ( ( ( set_int2 @ X3 )
% 13.77/7.78 = A4 )
% 13.77/7.78 & ( sorted_wrt_int @ ord_less_eq_int @ X3 )
% 13.77/7.78 & ( distinct_int @ X3 )
% 13.77/7.78 & ! [Y5: list_int] :
% 13.77/7.78 ( ( ( ( set_int2 @ Y5 )
% 13.77/7.78 = A4 )
% 13.77/7.78 & ( sorted_wrt_int @ ord_less_eq_int @ Y5 )
% 13.77/7.78 & ( distinct_int @ Y5 ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5881_distinct__Ex1,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBTi,X: vEBT_VEBTi] :
% 13.77/7.78 ( ( distinct_VEBT_VEBTi @ Xs )
% 13.77/7.78 => ( ( member_VEBT_VEBTi @ X @ ( set_VEBT_VEBTi2 @ Xs ) )
% 13.77/7.78 => ? [X3: nat] :
% 13.77/7.78 ( ( ord_less_nat @ X3 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 & ( ( nth_VEBT_VEBTi @ Xs @ X3 )
% 13.77/7.78 = X )
% 13.77/7.78 & ! [Y5: nat] :
% 13.77/7.78 ( ( ( ord_less_nat @ Y5 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 & ( ( nth_VEBT_VEBTi @ Xs @ Y5 )
% 13.77/7.78 = X ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5882_distinct__Ex1,axiom,
% 13.77/7.78 ! [Xs: list_int,X: int] :
% 13.77/7.78 ( ( distinct_int @ Xs )
% 13.77/7.78 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.78 => ? [X3: nat] :
% 13.77/7.78 ( ( ord_less_nat @ X3 @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 & ( ( nth_int @ Xs @ X3 )
% 13.77/7.78 = X )
% 13.77/7.78 & ! [Y5: nat] :
% 13.77/7.78 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 & ( ( nth_int @ Xs @ Y5 )
% 13.77/7.78 = X ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5883_distinct__Ex1,axiom,
% 13.77/7.78 ! [Xs: list_set_nat,X: set_nat] :
% 13.77/7.78 ( ( distinct_set_nat @ Xs )
% 13.77/7.78 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 13.77/7.78 => ? [X3: nat] :
% 13.77/7.78 ( ( ord_less_nat @ X3 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.78 & ( ( nth_set_nat @ Xs @ X3 )
% 13.77/7.78 = X )
% 13.77/7.78 & ! [Y5: nat] :
% 13.77/7.78 ( ( ( ord_less_nat @ Y5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 13.77/7.78 & ( ( nth_set_nat @ Xs @ Y5 )
% 13.77/7.78 = X ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5884_distinct__Ex1,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.78 ( ( distinct_VEBT_VEBT @ Xs )
% 13.77/7.78 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.78 => ? [X3: nat] :
% 13.77/7.78 ( ( ord_less_nat @ X3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 & ( ( nth_VEBT_VEBT @ Xs @ X3 )
% 13.77/7.78 = X )
% 13.77/7.78 & ! [Y5: nat] :
% 13.77/7.78 ( ( ( ord_less_nat @ Y5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 & ( ( nth_VEBT_VEBT @ Xs @ Y5 )
% 13.77/7.78 = X ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5885_distinct__Ex1,axiom,
% 13.77/7.78 ! [Xs: list_real,X: real] :
% 13.77/7.78 ( ( distinct_real @ Xs )
% 13.77/7.78 => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 13.77/7.78 => ? [X3: nat] :
% 13.77/7.78 ( ( ord_less_nat @ X3 @ ( size_size_list_real @ Xs ) )
% 13.77/7.78 & ( ( nth_real @ Xs @ X3 )
% 13.77/7.78 = X )
% 13.77/7.78 & ! [Y5: nat] :
% 13.77/7.78 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_real @ Xs ) )
% 13.77/7.78 & ( ( nth_real @ Xs @ Y5 )
% 13.77/7.78 = X ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5886_distinct__Ex1,axiom,
% 13.77/7.78 ! [Xs: list_o,X: $o] :
% 13.77/7.78 ( ( distinct_o @ Xs )
% 13.77/7.78 => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 13.77/7.78 => ? [X3: nat] :
% 13.77/7.78 ( ( ord_less_nat @ X3 @ ( size_size_list_o @ Xs ) )
% 13.77/7.78 & ( ( nth_o @ Xs @ X3 )
% 13.77/7.78 = X )
% 13.77/7.78 & ! [Y5: nat] :
% 13.77/7.78 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_o @ Xs ) )
% 13.77/7.78 & ( ( nth_o @ Xs @ Y5 )
% 13.77/7.78 = X ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5887_distinct__Ex1,axiom,
% 13.77/7.78 ! [Xs: list_nat,X: nat] :
% 13.77/7.78 ( ( distinct_nat @ Xs )
% 13.77/7.78 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.78 => ? [X3: nat] :
% 13.77/7.78 ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 & ( ( nth_nat @ Xs @ X3 )
% 13.77/7.78 = X )
% 13.77/7.78 & ! [Y5: nat] :
% 13.77/7.78 ( ( ( ord_less_nat @ Y5 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 & ( ( nth_nat @ Xs @ Y5 )
% 13.77/7.78 = X ) )
% 13.77/7.78 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5888_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 13.77/7.78 ! [Xs: list_real] :
% 13.77/7.78 ( ( sorted_wrt_real @ ord_less_eq_real @ Xs )
% 13.77/7.78 => ( ( distinct_real @ Xs )
% 13.77/7.78 => ( ( linord4252657396651189596t_real @ ( set_real2 @ Xs ) )
% 13.77/7.78 = Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5889_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 13.77/7.78 ! [Xs: list_o] :
% 13.77/7.78 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 13.77/7.78 => ( ( distinct_o @ Xs )
% 13.77/7.78 => ( ( linord3142498349692569832_set_o @ ( set_o2 @ Xs ) )
% 13.77/7.78 = Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5890_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 13.77/7.78 ! [Xs: list_rat] :
% 13.77/7.78 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.78 => ( ( distinct_rat @ Xs )
% 13.77/7.78 => ( ( linord1979837681955606664et_rat @ ( set_rat2 @ Xs ) )
% 13.77/7.78 = Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5891_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 13.77/7.78 ! [Xs: list_num] :
% 13.77/7.78 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.78 => ( ( distinct_num @ Xs )
% 13.77/7.78 => ( ( linord8395671565052656842et_num @ ( set_num2 @ Xs ) )
% 13.77/7.78 = Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5892_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 13.77/7.78 ! [Xs: list_int] :
% 13.77/7.78 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.78 => ( ( distinct_int @ Xs )
% 13.77/7.78 => ( ( linord2612477271533052124et_int @ ( set_int2 @ Xs ) )
% 13.77/7.78 = Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5893_sorted__list__of__set_Oidem__if__sorted__distinct,axiom,
% 13.77/7.78 ! [Xs: list_nat] :
% 13.77/7.78 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.78 => ( ( distinct_nat @ Xs )
% 13.77/7.78 => ( ( linord2614967742042102400et_nat @ ( set_nat2 @ Xs ) )
% 13.77/7.78 = Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5894_distinct__sorted__mono,axiom,
% 13.77/7.78 ! [L: list_o,I: nat,J: nat] :
% 13.77/7.78 ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 13.77/7.78 => ( ( distinct_o @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ J )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 13.77/7.78 => ( ord_less_o @ ( nth_o @ L @ I ) @ ( nth_o @ L @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5895_distinct__sorted__mono,axiom,
% 13.77/7.78 ! [L: list_real,I: nat,J: nat] :
% 13.77/7.78 ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 13.77/7.78 => ( ( distinct_real @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ J )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 13.77/7.78 => ( ord_less_real @ ( nth_real @ L @ I ) @ ( nth_real @ L @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5896_distinct__sorted__mono,axiom,
% 13.77/7.78 ! [L: list_rat,I: nat,J: nat] :
% 13.77/7.78 ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 13.77/7.78 => ( ( distinct_rat @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ J )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 13.77/7.78 => ( ord_less_rat @ ( nth_rat @ L @ I ) @ ( nth_rat @ L @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5897_distinct__sorted__mono,axiom,
% 13.77/7.78 ! [L: list_num,I: nat,J: nat] :
% 13.77/7.78 ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 13.77/7.78 => ( ( distinct_num @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ J )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 13.77/7.78 => ( ord_less_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5898_distinct__sorted__mono,axiom,
% 13.77/7.78 ! [L: list_nat,I: nat,J: nat] :
% 13.77/7.78 ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 13.77/7.78 => ( ( distinct_nat @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ J )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 13.77/7.78 => ( ord_less_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5899_distinct__sorted__mono,axiom,
% 13.77/7.78 ! [L: list_int,I: nat,J: nat] :
% 13.77/7.78 ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 13.77/7.78 => ( ( distinct_int @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ J )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 13.77/7.78 => ( ord_less_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5900_distinct__sorted__strict__mono__iff,axiom,
% 13.77/7.78 ! [L: list_o,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_o @ L )
% 13.77/7.78 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 13.77/7.78 => ( ( ord_less_o @ ( nth_o @ L @ I ) @ ( nth_o @ L @ J ) )
% 13.77/7.78 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5901_distinct__sorted__strict__mono__iff,axiom,
% 13.77/7.78 ! [L: list_real,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_real @ L )
% 13.77/7.78 => ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 13.77/7.78 => ( ( ord_less_real @ ( nth_real @ L @ I ) @ ( nth_real @ L @ J ) )
% 13.77/7.78 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5902_distinct__sorted__strict__mono__iff,axiom,
% 13.77/7.78 ! [L: list_rat,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_rat @ L )
% 13.77/7.78 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_rat @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 13.77/7.78 => ( ( ord_less_rat @ ( nth_rat @ L @ I ) @ ( nth_rat @ L @ J ) )
% 13.77/7.78 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5903_distinct__sorted__strict__mono__iff,axiom,
% 13.77/7.78 ! [L: list_num,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_num @ L )
% 13.77/7.78 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_num @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 13.77/7.78 => ( ( ord_less_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) )
% 13.77/7.78 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5904_distinct__sorted__strict__mono__iff,axiom,
% 13.77/7.78 ! [L: list_nat,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_nat @ L )
% 13.77/7.78 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) )
% 13.77/7.78 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5905_distinct__sorted__strict__mono__iff,axiom,
% 13.77/7.78 ! [L: list_int,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_int @ L )
% 13.77/7.78 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 13.77/7.78 => ( ( ord_less_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) )
% 13.77/7.78 = ( ord_less_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5906_distinct__sorted__mono__iff,axiom,
% 13.77/7.78 ! [L: list_real,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_real @ L )
% 13.77/7.78 => ( ( sorted_wrt_real @ ord_less_eq_real @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_real @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_real @ L ) )
% 13.77/7.78 => ( ( ord_less_eq_real @ ( nth_real @ L @ I ) @ ( nth_real @ L @ J ) )
% 13.77/7.78 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5907_distinct__sorted__mono__iff,axiom,
% 13.77/7.78 ! [L: list_o,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_o @ L )
% 13.77/7.78 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_o @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 13.77/7.78 => ( ( ord_less_eq_o @ ( nth_o @ L @ I ) @ ( nth_o @ L @ J ) )
% 13.77/7.78 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5908_distinct__sorted__mono__iff,axiom,
% 13.77/7.78 ! [L: list_rat,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_rat @ L )
% 13.77/7.78 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_rat @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 13.77/7.78 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I ) @ ( nth_rat @ L @ J ) )
% 13.77/7.78 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5909_distinct__sorted__mono__iff,axiom,
% 13.77/7.78 ! [L: list_num,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_num @ L )
% 13.77/7.78 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_num @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 13.77/7.78 => ( ( ord_less_eq_num @ ( nth_num @ L @ I ) @ ( nth_num @ L @ J ) )
% 13.77/7.78 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5910_distinct__sorted__mono__iff,axiom,
% 13.77/7.78 ! [L: list_nat,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_nat @ L )
% 13.77/7.78 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 13.77/7.78 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I ) @ ( nth_nat @ L @ J ) )
% 13.77/7.78 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5911_distinct__sorted__mono__iff,axiom,
% 13.77/7.78 ! [L: list_int,I: nat,J: nat] :
% 13.77/7.78 ( ( distinct_int @ L )
% 13.77/7.78 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ L ) )
% 13.77/7.78 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 13.77/7.78 => ( ( ord_less_eq_int @ ( nth_int @ L @ I ) @ ( nth_int @ L @ J ) )
% 13.77/7.78 = ( ord_less_eq_nat @ I @ J ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5912_distinct__list__update,axiom,
% 13.77/7.78 ! [Xs: list_set_nat,A: set_nat,I: nat] :
% 13.77/7.78 ( ( distinct_set_nat @ Xs )
% 13.77/7.78 => ( ~ ( member_set_nat @ A @ ( minus_2163939370556025621et_nat @ ( set_set_nat2 @ Xs ) @ ( insert_set_nat @ ( nth_set_nat @ Xs @ I ) @ bot_bot_set_set_nat ) ) )
% 13.77/7.78 => ( distinct_set_nat @ ( list_update_set_nat @ Xs @ I @ A ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5913_distinct__list__update,axiom,
% 13.77/7.78 ! [Xs: list_real,A: real,I: nat] :
% 13.77/7.78 ( ( distinct_real @ Xs )
% 13.77/7.78 => ( ~ ( member_real @ A @ ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ ( nth_real @ Xs @ I ) @ bot_bot_set_real ) ) )
% 13.77/7.78 => ( distinct_real @ ( list_update_real @ Xs @ I @ A ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5914_distinct__list__update,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBTi,A: vEBT_VEBTi,I: nat] :
% 13.77/7.78 ( ( distinct_VEBT_VEBTi @ Xs )
% 13.77/7.78 => ( ~ ( member_VEBT_VEBTi @ A @ ( minus_3697805406911847364_VEBTi @ ( set_VEBT_VEBTi2 @ Xs ) @ ( insert_VEBT_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ I ) @ bot_bo8982466882572371071_VEBTi ) ) )
% 13.77/7.78 => ( distinct_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ A ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5915_distinct__list__update,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBT,A: vEBT_VEBT,I: nat] :
% 13.77/7.78 ( ( distinct_VEBT_VEBT @ Xs )
% 13.77/7.78 => ( ~ ( member_VEBT_VEBT @ A @ ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ I ) @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.78 => ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ A ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5916_distinct__list__update,axiom,
% 13.77/7.78 ! [Xs: list_int,A: int,I: nat] :
% 13.77/7.78 ( ( distinct_int @ Xs )
% 13.77/7.78 => ( ~ ( member_int @ A @ ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ ( nth_int @ Xs @ I ) @ bot_bot_set_int ) ) )
% 13.77/7.78 => ( distinct_int @ ( list_update_int @ Xs @ I @ A ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5917_distinct__list__update,axiom,
% 13.77/7.78 ! [Xs: list_o,A: $o,I: nat] :
% 13.77/7.78 ( ( distinct_o @ Xs )
% 13.77/7.78 => ( ~ ( member_o @ A @ ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ ( nth_o @ Xs @ I ) @ bot_bot_set_o ) ) )
% 13.77/7.78 => ( distinct_o @ ( list_update_o @ Xs @ I @ A ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5918_distinct__list__update,axiom,
% 13.77/7.78 ! [Xs: list_nat,A: nat,I: nat] :
% 13.77/7.78 ( ( distinct_nat @ Xs )
% 13.77/7.78 => ( ~ ( member_nat @ A @ ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ ( nth_nat @ Xs @ I ) @ bot_bot_set_nat ) ) )
% 13.77/7.78 => ( distinct_nat @ ( list_update_nat @ Xs @ I @ A ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5919_vebt__insert_Osimps_I4_J,axiom,
% 13.77/7.78 ! [V2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5920_heaphelp,axiom,
% 13.77/7.78 ! [Xa2: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 13.77/7.78 ( ( rep_assn
% 13.77/7.78 @ ( times_times_assn
% 13.77/7.78 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa2 @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb ) )
% 13.77/7.78 @ ( pure_assn
% 13.77/7.78 @ ( ( none_P5556105721700978146at_nat = none_P5556105721700978146at_nat )
% 13.77/7.78 & ( N = N ) ) ) )
% 13.77/7.78 @ ( pure_assn
% 13.77/7.78 @ ( Xc
% 13.77/7.78 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa2 @ Xb ) ) ) )
% 13.77/7.78 @ H2 )
% 13.77/7.78 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5921_heaphelp,axiom,
% 13.77/7.78 ! [Xa2: array_VEBT_VEBTi,Tree_is: list_VEBT_VEBTi,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Xb: vEBT_VEBTi,N: nat,Xc: vEBT_VEBTi,H2: produc3658429121746597890et_nat] :
% 13.77/7.78 ( ( rep_assn
% 13.77/7.78 @ ( times_times_assn
% 13.77/7.78 @ ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Xa2 @ Tree_is ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ TreeList @ Tree_is ) ) @ ( vEBT_vebt_assn_raw @ Summary @ Xb ) )
% 13.77/7.78 @ ( pure_assn
% 13.77/7.78 @ ( ( none_nat = none_nat )
% 13.77/7.78 & ( N = N ) ) ) )
% 13.77/7.78 @ ( pure_assn
% 13.77/7.78 @ ( Xc
% 13.77/7.78 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ N @ Xa2 @ Xb ) ) ) )
% 13.77/7.78 @ H2 )
% 13.77/7.78 => ( rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_Node @ none_P5556105721700978146at_nat @ N @ TreeList @ Summary ) @ Xc ) @ H2 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5922_vebt__insert_Osimps_I3_J,axiom,
% 13.77/7.78 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 13.77/7.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X )
% 13.77/7.78 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5923_vebt__insert_Osimps_I2_J,axiom,
% 13.77/7.78 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 13.77/7.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) @ X )
% 13.77/7.78 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5924_mergesort__remdups__correct,axiom,
% 13.77/7.78 ! [L: list_real] :
% 13.77/7.78 ( ( distinct_real @ ( merges7559785487730971421s_real @ L ) )
% 13.77/7.78 & ( sorted_wrt_real @ ord_less_eq_real @ ( merges7559785487730971421s_real @ L ) )
% 13.77/7.78 & ( ( set_real2 @ ( merges7559785487730971421s_real @ L ) )
% 13.77/7.78 = ( set_real2 @ L ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5925_mergesort__remdups__correct,axiom,
% 13.77/7.78 ! [L: list_o] :
% 13.77/7.78 ( ( distinct_o @ ( mergesort_remdups_o @ L ) )
% 13.77/7.78 & ( sorted_wrt_o @ ord_less_eq_o @ ( mergesort_remdups_o @ L ) )
% 13.77/7.78 & ( ( set_o2 @ ( mergesort_remdups_o @ L ) )
% 13.77/7.78 = ( set_o2 @ L ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5926_mergesort__remdups__correct,axiom,
% 13.77/7.78 ! [L: list_rat] :
% 13.77/7.78 ( ( distinct_rat @ ( merges1021483306759835337ps_rat @ L ) )
% 13.77/7.78 & ( sorted_wrt_rat @ ord_less_eq_rat @ ( merges1021483306759835337ps_rat @ L ) )
% 13.77/7.78 & ( ( set_rat2 @ ( merges1021483306759835337ps_rat @ L ) )
% 13.77/7.78 = ( set_rat2 @ L ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5927_mergesort__remdups__correct,axiom,
% 13.77/7.78 ! [L: list_num] :
% 13.77/7.78 ( ( distinct_num @ ( merges7437317189856885515ps_num @ L ) )
% 13.77/7.78 & ( sorted_wrt_num @ ord_less_eq_num @ ( merges7437317189856885515ps_num @ L ) )
% 13.77/7.78 & ( ( set_num2 @ ( merges7437317189856885515ps_num @ L ) )
% 13.77/7.78 = ( set_num2 @ L ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5928_mergesort__remdups__correct,axiom,
% 13.77/7.78 ! [L: list_nat] :
% 13.77/7.78 ( ( distinct_nat @ ( merges1656613366846331073ps_nat @ L ) )
% 13.77/7.78 & ( sorted_wrt_nat @ ord_less_eq_nat @ ( merges1656613366846331073ps_nat @ L ) )
% 13.77/7.78 & ( ( set_nat2 @ ( merges1656613366846331073ps_nat @ L ) )
% 13.77/7.78 = ( set_nat2 @ L ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5929_mergesort__remdups__correct,axiom,
% 13.77/7.78 ! [L: list_int] :
% 13.77/7.78 ( ( distinct_int @ ( merges1654122896337280797ps_int @ L ) )
% 13.77/7.78 & ( sorted_wrt_int @ ord_less_eq_int @ ( merges1654122896337280797ps_int @ L ) )
% 13.77/7.78 & ( ( set_int2 @ ( merges1654122896337280797ps_int @ L ) )
% 13.77/7.78 = ( set_int2 @ L ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5930_last__take__nth__conv,axiom,
% 13.77/7.78 ! [N: nat,L: list_VEBT_VEBTi] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_s7982070591426661849_VEBTi @ L ) )
% 13.77/7.78 => ( ( N != zero_zero_nat )
% 13.77/7.78 => ( ( last_VEBT_VEBTi @ ( take_VEBT_VEBTi @ N @ L ) )
% 13.77/7.78 = ( nth_VEBT_VEBTi @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5931_last__take__nth__conv,axiom,
% 13.77/7.78 ! [N: nat,L: list_int] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ L ) )
% 13.77/7.78 => ( ( N != zero_zero_nat )
% 13.77/7.78 => ( ( last_int @ ( take_int @ N @ L ) )
% 13.77/7.78 = ( nth_int @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5932_last__take__nth__conv,axiom,
% 13.77/7.78 ! [N: nat,L: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.78 => ( ( N != zero_zero_nat )
% 13.77/7.78 => ( ( last_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ L ) )
% 13.77/7.78 = ( nth_VEBT_VEBT @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5933_last__take__nth__conv,axiom,
% 13.77/7.78 ! [N: nat,L: list_real] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ L ) )
% 13.77/7.78 => ( ( N != zero_zero_nat )
% 13.77/7.78 => ( ( last_real @ ( take_real @ N @ L ) )
% 13.77/7.78 = ( nth_real @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5934_last__take__nth__conv,axiom,
% 13.77/7.78 ! [N: nat,L: list_o] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ L ) )
% 13.77/7.78 => ( ( N != zero_zero_nat )
% 13.77/7.78 => ( ( last_o @ ( take_o @ N @ L ) )
% 13.77/7.78 = ( nth_o @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5935_last__take__nth__conv,axiom,
% 13.77/7.78 ! [N: nat,L: list_nat] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ L ) )
% 13.77/7.78 => ( ( N != zero_zero_nat )
% 13.77/7.78 => ( ( last_nat @ ( take_nat @ N @ L ) )
% 13.77/7.78 = ( nth_nat @ L @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5936_VEBTi_Oinject_I1_J,axiom,
% 13.77/7.78 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,Y11: option4927543243414619207at_nat,Y12: nat,Y13: array_VEBT_VEBTi,Y14: vEBT_VEBTi] :
% 13.77/7.78 ( ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 13.77/7.78 = ( vEBT_Nodei @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 13.77/7.78 = ( ( X11 = Y11 )
% 13.77/7.78 & ( X12 = Y12 )
% 13.77/7.78 & ( X13 = Y13 )
% 13.77/7.78 & ( X14 = Y14 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5937_vebt__assn__raw_Osimps_I4_J,axiom,
% 13.77/7.78 ! [Vd2: $o,Ve2: $o,V2: option4927543243414619207at_nat,Va2: nat,Vb: array_VEBT_VEBTi,Vc: vEBT_VEBTi] :
% 13.77/7.78 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ Vd2 @ Ve2 ) @ ( vEBT_Nodei @ V2 @ Va2 @ Vb @ Vc ) )
% 13.77/7.78 = bot_bot_assn ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5938_subset__subseqs,axiom,
% 13.77/7.78 ! [X6: set_VEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_le4337996190870823476T_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.78 => ( member_set_VEBT_VEBT @ X6 @ ( image_6463372868993444447T_VEBT @ set_VEBT_VEBT2 @ ( set_list_VEBT_VEBT2 @ ( subseqs_VEBT_VEBT @ Xs ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5939_subset__subseqs,axiom,
% 13.77/7.78 ! [X6: set_nat,Xs: list_nat] :
% 13.77/7.78 ( ( ord_less_eq_set_nat @ X6 @ ( set_nat2 @ Xs ) )
% 13.77/7.78 => ( member_set_nat @ X6 @ ( image_1775855109352712557et_nat @ set_nat2 @ ( set_list_nat2 @ ( subseqs_nat @ Xs ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5940_subset__subseqs,axiom,
% 13.77/7.78 ! [X6: set_real,Xs: list_real] :
% 13.77/7.78 ( ( ord_less_eq_set_real @ X6 @ ( set_real2 @ Xs ) )
% 13.77/7.78 => ( member_set_real @ X6 @ ( image_6239767680843085477t_real @ set_real2 @ ( set_list_real2 @ ( subseqs_real @ Xs ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5941_subset__subseqs,axiom,
% 13.77/7.78 ! [X6: set_o,Xs: list_o] :
% 13.77/7.78 ( ( ord_less_eq_set_o @ X6 @ ( set_o2 @ Xs ) )
% 13.77/7.78 => ( member_set_o @ X6 @ ( image_list_o_set_o @ set_o2 @ ( set_list_o2 @ ( subseqs_o @ Xs ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5942_subset__subseqs,axiom,
% 13.77/7.78 ! [X6: set_int,Xs: list_int] :
% 13.77/7.78 ( ( ord_less_eq_set_int @ X6 @ ( set_int2 @ Xs ) )
% 13.77/7.78 => ( member_set_int @ X6 @ ( image_3606813740839090725et_int @ set_int2 @ ( set_list_int2 @ ( subseqs_int @ Xs ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5943_set__remove1__eq,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.78 ( ( distinct_VEBT_VEBT @ Xs )
% 13.77/7.78 => ( ( set_VEBT_VEBT2 @ ( remove1_VEBT_VEBT @ X @ Xs ) )
% 13.77/7.78 = ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5944_set__remove1__eq,axiom,
% 13.77/7.78 ! [Xs: list_real,X: real] :
% 13.77/7.78 ( ( distinct_real @ Xs )
% 13.77/7.78 => ( ( set_real2 @ ( remove1_real @ X @ Xs ) )
% 13.77/7.78 = ( minus_minus_set_real @ ( set_real2 @ Xs ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5945_set__remove1__eq,axiom,
% 13.77/7.78 ! [Xs: list_int,X: int] :
% 13.77/7.78 ( ( distinct_int @ Xs )
% 13.77/7.78 => ( ( set_int2 @ ( remove1_int @ X @ Xs ) )
% 13.77/7.78 = ( minus_minus_set_int @ ( set_int2 @ Xs ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5946_set__remove1__eq,axiom,
% 13.77/7.78 ! [Xs: list_o,X: $o] :
% 13.77/7.78 ( ( distinct_o @ Xs )
% 13.77/7.78 => ( ( set_o2 @ ( remove1_o @ X @ Xs ) )
% 13.77/7.78 = ( minus_minus_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5947_set__remove1__eq,axiom,
% 13.77/7.78 ! [Xs: list_nat,X: nat] :
% 13.77/7.78 ( ( distinct_nat @ Xs )
% 13.77/7.78 => ( ( set_nat2 @ ( remove1_nat @ X @ Xs ) )
% 13.77/7.78 = ( minus_minus_set_nat @ ( set_nat2 @ Xs ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5948_lex__take__index,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi,R: set_Pr2227491710730465451_VEBTi] :
% 13.77/7.78 ( ( member4173000155140927252_VEBTi @ ( produc4384243565435462691_VEBTi @ Xs @ Ys ) @ ( lex_VEBT_VEBTi @ R ) )
% 13.77/7.78 => ~ ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I2 @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 13.77/7.78 => ( ( ( take_VEBT_VEBTi @ I2 @ Xs )
% 13.77/7.78 = ( take_VEBT_VEBTi @ I2 @ Ys ) )
% 13.77/7.78 => ~ ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ I2 ) @ ( nth_VEBT_VEBTi @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5949_lex__take__index,axiom,
% 13.77/7.78 ! [Xs: list_uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.78 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( lex_uint32 @ R ) )
% 13.77/7.78 => ~ ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_s4844771616002835472uint32 @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I2 @ ( size_s4844771616002835472uint32 @ Ys ) )
% 13.77/7.78 => ( ( ( take_uint32 @ I2 @ Xs )
% 13.77/7.78 = ( take_uint32 @ I2 @ Ys ) )
% 13.77/7.78 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ I2 ) @ ( nth_uint32 @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5950_lex__take__index,axiom,
% 13.77/7.78 ! [Xs: list_int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.78 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( lex_int @ R ) )
% 13.77/7.78 => ~ ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 13.77/7.78 => ( ( ( take_int @ I2 @ Xs )
% 13.77/7.78 = ( take_int @ I2 @ Ys ) )
% 13.77/7.78 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5951_lex__take__index,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 13.77/7.78 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( lex_VEBT_VEBT @ R ) )
% 13.77/7.78 => ~ ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.78 => ( ( ( take_VEBT_VEBT @ I2 @ Xs )
% 13.77/7.78 = ( take_VEBT_VEBT @ I2 @ Ys ) )
% 13.77/7.78 => ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5952_lex__take__index,axiom,
% 13.77/7.78 ! [Xs: list_real,Ys: list_real,R: set_Pr6218003697084177305l_real] :
% 13.77/7.78 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Xs @ Ys ) @ ( lex_real @ R ) )
% 13.77/7.78 => ~ ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Ys ) )
% 13.77/7.78 => ( ( ( take_real @ I2 @ Xs )
% 13.77/7.78 = ( take_real @ I2 @ Ys ) )
% 13.77/7.78 => ~ ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ I2 ) @ ( nth_real @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5953_lex__take__index,axiom,
% 13.77/7.78 ! [Xs: list_o,Ys: list_o,R: set_Product_prod_o_o] :
% 13.77/7.78 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( lex_o @ R ) )
% 13.77/7.78 => ~ ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 13.77/7.78 => ( ( ( take_o @ I2 @ Xs )
% 13.77/7.78 = ( take_o @ I2 @ Ys ) )
% 13.77/7.78 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ I2 ) @ ( nth_o @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5954_lex__take__index,axiom,
% 13.77/7.78 ! [Xs: list_nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.78 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( lex_nat @ R ) )
% 13.77/7.78 => ~ ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 13.77/7.78 => ( ( ( take_nat @ I2 @ Xs )
% 13.77/7.78 = ( take_nat @ I2 @ Ys ) )
% 13.77/7.78 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5955_take__butlast__conv,axiom,
% 13.77/7.78 ! [L: list_VEBT_VEBT] :
% 13.77/7.78 ( ( take_VEBT_VEBT @ ( minus_minus_nat @ ( size_s6755466524823107622T_VEBT @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_VEBT_VEBT @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5956_take__butlast__conv,axiom,
% 13.77/7.78 ! [L: list_real] :
% 13.77/7.78 ( ( take_real @ ( minus_minus_nat @ ( size_size_list_real @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_real @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5957_take__butlast__conv,axiom,
% 13.77/7.78 ! [L: list_o] :
% 13.77/7.78 ( ( take_o @ ( minus_minus_nat @ ( size_size_list_o @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_o @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5958_take__butlast__conv,axiom,
% 13.77/7.78 ! [L: list_nat] :
% 13.77/7.78 ( ( take_nat @ ( minus_minus_nat @ ( size_size_list_nat @ L ) @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_nat @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5959_take__minus__one__conv__butlast,axiom,
% 13.77/7.78 ! [N: nat,L: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ L ) )
% 13.77/7.78 => ( ( take_VEBT_VEBT @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ L ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5960_take__minus__one__conv__butlast,axiom,
% 13.77/7.78 ! [N: nat,L: list_real] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ L ) )
% 13.77/7.78 => ( ( take_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_real @ ( take_real @ N @ L ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5961_take__minus__one__conv__butlast,axiom,
% 13.77/7.78 ! [N: nat,L: list_o] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ L ) )
% 13.77/7.78 => ( ( take_o @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_o @ ( take_o @ N @ L ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5962_take__minus__one__conv__butlast,axiom,
% 13.77/7.78 ! [N: nat,L: list_nat] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ L ) )
% 13.77/7.78 => ( ( take_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ L )
% 13.77/7.78 = ( butlast_nat @ ( take_nat @ N @ L ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5963_Cons__in__lex,axiom,
% 13.77/7.78 ! [X: uint32,Xs: list_uint32,Y: uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.78 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Ys ) ) @ ( lex_uint32 @ R ) )
% 13.77/7.78 = ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 13.77/7.78 & ( ( size_s4844771616002835472uint32 @ Xs )
% 13.77/7.78 = ( size_s4844771616002835472uint32 @ Ys ) ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( lex_uint32 @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5964_Cons__in__lex,axiom,
% 13.77/7.78 ! [X: int,Xs: list_int,Y: int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.78 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( lex_int @ R ) )
% 13.77/7.78 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 13.77/7.78 & ( ( size_size_list_int @ Xs )
% 13.77/7.78 = ( size_size_list_int @ Ys ) ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( lex_int @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5965_Cons__in__lex,axiom,
% 13.77/7.78 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT,Y: vEBT_VEBT,Ys: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 13.77/7.78 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs ) @ ( cons_VEBT_VEBT @ Y @ Ys ) ) @ ( lex_VEBT_VEBT @ R ) )
% 13.77/7.78 = ( ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y ) @ R )
% 13.77/7.78 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( lex_VEBT_VEBT @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5966_Cons__in__lex,axiom,
% 13.77/7.78 ! [X: real,Xs: list_real,Y: real,Ys: list_real,R: set_Pr6218003697084177305l_real] :
% 13.77/7.78 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ ( cons_real @ X @ Xs ) @ ( cons_real @ Y @ Ys ) ) @ ( lex_real @ R ) )
% 13.77/7.78 = ( ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X @ Y ) @ R )
% 13.77/7.78 & ( ( size_size_list_real @ Xs )
% 13.77/7.78 = ( size_size_list_real @ Ys ) ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Xs @ Ys ) @ ( lex_real @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5967_Cons__in__lex,axiom,
% 13.77/7.78 ! [X: $o,Xs: list_o,Y: $o,Ys: list_o,R: set_Product_prod_o_o] :
% 13.77/7.78 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Ys ) ) @ ( lex_o @ R ) )
% 13.77/7.78 = ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 13.77/7.78 & ( ( size_size_list_o @ Xs )
% 13.77/7.78 = ( size_size_list_o @ Ys ) ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( lex_o @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5968_Cons__in__lex,axiom,
% 13.77/7.78 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.78 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( lex_nat @ R ) )
% 13.77/7.78 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 13.77/7.78 & ( ( size_size_list_nat @ Xs )
% 13.77/7.78 = ( size_size_list_nat @ Ys ) ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( lex_nat @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5969_butlast__update_H,axiom,
% 13.77/7.78 ! [L: list_nat,I: nat,X: nat] :
% 13.77/7.78 ( ( list_update_nat @ ( butlast_nat @ L ) @ I @ X )
% 13.77/7.78 = ( butlast_nat @ ( list_update_nat @ L @ I @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5970_butlast__update_H,axiom,
% 13.77/7.78 ! [L: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi] :
% 13.77/7.78 ( ( list_u6098035379799741383_VEBTi @ ( butlast_VEBT_VEBTi @ L ) @ I @ X )
% 13.77/7.78 = ( butlast_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ L @ I @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5971_butlast__update_H,axiom,
% 13.77/7.78 ! [L: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 13.77/7.78 ( ( list_u1324408373059187874T_VEBT @ ( butlast_VEBT_VEBT @ L ) @ I @ X )
% 13.77/7.78 = ( butlast_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ L @ I @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5972_foldl__absorb1,axiom,
% 13.77/7.78 ! [X: rat,Zs: list_rat] :
% 13.77/7.78 ( ( times_times_rat @ X @ ( foldl_rat_rat @ times_times_rat @ one_one_rat @ Zs ) )
% 13.77/7.78 = ( foldl_rat_rat @ times_times_rat @ X @ Zs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5973_foldl__absorb1,axiom,
% 13.77/7.78 ! [X: assn,Zs: list_assn] :
% 13.77/7.78 ( ( times_times_assn @ X @ ( foldl_assn_assn @ times_times_assn @ one_one_assn @ Zs ) )
% 13.77/7.78 = ( foldl_assn_assn @ times_times_assn @ X @ Zs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5974_foldl__absorb1,axiom,
% 13.77/7.78 ! [X: uint32,Zs: list_uint32] :
% 13.77/7.78 ( ( times_times_uint32 @ X @ ( foldl_uint32_uint32 @ times_times_uint32 @ one_one_uint32 @ Zs ) )
% 13.77/7.78 = ( foldl_uint32_uint32 @ times_times_uint32 @ X @ Zs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5975_foldl__absorb1,axiom,
% 13.77/7.78 ! [X: real,Zs: list_real] :
% 13.77/7.78 ( ( times_times_real @ X @ ( foldl_real_real @ times_times_real @ one_one_real @ Zs ) )
% 13.77/7.78 = ( foldl_real_real @ times_times_real @ X @ Zs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5976_foldl__absorb1,axiom,
% 13.77/7.78 ! [X: nat,Zs: list_nat] :
% 13.77/7.78 ( ( times_times_nat @ X @ ( foldl_nat_nat @ times_times_nat @ one_one_nat @ Zs ) )
% 13.77/7.78 = ( foldl_nat_nat @ times_times_nat @ X @ Zs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5977_foldl__absorb1,axiom,
% 13.77/7.78 ! [X: int,Zs: list_int] :
% 13.77/7.78 ( ( times_times_int @ X @ ( foldl_int_int @ times_times_int @ one_one_int @ Zs ) )
% 13.77/7.78 = ( foldl_int_int @ times_times_int @ X @ Zs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5978_set__remove1__subset,axiom,
% 13.77/7.78 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( remove1_VEBT_VEBT @ X @ Xs ) ) @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5979_set__remove1__subset,axiom,
% 13.77/7.78 ! [X: nat,Xs: list_nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( remove1_nat @ X @ Xs ) ) @ ( set_nat2 @ Xs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5980_set__remove1__subset,axiom,
% 13.77/7.78 ! [X: real,Xs: list_real] : ( ord_less_eq_set_real @ ( set_real2 @ ( remove1_real @ X @ Xs ) ) @ ( set_real2 @ Xs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5981_set__remove1__subset,axiom,
% 13.77/7.78 ! [X: $o,Xs: list_o] : ( ord_less_eq_set_o @ ( set_o2 @ ( remove1_o @ X @ Xs ) ) @ ( set_o2 @ Xs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5982_set__remove1__subset,axiom,
% 13.77/7.78 ! [X: int,Xs: list_int] : ( ord_less_eq_set_int @ ( set_int2 @ ( remove1_int @ X @ Xs ) ) @ ( set_int2 @ Xs ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5983_sorted__remove1,axiom,
% 13.77/7.78 ! [Xs: list_rat,A: rat] :
% 13.77/7.78 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 13.77/7.78 => ( sorted_wrt_rat @ ord_less_eq_rat @ ( remove1_rat @ A @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5984_sorted__remove1,axiom,
% 13.77/7.78 ! [Xs: list_num,A: num] :
% 13.77/7.78 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 13.77/7.78 => ( sorted_wrt_num @ ord_less_eq_num @ ( remove1_num @ A @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5985_sorted__remove1,axiom,
% 13.77/7.78 ! [Xs: list_nat,A: nat] :
% 13.77/7.78 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 13.77/7.78 => ( sorted_wrt_nat @ ord_less_eq_nat @ ( remove1_nat @ A @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5986_sorted__remove1,axiom,
% 13.77/7.78 ! [Xs: list_int,A: int] :
% 13.77/7.78 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 13.77/7.78 => ( sorted_wrt_int @ ord_less_eq_int @ ( remove1_int @ A @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5987_nth__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_VEBT_VEBTi] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_s7982070591426661849_VEBTi @ ( butlast_VEBT_VEBTi @ Xs ) ) )
% 13.77/7.78 => ( ( nth_VEBT_VEBTi @ ( butlast_VEBT_VEBTi @ Xs ) @ N )
% 13.77/7.78 = ( nth_VEBT_VEBTi @ Xs @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5988_nth__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_int] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_size_list_int @ ( butlast_int @ Xs ) ) )
% 13.77/7.78 => ( ( nth_int @ ( butlast_int @ Xs ) @ N )
% 13.77/7.78 = ( nth_int @ Xs @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5989_nth__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ ( butlast_VEBT_VEBT @ Xs ) ) )
% 13.77/7.78 => ( ( nth_VEBT_VEBT @ ( butlast_VEBT_VEBT @ Xs ) @ N )
% 13.77/7.78 = ( nth_VEBT_VEBT @ Xs @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5990_nth__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_real] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_size_list_real @ ( butlast_real @ Xs ) ) )
% 13.77/7.78 => ( ( nth_real @ ( butlast_real @ Xs ) @ N )
% 13.77/7.78 = ( nth_real @ Xs @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5991_nth__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_o] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_size_list_o @ ( butlast_o @ Xs ) ) )
% 13.77/7.78 => ( ( nth_o @ ( butlast_o @ Xs ) @ N )
% 13.77/7.78 = ( nth_o @ Xs @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5992_nth__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_nat] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_size_list_nat @ ( butlast_nat @ Xs ) ) )
% 13.77/7.78 => ( ( nth_nat @ ( butlast_nat @ Xs ) @ N )
% 13.77/7.78 = ( nth_nat @ Xs @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5993_take__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 => ( ( take_VEBT_VEBT @ N @ ( butlast_VEBT_VEBT @ Xs ) )
% 13.77/7.78 = ( take_VEBT_VEBT @ N @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5994_take__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_real] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.78 => ( ( take_real @ N @ ( butlast_real @ Xs ) )
% 13.77/7.78 = ( take_real @ N @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5995_take__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_o] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.78 => ( ( take_o @ N @ ( butlast_o @ Xs ) )
% 13.77/7.78 = ( take_o @ N @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5996_take__butlast,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_nat] :
% 13.77/7.78 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 => ( ( take_nat @ N @ ( butlast_nat @ Xs ) )
% 13.77/7.78 = ( take_nat @ N @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5997_distinct__butlast__swap,axiom,
% 13.77/7.78 ! [Pq: list_nat,I: nat] :
% 13.77/7.78 ( ( distinct_nat @ Pq )
% 13.77/7.78 => ( distinct_nat @ ( butlast_nat @ ( list_update_nat @ Pq @ I @ ( last_nat @ Pq ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5998_distinct__butlast__swap,axiom,
% 13.77/7.78 ! [Pq: list_VEBT_VEBTi,I: nat] :
% 13.77/7.78 ( ( distinct_VEBT_VEBTi @ Pq )
% 13.77/7.78 => ( distinct_VEBT_VEBTi @ ( butlast_VEBT_VEBTi @ ( list_u6098035379799741383_VEBTi @ Pq @ I @ ( last_VEBT_VEBTi @ Pq ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_5999_distinct__butlast__swap,axiom,
% 13.77/7.78 ! [Pq: list_VEBT_VEBT,I: nat] :
% 13.77/7.78 ( ( distinct_VEBT_VEBT @ Pq )
% 13.77/7.78 => ( distinct_VEBT_VEBT @ ( butlast_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Pq @ I @ ( last_VEBT_VEBT @ Pq ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6000_butlast__take,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 => ( ( butlast_VEBT_VEBT @ ( take_VEBT_VEBT @ N @ Xs ) )
% 13.77/7.78 = ( take_VEBT_VEBT @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6001_butlast__take,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_real] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs ) )
% 13.77/7.78 => ( ( butlast_real @ ( take_real @ N @ Xs ) )
% 13.77/7.78 = ( take_real @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6002_butlast__take,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_o] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs ) )
% 13.77/7.78 => ( ( butlast_o @ ( take_o @ N @ Xs ) )
% 13.77/7.78 = ( take_o @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6003_butlast__take,axiom,
% 13.77/7.78 ! [N: nat,Xs: list_nat] :
% 13.77/7.78 ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 => ( ( butlast_nat @ ( take_nat @ N @ Xs ) )
% 13.77/7.78 = ( take_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ Xs ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6004_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 13.77/7.78 ! [A4: set_Code_integer,X: code_integer] :
% 13.77/7.78 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.78 => ( ( linord2324613341767563021nteger @ ( minus_2355218937544613996nteger @ A4 @ ( insert_Code_integer @ X @ bot_bo3990330152332043303nteger ) ) )
% 13.77/7.78 = ( remove1_Code_integer @ X @ ( linord2324613341767563021nteger @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6005_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 13.77/7.78 ! [A4: set_int,X: int] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ( ( linord2612477271533052124et_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) )
% 13.77/7.78 = ( remove1_int @ X @ ( linord2612477271533052124et_int @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6006_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 13.77/7.78 ! [A4: set_o,X: $o] :
% 13.77/7.78 ( ( finite_finite_o @ A4 )
% 13.77/7.78 => ( ( linord3142498349692569832_set_o @ ( minus_minus_set_o @ A4 @ ( insert_o @ X @ bot_bot_set_o ) ) )
% 13.77/7.78 = ( remove1_o @ X @ ( linord3142498349692569832_set_o @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6007_sorted__list__of__set_Osorted__key__list__of__set__remove,axiom,
% 13.77/7.78 ! [A4: set_nat,X: nat] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ( ( linord2614967742042102400et_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 13.77/7.78 = ( remove1_nat @ X @ ( linord2614967742042102400et_nat @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6008_Cons__lenlex__iff,axiom,
% 13.77/7.78 ! [M: uint32,Ms: list_uint32,N: uint32,Ns: list_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.78 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ M @ Ms ) @ ( cons_uint32 @ N @ Ns ) ) @ ( lenlex_uint32 @ R ) )
% 13.77/7.78 = ( ( ord_less_nat @ ( size_s4844771616002835472uint32 @ Ms ) @ ( size_s4844771616002835472uint32 @ Ns ) )
% 13.77/7.78 | ( ( ( size_s4844771616002835472uint32 @ Ms )
% 13.77/7.78 = ( size_s4844771616002835472uint32 @ Ns ) )
% 13.77/7.78 & ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ M @ N ) @ R ) )
% 13.77/7.78 | ( ( M = N )
% 13.77/7.78 & ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Ms @ Ns ) @ ( lenlex_uint32 @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6009_Cons__lenlex__iff,axiom,
% 13.77/7.78 ! [M: int,Ms: list_int,N: int,Ns: list_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.78 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ M @ Ms ) @ ( cons_int @ N @ Ns ) ) @ ( lenlex_int @ R ) )
% 13.77/7.78 = ( ( ord_less_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) )
% 13.77/7.78 | ( ( ( size_size_list_int @ Ms )
% 13.77/7.78 = ( size_size_list_int @ Ns ) )
% 13.77/7.78 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ M @ N ) @ R ) )
% 13.77/7.78 | ( ( M = N )
% 13.77/7.78 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6010_Cons__lenlex__iff,axiom,
% 13.77/7.78 ! [M: vEBT_VEBT,Ms: list_VEBT_VEBT,N: vEBT_VEBT,Ns: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 13.77/7.78 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ M @ Ms ) @ ( cons_VEBT_VEBT @ N @ Ns ) ) @ ( lenlex_VEBT_VEBT @ R ) )
% 13.77/7.78 = ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) )
% 13.77/7.78 | ( ( ( size_s6755466524823107622T_VEBT @ Ms )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ Ns ) )
% 13.77/7.78 & ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ M @ N ) @ R ) )
% 13.77/7.78 | ( ( M = N )
% 13.77/7.78 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6011_Cons__lenlex__iff,axiom,
% 13.77/7.78 ! [M: real,Ms: list_real,N: real,Ns: list_real,R: set_Pr6218003697084177305l_real] :
% 13.77/7.78 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ ( cons_real @ M @ Ms ) @ ( cons_real @ N @ Ns ) ) @ ( lenlex_real @ R ) )
% 13.77/7.78 = ( ( ord_less_nat @ ( size_size_list_real @ Ms ) @ ( size_size_list_real @ Ns ) )
% 13.77/7.78 | ( ( ( size_size_list_real @ Ms )
% 13.77/7.78 = ( size_size_list_real @ Ns ) )
% 13.77/7.78 & ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ M @ N ) @ R ) )
% 13.77/7.78 | ( ( M = N )
% 13.77/7.78 & ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Ms @ Ns ) @ ( lenlex_real @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6012_Cons__lenlex__iff,axiom,
% 13.77/7.78 ! [M: $o,Ms: list_o,N: $o,Ns: list_o,R: set_Product_prod_o_o] :
% 13.77/7.78 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ M @ Ms ) @ ( cons_o @ N @ Ns ) ) @ ( lenlex_o @ R ) )
% 13.77/7.78 = ( ( ord_less_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) )
% 13.77/7.78 | ( ( ( size_size_list_o @ Ms )
% 13.77/7.78 = ( size_size_list_o @ Ns ) )
% 13.77/7.78 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ M @ N ) @ R ) )
% 13.77/7.78 | ( ( M = N )
% 13.77/7.78 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6013_Cons__lenlex__iff,axiom,
% 13.77/7.78 ! [M: nat,Ms: list_nat,N: nat,Ns: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.78 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ M @ Ms ) @ ( cons_nat @ N @ Ns ) ) @ ( lenlex_nat @ R ) )
% 13.77/7.78 = ( ( ord_less_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) )
% 13.77/7.78 | ( ( ( size_size_list_nat @ Ms )
% 13.77/7.78 = ( size_size_list_nat @ Ns ) )
% 13.77/7.78 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ R ) )
% 13.77/7.78 | ( ( M = N )
% 13.77/7.78 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6014_listrel1__iff__update,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi,R: set_Pr2227491710730465451_VEBTi] :
% 13.77/7.78 ( ( member4173000155140927252_VEBTi @ ( produc4384243565435462691_VEBTi @ Xs @ Ys ) @ ( listrel1_VEBT_VEBTi @ R ) )
% 13.77/7.78 = ( ? [Y4: vEBT_VEBTi,N6: nat] :
% 13.77/7.78 ( ( member660371905731732212_VEBTi @ ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ N6 ) @ Y4 ) @ R )
% 13.77/7.78 & ( ord_less_nat @ N6 @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 & ( Ys
% 13.77/7.78 = ( list_u6098035379799741383_VEBTi @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6015_listrel1__iff__update,axiom,
% 13.77/7.78 ! [Xs: list_uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.78 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( listrel1_uint32 @ R ) )
% 13.77/7.78 = ( ? [Y4: uint32,N6: nat] :
% 13.77/7.78 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ N6 ) @ Y4 ) @ R )
% 13.77/7.78 & ( ord_less_nat @ N6 @ ( size_s4844771616002835472uint32 @ Xs ) )
% 13.77/7.78 & ( Ys
% 13.77/7.78 = ( list_update_uint32 @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6016_listrel1__iff__update,axiom,
% 13.77/7.78 ! [Xs: list_int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.78 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R ) )
% 13.77/7.78 = ( ? [Y4: int,N6: nat] :
% 13.77/7.78 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ ( nth_int @ Xs @ N6 ) @ Y4 ) @ R )
% 13.77/7.78 & ( ord_less_nat @ N6 @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 & ( Ys
% 13.77/7.78 = ( list_update_int @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6017_listrel1__iff__update,axiom,
% 13.77/7.78 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 13.77/7.78 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs @ Ys ) @ ( listrel1_VEBT_VEBT @ R ) )
% 13.77/7.78 = ( ? [Y4: vEBT_VEBT,N6: nat] :
% 13.77/7.78 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ N6 ) @ Y4 ) @ R )
% 13.77/7.78 & ( ord_less_nat @ N6 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 & ( Ys
% 13.77/7.78 = ( list_u1324408373059187874T_VEBT @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6018_listrel1__iff__update,axiom,
% 13.77/7.78 ! [Xs: list_real,Ys: list_real,R: set_Pr6218003697084177305l_real] :
% 13.77/7.78 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Xs @ Ys ) @ ( listrel1_real @ R ) )
% 13.77/7.78 = ( ? [Y4: real,N6: nat] :
% 13.77/7.78 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ ( nth_real @ Xs @ N6 ) @ Y4 ) @ R )
% 13.77/7.78 & ( ord_less_nat @ N6 @ ( size_size_list_real @ Xs ) )
% 13.77/7.78 & ( Ys
% 13.77/7.78 = ( list_update_real @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6019_listrel1__iff__update,axiom,
% 13.77/7.78 ! [Xs: list_o,Ys: list_o,R: set_Product_prod_o_o] :
% 13.77/7.78 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( listrel1_o @ R ) )
% 13.77/7.78 = ( ? [Y4: $o,N6: nat] :
% 13.77/7.78 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs @ N6 ) @ Y4 ) @ R )
% 13.77/7.78 & ( ord_less_nat @ N6 @ ( size_size_list_o @ Xs ) )
% 13.77/7.78 & ( Ys
% 13.77/7.78 = ( list_update_o @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6020_listrel1__iff__update,axiom,
% 13.77/7.78 ! [Xs: list_nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.78 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 13.77/7.78 = ( ? [Y4: nat,N6: nat] :
% 13.77/7.78 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ ( nth_nat @ Xs @ N6 ) @ Y4 ) @ R )
% 13.77/7.78 & ( ord_less_nat @ N6 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 & ( Ys
% 13.77/7.78 = ( list_update_nat @ Xs @ N6 @ Y4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6021_total__on__singleton,axiom,
% 13.77/7.78 ! [X: vEBT_VEBT] : ( total_on_VEBT_VEBT @ ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) @ ( insert494605675473494903T_VEBT @ ( produc537772716801021591T_VEBT @ X @ X ) @ bot_bo5088076668136028147T_VEBT ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6022_total__on__singleton,axiom,
% 13.77/7.78 ! [X: uint32] : ( total_on_uint32 @ ( insert_uint32 @ X @ bot_bot_set_uint32 ) @ ( insert4454361187789264009uint32 @ ( produc1400373151660368625uint32 @ X @ X ) @ bot_bo8438649754162204037uint32 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6023_total__on__singleton,axiom,
% 13.77/7.78 ! [X: nat] : ( total_on_nat @ ( insert_nat @ X @ bot_bot_set_nat ) @ ( insert8211810215607154385at_nat @ ( product_Pair_nat_nat @ X @ X ) @ bot_bo2099793752762293965at_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6024_total__on__singleton,axiom,
% 13.77/7.78 ! [X: int] : ( total_on_int @ ( insert_int @ X @ bot_bot_set_int ) @ ( insert5033312907999012233nt_int @ ( product_Pair_int_int @ X @ X ) @ bot_bo1796632182523588997nt_int ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6025_total__on__singleton,axiom,
% 13.77/7.78 ! [X: $o] : ( total_on_o @ ( insert_o @ X @ bot_bot_set_o ) @ ( insert6201435330877294327od_o_o @ ( product_Pair_o_o @ X @ X ) @ bot_bo7073875226086086771od_o_o ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6026_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBTi] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr6329974346453275474_VEBTi @ ( zip_VE793581609497812771_VEBTi @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc436343169921013763_VEBTi @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6027_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_int] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr2733638074192486473Ti_int @ ( zip_VEBT_VEBTi_int @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc7190175284220460154Ti_int @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6028_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_int,Ys: list_VEBT_VEBTi] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr5092243222550848201_VEBTi @ ( zip_int_VEBT_VEBTi @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc4497823428076633978_VEBTi @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6029_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_uint32,Ys: list_uint32] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_s4844771616002835472uint32 @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s4844771616002835472uint32 @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr6139322253122866368uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc1400373151660368625uint32 @ ( nth_uint32 @ Xs @ I ) @ ( nth_uint32 @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6030_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_int,Ys: list_int] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr4439495888332055232nt_int @ ( zip_int_int @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( product_Pair_int_int @ ( nth_int @ Xs @ I ) @ ( nth_int @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6031_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr8725177398587324397T_VEBT @ ( zip_VE7413257051550508102T_VEBT @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc7053807326796202854T_VEBT @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6032_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_int,Ys: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr3474266648193625910T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc3329399203697025711T_VEBT @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6033_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_real] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr3433448822664029129i_real @ ( zip_VEBT_VEBTi_real @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc8457151488442208762i_real @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_real @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6034_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_int,Ys: list_real] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_real @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr731366597535767232t_real @ ( zip_int_real @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc801115645435158769t_real @ ( nth_int @ Xs @ I ) @ ( nth_real @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6035_nth__zip,axiom,
% 13.77/7.78 ! [I: nat,Xs: list_VEBT_VEBTi,Ys: list_o] :
% 13.77/7.78 ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_o @ Ys ) )
% 13.77/7.78 => ( ( nth_Pr3306050735993963089EBTi_o @ ( zip_VEBT_VEBTi_o @ Xs @ Ys ) @ I )
% 13.77/7.78 = ( produc8194178580519725514EBTi_o @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_o @ Ys @ I ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6036_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBT > assn,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBT,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L7265847600308530106T_VEBT @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2497118539674116125T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L7265847600308530106T_VEBT @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6037_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: vEBT_VEBTi > nat > assn,Xs: list_VEBT_VEBTi,Xsi: list_nat,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L8930081998596925642Ti_nat @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L2809031099982602151Ti_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L8930081998596925642Ti_nat @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6038_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: vEBT_VEBTi > vEBT_VEBTi > assn,Xs: list_VEBT_VEBTi,Xsi: list_VEBT_VEBTi,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L1891944875198410415_VEBTi @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L886525131989349516_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1891944875198410415_VEBTi @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6039_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: vEBT_VEBTi > int > assn,Xs: list_VEBT_VEBTi,Xsi: list_int,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L8927591528087875366Ti_int @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s7982070591426661849_VEBTi @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBTi @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L2806540629473551875Ti_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s7982070591426661849_VEBTi @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L8927591528087875366Ti_int @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6040_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: int > vEBT_VEBT > assn,Xs: list_int,Xsi: list_VEBT_VEBT,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L1664421287176695555T_VEBT @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L2018189785592951398T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1664421287176695555T_VEBT @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6041_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: int > nat > assn,Xs: list_int,Xsi: list_nat,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L77084186935402305nt_nat @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8891422820522952478nt_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L77084186935402305nt_nat @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6042_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: int > vEBT_VEBTi > assn,Xs: list_int,Xsi: list_VEBT_VEBTi,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L6235239671944049190_VEBTi @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_VEBT_VEBTi @ Xsi @ I ) ) @ ( vEBT_L114188773329725699_VEBTi @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L6235239671944049190_VEBTi @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6043_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: int > int > assn,Xs: list_int,Xsi: list_int,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L74593716426352029nt_int @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_int @ Xs @ I ) @ ( nth_int @ Xsi @ I ) ) @ ( vEBT_L8888932350013902202nt_int @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L74593716426352029nt_int @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6044_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: vEBT_VEBT > vEBT_VEBT > assn,Xs: list_VEBT_VEBT,Xsi: list_VEBT_VEBT,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L1279224858307276611T_VEBT @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_VEBT_VEBT @ Xsi @ I ) ) @ ( vEBT_L3204528365124325536T_VEBT @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L1279224858307276611T_VEBT @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6045_rule__at__index,axiom,
% 13.77/7.78 ! [P2: assn,A4: vEBT_VEBT > nat > assn,Xs: list_VEBT_VEBT,Xsi: list_nat,F2: assn,I: nat,C2: heap_T8145700208782473153_VEBTi,Q4: vEBT_VEBTi > assn,F4: vEBT_VEBTi > assn] :
% 13.77/7.78 ( ( entails @ P2 @ ( times_times_assn @ ( vEBT_L8296926524756676353BT_nat @ A4 @ Xs @ Xsi ) @ F2 ) )
% 13.77/7.78 => ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 13.77/7.78 => ( ( hoare_1429296392585015714_VEBTi @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ F2 ) @ C2 @ Q4 )
% 13.77/7.78 => ( ! [R4: vEBT_VEBTi] : ( entails @ ( Q4 @ R4 ) @ ( times_times_assn @ ( times_times_assn @ ( A4 @ ( nth_VEBT_VEBT @ Xs @ I ) @ ( nth_nat @ Xsi @ I ) ) @ ( vEBT_L8650695023172932196BT_nat @ ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) @ ( insert_nat @ I @ bot_bot_set_nat ) ) @ A4 @ Xs @ Xsi ) ) @ ( F4 @ R4 ) ) )
% 13.77/7.78 => ( hoare_1429296392585015714_VEBTi @ P2 @ C2
% 13.77/7.78 @ ^ [R5: vEBT_VEBTi] : ( times_times_assn @ ( vEBT_L8296926524756676353BT_nat @ A4 @ Xs @ Xsi ) @ ( F4 @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6046_atLeast1__lessThan__eq__remove0,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.78 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6047_Bernoulli__inequality,axiom,
% 13.77/7.78 ! [X: real,N: nat] :
% 13.77/7.78 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.78 => ( 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 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6048_set__vebt_H__def,axiom,
% 13.77/7.78 ( vEBT_VEBT_set_vebt
% 13.77/7.78 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6049_of__nat__eq__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ( semiri5074537144036343181t_real @ M )
% 13.77/7.78 = ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.78 = ( M = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6050_of__nat__eq__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ( semiri1314217659103216013at_int @ M )
% 13.77/7.78 = ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.78 = ( M = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6051_of__nat__eq__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ( semiri4939895301339042750nteger @ M )
% 13.77/7.78 = ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.78 = ( M = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6052_image__ident,axiom,
% 13.77/7.78 ! [Y7: set_nat] :
% 13.77/7.78 ( ( image_nat_nat
% 13.77/7.78 @ ^ [X4: nat] : X4
% 13.77/7.78 @ Y7 )
% 13.77/7.78 = Y7 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6053_image__ident,axiom,
% 13.77/7.78 ! [Y7: set_int] :
% 13.77/7.78 ( ( image_int_int
% 13.77/7.78 @ ^ [X4: int] : X4
% 13.77/7.78 @ Y7 )
% 13.77/7.78 = Y7 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6054_finite__Collect__disjI,axiom,
% 13.77/7.78 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 13.77/7.78 ( ( finite8100373058378681591st_nat
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 | ( Q2 @ X4 ) ) ) )
% 13.77/7.78 = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 13.77/7.78 & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6055_finite__Collect__disjI,axiom,
% 13.77/7.78 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 13.77/7.78 ( ( finite1152437895449049373et_nat
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 | ( Q2 @ X4 ) ) ) )
% 13.77/7.78 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 13.77/7.78 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6056_finite__Collect__disjI,axiom,
% 13.77/7.78 ! [P2: nat > $o,Q2: nat > $o] :
% 13.77/7.78 ( ( finite_finite_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 | ( Q2 @ X4 ) ) ) )
% 13.77/7.78 = ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 13.77/7.78 & ( finite_finite_nat @ ( collect_nat @ Q2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6057_finite__Collect__disjI,axiom,
% 13.77/7.78 ! [P2: int > $o,Q2: int > $o] :
% 13.77/7.78 ( ( finite_finite_int
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 | ( Q2 @ X4 ) ) ) )
% 13.77/7.78 = ( ( finite_finite_int @ ( collect_int @ P2 ) )
% 13.77/7.78 & ( finite_finite_int @ ( collect_int @ Q2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6058_finite__Collect__disjI,axiom,
% 13.77/7.78 ! [P2: complex > $o,Q2: complex > $o] :
% 13.77/7.78 ( ( finite3207457112153483333omplex
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 | ( Q2 @ X4 ) ) ) )
% 13.77/7.78 = ( ( finite3207457112153483333omplex @ ( collect_complex @ P2 ) )
% 13.77/7.78 & ( finite3207457112153483333omplex @ ( collect_complex @ Q2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6059_finite__Collect__disjI,axiom,
% 13.77/7.78 ! [P2: code_integer > $o,Q2: code_integer > $o] :
% 13.77/7.78 ( ( finite6017078050557962740nteger
% 13.77/7.78 @ ( collect_Code_integer
% 13.77/7.78 @ ^ [X4: code_integer] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 | ( Q2 @ X4 ) ) ) )
% 13.77/7.78 = ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 13.77/7.78 & ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6060_finite__Collect__conjI,axiom,
% 13.77/7.78 ! [P2: list_nat > $o,Q2: list_nat > $o] :
% 13.77/7.78 ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 13.77/7.78 | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q2 ) ) )
% 13.77/7.78 => ( finite8100373058378681591st_nat
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6061_finite__Collect__conjI,axiom,
% 13.77/7.78 ! [P2: set_nat > $o,Q2: set_nat > $o] :
% 13.77/7.78 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 13.77/7.78 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) )
% 13.77/7.78 => ( finite1152437895449049373et_nat
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6062_finite__Collect__conjI,axiom,
% 13.77/7.78 ! [P2: nat > $o,Q2: nat > $o] :
% 13.77/7.78 ( ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 13.77/7.78 | ( finite_finite_nat @ ( collect_nat @ Q2 ) ) )
% 13.77/7.78 => ( finite_finite_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6063_finite__Collect__conjI,axiom,
% 13.77/7.78 ! [P2: int > $o,Q2: int > $o] :
% 13.77/7.78 ( ( ( finite_finite_int @ ( collect_int @ P2 ) )
% 13.77/7.78 | ( finite_finite_int @ ( collect_int @ Q2 ) ) )
% 13.77/7.78 => ( finite_finite_int
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6064_finite__Collect__conjI,axiom,
% 13.77/7.78 ! [P2: complex > $o,Q2: complex > $o] :
% 13.77/7.78 ( ( ( finite3207457112153483333omplex @ ( collect_complex @ P2 ) )
% 13.77/7.78 | ( finite3207457112153483333omplex @ ( collect_complex @ Q2 ) ) )
% 13.77/7.78 => ( finite3207457112153483333omplex
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6065_finite__Collect__conjI,axiom,
% 13.77/7.78 ! [P2: code_integer > $o,Q2: code_integer > $o] :
% 13.77/7.78 ( ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 13.77/7.78 | ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q2 ) ) )
% 13.77/7.78 => ( finite6017078050557962740nteger
% 13.77/7.78 @ ( collect_Code_integer
% 13.77/7.78 @ ^ [X4: code_integer] :
% 13.77/7.78 ( ( P2 @ X4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6066_succ__empty,axiom,
% 13.77/7.78 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.78 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.78 => ( ( ( vEBT_vebt_succ @ T @ X )
% 13.77/7.78 = none_nat )
% 13.77/7.78 = ( ( collect_nat
% 13.77/7.78 @ ^ [Y4: nat] :
% 13.77/7.78 ( ( vEBT_vebt_member @ T @ Y4 )
% 13.77/7.78 & ( ord_less_nat @ X @ Y4 ) ) )
% 13.77/7.78 = bot_bot_set_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6067_pred__empty,axiom,
% 13.77/7.78 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.78 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.78 => ( ( ( vEBT_vebt_pred @ T @ X )
% 13.77/7.78 = none_nat )
% 13.77/7.78 = ( ( collect_nat
% 13.77/7.78 @ ^ [Y4: nat] :
% 13.77/7.78 ( ( vEBT_vebt_member @ T @ Y4 )
% 13.77/7.78 & ( ord_less_nat @ Y4 @ X ) ) )
% 13.77/7.78 = bot_bot_set_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6068_foldr__mono,axiom,
% 13.77/7.78 ! [Xs: list_nat,Ys: list_nat,C2: nat,D: nat] :
% 13.77/7.78 ( ( ( size_size_list_nat @ Xs )
% 13.77/7.78 = ( size_size_list_nat @ Ys ) )
% 13.77/7.78 => ( ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 => ( ord_less_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) )
% 13.77/7.78 => ( ( ord_less_eq_nat @ C2 @ D )
% 13.77/7.78 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ C2 ) @ ( size_size_list_nat @ Ys ) ) @ ( foldr_nat_nat @ plus_plus_nat @ Ys @ D ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6069_lessThan__iff,axiom,
% 13.77/7.78 ! [I: set_nat,K: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 13.77/7.78 = ( ord_less_set_nat @ I @ K ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6070_lessThan__iff,axiom,
% 13.77/7.78 ! [I: rat,K: rat] :
% 13.77/7.78 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 13.77/7.78 = ( ord_less_rat @ I @ K ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6071_lessThan__iff,axiom,
% 13.77/7.78 ! [I: num,K: num] :
% 13.77/7.78 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 13.77/7.78 = ( ord_less_num @ I @ K ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6072_lessThan__iff,axiom,
% 13.77/7.78 ! [I: nat,K: nat] :
% 13.77/7.78 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 13.77/7.78 = ( ord_less_nat @ I @ K ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6073_lessThan__iff,axiom,
% 13.77/7.78 ! [I: int,K: int] :
% 13.77/7.78 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 13.77/7.78 = ( ord_less_int @ I @ K ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6074_lessThan__iff,axiom,
% 13.77/7.78 ! [I: real,K: real] :
% 13.77/7.78 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 13.77/7.78 = ( ord_less_real @ I @ K ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6075_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,A2: list_VEBT_VEBT,B2: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ B ) )
% 13.77/7.78 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 13.77/7.78 => ( ( ( zip_VE537291747668921783T_VEBT @ A @ B )
% 13.77/7.78 = ( zip_VE537291747668921783T_VEBT @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6076_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_VEBT_VEBT,B: list_real,A2: list_VEBT_VEBT,B2: list_real] :
% 13.77/7.78 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.78 = ( size_size_list_real @ B ) )
% 13.77/7.78 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.78 = ( size_size_list_real @ B2 ) )
% 13.77/7.78 => ( ( ( zip_VEBT_VEBT_real @ A @ B )
% 13.77/7.78 = ( zip_VEBT_VEBT_real @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6077_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_VEBT_VEBT,B: list_o,A2: list_VEBT_VEBT,B2: list_o] :
% 13.77/7.78 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.78 = ( size_size_list_o @ B ) )
% 13.77/7.78 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.78 = ( size_size_list_o @ B2 ) )
% 13.77/7.78 => ( ( ( zip_VEBT_VEBT_o @ A @ B )
% 13.77/7.78 = ( zip_VEBT_VEBT_o @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6078_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_VEBT_VEBT,B: list_nat,A2: list_VEBT_VEBT,B2: list_nat] :
% 13.77/7.78 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.78 = ( size_size_list_nat @ B ) )
% 13.77/7.78 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.78 = ( size_size_list_nat @ B2 ) )
% 13.77/7.78 => ( ( ( zip_VEBT_VEBT_nat @ A @ B )
% 13.77/7.78 = ( zip_VEBT_VEBT_nat @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6079_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_real,B: list_VEBT_VEBT,A2: list_real,B2: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ( size_size_list_real @ A )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ B ) )
% 13.77/7.78 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 13.77/7.78 => ( ( ( zip_real_VEBT_VEBT @ A @ B )
% 13.77/7.78 = ( zip_real_VEBT_VEBT @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6080_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_real,B: list_real,A2: list_real,B2: list_real] :
% 13.77/7.78 ( ( ( size_size_list_real @ A )
% 13.77/7.78 = ( size_size_list_real @ B ) )
% 13.77/7.78 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.78 = ( size_size_list_real @ B2 ) )
% 13.77/7.78 => ( ( ( zip_real_real @ A @ B )
% 13.77/7.78 = ( zip_real_real @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6081_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_real,B: list_o,A2: list_real,B2: list_o] :
% 13.77/7.78 ( ( ( size_size_list_real @ A )
% 13.77/7.78 = ( size_size_list_o @ B ) )
% 13.77/7.78 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.78 = ( size_size_list_o @ B2 ) )
% 13.77/7.78 => ( ( ( zip_real_o @ A @ B )
% 13.77/7.78 = ( zip_real_o @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6082_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_real,B: list_nat,A2: list_real,B2: list_nat] :
% 13.77/7.78 ( ( ( size_size_list_real @ A )
% 13.77/7.78 = ( size_size_list_nat @ B ) )
% 13.77/7.78 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.78 = ( size_size_list_nat @ B2 ) )
% 13.77/7.78 => ( ( ( zip_real_nat @ A @ B )
% 13.77/7.78 = ( zip_real_nat @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6083_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_o,B: list_VEBT_VEBT,A2: list_o,B2: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ( size_size_list_o @ A )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ B ) )
% 13.77/7.78 => ( ( ( size_size_list_o @ A2 )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 13.77/7.78 => ( ( ( zip_o_VEBT_VEBT @ A @ B )
% 13.77/7.78 = ( zip_o_VEBT_VEBT @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6084_zip__eq__zip__same__len,axiom,
% 13.77/7.78 ! [A: list_o,B: list_real,A2: list_o,B2: list_real] :
% 13.77/7.78 ( ( ( size_size_list_o @ A )
% 13.77/7.78 = ( size_size_list_real @ B ) )
% 13.77/7.78 => ( ( ( size_size_list_o @ A2 )
% 13.77/7.78 = ( size_size_list_real @ B2 ) )
% 13.77/7.78 => ( ( ( zip_o_real @ A @ B )
% 13.77/7.78 = ( zip_o_real @ A2 @ B2 ) )
% 13.77/7.78 = ( ( A = A2 )
% 13.77/7.78 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6085_finite__lessThan,axiom,
% 13.77/7.78 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6086_foldr__zero,axiom,
% 13.77/7.78 ! [Xs: list_nat,D: nat] :
% 13.77/7.78 ( ! [I2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 13.77/7.78 => ( ord_less_nat @ zero_zero_nat @ ( nth_nat @ Xs @ I2 ) ) )
% 13.77/7.78 => ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ ( minus_minus_nat @ ( foldr_nat_nat @ plus_plus_nat @ Xs @ D ) @ D ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6087_sum_Oneutral__const,axiom,
% 13.77/7.78 ! [A4: set_nat] :
% 13.77/7.78 ( ( groups3542108847815614940at_nat
% 13.77/7.78 @ ^ [Uu3: nat] : zero_zero_nat
% 13.77/7.78 @ A4 )
% 13.77/7.78 = zero_zero_nat ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6088_sum_Oneutral__const,axiom,
% 13.77/7.78 ! [A4: set_complex] :
% 13.77/7.78 ( ( groups7754918857620584856omplex
% 13.77/7.78 @ ^ [Uu3: complex] : zero_zero_complex
% 13.77/7.78 @ A4 )
% 13.77/7.78 = zero_zero_complex ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6089_sum_Oneutral__const,axiom,
% 13.77/7.78 ! [A4: set_nat] :
% 13.77/7.78 ( ( groups6591440286371151544t_real
% 13.77/7.78 @ ^ [Uu3: nat] : zero_zero_real
% 13.77/7.78 @ A4 )
% 13.77/7.78 = zero_zero_real ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6090_sum_Oneutral__const,axiom,
% 13.77/7.78 ! [A4: set_int] :
% 13.77/7.78 ( ( groups4538972089207619220nt_int
% 13.77/7.78 @ ^ [Uu3: int] : zero_zero_int
% 13.77/7.78 @ A4 )
% 13.77/7.78 = zero_zero_int ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6091_singleton__conv2,axiom,
% 13.77/7.78 ! [A: vEBT_VEBT] :
% 13.77/7.78 ( ( collect_VEBT_VEBT
% 13.77/7.78 @ ( ^ [Y6: vEBT_VEBT,Z4: vEBT_VEBT] : ( Y6 = Z4 )
% 13.77/7.78 @ A ) )
% 13.77/7.78 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6092_singleton__conv2,axiom,
% 13.77/7.78 ! [A: complex] :
% 13.77/7.78 ( ( collect_complex
% 13.77/7.78 @ ( ^ [Y6: complex,Z4: complex] : ( Y6 = Z4 )
% 13.77/7.78 @ A ) )
% 13.77/7.78 = ( insert_complex @ A @ bot_bot_set_complex ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6093_singleton__conv2,axiom,
% 13.77/7.78 ! [A: list_nat] :
% 13.77/7.78 ( ( collect_list_nat
% 13.77/7.78 @ ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 )
% 13.77/7.78 @ A ) )
% 13.77/7.78 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6094_singleton__conv2,axiom,
% 13.77/7.78 ! [A: set_nat] :
% 13.77/7.78 ( ( collect_set_nat
% 13.77/7.78 @ ( ^ [Y6: set_nat,Z4: set_nat] : ( Y6 = Z4 )
% 13.77/7.78 @ A ) )
% 13.77/7.78 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6095_singleton__conv2,axiom,
% 13.77/7.78 ! [A: nat] :
% 13.77/7.78 ( ( collect_nat
% 13.77/7.78 @ ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.78 @ A ) )
% 13.77/7.78 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6096_singleton__conv2,axiom,
% 13.77/7.78 ! [A: int] :
% 13.77/7.78 ( ( collect_int
% 13.77/7.78 @ ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.78 @ A ) )
% 13.77/7.78 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6097_singleton__conv2,axiom,
% 13.77/7.78 ! [A: $o] :
% 13.77/7.78 ( ( collect_o
% 13.77/7.78 @ ( ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 )
% 13.77/7.78 @ A ) )
% 13.77/7.78 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6098_singleton__conv,axiom,
% 13.77/7.78 ! [A: vEBT_VEBT] :
% 13.77/7.78 ( ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] : ( X4 = A ) )
% 13.77/7.78 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6099_singleton__conv,axiom,
% 13.77/7.78 ! [A: complex] :
% 13.77/7.78 ( ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] : ( X4 = A ) )
% 13.77/7.78 = ( insert_complex @ A @ bot_bot_set_complex ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6100_singleton__conv,axiom,
% 13.77/7.78 ! [A: list_nat] :
% 13.77/7.78 ( ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] : ( X4 = A ) )
% 13.77/7.78 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6101_singleton__conv,axiom,
% 13.77/7.78 ! [A: set_nat] :
% 13.77/7.78 ( ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] : ( X4 = A ) )
% 13.77/7.78 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6102_singleton__conv,axiom,
% 13.77/7.78 ! [A: nat] :
% 13.77/7.78 ( ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] : ( X4 = A ) )
% 13.77/7.78 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6103_singleton__conv,axiom,
% 13.77/7.78 ! [A: int] :
% 13.77/7.78 ( ( collect_int
% 13.77/7.78 @ ^ [X4: int] : ( X4 = A ) )
% 13.77/7.78 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6104_singleton__conv,axiom,
% 13.77/7.78 ! [A: $o] :
% 13.77/7.78 ( ( collect_o
% 13.77/7.78 @ ^ [X4: $o] : ( X4 = A ) )
% 13.77/7.78 = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6105_finite__Collect__less__nat,axiom,
% 13.77/7.78 ! [K: nat] :
% 13.77/7.78 ( finite_finite_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [N6: nat] : ( ord_less_nat @ N6 @ K ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6106_finite__Collect__le__nat,axiom,
% 13.77/7.78 ! [K: nat] :
% 13.77/7.78 ( finite_finite_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [N6: nat] : ( ord_less_eq_nat @ N6 @ K ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6107_card__Collect__less__nat,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( finite_card_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 13.77/7.78 = N ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6108_of__nat__eq__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ( semiri681578069525770553at_rat @ M )
% 13.77/7.78 = zero_zero_rat )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6109_of__nat__eq__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ( semiri1316708129612266289at_nat @ M )
% 13.77/7.78 = zero_zero_nat )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6110_of__nat__eq__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ( semiri5074537144036343181t_real @ M )
% 13.77/7.78 = zero_zero_real )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6111_of__nat__eq__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ( semiri1314217659103216013at_int @ M )
% 13.77/7.78 = zero_zero_int )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6112_of__nat__eq__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ( semiri4939895301339042750nteger @ M )
% 13.77/7.78 = zero_z3403309356797280102nteger )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6113_of__nat__0__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( zero_zero_rat
% 13.77/7.78 = ( semiri681578069525770553at_rat @ N ) )
% 13.77/7.78 = ( zero_zero_nat = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6114_of__nat__0__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( zero_zero_nat
% 13.77/7.78 = ( semiri1316708129612266289at_nat @ N ) )
% 13.77/7.78 = ( zero_zero_nat = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6115_of__nat__0__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( zero_zero_real
% 13.77/7.78 = ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.78 = ( zero_zero_nat = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6116_of__nat__0__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( zero_zero_int
% 13.77/7.78 = ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.78 = ( zero_zero_nat = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6117_of__nat__0__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( zero_z3403309356797280102nteger
% 13.77/7.78 = ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.78 = ( zero_zero_nat = N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6118_semiring__1__class_Oof__nat__0,axiom,
% 13.77/7.78 ( ( semiri2565882477558803405uint32 @ zero_zero_nat )
% 13.77/7.78 = zero_zero_uint32 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6119_semiring__1__class_Oof__nat__0,axiom,
% 13.77/7.78 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 13.77/7.78 = zero_zero_rat ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6120_semiring__1__class_Oof__nat__0,axiom,
% 13.77/7.78 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 13.77/7.78 = zero_zero_nat ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6121_semiring__1__class_Oof__nat__0,axiom,
% 13.77/7.78 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 13.77/7.78 = zero_zero_real ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6122_semiring__1__class_Oof__nat__0,axiom,
% 13.77/7.78 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 13.77/7.78 = zero_zero_int ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6123_semiring__1__class_Oof__nat__0,axiom,
% 13.77/7.78 ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 13.77/7.78 = zero_z3403309356797280102nteger ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6124_of__nat__less__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 13.77/7.78 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6125_of__nat__less__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 13.77/7.78 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6126_of__nat__less__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.78 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6127_of__nat__less__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.78 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6128_of__nat__less__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.78 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6129_of__nat__le__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.78 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6130_of__nat__le__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.78 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6131_of__nat__le__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 13.77/7.78 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6132_of__nat__le__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 13.77/7.78 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6133_of__nat__le__iff,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.78 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6134_of__nat__add,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 13.77/7.78 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6135_of__nat__add,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 13.77/7.78 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6136_of__nat__add,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 13.77/7.78 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6137_of__nat__add,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 13.77/7.78 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6138_of__nat__add,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N ) )
% 13.77/7.78 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6139_of__nat__1,axiom,
% 13.77/7.78 ( ( semiri2565882477558803405uint32 @ one_one_nat )
% 13.77/7.78 = one_one_uint32 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6140_of__nat__1,axiom,
% 13.77/7.78 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 13.77/7.78 = one_one_rat ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6141_of__nat__1,axiom,
% 13.77/7.78 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 13.77/7.78 = one_one_nat ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6142_of__nat__1,axiom,
% 13.77/7.78 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 13.77/7.78 = one_one_real ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6143_of__nat__1,axiom,
% 13.77/7.78 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 13.77/7.78 = one_one_int ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6144_of__nat__1,axiom,
% 13.77/7.78 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 13.77/7.78 = one_one_Code_integer ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6145_of__nat__1__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( one_one_rat
% 13.77/7.78 = ( semiri681578069525770553at_rat @ N ) )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6146_of__nat__1__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( one_one_nat
% 13.77/7.78 = ( semiri1316708129612266289at_nat @ N ) )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6147_of__nat__1__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( one_one_real
% 13.77/7.78 = ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6148_of__nat__1__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( one_one_int
% 13.77/7.78 = ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6149_of__nat__1__eq__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( one_one_Code_integer
% 13.77/7.78 = ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6150_of__nat__eq__1__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ( semiri681578069525770553at_rat @ N )
% 13.77/7.78 = one_one_rat )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6151_of__nat__eq__1__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ( semiri1316708129612266289at_nat @ N )
% 13.77/7.78 = one_one_nat )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6152_of__nat__eq__1__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ( semiri5074537144036343181t_real @ N )
% 13.77/7.78 = one_one_real )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6153_of__nat__eq__1__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ( semiri1314217659103216013at_int @ N )
% 13.77/7.78 = one_one_int )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6154_of__nat__eq__1__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ( semiri4939895301339042750nteger @ N )
% 13.77/7.78 = one_one_Code_integer )
% 13.77/7.78 = ( N = one_one_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6155_of__nat__mult,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri2565882477558803405uint32 @ ( times_times_nat @ M @ N ) )
% 13.77/7.78 = ( times_times_uint32 @ ( semiri2565882477558803405uint32 @ M ) @ ( semiri2565882477558803405uint32 @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6156_of__nat__mult,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 13.77/7.78 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6157_of__nat__mult,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 13.77/7.78 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6158_of__nat__mult,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 13.77/7.78 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6159_of__nat__mult,axiom,
% 13.77/7.78 ! [M: nat,N: nat] :
% 13.77/7.78 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 13.77/7.78 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6160_lessThan__subset__iff,axiom,
% 13.77/7.78 ! [X: rat,Y: rat] :
% 13.77/7.78 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 13.77/7.78 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6161_lessThan__subset__iff,axiom,
% 13.77/7.78 ! [X: num,Y: num] :
% 13.77/7.78 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 13.77/7.78 = ( ord_less_eq_num @ X @ Y ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6162_lessThan__subset__iff,axiom,
% 13.77/7.78 ! [X: nat,Y: nat] :
% 13.77/7.78 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 13.77/7.78 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6163_lessThan__subset__iff,axiom,
% 13.77/7.78 ! [X: int,Y: int] :
% 13.77/7.78 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 13.77/7.78 = ( ord_less_eq_int @ X @ Y ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6164_lessThan__subset__iff,axiom,
% 13.77/7.78 ! [X: real,Y: real] :
% 13.77/7.78 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 13.77/7.78 = ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6165_lessThan__0,axiom,
% 13.77/7.78 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 13.77/7.78 = bot_bot_set_nat ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6166_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > uint32] :
% 13.77/7.78 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.78 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups8325533452322294502uint32
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups8325533452322294502uint32
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6167_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_real,A: real,B: real > uint32] :
% 13.77/7.78 ( ( finite_finite_real @ S3 )
% 13.77/7.78 => ( ( ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups5944083974425963860uint32
% 13.77/7.78 @ ^ [K3: real] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups5944083974425963860uint32
% 13.77/7.78 @ ^ [K3: real] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6168_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_nat,A: nat,B: nat > uint32] :
% 13.77/7.78 ( ( finite_finite_nat @ S3 )
% 13.77/7.78 => ( ( ( member_nat @ A @ S3 )
% 13.77/7.78 => ( ( groups833757482993574392uint32
% 13.77/7.78 @ ^ [K3: nat] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_nat @ A @ S3 )
% 13.77/7.78 => ( ( groups833757482993574392uint32
% 13.77/7.78 @ ^ [K3: nat] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6169_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_int,A: int,B: int > uint32] :
% 13.77/7.78 ( ( finite_finite_int @ S3 )
% 13.77/7.78 => ( ( ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups5712668689793887828uint32
% 13.77/7.78 @ ^ [K3: int] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups5712668689793887828uint32
% 13.77/7.78 @ ^ [K3: int] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6170_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_complex,A: complex,B: complex > uint32] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.78 => ( ( ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups8736914816313324502uint32
% 13.77/7.78 @ ^ [K3: complex] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups8736914816313324502uint32
% 13.77/7.78 @ ^ [K3: complex] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6171_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_Code_integer,A: code_integer,B: code_integer > uint32] :
% 13.77/7.78 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.78 => ( ( ( member_Code_integer @ A @ S3 )
% 13.77/7.78 => ( ( groups8847630953604152069uint32
% 13.77/7.78 @ ^ [K3: code_integer] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_Code_integer @ A @ S3 )
% 13.77/7.78 => ( ( groups8847630953604152069uint32
% 13.77/7.78 @ ^ [K3: code_integer] : ( if_uint32 @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6172_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 13.77/7.78 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.78 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups2240296850493347238T_real
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups2240296850493347238T_real
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6173_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_real,A: real,B: real > real] :
% 13.77/7.78 ( ( finite_finite_real @ S3 )
% 13.77/7.78 => ( ( ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups8097168146408367636l_real
% 13.77/7.78 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups8097168146408367636l_real
% 13.77/7.78 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6174_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_int,A: int,B: int > real] :
% 13.77/7.78 ( ( finite_finite_int @ S3 )
% 13.77/7.78 => ( ( ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups8778361861064173332t_real
% 13.77/7.78 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups8778361861064173332t_real
% 13.77/7.78 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6175_sum_Odelta_H,axiom,
% 13.77/7.78 ! [S3: set_complex,A: complex,B: complex > real] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.78 => ( ( ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups5808333547571424918x_real
% 13.77/7.78 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups5808333547571424918x_real
% 13.77/7.78 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6176_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > uint32] :
% 13.77/7.78 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.78 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups8325533452322294502uint32
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups8325533452322294502uint32
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6177_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_real,A: real,B: real > uint32] :
% 13.77/7.78 ( ( finite_finite_real @ S3 )
% 13.77/7.78 => ( ( ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups5944083974425963860uint32
% 13.77/7.78 @ ^ [K3: real] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups5944083974425963860uint32
% 13.77/7.78 @ ^ [K3: real] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6178_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_nat,A: nat,B: nat > uint32] :
% 13.77/7.78 ( ( finite_finite_nat @ S3 )
% 13.77/7.78 => ( ( ( member_nat @ A @ S3 )
% 13.77/7.78 => ( ( groups833757482993574392uint32
% 13.77/7.78 @ ^ [K3: nat] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_nat @ A @ S3 )
% 13.77/7.78 => ( ( groups833757482993574392uint32
% 13.77/7.78 @ ^ [K3: nat] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6179_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_int,A: int,B: int > uint32] :
% 13.77/7.78 ( ( finite_finite_int @ S3 )
% 13.77/7.78 => ( ( ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups5712668689793887828uint32
% 13.77/7.78 @ ^ [K3: int] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups5712668689793887828uint32
% 13.77/7.78 @ ^ [K3: int] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6180_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_complex,A: complex,B: complex > uint32] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.78 => ( ( ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups8736914816313324502uint32
% 13.77/7.78 @ ^ [K3: complex] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups8736914816313324502uint32
% 13.77/7.78 @ ^ [K3: complex] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6181_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_Code_integer,A: code_integer,B: code_integer > uint32] :
% 13.77/7.78 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.78 => ( ( ( member_Code_integer @ A @ S3 )
% 13.77/7.78 => ( ( groups8847630953604152069uint32
% 13.77/7.78 @ ^ [K3: code_integer] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_Code_integer @ A @ S3 )
% 13.77/7.78 => ( ( groups8847630953604152069uint32
% 13.77/7.78 @ ^ [K3: code_integer] : ( if_uint32 @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_uint32 )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_uint32 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6182_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real] :
% 13.77/7.78 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.78 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups2240296850493347238T_real
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.78 => ( ( groups2240296850493347238T_real
% 13.77/7.78 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6183_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_real,A: real,B: real > real] :
% 13.77/7.78 ( ( finite_finite_real @ S3 )
% 13.77/7.78 => ( ( ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups8097168146408367636l_real
% 13.77/7.78 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_real @ A @ S3 )
% 13.77/7.78 => ( ( groups8097168146408367636l_real
% 13.77/7.78 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6184_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_int,A: int,B: int > real] :
% 13.77/7.78 ( ( finite_finite_int @ S3 )
% 13.77/7.78 => ( ( ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups8778361861064173332t_real
% 13.77/7.78 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_int @ A @ S3 )
% 13.77/7.78 => ( ( groups8778361861064173332t_real
% 13.77/7.78 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6185_sum_Odelta,axiom,
% 13.77/7.78 ! [S3: set_complex,A: complex,B: complex > real] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.78 => ( ( ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups5808333547571424918x_real
% 13.77/7.78 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = ( B @ A ) ) )
% 13.77/7.78 & ( ~ ( member_complex @ A @ S3 )
% 13.77/7.78 => ( ( groups5808333547571424918x_real
% 13.77/7.78 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 13.77/7.78 @ S3 )
% 13.77/7.78 = zero_zero_real ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6186_foldl__length,axiom,
% 13.77/7.78 ! [L: list_VEBT_VEBT] :
% 13.77/7.78 ( ( foldl_nat_VEBT_VEBT
% 13.77/7.78 @ ^ [I3: nat,X4: vEBT_VEBT] : ( suc @ I3 )
% 13.77/7.78 @ zero_zero_nat
% 13.77/7.78 @ L )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6187_foldl__length,axiom,
% 13.77/7.78 ! [L: list_real] :
% 13.77/7.78 ( ( foldl_nat_real
% 13.77/7.78 @ ^ [I3: nat,X4: real] : ( suc @ I3 )
% 13.77/7.78 @ zero_zero_nat
% 13.77/7.78 @ L )
% 13.77/7.78 = ( size_size_list_real @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6188_foldl__length,axiom,
% 13.77/7.78 ! [L: list_o] :
% 13.77/7.78 ( ( foldl_nat_o
% 13.77/7.78 @ ^ [I3: nat,X4: $o] : ( suc @ I3 )
% 13.77/7.78 @ zero_zero_nat
% 13.77/7.78 @ L )
% 13.77/7.78 = ( size_size_list_o @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6189_foldl__length,axiom,
% 13.77/7.78 ! [L: list_nat] :
% 13.77/7.78 ( ( foldl_nat_nat
% 13.77/7.78 @ ^ [I3: nat,X4: nat] : ( suc @ I3 )
% 13.77/7.78 @ zero_zero_nat
% 13.77/7.78 @ L )
% 13.77/7.78 = ( size_size_list_nat @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6190_card__Collect__le__nat,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( finite_card_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 13.77/7.78 = ( suc @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6191_finite__Collect__subsets,axiom,
% 13.77/7.78 ! [A4: set_nat] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ( finite1152437895449049373et_nat
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6192_finite__Collect__subsets,axiom,
% 13.77/7.78 ! [A4: set_complex] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.78 => ( finite6551019134538273531omplex
% 13.77/7.78 @ ( collect_set_complex
% 13.77/7.78 @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6193_finite__Collect__subsets,axiom,
% 13.77/7.78 ! [A4: set_Code_integer] :
% 13.77/7.78 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.78 => ( finite6931041176100689706nteger
% 13.77/7.78 @ ( collec574505750873337192nteger
% 13.77/7.78 @ ^ [B6: set_Code_integer] : ( ord_le7084787975880047091nteger @ B6 @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6194_finite__Collect__subsets,axiom,
% 13.77/7.78 ! [A4: set_int] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ( finite6197958912794628473et_int
% 13.77/7.78 @ ( collect_set_int
% 13.77/7.78 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A4 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6195_of__nat__le__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6196_of__nat__le__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6197_of__nat__le__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6198_of__nat__le__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6199_of__nat__le__0__iff,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 13.77/7.78 = ( M = zero_zero_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6200_of__nat__Suc,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( semiri2565882477558803405uint32 @ ( suc @ M ) )
% 13.77/7.78 = ( plus_plus_uint32 @ one_one_uint32 @ ( semiri2565882477558803405uint32 @ M ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6201_of__nat__Suc,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 13.77/7.78 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6202_of__nat__Suc,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 13.77/7.78 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6203_of__nat__Suc,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 13.77/7.78 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6204_of__nat__Suc,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 13.77/7.78 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6205_of__nat__Suc,axiom,
% 13.77/7.78 ! [M: nat] :
% 13.77/7.78 ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 13.77/7.78 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6206_sum_OlessThan__Suc,axiom,
% 13.77/7.78 ! [G: nat > rat,N: nat] :
% 13.77/7.78 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.78 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6207_sum_OlessThan__Suc,axiom,
% 13.77/7.78 ! [G: nat > int,N: nat] :
% 13.77/7.78 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.78 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6208_sum_OlessThan__Suc,axiom,
% 13.77/7.78 ! [G: nat > nat,N: nat] :
% 13.77/7.78 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.78 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6209_sum_OlessThan__Suc,axiom,
% 13.77/7.78 ! [G: nat > real,N: nat] :
% 13.77/7.78 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.78 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6210_single__Diff__lessThan,axiom,
% 13.77/7.78 ! [K: $o] :
% 13.77/7.78 ( ( minus_minus_set_o @ ( insert_o @ K @ bot_bot_set_o ) @ ( set_ord_lessThan_o @ K ) )
% 13.77/7.78 = ( insert_o @ K @ bot_bot_set_o ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6211_single__Diff__lessThan,axiom,
% 13.77/7.78 ! [K: nat] :
% 13.77/7.78 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 13.77/7.78 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6212_single__Diff__lessThan,axiom,
% 13.77/7.78 ! [K: int] :
% 13.77/7.78 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 13.77/7.78 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6213_single__Diff__lessThan,axiom,
% 13.77/7.78 ! [K: real] :
% 13.77/7.78 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 13.77/7.78 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6214_Cons__listrel1__Cons,axiom,
% 13.77/7.78 ! [X: $o,Xs: list_o,Y: $o,Ys: list_o,R: set_Product_prod_o_o] :
% 13.77/7.78 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Ys ) ) @ ( listrel1_o @ R ) )
% 13.77/7.78 = ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 13.77/7.78 & ( Xs = Ys ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Ys ) @ ( listrel1_o @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6215_Cons__listrel1__Cons,axiom,
% 13.77/7.78 ! [X: uint32,Xs: list_uint32,Y: uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.78 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Ys ) ) @ ( listrel1_uint32 @ R ) )
% 13.77/7.78 = ( ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 13.77/7.78 & ( Xs = Ys ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Ys ) @ ( listrel1_uint32 @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6216_Cons__listrel1__Cons,axiom,
% 13.77/7.78 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.78 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 13.77/7.78 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 13.77/7.78 & ( Xs = Ys ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6217_Cons__listrel1__Cons,axiom,
% 13.77/7.78 ! [X: int,Xs: list_int,Y: int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.78 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel1_int @ R ) )
% 13.77/7.78 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 13.77/7.78 & ( Xs = Ys ) )
% 13.77/7.78 | ( ( X = Y )
% 13.77/7.78 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Ys ) @ ( listrel1_int @ R ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6218_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: int,Xs: list_int,Y: nat,Ys: list_nat] :
% 13.77/7.78 ( ( zip_int_nat @ ( cons_int @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P7512249878480867347nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( zip_int_nat @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6219_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: int,Xs: list_int,Y: $o,Ys: list_o] :
% 13.77/7.78 ( ( zip_int_o @ ( cons_int @ X @ Xs ) @ ( cons_o @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P7321330006258091179_int_o @ ( product_Pair_int_o @ X @ Y ) @ ( zip_int_o @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6220_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: nat,Xs: list_nat,Y: int,Ys: list_int] :
% 13.77/7.78 ( ( zip_nat_int @ ( cons_nat @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P2335045147070616083at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( zip_nat_int @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6221_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: nat,Xs: list_nat,Y: $o,Ys: list_o] :
% 13.77/7.78 ( ( zip_nat_o @ ( cons_nat @ X @ Xs ) @ ( cons_o @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P9142372351690779143_nat_o @ ( product_Pair_nat_o @ X @ Y ) @ ( zip_nat_o @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6222_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: $o,Xs: list_o,Y: int,Ys: list_int] :
% 13.77/7.78 ( ( zip_o_int @ ( cons_o @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P1455986808126089405_o_int @ ( product_Pair_o_int @ X @ Y ) @ ( zip_o_int @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6223_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: $o,Xs: list_o,Y: nat,Ys: list_nat] :
% 13.77/7.78 ( ( zip_o_nat @ ( cons_o @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P5633837827635286113_o_nat @ ( product_Pair_o_nat @ X @ Y ) @ ( zip_o_nat @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6224_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: $o,Xs: list_o,Y: $o,Ys: list_o] :
% 13.77/7.78 ( ( zip_o_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P8766293264717362397od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( zip_o_o @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6225_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: uint32,Xs: list_uint32,Y: uint32,Ys: list_uint32] :
% 13.77/7.78 ( ( zip_uint32_uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P3149448846263281007uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( zip_uint32_uint32 @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6226_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 13.77/7.78 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6227_zip__Cons__Cons,axiom,
% 13.77/7.78 ! [X: int,Xs: list_int,Y: int,Ys: list_int] :
% 13.77/7.78 ( ( zip_int_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Ys ) )
% 13.77/7.78 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs @ Ys ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6228_Max__const,axiom,
% 13.77/7.78 ! [A4: set_nat,C2: int] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.78 => ( ( lattic8263393255366662781ax_int
% 13.77/7.78 @ ( image_nat_int
% 13.77/7.78 @ ^ [Uu3: nat] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6229_Max__const,axiom,
% 13.77/7.78 ! [A4: set_int,C2: int] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_int )
% 13.77/7.78 => ( ( lattic8263393255366662781ax_int
% 13.77/7.78 @ ( image_int_int
% 13.77/7.78 @ ^ [Uu3: int] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6230_Max__const,axiom,
% 13.77/7.78 ! [A4: set_complex,C2: nat] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_complex )
% 13.77/7.78 => ( ( lattic8265883725875713057ax_nat
% 13.77/7.78 @ ( image_complex_nat
% 13.77/7.78 @ ^ [Uu3: complex] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6231_Max__const,axiom,
% 13.77/7.78 ! [A4: set_Code_integer,C2: nat] :
% 13.77/7.78 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.78 => ( ( lattic8265883725875713057ax_nat
% 13.77/7.78 @ ( image_951025933927791156er_nat
% 13.77/7.78 @ ^ [Uu3: code_integer] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6232_Max__const,axiom,
% 13.77/7.78 ! [A4: set_nat,C2: nat] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.78 => ( ( lattic8265883725875713057ax_nat
% 13.77/7.78 @ ( image_nat_nat
% 13.77/7.78 @ ^ [Uu3: nat] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6233_Max__const,axiom,
% 13.77/7.78 ! [A4: set_int,C2: nat] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_int )
% 13.77/7.78 => ( ( lattic8265883725875713057ax_nat
% 13.77/7.78 @ ( image_int_nat
% 13.77/7.78 @ ^ [Uu3: int] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6234_Max__const,axiom,
% 13.77/7.78 ! [A4: set_o,C2: nat] :
% 13.77/7.78 ( ( finite_finite_o @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_o )
% 13.77/7.78 => ( ( lattic8265883725875713057ax_nat
% 13.77/7.78 @ ( image_o_nat
% 13.77/7.78 @ ^ [Uu3: $o] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6235_Min__const,axiom,
% 13.77/7.78 ! [A4: set_nat,C2: int] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.78 => ( ( lattic8718645017227715691in_int
% 13.77/7.78 @ ( image_nat_int
% 13.77/7.78 @ ^ [Uu3: nat] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6236_Min__const,axiom,
% 13.77/7.78 ! [A4: set_int,C2: int] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_int )
% 13.77/7.78 => ( ( lattic8718645017227715691in_int
% 13.77/7.78 @ ( image_int_int
% 13.77/7.78 @ ^ [Uu3: int] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6237_Min__const,axiom,
% 13.77/7.78 ! [A4: set_complex,C2: nat] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_complex )
% 13.77/7.78 => ( ( lattic8721135487736765967in_nat
% 13.77/7.78 @ ( image_complex_nat
% 13.77/7.78 @ ^ [Uu3: complex] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6238_Min__const,axiom,
% 13.77/7.78 ! [A4: set_Code_integer,C2: nat] :
% 13.77/7.78 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bo3990330152332043303nteger )
% 13.77/7.78 => ( ( lattic8721135487736765967in_nat
% 13.77/7.78 @ ( image_951025933927791156er_nat
% 13.77/7.78 @ ^ [Uu3: code_integer] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6239_Min__const,axiom,
% 13.77/7.78 ! [A4: set_nat,C2: nat] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.78 => ( ( lattic8721135487736765967in_nat
% 13.77/7.78 @ ( image_nat_nat
% 13.77/7.78 @ ^ [Uu3: nat] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6240_Min__const,axiom,
% 13.77/7.78 ! [A4: set_int,C2: nat] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_int )
% 13.77/7.78 => ( ( lattic8721135487736765967in_nat
% 13.77/7.78 @ ( image_int_nat
% 13.77/7.78 @ ^ [Uu3: int] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6241_Min__const,axiom,
% 13.77/7.78 ! [A4: set_o,C2: nat] :
% 13.77/7.78 ( ( finite_finite_o @ A4 )
% 13.77/7.78 => ( ( A4 != bot_bot_set_o )
% 13.77/7.78 => ( ( lattic8721135487736765967in_nat
% 13.77/7.78 @ ( image_o_nat
% 13.77/7.78 @ ^ [Uu3: $o] : C2
% 13.77/7.78 @ A4 ) )
% 13.77/7.78 = C2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6242_foldr__length,axiom,
% 13.77/7.78 ! [L: list_VEBT_VEBT] :
% 13.77/7.78 ( ( foldr_VEBT_VEBT_nat
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] : suc
% 13.77/7.78 @ L
% 13.77/7.78 @ zero_zero_nat )
% 13.77/7.78 = ( size_s6755466524823107622T_VEBT @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6243_foldr__length,axiom,
% 13.77/7.78 ! [L: list_real] :
% 13.77/7.78 ( ( foldr_real_nat
% 13.77/7.78 @ ^ [X4: real] : suc
% 13.77/7.78 @ L
% 13.77/7.78 @ zero_zero_nat )
% 13.77/7.78 = ( size_size_list_real @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6244_foldr__length,axiom,
% 13.77/7.78 ! [L: list_o] :
% 13.77/7.78 ( ( foldr_o_nat
% 13.77/7.78 @ ^ [X4: $o] : suc
% 13.77/7.78 @ L
% 13.77/7.78 @ zero_zero_nat )
% 13.77/7.78 = ( size_size_list_o @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6245_foldr__length,axiom,
% 13.77/7.78 ! [L: list_nat] :
% 13.77/7.78 ( ( foldr_nat_nat
% 13.77/7.78 @ ^ [X4: nat] : suc
% 13.77/7.78 @ L
% 13.77/7.78 @ zero_zero_nat )
% 13.77/7.78 = ( size_size_list_nat @ L ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6246_of__nat__0__less__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 13.77/7.78 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6247_of__nat__0__less__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 13.77/7.78 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6248_of__nat__0__less__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.78 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6249_of__nat__0__less__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.78 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6250_of__nat__0__less__iff,axiom,
% 13.77/7.78 ! [N: nat] :
% 13.77/7.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.78 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6251_of__nat__power__less__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6252_of__nat__power__less__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6253_of__nat__power__less__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6254_of__nat__power__less__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6255_of__nat__power__less__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6256_of__nat__less__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 13.77/7.78 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6257_of__nat__less__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 13.77/7.78 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6258_of__nat__less__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 13.77/7.78 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6259_of__nat__less__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 13.77/7.78 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6260_of__nat__less__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 13.77/7.78 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6261_of__nat__le__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 13.77/7.78 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6262_of__nat__le__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 13.77/7.78 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6263_of__nat__le__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 13.77/7.78 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6264_of__nat__le__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 13.77/7.78 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6265_of__nat__le__of__nat__power__cancel__iff,axiom,
% 13.77/7.78 ! [B: nat,W2: nat,X: nat] :
% 13.77/7.78 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 13.77/7.78 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6266_of__nat__power__le__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6267_of__nat__power__le__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6268_of__nat__power__le__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6269_of__nat__power__le__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6270_of__nat__power__le__of__nat__cancel__iff,axiom,
% 13.77/7.78 ! [X: nat,B: nat,W2: nat] :
% 13.77/7.78 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 13.77/7.78 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6271_of__nat__zero__less__power__iff,axiom,
% 13.77/7.78 ! [X: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 13.77/7.78 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 13.77/7.78 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6272_of__nat__zero__less__power__iff,axiom,
% 13.77/7.78 ! [X: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 13.77/7.78 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 13.77/7.78 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6273_of__nat__zero__less__power__iff,axiom,
% 13.77/7.78 ! [X: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 13.77/7.78 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 13.77/7.78 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6274_of__nat__zero__less__power__iff,axiom,
% 13.77/7.78 ! [X: nat,N: nat] :
% 13.77/7.78 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 13.77/7.78 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 13.77/7.78 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6275_of__nat__zero__less__power__iff,axiom,
% 13.77/7.78 ! [X: nat,N: nat] :
% 13.77/7.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X ) @ N ) )
% 13.77/7.78 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 13.77/7.78 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6276_sum__zero__power,axiom,
% 13.77/7.78 ! [A4: set_nat,C2: nat > rat] :
% 13.77/7.78 ( ( ( ( finite_finite_nat @ A4 )
% 13.77/7.78 & ( member_nat @ zero_zero_nat @ A4 ) )
% 13.77/7.78 => ( ( groups2906978787729119204at_rat
% 13.77/7.78 @ ^ [I3: nat] : ( times_times_rat @ ( C2 @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 13.77/7.78 @ A4 )
% 13.77/7.78 = ( C2 @ zero_zero_nat ) ) )
% 13.77/7.78 & ( ~ ( ( finite_finite_nat @ A4 )
% 13.77/7.78 & ( member_nat @ zero_zero_nat @ A4 ) )
% 13.77/7.78 => ( ( groups2906978787729119204at_rat
% 13.77/7.78 @ ^ [I3: nat] : ( times_times_rat @ ( C2 @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 13.77/7.78 @ A4 )
% 13.77/7.78 = zero_zero_rat ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6277_sum__zero__power,axiom,
% 13.77/7.78 ! [A4: set_nat,C2: nat > complex] :
% 13.77/7.78 ( ( ( ( finite_finite_nat @ A4 )
% 13.77/7.78 & ( member_nat @ zero_zero_nat @ A4 ) )
% 13.77/7.78 => ( ( groups2073611262835488442omplex
% 13.77/7.78 @ ^ [I3: nat] : ( times_times_complex @ ( C2 @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 13.77/7.78 @ A4 )
% 13.77/7.78 = ( C2 @ zero_zero_nat ) ) )
% 13.77/7.78 & ( ~ ( ( finite_finite_nat @ A4 )
% 13.77/7.78 & ( member_nat @ zero_zero_nat @ A4 ) )
% 13.77/7.78 => ( ( groups2073611262835488442omplex
% 13.77/7.78 @ ^ [I3: nat] : ( times_times_complex @ ( C2 @ I3 ) @ ( power_power_complex @ zero_zero_complex @ I3 ) )
% 13.77/7.78 @ A4 )
% 13.77/7.78 = zero_zero_complex ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6278_sum__zero__power,axiom,
% 13.77/7.78 ! [A4: set_nat,C2: nat > real] :
% 13.77/7.78 ( ( ( ( finite_finite_nat @ A4 )
% 13.77/7.78 & ( member_nat @ zero_zero_nat @ A4 ) )
% 13.77/7.78 => ( ( groups6591440286371151544t_real
% 13.77/7.78 @ ^ [I3: nat] : ( times_times_real @ ( C2 @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 13.77/7.78 @ A4 )
% 13.77/7.78 = ( C2 @ zero_zero_nat ) ) )
% 13.77/7.78 & ( ~ ( ( finite_finite_nat @ A4 )
% 13.77/7.78 & ( member_nat @ zero_zero_nat @ A4 ) )
% 13.77/7.78 => ( ( groups6591440286371151544t_real
% 13.77/7.78 @ ^ [I3: nat] : ( times_times_real @ ( C2 @ I3 ) @ ( power_power_real @ zero_zero_real @ I3 ) )
% 13.77/7.78 @ A4 )
% 13.77/7.78 = zero_zero_real ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6279_finite__lists__distinct__length__eq,axiom,
% 13.77/7.78 ! [A4: set_complex,N: nat] :
% 13.77/7.78 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.78 => ( finite8712137658972009173omplex
% 13.77/7.78 @ ( collect_list_complex
% 13.77/7.78 @ ^ [Xs2: list_complex] :
% 13.77/7.78 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 13.77/7.78 = N )
% 13.77/7.78 & ( distinct_complex @ Xs2 )
% 13.77/7.78 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6280_finite__lists__distinct__length__eq,axiom,
% 13.77/7.78 ! [A4: set_Code_integer,N: nat] :
% 13.77/7.78 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.78 => ( finite1283093830868386564nteger
% 13.77/7.78 @ ( collec3483841146883906114nteger
% 13.77/7.78 @ ^ [Xs2: list_Code_integer] :
% 13.77/7.78 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 13.77/7.78 = N )
% 13.77/7.78 & ( distin1543349897113766820nteger @ Xs2 )
% 13.77/7.78 & ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6281_finite__lists__distinct__length__eq,axiom,
% 13.77/7.78 ! [A4: set_VEBT_VEBT,N: nat] :
% 13.77/7.78 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.78 => ( finite3004134309566078307T_VEBT
% 13.77/7.78 @ ( collec5608196760682091941T_VEBT
% 13.77/7.78 @ ^ [Xs2: list_VEBT_VEBT] :
% 13.77/7.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 13.77/7.78 = N )
% 13.77/7.78 & ( distinct_VEBT_VEBT @ Xs2 )
% 13.77/7.78 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6282_finite__lists__distinct__length__eq,axiom,
% 13.77/7.78 ! [A4: set_real,N: nat] :
% 13.77/7.78 ( ( finite_finite_real @ A4 )
% 13.77/7.78 => ( finite306553202115118035t_real
% 13.77/7.78 @ ( collect_list_real
% 13.77/7.78 @ ^ [Xs2: list_real] :
% 13.77/7.78 ( ( ( size_size_list_real @ Xs2 )
% 13.77/7.78 = N )
% 13.77/7.78 & ( distinct_real @ Xs2 )
% 13.77/7.78 & ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6283_finite__lists__distinct__length__eq,axiom,
% 13.77/7.78 ! [A4: set_o,N: nat] :
% 13.77/7.78 ( ( finite_finite_o @ A4 )
% 13.77/7.78 => ( finite_finite_list_o
% 13.77/7.78 @ ( collect_list_o
% 13.77/7.78 @ ^ [Xs2: list_o] :
% 13.77/7.78 ( ( ( size_size_list_o @ Xs2 )
% 13.77/7.78 = N )
% 13.77/7.78 & ( distinct_o @ Xs2 )
% 13.77/7.78 & ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6284_finite__lists__distinct__length__eq,axiom,
% 13.77/7.78 ! [A4: set_nat,N: nat] :
% 13.77/7.78 ( ( finite_finite_nat @ A4 )
% 13.77/7.78 => ( finite8100373058378681591st_nat
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [Xs2: list_nat] :
% 13.77/7.78 ( ( ( size_size_list_nat @ Xs2 )
% 13.77/7.78 = N )
% 13.77/7.78 & ( distinct_nat @ Xs2 )
% 13.77/7.78 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6285_finite__lists__distinct__length__eq,axiom,
% 13.77/7.78 ! [A4: set_int,N: nat] :
% 13.77/7.78 ( ( finite_finite_int @ A4 )
% 13.77/7.78 => ( finite3922522038869484883st_int
% 13.77/7.78 @ ( collect_list_int
% 13.77/7.78 @ ^ [Xs2: list_int] :
% 13.77/7.78 ( ( ( size_size_list_int @ Xs2 )
% 13.77/7.78 = N )
% 13.77/7.78 & ( distinct_int @ Xs2 )
% 13.77/7.78 & ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6286_vebt__memberi_H__rf__abstr,axiom,
% 13.77/7.78 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.78 ( hoare_hoare_triple_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X )
% 13.77/7.78 @ ^ [R5: $o] :
% 13.77/7.78 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.78 @ ( pure_assn
% 13.77/7.78 @ ( R5
% 13.77/7.78 = ( vEBT_vebt_member @ T @ X ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6287_vebt__succi_H__rf__abstr,axiom,
% 13.77/7.78 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.78 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.78 => ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X )
% 13.77/7.78 @ ^ [R5: option_nat] :
% 13.77/7.78 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.78 @ ( pure_assn
% 13.77/7.78 @ ( R5
% 13.77/7.78 = ( vEBT_vebt_succ @ T @ X ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6288_vebt__pred_H__rf__abstr,axiom,
% 13.77/7.78 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.78 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.78 => ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X )
% 13.77/7.78 @ ^ [R5: option_nat] :
% 13.77/7.78 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.78 @ ( pure_assn
% 13.77/7.78 @ ( R5
% 13.77/7.78 = ( vEBT_vebt_pred @ T @ X ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6289_vebt__inserti_H__rf__abstr,axiom,
% 13.77/7.78 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( hoare_1429296392585015714_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6290_pred__equals__eq2,axiom,
% 13.77/7.78 ! [R2: set_Pr1773385645901665561uint32,S3: set_Pr1773385645901665561uint32] :
% 13.77/7.78 ( ( ( ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R2 ) )
% 13.77/7.78 = ( ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ S3 ) ) )
% 13.77/7.78 = ( R2 = S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6291_pred__equals__eq2,axiom,
% 13.77/7.78 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 13.77/7.78 ( ( ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R2 ) )
% 13.77/7.78 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S3 ) ) )
% 13.77/7.78 = ( R2 = S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6292_pred__equals__eq2,axiom,
% 13.77/7.78 ! [R2: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 13.77/7.78 ( ( ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R2 ) )
% 13.77/7.78 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S3 ) ) )
% 13.77/7.78 = ( R2 = S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6293_pred__equals__eq2,axiom,
% 13.77/7.78 ! [R2: set_Pr3286484037609594932et_nat,S3: set_Pr3286484037609594932et_nat] :
% 13.77/7.78 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R2 ) )
% 13.77/7.78 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S3 ) ) )
% 13.77/7.78 = ( R2 = S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6294_pred__equals__eq2,axiom,
% 13.77/7.78 ! [R2: set_Pr8536935166611901872et_nat,S3: set_Pr8536935166611901872et_nat] :
% 13.77/7.78 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R2 ) )
% 13.77/7.78 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S3 ) ) )
% 13.77/7.78 = ( R2 = S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6295_pred__subset__eq,axiom,
% 13.77/7.78 ! [R2: set_nat,S3: set_nat] :
% 13.77/7.78 ( ( ord_less_eq_nat_o
% 13.77/7.78 @ ^ [X4: nat] : ( member_nat @ X4 @ R2 )
% 13.77/7.78 @ ^ [X4: nat] : ( member_nat @ X4 @ S3 ) )
% 13.77/7.78 = ( ord_less_eq_set_nat @ R2 @ S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6296_pred__subset__eq,axiom,
% 13.77/7.78 ! [R2: set_VEBT_VEBT,S3: set_VEBT_VEBT] :
% 13.77/7.78 ( ( ord_le418104280809901481VEBT_o
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ R2 )
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ S3 ) )
% 13.77/7.78 = ( ord_le4337996190870823476T_VEBT @ R2 @ S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6297_pred__subset__eq,axiom,
% 13.77/7.78 ! [R2: set_real,S3: set_real] :
% 13.77/7.78 ( ( ord_less_eq_real_o
% 13.77/7.78 @ ^ [X4: real] : ( member_real @ X4 @ R2 )
% 13.77/7.78 @ ^ [X4: real] : ( member_real @ X4 @ S3 ) )
% 13.77/7.78 = ( ord_less_eq_set_real @ R2 @ S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6298_pred__subset__eq,axiom,
% 13.77/7.78 ! [R2: set_set_nat,S3: set_set_nat] :
% 13.77/7.78 ( ( ord_le3964352015994296041_nat_o
% 13.77/7.78 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R2 )
% 13.77/7.78 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S3 ) )
% 13.77/7.78 = ( ord_le6893508408891458716et_nat @ R2 @ S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6299_pred__subset__eq,axiom,
% 13.77/7.78 ! [R2: set_int,S3: set_int] :
% 13.77/7.78 ( ( ord_less_eq_int_o
% 13.77/7.78 @ ^ [X4: int] : ( member_int @ X4 @ R2 )
% 13.77/7.78 @ ^ [X4: int] : ( member_int @ X4 @ S3 ) )
% 13.77/7.78 = ( ord_less_eq_set_int @ R2 @ S3 ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6300_less__eq__set__def,axiom,
% 13.77/7.78 ( ord_less_eq_set_nat
% 13.77/7.78 = ( ^ [A6: set_nat,B6: set_nat] :
% 13.77/7.78 ( ord_less_eq_nat_o
% 13.77/7.78 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 13.77/7.78 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6301_less__eq__set__def,axiom,
% 13.77/7.78 ( ord_le4337996190870823476T_VEBT
% 13.77/7.78 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.78 ( ord_le418104280809901481VEBT_o
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 )
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6302_less__eq__set__def,axiom,
% 13.77/7.78 ( ord_less_eq_set_real
% 13.77/7.78 = ( ^ [A6: set_real,B6: set_real] :
% 13.77/7.78 ( ord_less_eq_real_o
% 13.77/7.78 @ ^ [X4: real] : ( member_real @ X4 @ A6 )
% 13.77/7.78 @ ^ [X4: real] : ( member_real @ X4 @ B6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6303_less__eq__set__def,axiom,
% 13.77/7.78 ( ord_le6893508408891458716et_nat
% 13.77/7.78 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 13.77/7.78 ( ord_le3964352015994296041_nat_o
% 13.77/7.78 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 13.77/7.78 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6304_less__eq__set__def,axiom,
% 13.77/7.78 ( ord_less_eq_set_int
% 13.77/7.78 = ( ^ [A6: set_int,B6: set_int] :
% 13.77/7.78 ( ord_less_eq_int_o
% 13.77/7.78 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 13.77/7.78 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6305_Collect__subset,axiom,
% 13.77/7.78 ! [A4: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.78 ( ord_le4337996190870823476T_VEBT
% 13.77/7.78 @ ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ A4 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6306_Collect__subset,axiom,
% 13.77/7.78 ! [A4: set_real,P2: real > $o] :
% 13.77/7.78 ( ord_less_eq_set_real
% 13.77/7.78 @ ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ( ( member_real @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ A4 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6307_Collect__subset,axiom,
% 13.77/7.78 ! [A4: set_complex,P2: complex > $o] :
% 13.77/7.78 ( ord_le211207098394363844omplex
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( member_complex @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ A4 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6308_Collect__subset,axiom,
% 13.77/7.78 ! [A4: set_list_nat,P2: list_nat > $o] :
% 13.77/7.78 ( ord_le6045566169113846134st_nat
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ A4 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6309_Collect__subset,axiom,
% 13.77/7.78 ! [A4: set_set_nat,P2: set_nat > $o] :
% 13.77/7.78 ( ord_le6893508408891458716et_nat
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ A4 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6310_Collect__subset,axiom,
% 13.77/7.78 ! [A4: set_nat,P2: nat > $o] :
% 13.77/7.78 ( ord_less_eq_set_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( member_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ A4 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6311_Collect__subset,axiom,
% 13.77/7.78 ! [A4: set_int,P2: int > $o] :
% 13.77/7.78 ( ord_less_eq_set_int
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( member_int @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ A4 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6312_prop__restrict,axiom,
% 13.77/7.78 ! [X: vEBT_VEBT,Z6: set_VEBT_VEBT,X6: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X @ Z6 )
% 13.77/7.78 => ( ( ord_le4337996190870823476T_VEBT @ Z6
% 13.77/7.78 @ ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 => ( P2 @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6313_prop__restrict,axiom,
% 13.77/7.78 ! [X: real,Z6: set_real,X6: set_real,P2: real > $o] :
% 13.77/7.78 ( ( member_real @ X @ Z6 )
% 13.77/7.78 => ( ( ord_less_eq_set_real @ Z6
% 13.77/7.78 @ ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ( ( member_real @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 => ( P2 @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6314_prop__restrict,axiom,
% 13.77/7.78 ! [X: complex,Z6: set_complex,X6: set_complex,P2: complex > $o] :
% 13.77/7.78 ( ( member_complex @ X @ Z6 )
% 13.77/7.78 => ( ( ord_le211207098394363844omplex @ Z6
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( member_complex @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 => ( P2 @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6315_prop__restrict,axiom,
% 13.77/7.78 ! [X: list_nat,Z6: set_list_nat,X6: set_list_nat,P2: list_nat > $o] :
% 13.77/7.78 ( ( member_list_nat @ X @ Z6 )
% 13.77/7.78 => ( ( ord_le6045566169113846134st_nat @ Z6
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 => ( P2 @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6316_prop__restrict,axiom,
% 13.77/7.78 ! [X: set_nat,Z6: set_set_nat,X6: set_set_nat,P2: set_nat > $o] :
% 13.77/7.78 ( ( member_set_nat @ X @ Z6 )
% 13.77/7.78 => ( ( ord_le6893508408891458716et_nat @ Z6
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 => ( P2 @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6317_prop__restrict,axiom,
% 13.77/7.78 ! [X: nat,Z6: set_nat,X6: set_nat,P2: nat > $o] :
% 13.77/7.78 ( ( member_nat @ X @ Z6 )
% 13.77/7.78 => ( ( ord_less_eq_set_nat @ Z6
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( member_nat @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 => ( P2 @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6318_prop__restrict,axiom,
% 13.77/7.78 ! [X: int,Z6: set_int,X6: set_int,P2: int > $o] :
% 13.77/7.78 ( ( member_int @ X @ Z6 )
% 13.77/7.78 => ( ( ord_less_eq_set_int @ Z6
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( member_int @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 => ( P2 @ X ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6319_Collect__restrict,axiom,
% 13.77/7.78 ! [X6: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.78 ( ord_le4337996190870823476T_VEBT
% 13.77/7.78 @ ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ X6 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6320_Collect__restrict,axiom,
% 13.77/7.78 ! [X6: set_real,P2: real > $o] :
% 13.77/7.78 ( ord_less_eq_set_real
% 13.77/7.78 @ ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ( ( member_real @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ X6 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6321_Collect__restrict,axiom,
% 13.77/7.78 ! [X6: set_complex,P2: complex > $o] :
% 13.77/7.78 ( ord_le211207098394363844omplex
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( member_complex @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ X6 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6322_Collect__restrict,axiom,
% 13.77/7.78 ! [X6: set_list_nat,P2: list_nat > $o] :
% 13.77/7.78 ( ord_le6045566169113846134st_nat
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ X6 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6323_Collect__restrict,axiom,
% 13.77/7.78 ! [X6: set_set_nat,P2: set_nat > $o] :
% 13.77/7.78 ( ord_le6893508408891458716et_nat
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ X6 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6324_Collect__restrict,axiom,
% 13.77/7.78 ! [X6: set_nat,P2: nat > $o] :
% 13.77/7.78 ( ord_less_eq_set_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( member_nat @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ X6 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6325_Collect__restrict,axiom,
% 13.77/7.78 ! [X6: set_int,P2: int > $o] :
% 13.77/7.78 ( ord_less_eq_set_int
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( member_int @ X4 @ X6 )
% 13.77/7.78 & ( P2 @ X4 ) ) )
% 13.77/7.78 @ X6 ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6326_subset__CollectI,axiom,
% 13.77/7.78 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,Q2: vEBT_VEBT > $o,P2: vEBT_VEBT > $o] :
% 13.77/7.78 ( ( ord_le4337996190870823476T_VEBT @ B4 @ A4 )
% 13.77/7.78 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X3 @ B4 )
% 13.77/7.78 => ( ( Q2 @ X3 )
% 13.77/7.78 => ( P2 @ X3 ) ) )
% 13.77/7.78 => ( ord_le4337996190870823476T_VEBT
% 13.77/7.78 @ ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X4 @ B4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) )
% 13.77/7.78 @ ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6327_subset__CollectI,axiom,
% 13.77/7.78 ! [B4: set_real,A4: set_real,Q2: real > $o,P2: real > $o] :
% 13.77/7.78 ( ( ord_less_eq_set_real @ B4 @ A4 )
% 13.77/7.78 => ( ! [X3: real] :
% 13.77/7.78 ( ( member_real @ X3 @ B4 )
% 13.77/7.78 => ( ( Q2 @ X3 )
% 13.77/7.78 => ( P2 @ X3 ) ) )
% 13.77/7.78 => ( ord_less_eq_set_real
% 13.77/7.78 @ ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ( ( member_real @ X4 @ B4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) )
% 13.77/7.78 @ ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ( ( member_real @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6328_subset__CollectI,axiom,
% 13.77/7.78 ! [B4: set_complex,A4: set_complex,Q2: complex > $o,P2: complex > $o] :
% 13.77/7.78 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.78 => ( ! [X3: complex] :
% 13.77/7.78 ( ( member_complex @ X3 @ B4 )
% 13.77/7.78 => ( ( Q2 @ X3 )
% 13.77/7.78 => ( P2 @ X3 ) ) )
% 13.77/7.78 => ( ord_le211207098394363844omplex
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( member_complex @ X4 @ B4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) )
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( member_complex @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6329_subset__CollectI,axiom,
% 13.77/7.78 ! [B4: set_list_nat,A4: set_list_nat,Q2: list_nat > $o,P2: list_nat > $o] :
% 13.77/7.78 ( ( ord_le6045566169113846134st_nat @ B4 @ A4 )
% 13.77/7.78 => ( ! [X3: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X3 @ B4 )
% 13.77/7.78 => ( ( Q2 @ X3 )
% 13.77/7.78 => ( P2 @ X3 ) ) )
% 13.77/7.78 => ( ord_le6045566169113846134st_nat
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X4 @ B4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) )
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6330_subset__CollectI,axiom,
% 13.77/7.78 ! [B4: set_set_nat,A4: set_set_nat,Q2: set_nat > $o,P2: set_nat > $o] :
% 13.77/7.78 ( ( ord_le6893508408891458716et_nat @ B4 @ A4 )
% 13.77/7.78 => ( ! [X3: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X3 @ B4 )
% 13.77/7.78 => ( ( Q2 @ X3 )
% 13.77/7.78 => ( P2 @ X3 ) ) )
% 13.77/7.78 => ( ord_le6893508408891458716et_nat
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X4 @ B4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) )
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6331_subset__CollectI,axiom,
% 13.77/7.78 ! [B4: set_nat,A4: set_nat,Q2: nat > $o,P2: nat > $o] :
% 13.77/7.78 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.78 => ( ! [X3: nat] :
% 13.77/7.78 ( ( member_nat @ X3 @ B4 )
% 13.77/7.78 => ( ( Q2 @ X3 )
% 13.77/7.78 => ( P2 @ X3 ) ) )
% 13.77/7.78 => ( ord_less_eq_set_nat
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( member_nat @ X4 @ B4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) )
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( member_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6332_subset__CollectI,axiom,
% 13.77/7.78 ! [B4: set_int,A4: set_int,Q2: int > $o,P2: int > $o] :
% 13.77/7.78 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.77/7.78 => ( ! [X3: int] :
% 13.77/7.78 ( ( member_int @ X3 @ B4 )
% 13.77/7.78 => ( ( Q2 @ X3 )
% 13.77/7.78 => ( P2 @ X3 ) ) )
% 13.77/7.78 => ( ord_less_eq_set_int
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( member_int @ X4 @ B4 )
% 13.77/7.78 & ( Q2 @ X4 ) ) )
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( member_int @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6333_subset__Collect__iff,axiom,
% 13.77/7.78 ! [B4: set_VEBT_VEBT,A4: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.78 ( ( ord_le4337996190870823476T_VEBT @ B4 @ A4 )
% 13.77/7.78 => ( ( ord_le4337996190870823476T_VEBT @ B4
% 13.77/7.78 @ ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 = ( ! [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( member_VEBT_VEBT @ X4 @ B4 )
% 13.77/7.78 => ( P2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6334_subset__Collect__iff,axiom,
% 13.77/7.78 ! [B4: set_real,A4: set_real,P2: real > $o] :
% 13.77/7.78 ( ( ord_less_eq_set_real @ B4 @ A4 )
% 13.77/7.78 => ( ( ord_less_eq_set_real @ B4
% 13.77/7.78 @ ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ( ( member_real @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 = ( ! [X4: real] :
% 13.77/7.78 ( ( member_real @ X4 @ B4 )
% 13.77/7.78 => ( P2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6335_subset__Collect__iff,axiom,
% 13.77/7.78 ! [B4: set_complex,A4: set_complex,P2: complex > $o] :
% 13.77/7.78 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 13.77/7.78 => ( ( ord_le211207098394363844omplex @ B4
% 13.77/7.78 @ ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( member_complex @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 = ( ! [X4: complex] :
% 13.77/7.78 ( ( member_complex @ X4 @ B4 )
% 13.77/7.78 => ( P2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6336_subset__Collect__iff,axiom,
% 13.77/7.78 ! [B4: set_list_nat,A4: set_list_nat,P2: list_nat > $o] :
% 13.77/7.78 ( ( ord_le6045566169113846134st_nat @ B4 @ A4 )
% 13.77/7.78 => ( ( ord_le6045566169113846134st_nat @ B4
% 13.77/7.78 @ ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 = ( ! [X4: list_nat] :
% 13.77/7.78 ( ( member_list_nat @ X4 @ B4 )
% 13.77/7.78 => ( P2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6337_subset__Collect__iff,axiom,
% 13.77/7.78 ! [B4: set_set_nat,A4: set_set_nat,P2: set_nat > $o] :
% 13.77/7.78 ( ( ord_le6893508408891458716et_nat @ B4 @ A4 )
% 13.77/7.78 => ( ( ord_le6893508408891458716et_nat @ B4
% 13.77/7.78 @ ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 = ( ! [X4: set_nat] :
% 13.77/7.78 ( ( member_set_nat @ X4 @ B4 )
% 13.77/7.78 => ( P2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6338_subset__Collect__iff,axiom,
% 13.77/7.78 ! [B4: set_nat,A4: set_nat,P2: nat > $o] :
% 13.77/7.78 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 13.77/7.78 => ( ( ord_less_eq_set_nat @ B4
% 13.77/7.78 @ ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( member_nat @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 = ( ! [X4: nat] :
% 13.77/7.78 ( ( member_nat @ X4 @ B4 )
% 13.77/7.78 => ( P2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6339_subset__Collect__iff,axiom,
% 13.77/7.78 ! [B4: set_int,A4: set_int,P2: int > $o] :
% 13.77/7.78 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 13.77/7.78 => ( ( ord_less_eq_set_int @ B4
% 13.77/7.78 @ ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( member_int @ X4 @ A4 )
% 13.77/7.78 & ( P2 @ X4 ) ) ) )
% 13.77/7.78 = ( ! [X4: int] :
% 13.77/7.78 ( ( member_int @ X4 @ B4 )
% 13.77/7.78 => ( P2 @ X4 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6340_insert__compr,axiom,
% 13.77/7.78 ( insert_o
% 13.77/7.78 = ( ^ [A7: $o,B6: set_o] :
% 13.77/7.78 ( collect_o
% 13.77/7.78 @ ^ [X4: $o] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6341_insert__compr,axiom,
% 13.77/7.78 ( insert_VEBT_VEBT
% 13.77/7.78 = ( ^ [A7: vEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.78 ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6342_insert__compr,axiom,
% 13.77/7.78 ( insert_real
% 13.77/7.78 = ( ^ [A7: real,B6: set_real] :
% 13.77/7.78 ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_real @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6343_insert__compr,axiom,
% 13.77/7.78 ( insert_complex
% 13.77/7.78 = ( ^ [A7: complex,B6: set_complex] :
% 13.77/7.78 ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_complex @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6344_insert__compr,axiom,
% 13.77/7.78 ( insert_list_nat
% 13.77/7.78 = ( ^ [A7: list_nat,B6: set_list_nat] :
% 13.77/7.78 ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6345_insert__compr,axiom,
% 13.77/7.78 ( insert_set_nat
% 13.77/7.78 = ( ^ [A7: set_nat,B6: set_set_nat] :
% 13.77/7.78 ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6346_insert__compr,axiom,
% 13.77/7.78 ( insert_nat
% 13.77/7.78 = ( ^ [A7: nat,B6: set_nat] :
% 13.77/7.78 ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6347_insert__compr,axiom,
% 13.77/7.78 ( insert_int
% 13.77/7.78 = ( ^ [A7: int,B6: set_int] :
% 13.77/7.78 ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ( ( X4 = A7 )
% 13.77/7.78 | ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6348_insert__Collect,axiom,
% 13.77/7.78 ! [A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.78 ( ( insert_VEBT_VEBT @ A @ ( collect_VEBT_VEBT @ P2 ) )
% 13.77/7.78 = ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [U2: vEBT_VEBT] :
% 13.77/7.78 ( ( U2 != A )
% 13.77/7.78 => ( P2 @ U2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6349_insert__Collect,axiom,
% 13.77/7.78 ! [A: $o,P2: $o > $o] :
% 13.77/7.78 ( ( insert_o @ A @ ( collect_o @ P2 ) )
% 13.77/7.78 = ( collect_o
% 13.77/7.78 @ ^ [U2: $o] :
% 13.77/7.78 ( ( U2 != A )
% 13.77/7.78 => ( P2 @ U2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6350_insert__Collect,axiom,
% 13.77/7.78 ! [A: complex,P2: complex > $o] :
% 13.77/7.78 ( ( insert_complex @ A @ ( collect_complex @ P2 ) )
% 13.77/7.78 = ( collect_complex
% 13.77/7.78 @ ^ [U2: complex] :
% 13.77/7.78 ( ( U2 != A )
% 13.77/7.78 => ( P2 @ U2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6351_insert__Collect,axiom,
% 13.77/7.78 ! [A: list_nat,P2: list_nat > $o] :
% 13.77/7.78 ( ( insert_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 13.77/7.78 = ( collect_list_nat
% 13.77/7.78 @ ^ [U2: list_nat] :
% 13.77/7.78 ( ( U2 != A )
% 13.77/7.78 => ( P2 @ U2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6352_insert__Collect,axiom,
% 13.77/7.78 ! [A: set_nat,P2: set_nat > $o] :
% 13.77/7.78 ( ( insert_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 13.77/7.78 = ( collect_set_nat
% 13.77/7.78 @ ^ [U2: set_nat] :
% 13.77/7.78 ( ( U2 != A )
% 13.77/7.78 => ( P2 @ U2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6353_insert__Collect,axiom,
% 13.77/7.78 ! [A: nat,P2: nat > $o] :
% 13.77/7.78 ( ( insert_nat @ A @ ( collect_nat @ P2 ) )
% 13.77/7.78 = ( collect_nat
% 13.77/7.78 @ ^ [U2: nat] :
% 13.77/7.78 ( ( U2 != A )
% 13.77/7.78 => ( P2 @ U2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6354_insert__Collect,axiom,
% 13.77/7.78 ! [A: int,P2: int > $o] :
% 13.77/7.78 ( ( insert_int @ A @ ( collect_int @ P2 ) )
% 13.77/7.78 = ( collect_int
% 13.77/7.78 @ ^ [U2: int] :
% 13.77/7.78 ( ( U2 != A )
% 13.77/7.78 => ( P2 @ U2 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6355_Compl__eq,axiom,
% 13.77/7.78 ( uminus8041839845116263051T_VEBT
% 13.77/7.78 = ( ^ [A6: set_VEBT_VEBT] :
% 13.77/7.78 ( collect_VEBT_VEBT
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.78 ~ ( member_VEBT_VEBT @ X4 @ A6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6356_Compl__eq,axiom,
% 13.77/7.78 ( uminus612125837232591019t_real
% 13.77/7.78 = ( ^ [A6: set_real] :
% 13.77/7.78 ( collect_real
% 13.77/7.78 @ ^ [X4: real] :
% 13.77/7.78 ~ ( member_real @ X4 @ A6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6357_Compl__eq,axiom,
% 13.77/7.78 ( uminus8566677241136511917omplex
% 13.77/7.78 = ( ^ [A6: set_complex] :
% 13.77/7.78 ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ~ ( member_complex @ X4 @ A6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6358_Compl__eq,axiom,
% 13.77/7.78 ( uminus3195874150345416415st_nat
% 13.77/7.78 = ( ^ [A6: set_list_nat] :
% 13.77/7.78 ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ~ ( member_list_nat @ X4 @ A6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6359_Compl__eq,axiom,
% 13.77/7.78 ( uminus613421341184616069et_nat
% 13.77/7.78 = ( ^ [A6: set_set_nat] :
% 13.77/7.78 ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ~ ( member_set_nat @ X4 @ A6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6360_Compl__eq,axiom,
% 13.77/7.78 ( uminus5710092332889474511et_nat
% 13.77/7.78 = ( ^ [A6: set_nat] :
% 13.77/7.78 ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ~ ( member_nat @ X4 @ A6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6361_Compl__eq,axiom,
% 13.77/7.78 ( uminus1532241313380277803et_int
% 13.77/7.78 = ( ^ [A6: set_int] :
% 13.77/7.78 ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ~ ( member_int @ X4 @ A6 ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6362_Collect__neg__eq,axiom,
% 13.77/7.78 ! [P2: complex > $o] :
% 13.77/7.78 ( ( collect_complex
% 13.77/7.78 @ ^ [X4: complex] :
% 13.77/7.78 ~ ( P2 @ X4 ) )
% 13.77/7.78 = ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6363_Collect__neg__eq,axiom,
% 13.77/7.78 ! [P2: list_nat > $o] :
% 13.77/7.78 ( ( collect_list_nat
% 13.77/7.78 @ ^ [X4: list_nat] :
% 13.77/7.78 ~ ( P2 @ X4 ) )
% 13.77/7.78 = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6364_Collect__neg__eq,axiom,
% 13.77/7.78 ! [P2: set_nat > $o] :
% 13.77/7.78 ( ( collect_set_nat
% 13.77/7.78 @ ^ [X4: set_nat] :
% 13.77/7.78 ~ ( P2 @ X4 ) )
% 13.77/7.78 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6365_Collect__neg__eq,axiom,
% 13.77/7.78 ! [P2: nat > $o] :
% 13.77/7.78 ( ( collect_nat
% 13.77/7.78 @ ^ [X4: nat] :
% 13.77/7.78 ~ ( P2 @ X4 ) )
% 13.77/7.78 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6366_Collect__neg__eq,axiom,
% 13.77/7.78 ! [P2: int > $o] :
% 13.77/7.78 ( ( collect_int
% 13.77/7.78 @ ^ [X4: int] :
% 13.77/7.78 ~ ( P2 @ X4 ) )
% 13.77/7.78 = ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6367_uminus__set__def,axiom,
% 13.77/7.78 ( uminus8041839845116263051T_VEBT
% 13.77/7.78 = ( ^ [A6: set_VEBT_VEBT] :
% 13.77/7.78 ( collect_VEBT_VEBT
% 13.77/7.78 @ ( uminus2746543603091002386VEBT_o
% 13.77/7.78 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6368_uminus__set__def,axiom,
% 13.77/7.78 ( uminus612125837232591019t_real
% 13.77/7.78 = ( ^ [A6: set_real] :
% 13.77/7.78 ( collect_real
% 13.77/7.78 @ ( uminus_uminus_real_o
% 13.77/7.78 @ ^ [X4: real] : ( member_real @ X4 @ A6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6369_uminus__set__def,axiom,
% 13.77/7.78 ( uminus8566677241136511917omplex
% 13.77/7.78 = ( ^ [A6: set_complex] :
% 13.77/7.78 ( collect_complex
% 13.77/7.78 @ ( uminus1680532995456772888plex_o
% 13.77/7.78 @ ^ [X4: complex] : ( member_complex @ X4 @ A6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6370_uminus__set__def,axiom,
% 13.77/7.78 ( uminus3195874150345416415st_nat
% 13.77/7.78 = ( ^ [A6: set_list_nat] :
% 13.77/7.78 ( collect_list_nat
% 13.77/7.78 @ ( uminus5770388063884162150_nat_o
% 13.77/7.78 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6371_uminus__set__def,axiom,
% 13.77/7.78 ( uminus613421341184616069et_nat
% 13.77/7.78 = ( ^ [A6: set_set_nat] :
% 13.77/7.78 ( collect_set_nat
% 13.77/7.78 @ ( uminus6401447641752708672_nat_o
% 13.77/7.78 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 ) ) ) ) ) ).
% 13.77/7.78
% 13.77/7.78 thf(fact_6372_uminus__set__def,axiom,
% 13.77/7.78 ( uminus5710092332889474511et_nat
% 13.77/7.78 = ( ^ [A6: set_nat] :
% 13.77/7.78 ( collect_nat
% 13.77/7.78 @ ( uminus_uminus_nat_o
% 13.77/7.79 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6373_uminus__set__def,axiom,
% 13.77/7.79 ( uminus1532241313380277803et_int
% 13.77/7.79 = ( ^ [A6: set_int] :
% 13.77/7.79 ( collect_int
% 13.77/7.79 @ ( uminus_uminus_int_o
% 13.77/7.79 @ ^ [X4: int] : ( member_int @ X4 @ A6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6374_lessThan__def,axiom,
% 13.77/7.79 ( set_or890127255671739683et_nat
% 13.77/7.79 = ( ^ [U2: set_nat] :
% 13.77/7.79 ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U2 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6375_lessThan__def,axiom,
% 13.77/7.79 ( set_ord_lessThan_rat
% 13.77/7.79 = ( ^ [U2: rat] :
% 13.77/7.79 ( collect_rat
% 13.77/7.79 @ ^ [X4: rat] : ( ord_less_rat @ X4 @ U2 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6376_lessThan__def,axiom,
% 13.77/7.79 ( set_ord_lessThan_num
% 13.77/7.79 = ( ^ [U2: num] :
% 13.77/7.79 ( collect_num
% 13.77/7.79 @ ^ [X4: num] : ( ord_less_num @ X4 @ U2 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6377_lessThan__def,axiom,
% 13.77/7.79 ( set_ord_lessThan_nat
% 13.77/7.79 = ( ^ [U2: nat] :
% 13.77/7.79 ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U2 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6378_lessThan__def,axiom,
% 13.77/7.79 ( set_ord_lessThan_int
% 13.77/7.79 = ( ^ [U2: int] :
% 13.77/7.79 ( collect_int
% 13.77/7.79 @ ^ [X4: int] : ( ord_less_int @ X4 @ U2 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6379_lessThan__def,axiom,
% 13.77/7.79 ( set_or5984915006950818249n_real
% 13.77/7.79 = ( ^ [U2: real] :
% 13.77/7.79 ( collect_real
% 13.77/7.79 @ ^ [X4: real] : ( ord_less_real @ X4 @ U2 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6380_less__set__def,axiom,
% 13.77/7.79 ( ord_less_set_nat
% 13.77/7.79 = ( ^ [A6: set_nat,B6: set_nat] :
% 13.77/7.79 ( ord_less_nat_o
% 13.77/7.79 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6381_less__set__def,axiom,
% 13.77/7.79 ( ord_le3480810397992357184T_VEBT
% 13.77/7.79 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.79 ( ord_less_VEBT_VEBT_o
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6382_less__set__def,axiom,
% 13.77/7.79 ( ord_less_set_real
% 13.77/7.79 = ( ^ [A6: set_real,B6: set_real] :
% 13.77/7.79 ( ord_less_real_o
% 13.77/7.79 @ ^ [X4: real] : ( member_real @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: real] : ( member_real @ X4 @ B6 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6383_less__set__def,axiom,
% 13.77/7.79 ( ord_less_set_int
% 13.77/7.79 = ( ^ [A6: set_int,B6: set_int] :
% 13.77/7.79 ( ord_less_int_o
% 13.77/7.79 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6384_less__set__def,axiom,
% 13.77/7.79 ( ord_less_set_set_nat
% 13.77/7.79 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 13.77/7.79 ( ord_less_set_nat_o
% 13.77/7.79 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6385_Set_Oempty__def,axiom,
% 13.77/7.79 ( bot_bot_set_complex
% 13.77/7.79 = ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] : $false ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6386_Set_Oempty__def,axiom,
% 13.77/7.79 ( bot_bot_set_list_nat
% 13.77/7.79 = ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] : $false ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6387_Set_Oempty__def,axiom,
% 13.77/7.79 ( bot_bot_set_set_nat
% 13.77/7.79 = ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] : $false ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6388_Set_Oempty__def,axiom,
% 13.77/7.79 ( bot_bot_set_nat
% 13.77/7.79 = ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] : $false ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6389_Set_Oempty__def,axiom,
% 13.77/7.79 ( bot_bot_set_int
% 13.77/7.79 = ( collect_int
% 13.77/7.79 @ ^ [X4: int] : $false ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6390_Set_Oempty__def,axiom,
% 13.77/7.79 ( bot_bot_set_o
% 13.77/7.79 = ( collect_o
% 13.77/7.79 @ ^ [X4: $o] : $false ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6391_minus__set__def,axiom,
% 13.77/7.79 ( minus_5127226145743854075T_VEBT
% 13.77/7.79 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.79 ( collect_VEBT_VEBT
% 13.77/7.79 @ ( minus_2794559001203777698VEBT_o
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6392_minus__set__def,axiom,
% 13.77/7.79 ( minus_minus_set_real
% 13.77/7.79 = ( ^ [A6: set_real,B6: set_real] :
% 13.77/7.79 ( collect_real
% 13.77/7.79 @ ( minus_minus_real_o
% 13.77/7.79 @ ^ [X4: real] : ( member_real @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: real] : ( member_real @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6393_minus__set__def,axiom,
% 13.77/7.79 ( minus_811609699411566653omplex
% 13.77/7.79 = ( ^ [A6: set_complex,B6: set_complex] :
% 13.77/7.79 ( collect_complex
% 13.77/7.79 @ ( minus_8727706125548526216plex_o
% 13.77/7.79 @ ^ [X4: complex] : ( member_complex @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: complex] : ( member_complex @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6394_minus__set__def,axiom,
% 13.77/7.79 ( minus_7954133019191499631st_nat
% 13.77/7.79 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 13.77/7.79 ( collect_list_nat
% 13.77/7.79 @ ( minus_1139252259498527702_nat_o
% 13.77/7.79 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6395_minus__set__def,axiom,
% 13.77/7.79 ( minus_2163939370556025621et_nat
% 13.77/7.79 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 13.77/7.79 ( collect_set_nat
% 13.77/7.79 @ ( minus_6910147592129066416_nat_o
% 13.77/7.79 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6396_minus__set__def,axiom,
% 13.77/7.79 ( minus_minus_set_int
% 13.77/7.79 = ( ^ [A6: set_int,B6: set_int] :
% 13.77/7.79 ( collect_int
% 13.77/7.79 @ ( minus_minus_int_o
% 13.77/7.79 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6397_minus__set__def,axiom,
% 13.77/7.79 ( minus_minus_set_nat
% 13.77/7.79 = ( ^ [A6: set_nat,B6: set_nat] :
% 13.77/7.79 ( collect_nat
% 13.77/7.79 @ ( minus_minus_nat_o
% 13.77/7.79 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 13.77/7.79 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6398_set__diff__eq,axiom,
% 13.77/7.79 ( minus_5127226145743854075T_VEBT
% 13.77/7.79 = ( ^ [A6: set_VEBT_VEBT,B6: set_VEBT_VEBT] :
% 13.77/7.79 ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ A6 )
% 13.77/7.79 & ~ ( member_VEBT_VEBT @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6399_set__diff__eq,axiom,
% 13.77/7.79 ( minus_minus_set_real
% 13.77/7.79 = ( ^ [A6: set_real,B6: set_real] :
% 13.77/7.79 ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ A6 )
% 13.77/7.79 & ~ ( member_real @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6400_set__diff__eq,axiom,
% 13.77/7.79 ( minus_811609699411566653omplex
% 13.77/7.79 = ( ^ [A6: set_complex,B6: set_complex] :
% 13.77/7.79 ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( member_complex @ X4 @ A6 )
% 13.77/7.79 & ~ ( member_complex @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6401_set__diff__eq,axiom,
% 13.77/7.79 ( minus_7954133019191499631st_nat
% 13.77/7.79 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 13.77/7.79 ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] :
% 13.77/7.79 ( ( member_list_nat @ X4 @ A6 )
% 13.77/7.79 & ~ ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6402_set__diff__eq,axiom,
% 13.77/7.79 ( minus_2163939370556025621et_nat
% 13.77/7.79 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 13.77/7.79 ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] :
% 13.77/7.79 ( ( member_set_nat @ X4 @ A6 )
% 13.77/7.79 & ~ ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6403_set__diff__eq,axiom,
% 13.77/7.79 ( minus_minus_set_int
% 13.77/7.79 = ( ^ [A6: set_int,B6: set_int] :
% 13.77/7.79 ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A6 )
% 13.77/7.79 & ~ ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6404_set__diff__eq,axiom,
% 13.77/7.79 ( minus_minus_set_nat
% 13.77/7.79 = ( ^ [A6: set_nat,B6: set_nat] :
% 13.77/7.79 ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( member_nat @ X4 @ A6 )
% 13.77/7.79 & ~ ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6405_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,B4: set_nat,R2: vEBT_VEBT > nat > $o] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: nat] :
% 13.77/7.79 ( ( member_nat @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6406_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_real,B4: set_nat,R2: real > nat > $o] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: nat] :
% 13.77/7.79 ( ( member_nat @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6407_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,B4: set_int,R2: vEBT_VEBT > int > $o] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite_finite_int @ B4 )
% 13.77/7.79 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: int] :
% 13.77/7.79 ( ( member_int @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: int] :
% 13.77/7.79 ( ( member_int @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6408_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_real,B4: set_int,R2: real > int > $o] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite_finite_int @ B4 )
% 13.77/7.79 => ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: int] :
% 13.77/7.79 ( ( member_int @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: int] :
% 13.77/7.79 ( ( member_int @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6409_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,B4: set_complex,R2: vEBT_VEBT > complex > $o] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.79 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: complex] :
% 13.77/7.79 ( ( member_complex @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: complex] :
% 13.77/7.79 ( ( member_complex @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6410_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_real,B4: set_complex,R2: real > complex > $o] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.79 => ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: complex] :
% 13.77/7.79 ( ( member_complex @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: complex] :
% 13.77/7.79 ( ( member_complex @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6411_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,B4: set_Code_integer,R2: vEBT_VEBT > code_integer > $o] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.79 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6412_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_real,B4: set_Code_integer,R2: real > code_integer > $o] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite6017078050557962740nteger @ B4 )
% 13.77/7.79 => ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6413_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_nat,B4: set_nat,R2: nat > nat > $o] :
% 13.77/7.79 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ! [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: nat] :
% 13.77/7.79 ( ( member_nat @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [A7: nat] :
% 13.77/7.79 ( ( member_nat @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6414_pigeonhole__infinite__rel,axiom,
% 13.77/7.79 ! [A4: set_nat,B4: set_int,R2: nat > int > $o] :
% 13.77/7.79 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.79 => ( ( finite_finite_int @ B4 )
% 13.77/7.79 => ( ! [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ A4 )
% 13.77/7.79 => ? [Xa: int] :
% 13.77/7.79 ( ( member_int @ Xa @ B4 )
% 13.77/7.79 & ( R2 @ X3 @ Xa ) ) )
% 13.77/7.79 => ? [X3: int] :
% 13.77/7.79 ( ( member_int @ X3 @ B4 )
% 13.77/7.79 & ~ ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [A7: nat] :
% 13.77/7.79 ( ( member_nat @ A7 @ A4 )
% 13.77/7.79 & ( R2 @ A7 @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6415_not__finite__existsD,axiom,
% 13.77/7.79 ! [P2: list_nat > $o] :
% 13.77/7.79 ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P2 ) )
% 13.77/7.79 => ? [X_1: list_nat] : ( P2 @ X_1 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6416_not__finite__existsD,axiom,
% 13.77/7.79 ! [P2: set_nat > $o] :
% 13.77/7.79 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P2 ) )
% 13.77/7.79 => ? [X_1: set_nat] : ( P2 @ X_1 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6417_not__finite__existsD,axiom,
% 13.77/7.79 ! [P2: nat > $o] :
% 13.77/7.79 ( ~ ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 13.77/7.79 => ? [X_1: nat] : ( P2 @ X_1 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6418_not__finite__existsD,axiom,
% 13.77/7.79 ! [P2: int > $o] :
% 13.77/7.79 ( ~ ( finite_finite_int @ ( collect_int @ P2 ) )
% 13.77/7.79 => ? [X_1: int] : ( P2 @ X_1 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6419_not__finite__existsD,axiom,
% 13.77/7.79 ! [P2: complex > $o] :
% 13.77/7.79 ( ~ ( finite3207457112153483333omplex @ ( collect_complex @ P2 ) )
% 13.77/7.79 => ? [X_1: complex] : ( P2 @ X_1 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6420_not__finite__existsD,axiom,
% 13.77/7.79 ! [P2: code_integer > $o] :
% 13.77/7.79 ( ~ ( finite6017078050557962740nteger @ ( collect_Code_integer @ P2 ) )
% 13.77/7.79 => ? [X_1: code_integer] : ( P2 @ X_1 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6421_imageE,axiom,
% 13.77/7.79 ! [B: nat,F: nat > nat,A4: set_nat] :
% 13.77/7.79 ( ( member_nat @ B @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: nat] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_nat @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6422_imageE,axiom,
% 13.77/7.79 ! [B: nat,F: vEBT_VEBT > nat,A4: set_VEBT_VEBT] :
% 13.77/7.79 ( ( member_nat @ B @ ( image_VEBT_VEBT_nat @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_VEBT_VEBT @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6423_imageE,axiom,
% 13.77/7.79 ! [B: nat,F: real > nat,A4: set_real] :
% 13.77/7.79 ( ( member_nat @ B @ ( image_real_nat @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: real] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_real @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6424_imageE,axiom,
% 13.77/7.79 ! [B: nat,F: int > nat,A4: set_int] :
% 13.77/7.79 ( ( member_nat @ B @ ( image_int_nat @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: int] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_int @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6425_imageE,axiom,
% 13.77/7.79 ! [B: vEBT_VEBT,F: nat > vEBT_VEBT,A4: set_nat] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ B @ ( image_nat_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: nat] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_nat @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6426_imageE,axiom,
% 13.77/7.79 ! [B: vEBT_VEBT,F: vEBT_VEBT > vEBT_VEBT,A4: set_VEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ B @ ( image_3375948659692109573T_VEBT @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_VEBT_VEBT @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6427_imageE,axiom,
% 13.77/7.79 ! [B: vEBT_VEBT,F: real > vEBT_VEBT,A4: set_real] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ B @ ( image_real_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: real] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_real @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6428_imageE,axiom,
% 13.77/7.79 ! [B: vEBT_VEBT,F: int > vEBT_VEBT,A4: set_int] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ B @ ( image_int_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: int] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_int @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6429_imageE,axiom,
% 13.77/7.79 ! [B: real,F: nat > real,A4: set_nat] :
% 13.77/7.79 ( ( member_real @ B @ ( image_nat_real @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: nat] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_nat @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6430_imageE,axiom,
% 13.77/7.79 ! [B: real,F: vEBT_VEBT > real,A4: set_VEBT_VEBT] :
% 13.77/7.79 ( ( member_real @ B @ ( image_VEBT_VEBT_real @ F @ A4 ) )
% 13.77/7.79 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( B
% 13.77/7.79 = ( F @ X3 ) )
% 13.77/7.79 => ~ ( member_VEBT_VEBT @ X3 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6431_image__image,axiom,
% 13.77/7.79 ! [F: nat > nat,G: nat > nat,A4: set_nat] :
% 13.77/7.79 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ A4 ) )
% 13.77/7.79 = ( image_nat_nat
% 13.77/7.79 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6432_image__image,axiom,
% 13.77/7.79 ! [F: nat > nat,G: int > nat,A4: set_int] :
% 13.77/7.79 ( ( image_nat_nat @ F @ ( image_int_nat @ G @ A4 ) )
% 13.77/7.79 = ( image_int_nat
% 13.77/7.79 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6433_image__image,axiom,
% 13.77/7.79 ! [F: nat > int,G: nat > nat,A4: set_nat] :
% 13.77/7.79 ( ( image_nat_int @ F @ ( image_nat_nat @ G @ A4 ) )
% 13.77/7.79 = ( image_nat_int
% 13.77/7.79 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6434_image__image,axiom,
% 13.77/7.79 ! [F: nat > int,G: int > nat,A4: set_int] :
% 13.77/7.79 ( ( image_nat_int @ F @ ( image_int_nat @ G @ A4 ) )
% 13.77/7.79 = ( image_int_int
% 13.77/7.79 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6435_image__image,axiom,
% 13.77/7.79 ! [F: int > nat,G: nat > int,A4: set_nat] :
% 13.77/7.79 ( ( image_int_nat @ F @ ( image_nat_int @ G @ A4 ) )
% 13.77/7.79 = ( image_nat_nat
% 13.77/7.79 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6436_image__image,axiom,
% 13.77/7.79 ! [F: int > nat,G: int > int,A4: set_int] :
% 13.77/7.79 ( ( image_int_nat @ F @ ( image_int_int @ G @ A4 ) )
% 13.77/7.79 = ( image_int_nat
% 13.77/7.79 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6437_image__image,axiom,
% 13.77/7.79 ! [F: int > int,G: nat > int,A4: set_nat] :
% 13.77/7.79 ( ( image_int_int @ F @ ( image_nat_int @ G @ A4 ) )
% 13.77/7.79 = ( image_nat_int
% 13.77/7.79 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6438_image__image,axiom,
% 13.77/7.79 ! [F: int > int,G: int > int,A4: set_int] :
% 13.77/7.79 ( ( image_int_int @ F @ ( image_int_int @ G @ A4 ) )
% 13.77/7.79 = ( image_int_int
% 13.77/7.79 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6439_image__image,axiom,
% 13.77/7.79 ! [F: set_nat > nat,G: nat > set_nat,A4: set_nat] :
% 13.77/7.79 ( ( image_set_nat_nat @ F @ ( image_nat_set_nat @ G @ A4 ) )
% 13.77/7.79 = ( image_nat_nat
% 13.77/7.79 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6440_image__image,axiom,
% 13.77/7.79 ! [F: set_nat > int,G: nat > set_nat,A4: set_nat] :
% 13.77/7.79 ( ( image_set_nat_int @ F @ ( image_nat_set_nat @ G @ A4 ) )
% 13.77/7.79 = ( image_nat_int
% 13.77/7.79 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6441_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: vEBT_VEBT > vEBT_VEBT,A4: set_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 13.77/7.79 ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ ( image_3375948659692109573T_VEBT @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_3375948659692109573T_VEBT @ F
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6442_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: real > vEBT_VEBT,A4: set_real,P2: vEBT_VEBT > $o] :
% 13.77/7.79 ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ ( image_real_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_real_VEBT_VEBT @ F
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6443_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: vEBT_VEBT > real,A4: set_VEBT_VEBT,P2: real > $o] :
% 13.77/7.79 ( ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ ( image_VEBT_VEBT_real @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_VEBT_VEBT_real @ F
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6444_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: real > real,A4: set_real,P2: real > $o] :
% 13.77/7.79 ( ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ ( image_real_real @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_real_real @ F
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6445_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: complex > vEBT_VEBT,A4: set_complex,P2: vEBT_VEBT > $o] :
% 13.77/7.79 ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ ( image_932796090930683071T_VEBT @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_932796090930683071T_VEBT @ F
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( member_complex @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6446_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: complex > real,A4: set_complex,P2: real > $o] :
% 13.77/7.79 ( ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ ( image_complex_real @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_complex_real @ F
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( member_complex @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6447_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: nat > vEBT_VEBT,A4: set_nat,P2: vEBT_VEBT > $o] :
% 13.77/7.79 ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ ( image_nat_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_nat_VEBT_VEBT @ F
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( member_nat @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6448_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: nat > real,A4: set_nat,P2: real > $o] :
% 13.77/7.79 ( ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ ( image_nat_real @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_nat_real @ F
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( member_nat @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6449_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: int > vEBT_VEBT,A4: set_int,P2: vEBT_VEBT > $o] :
% 13.77/7.79 ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ ( image_int_VEBT_VEBT @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_int_VEBT_VEBT @ F
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6450_Compr__image__eq,axiom,
% 13.77/7.79 ! [F: int > real,A4: set_int,P2: real > $o] :
% 13.77/7.79 ( ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ ( image_int_real @ F @ A4 ) )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( image_int_real @ F
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ ( F @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6451_lambda__zero,axiom,
% 13.77/7.79 ( ( ^ [H4: rat] : zero_zero_rat )
% 13.77/7.79 = ( times_times_rat @ zero_zero_rat ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6452_lambda__zero,axiom,
% 13.77/7.79 ( ( ^ [H4: uint32] : zero_zero_uint32 )
% 13.77/7.79 = ( times_times_uint32 @ zero_zero_uint32 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6453_lambda__zero,axiom,
% 13.77/7.79 ( ( ^ [H4: real] : zero_zero_real )
% 13.77/7.79 = ( times_times_real @ zero_zero_real ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6454_lambda__zero,axiom,
% 13.77/7.79 ( ( ^ [H4: nat] : zero_zero_nat )
% 13.77/7.79 = ( times_times_nat @ zero_zero_nat ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6455_lambda__zero,axiom,
% 13.77/7.79 ( ( ^ [H4: int] : zero_zero_int )
% 13.77/7.79 = ( times_times_int @ zero_zero_int ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6456_sum_Onat__diff__reindex,axiom,
% 13.77/7.79 ! [G: nat > nat,N: nat] :
% 13.77/7.79 ( ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.79 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6457_sum_Onat__diff__reindex,axiom,
% 13.77/7.79 ! [G: nat > real,N: nat] :
% 13.77/7.79 ( ( groups6591440286371151544t_real
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.79 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6458_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_nat,F: nat > rat,G: nat > rat] :
% 13.77/7.79 ( ! [I2: nat] :
% 13.77/7.79 ( ( member_nat @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K4 ) @ ( groups2906978787729119204at_rat @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6459_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_VEBT_VEBT,F: vEBT_VEBT > rat,G: vEBT_VEBT > rat] :
% 13.77/7.79 ( ! [I2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_rat @ ( groups136491112297645522BT_rat @ F @ K4 ) @ ( groups136491112297645522BT_rat @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6460_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_real,F: real > rat,G: real > rat] :
% 13.77/7.79 ( ! [I2: real] :
% 13.77/7.79 ( ( member_real @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K4 ) @ ( groups1300246762558778688al_rat @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6461_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_int,F: int > rat,G: int > rat] :
% 13.77/7.79 ( ! [I2: int] :
% 13.77/7.79 ( ( member_int @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K4 ) @ ( groups3906332499630173760nt_rat @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6462_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_VEBT_VEBT,F: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 13.77/7.79 ( ! [I2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_nat @ ( groups771621172384141258BT_nat @ F @ K4 ) @ ( groups771621172384141258BT_nat @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6463_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_real,F: real > nat,G: real > nat] :
% 13.77/7.79 ( ! [I2: real] :
% 13.77/7.79 ( ( member_real @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K4 ) @ ( groups1935376822645274424al_nat @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6464_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_int,F: int > nat,G: int > nat] :
% 13.77/7.79 ( ! [I2: int] :
% 13.77/7.79 ( ( member_int @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K4 ) @ ( groups4541462559716669496nt_nat @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6465_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_nat,F: nat > int,G: nat > int] :
% 13.77/7.79 ( ! [I2: nat] :
% 13.77/7.79 ( ( member_nat @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K4 ) @ ( groups3539618377306564664at_int @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6466_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_VEBT_VEBT,F: vEBT_VEBT > int,G: vEBT_VEBT > int] :
% 13.77/7.79 ( ! [I2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_int @ ( groups769130701875090982BT_int @ F @ K4 ) @ ( groups769130701875090982BT_int @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6467_sum__mono,axiom,
% 13.77/7.79 ! [K4: set_real,F: real > int,G: real > int] :
% 13.77/7.79 ( ! [I2: real] :
% 13.77/7.79 ( ( member_real @ I2 @ K4 )
% 13.77/7.79 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 13.77/7.79 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K4 ) @ ( groups1932886352136224148al_int @ G @ K4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6468_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ ( image_VEBT_VEBT_nat @ F @ A4 ) )
% 13.77/7.79 => ? [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6469_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_real,F: real > nat] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ ( image_real_nat @ F @ A4 ) )
% 13.77/7.79 => ? [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6470_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite_finite_int @ ( image_VEBT_VEBT_int @ F @ A4 ) )
% 13.77/7.79 => ? [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6471_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_real,F: real > int] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite_finite_int @ ( image_real_int @ F @ A4 ) )
% 13.77/7.79 => ? [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6472_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > complex] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ ( image_3793382806556112285omplex @ F @ A4 ) )
% 13.77/7.79 => ? [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6473_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_real,F: real > complex] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ ( image_real_complex @ F @ A4 ) )
% 13.77/7.79 => ? [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6474_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > code_integer] :
% 13.77/7.79 ( ~ ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite6017078050557962740nteger @ ( image_2092689629700589388nteger @ F @ A4 ) )
% 13.77/7.79 => ? [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [A7: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6475_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_real,F: real > code_integer] :
% 13.77/7.79 ( ~ ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite6017078050557962740nteger @ ( image_4958697645175560720nteger @ F @ A4 ) )
% 13.77/7.79 => ? [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [A7: real] :
% 13.77/7.79 ( ( member_real @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6476_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_nat,F: nat > nat] :
% 13.77/7.79 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ ( image_nat_nat @ F @ A4 ) )
% 13.77/7.79 => ? [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [A7: nat] :
% 13.77/7.79 ( ( member_nat @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6477_pigeonhole__infinite,axiom,
% 13.77/7.79 ! [A4: set_nat,F: nat > int] :
% 13.77/7.79 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.79 => ( ( finite_finite_int @ ( image_nat_int @ F @ A4 ) )
% 13.77/7.79 => ? [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ A4 )
% 13.77/7.79 & ~ ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [A7: nat] :
% 13.77/7.79 ( ( member_nat @ A7 @ A4 )
% 13.77/7.79 & ( ( F @ A7 )
% 13.77/7.79 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6478_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: complex > $o,F: complex > nat,B4: set_nat] :
% 13.77/7.79 ( ! [X3: complex] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_less_eq_set_nat @ ( image_complex_nat @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6479_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: complex > $o,F: complex > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.79 ( ! [X3: complex] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_le4337996190870823476T_VEBT @ ( image_932796090930683071T_VEBT @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6480_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: complex > $o,F: complex > real,B4: set_real] :
% 13.77/7.79 ( ! [X3: complex] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_less_eq_set_real @ ( image_complex_real @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6481_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: nat > $o,F: nat > nat,B4: set_nat] :
% 13.77/7.79 ( ! [X3: nat] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( collect_nat @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6482_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: nat > $o,F: nat > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.79 ( ! [X3: nat] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_le4337996190870823476T_VEBT @ ( image_nat_VEBT_VEBT @ F @ ( collect_nat @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6483_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: nat > $o,F: nat > real,B4: set_real] :
% 13.77/7.79 ( ! [X3: nat] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_less_eq_set_real @ ( image_nat_real @ F @ ( collect_nat @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6484_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: int > $o,F: int > nat,B4: set_nat] :
% 13.77/7.79 ( ! [X3: int] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_nat @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( collect_int @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6485_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: int > $o,F: int > vEBT_VEBT,B4: set_VEBT_VEBT] :
% 13.77/7.79 ( ! [X3: int] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_VEBT_VEBT @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_le4337996190870823476T_VEBT @ ( image_int_VEBT_VEBT @ F @ ( collect_int @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6486_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: int > $o,F: int > real,B4: set_real] :
% 13.77/7.79 ( ! [X3: int] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_real @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_less_eq_set_real @ ( image_int_real @ F @ ( collect_int @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6487_image__Collect__subsetI,axiom,
% 13.77/7.79 ! [P2: complex > $o,F: complex > int,B4: set_int] :
% 13.77/7.79 ( ! [X3: complex] :
% 13.77/7.79 ( ( P2 @ X3 )
% 13.77/7.79 => ( member_int @ ( F @ X3 ) @ B4 ) )
% 13.77/7.79 => ( ord_less_eq_set_int @ ( image_complex_int @ F @ ( collect_complex @ P2 ) ) @ B4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6488_Collect__conv__if2,axiom,
% 13.77/7.79 ! [P2: vEBT_VEBT > $o,A: vEBT_VEBT] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6489_Collect__conv__if2,axiom,
% 13.77/7.79 ! [P2: complex > $o,A: complex] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_complex ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6490_Collect__conv__if2,axiom,
% 13.77/7.79 ! [P2: list_nat > $o,A: list_nat] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_list_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6491_Collect__conv__if2,axiom,
% 13.77/7.79 ! [P2: set_nat > $o,A: set_nat] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6492_Collect__conv__if2,axiom,
% 13.77/7.79 ! [P2: nat > $o,A: nat] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6493_Collect__conv__if2,axiom,
% 13.77/7.79 ! [P2: int > $o,A: int] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_int ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6494_Collect__conv__if2,axiom,
% 13.77/7.79 ! [P2: $o > $o,A: $o] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_o
% 13.77/7.79 @ ^ [X4: $o] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_o
% 13.77/7.79 @ ^ [X4: $o] :
% 13.77/7.79 ( ( A = X4 )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_o ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6495_Collect__conv__if,axiom,
% 13.77/7.79 ! [P2: vEBT_VEBT > $o,A: vEBT_VEBT] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6496_Collect__conv__if,axiom,
% 13.77/7.79 ! [P2: complex > $o,A: complex] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_complex ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6497_Collect__conv__if,axiom,
% 13.77/7.79 ! [P2: list_nat > $o,A: list_nat] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_list_nat @ A @ bot_bot_set_list_nat ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_list_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6498_Collect__conv__if,axiom,
% 13.77/7.79 ! [P2: set_nat > $o,A: set_nat] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6499_Collect__conv__if,axiom,
% 13.77/7.79 ! [P2: nat > $o,A: nat] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6500_Collect__conv__if,axiom,
% 13.77/7.79 ! [P2: int > $o,A: int] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_int @ A @ bot_bot_set_int ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_int ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6501_Collect__conv__if,axiom,
% 13.77/7.79 ! [P2: $o > $o,A: $o] :
% 13.77/7.79 ( ( ( P2 @ A )
% 13.77/7.79 => ( ( collect_o
% 13.77/7.79 @ ^ [X4: $o] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = ( insert_o @ A @ bot_bot_set_o ) ) )
% 13.77/7.79 & ( ~ ( P2 @ A )
% 13.77/7.79 => ( ( collect_o
% 13.77/7.79 @ ^ [X4: $o] :
% 13.77/7.79 ( ( X4 = A )
% 13.77/7.79 & ( P2 @ X4 ) ) )
% 13.77/7.79 = bot_bot_set_o ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6502_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,B4: set_nat,G: vEBT_VEBT > nat > nat,R2: vEBT_VEBT > nat > $o] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ( groups771621172384141258BT_nat
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( ( member_nat @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups771621172384141258BT_nat
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6503_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_real,B4: set_nat,G: real > nat > nat,R2: real > nat > $o] :
% 13.77/7.79 ( ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ( groups1935376822645274424al_nat
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( ( member_nat @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups1935376822645274424al_nat
% 13.77/7.79 @ ^ [X4: real] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6504_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_int,B4: set_nat,G: int > nat > nat,R2: int > nat > $o] :
% 13.77/7.79 ( ( finite_finite_int @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ( groups4541462559716669496nt_nat
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( ( member_nat @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups4541462559716669496nt_nat
% 13.77/7.79 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6505_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_complex,B4: set_nat,G: complex > nat > nat,R2: complex > nat > $o] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ( groups5693394587270226106ex_nat
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( ( member_nat @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups5693394587270226106ex_nat
% 13.77/7.79 @ ^ [X4: complex] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( member_complex @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6506_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_Code_integer,B4: set_nat,G: code_integer > nat > nat,R2: code_integer > nat > $o] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.79 => ( ( finite_finite_nat @ B4 )
% 13.77/7.79 => ( ( groups7237345082560585321er_nat
% 13.77/7.79 @ ^ [X4: code_integer] :
% 13.77/7.79 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( ( member_nat @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups7237345082560585321er_nat
% 13.77/7.79 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6507_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,B4: set_complex,G: vEBT_VEBT > complex > complex,R2: vEBT_VEBT > complex > $o] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.79 => ( ( groups1794756597179926696omplex
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( groups7754918857620584856omplex @ ( G @ X4 )
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( ( member_complex @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups1794756597179926696omplex
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6508_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_real,B4: set_complex,G: real > complex > complex,R2: real > complex > $o] :
% 13.77/7.79 ( ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.79 => ( ( groups5754745047067104278omplex
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( groups7754918857620584856omplex @ ( G @ X4 )
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( ( member_complex @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups5754745047067104278omplex
% 13.77/7.79 @ ^ [X4: real] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6509_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_nat,B4: set_complex,G: nat > complex > complex,R2: nat > complex > $o] :
% 13.77/7.79 ( ( finite_finite_nat @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.79 => ( ( groups2073611262835488442omplex
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( groups7754918857620584856omplex @ ( G @ X4 )
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( ( member_complex @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups2073611262835488442omplex
% 13.77/7.79 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( member_nat @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6510_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_int,B4: set_complex,G: int > complex > complex,R2: int > complex > $o] :
% 13.77/7.79 ( ( finite_finite_int @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.79 => ( ( groups3049146728041665814omplex
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( groups7754918857620584856omplex @ ( G @ X4 )
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( ( member_complex @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups3049146728041665814omplex
% 13.77/7.79 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6511_sum_Oswap__restrict,axiom,
% 13.77/7.79 ! [A4: set_Code_integer,B4: set_complex,G: code_integer > complex > complex,R2: code_integer > complex > $o] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.79 => ( ( finite3207457112153483333omplex @ B4 )
% 13.77/7.79 => ( ( groups8024822376189712711omplex
% 13.77/7.79 @ ^ [X4: code_integer] :
% 13.77/7.79 ( groups7754918857620584856omplex @ ( G @ X4 )
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( ( member_complex @ Y4 @ B4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups8024822376189712711omplex
% 13.77/7.79 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.79 & ( R2 @ X4 @ Y4 ) ) ) )
% 13.77/7.79 @ B4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6512_sum__diff__distrib,axiom,
% 13.77/7.79 ! [Q2: int > nat,P2: int > nat,N: int] :
% 13.77/7.79 ( ! [X3: int] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 13.77/7.79 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P2 @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q2 @ ( set_ord_lessThan_int @ N ) ) )
% 13.77/7.79 = ( groups4541462559716669496nt_nat
% 13.77/7.79 @ ^ [X4: int] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 13.77/7.79 @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6513_sum__diff__distrib,axiom,
% 13.77/7.79 ! [Q2: real > nat,P2: real > nat,N: real] :
% 13.77/7.79 ( ! [X3: real] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 13.77/7.79 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P2 @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q2 @ ( set_or5984915006950818249n_real @ N ) ) )
% 13.77/7.79 = ( groups1935376822645274424al_nat
% 13.77/7.79 @ ^ [X4: real] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 13.77/7.79 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6514_sum__diff__distrib,axiom,
% 13.77/7.79 ! [Q2: nat > nat,P2: nat > nat,N: nat] :
% 13.77/7.79 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q2 @ X3 ) @ ( P2 @ X3 ) )
% 13.77/7.79 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P2 @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q2 @ ( set_ord_lessThan_nat @ N ) ) )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [X4: nat] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q2 @ X4 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6515_max__def__raw,axiom,
% 13.77/7.79 ( ord_max_Code_integer
% 13.77/7.79 = ( ^ [A7: code_integer,B7: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6516_max__def__raw,axiom,
% 13.77/7.79 ( ord_max_set_int
% 13.77/7.79 = ( ^ [A7: set_int,B7: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6517_max__def__raw,axiom,
% 13.77/7.79 ( ord_max_rat
% 13.77/7.79 = ( ^ [A7: rat,B7: rat] : ( if_rat @ ( ord_less_eq_rat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6518_max__def__raw,axiom,
% 13.77/7.79 ( ord_max_num
% 13.77/7.79 = ( ^ [A7: num,B7: num] : ( if_num @ ( ord_less_eq_num @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6519_max__def__raw,axiom,
% 13.77/7.79 ( ord_max_nat
% 13.77/7.79 = ( ^ [A7: nat,B7: nat] : ( if_nat @ ( ord_less_eq_nat @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6520_max__def__raw,axiom,
% 13.77/7.79 ( ord_max_int
% 13.77/7.79 = ( ^ [A7: int,B7: int] : ( if_int @ ( ord_less_eq_int @ A7 @ B7 ) @ B7 @ A7 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6521_pred__subset__eq2,axiom,
% 13.77/7.79 ! [R2: set_Pr1773385645901665561uint32,S3: set_Pr1773385645901665561uint32] :
% 13.77/7.79 ( ( ord_le5999336846926846542nt32_o
% 13.77/7.79 @ ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R2 )
% 13.77/7.79 @ ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ S3 ) )
% 13.77/7.79 = ( ord_le6429528607962791097uint32 @ R2 @ S3 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6522_pred__subset__eq2,axiom,
% 13.77/7.79 ! [R2: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 13.77/7.79 ( ( ord_le2646555220125990790_nat_o
% 13.77/7.79 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R2 )
% 13.77/7.79 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S3 ) )
% 13.77/7.79 = ( ord_le3146513528884898305at_nat @ R2 @ S3 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6523_pred__subset__eq2,axiom,
% 13.77/7.79 ! [R2: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 13.77/7.79 ( ( ord_le6741204236512500942_int_o
% 13.77/7.79 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R2 )
% 13.77/7.79 @ ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ S3 ) )
% 13.77/7.79 = ( ord_le2843351958646193337nt_int @ R2 @ S3 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6524_pred__subset__eq2,axiom,
% 13.77/7.79 ! [R2: set_Pr3286484037609594932et_nat,S3: set_Pr3286484037609594932et_nat] :
% 13.77/7.79 ( ( ord_le8000401564054156549_nat_o
% 13.77/7.79 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R2 )
% 13.77/7.79 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S3 ) )
% 13.77/7.79 = ( ord_le5966269811547037844et_nat @ R2 @ S3 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6525_pred__subset__eq2,axiom,
% 13.77/7.79 ! [R2: set_Pr8536935166611901872et_nat,S3: set_Pr8536935166611901872et_nat] :
% 13.77/7.79 ( ( ord_le6753239538765779593_nat_o
% 13.77/7.79 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R2 )
% 13.77/7.79 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S3 ) )
% 13.77/7.79 = ( ord_le4763372923235995152et_nat @ R2 @ S3 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6526_bot__empty__eq2,axiom,
% 13.77/7.79 ( bot_bo8112279147790955290nt32_o
% 13.77/7.79 = ( ^ [X4: uint32,Y4: uint32] : ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ bot_bo8438649754162204037uint32 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6527_bot__empty__eq2,axiom,
% 13.77/7.79 ( bot_bot_nat_nat_o
% 13.77/7.79 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6528_bot__empty__eq2,axiom,
% 13.77/7.79 ( bot_bot_int_int_o
% 13.77/7.79 = ( ^ [X4: int,Y4: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6529_bot__empty__eq2,axiom,
% 13.77/7.79 ( bot_bo5580076615179976505_nat_o
% 13.77/7.79 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6530_bot__empty__eq2,axiom,
% 13.77/7.79 ( bot_bo3790638025767943357_nat_o
% 13.77/7.79 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6531_finite__M__bounded__by__nat,axiom,
% 13.77/7.79 ! [P2: nat > $o,I: nat] :
% 13.77/7.79 ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [K3: nat] :
% 13.77/7.79 ( ( P2 @ K3 )
% 13.77/7.79 & ( ord_less_nat @ K3 @ I ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6532_finite__less__ub,axiom,
% 13.77/7.79 ! [F: nat > nat,U: nat] :
% 13.77/7.79 ( ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( F @ N2 ) )
% 13.77/7.79 => ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [N6: nat] : ( ord_less_eq_nat @ ( F @ N6 ) @ U ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6533_set__vebt__def,axiom,
% 13.77/7.79 ( vEBT_set_vebt
% 13.77/7.79 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6534_zip__inj,axiom,
% 13.77/7.79 ! [A: list_VEBT_VEBT,B: list_VEBT_VEBT,A2: list_VEBT_VEBT,B2: list_VEBT_VEBT] :
% 13.77/7.79 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ B ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 13.77/7.79 => ( ( ( zip_VE537291747668921783T_VEBT @ A @ B )
% 13.77/7.79 = ( zip_VE537291747668921783T_VEBT @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6535_zip__inj,axiom,
% 13.77/7.79 ! [A: list_VEBT_VEBT,B: list_real,A2: list_VEBT_VEBT,B2: list_real] :
% 13.77/7.79 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.79 = ( size_size_list_real @ B ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.79 = ( size_size_list_real @ B2 ) )
% 13.77/7.79 => ( ( ( zip_VEBT_VEBT_real @ A @ B )
% 13.77/7.79 = ( zip_VEBT_VEBT_real @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6536_zip__inj,axiom,
% 13.77/7.79 ! [A: list_VEBT_VEBT,B: list_o,A2: list_VEBT_VEBT,B2: list_o] :
% 13.77/7.79 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.79 = ( size_size_list_o @ B ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.79 = ( size_size_list_o @ B2 ) )
% 13.77/7.79 => ( ( ( zip_VEBT_VEBT_o @ A @ B )
% 13.77/7.79 = ( zip_VEBT_VEBT_o @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6537_zip__inj,axiom,
% 13.77/7.79 ! [A: list_VEBT_VEBT,B: list_nat,A2: list_VEBT_VEBT,B2: list_nat] :
% 13.77/7.79 ( ( ( size_s6755466524823107622T_VEBT @ A )
% 13.77/7.79 = ( size_size_list_nat @ B ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ A2 )
% 13.77/7.79 = ( size_size_list_nat @ B2 ) )
% 13.77/7.79 => ( ( ( zip_VEBT_VEBT_nat @ A @ B )
% 13.77/7.79 = ( zip_VEBT_VEBT_nat @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6538_zip__inj,axiom,
% 13.77/7.79 ! [A: list_real,B: list_VEBT_VEBT,A2: list_real,B2: list_VEBT_VEBT] :
% 13.77/7.79 ( ( ( size_size_list_real @ A )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ B ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 13.77/7.79 => ( ( ( zip_real_VEBT_VEBT @ A @ B )
% 13.77/7.79 = ( zip_real_VEBT_VEBT @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6539_zip__inj,axiom,
% 13.77/7.79 ! [A: list_real,B: list_real,A2: list_real,B2: list_real] :
% 13.77/7.79 ( ( ( size_size_list_real @ A )
% 13.77/7.79 = ( size_size_list_real @ B ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.79 = ( size_size_list_real @ B2 ) )
% 13.77/7.79 => ( ( ( zip_real_real @ A @ B )
% 13.77/7.79 = ( zip_real_real @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6540_zip__inj,axiom,
% 13.77/7.79 ! [A: list_real,B: list_o,A2: list_real,B2: list_o] :
% 13.77/7.79 ( ( ( size_size_list_real @ A )
% 13.77/7.79 = ( size_size_list_o @ B ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.79 = ( size_size_list_o @ B2 ) )
% 13.77/7.79 => ( ( ( zip_real_o @ A @ B )
% 13.77/7.79 = ( zip_real_o @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6541_zip__inj,axiom,
% 13.77/7.79 ! [A: list_real,B: list_nat,A2: list_real,B2: list_nat] :
% 13.77/7.79 ( ( ( size_size_list_real @ A )
% 13.77/7.79 = ( size_size_list_nat @ B ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ A2 )
% 13.77/7.79 = ( size_size_list_nat @ B2 ) )
% 13.77/7.79 => ( ( ( zip_real_nat @ A @ B )
% 13.77/7.79 = ( zip_real_nat @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6542_zip__inj,axiom,
% 13.77/7.79 ! [A: list_o,B: list_VEBT_VEBT,A2: list_o,B2: list_VEBT_VEBT] :
% 13.77/7.79 ( ( ( size_size_list_o @ A )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ B ) )
% 13.77/7.79 => ( ( ( size_size_list_o @ A2 )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ B2 ) )
% 13.77/7.79 => ( ( ( zip_o_VEBT_VEBT @ A @ B )
% 13.77/7.79 = ( zip_o_VEBT_VEBT @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6543_zip__inj,axiom,
% 13.77/7.79 ! [A: list_o,B: list_real,A2: list_o,B2: list_real] :
% 13.77/7.79 ( ( ( size_size_list_o @ A )
% 13.77/7.79 = ( size_size_list_real @ B ) )
% 13.77/7.79 => ( ( ( size_size_list_o @ A2 )
% 13.77/7.79 = ( size_size_list_real @ B2 ) )
% 13.77/7.79 => ( ( ( zip_o_real @ A @ B )
% 13.77/7.79 = ( zip_o_real @ A2 @ B2 ) )
% 13.77/7.79 => ( ( A = A2 )
% 13.77/7.79 & ( B = B2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6544_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P7413028617227757229T_VEBT] :
% 13.77/7.79 ~ ! [L1: list_VEBT_VEBT,L22: list_VEBT_VEBT] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_VE537291747668921783T_VEBT @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ L22 ) )
% 13.77/7.79 => ( ( size_s7466405169056248089T_VEBT @ L )
% 13.77/7.79 != ( size_s6755466524823107622T_VEBT @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6545_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P2623026923184700063T_real] :
% 13.77/7.79 ~ ! [L1: list_VEBT_VEBT,L22: list_real] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_VEBT_VEBT_real @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 13.77/7.79 = ( size_size_list_real @ L22 ) )
% 13.77/7.79 => ( ( size_s5035110155006384947T_real @ L )
% 13.77/7.79 != ( size_size_list_real @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6546_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P3126845725202233233VEBT_o] :
% 13.77/7.79 ~ ! [L1: list_VEBT_VEBT,L22: list_o] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_VEBT_VEBT_o @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 13.77/7.79 = ( size_size_list_o @ L22 ) )
% 13.77/7.79 => ( ( size_s9168528473962070013VEBT_o @ L )
% 13.77/7.79 != ( size_size_list_o @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6547_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P7037539587688870467BT_nat] :
% 13.77/7.79 ~ ! [L1: list_VEBT_VEBT,L22: list_nat] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_VEBT_VEBT_nat @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_s6755466524823107622T_VEBT @ L1 )
% 13.77/7.79 = ( size_size_list_nat @ L22 ) )
% 13.77/7.79 => ( ( size_s6152045936467909847BT_nat @ L )
% 13.77/7.79 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6548_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P877281246627933069T_VEBT] :
% 13.77/7.79 ~ ! [L1: list_real,L22: list_VEBT_VEBT] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_real_VEBT_VEBT @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ L1 )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ L22 ) )
% 13.77/7.79 => ( ( size_s3289364478449617953T_VEBT @ L )
% 13.77/7.79 != ( size_s6755466524823107622T_VEBT @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6549_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P8689742595348180415l_real] :
% 13.77/7.79 ~ ! [L1: list_real,L22: list_real] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_real_real @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ L1 )
% 13.77/7.79 = ( size_size_list_real @ L22 ) )
% 13.77/7.79 => ( ( size_s3932428310213730859l_real @ L )
% 13.77/7.79 != ( size_size_list_real @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6550_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P3595434254542482545real_o] :
% 13.77/7.79 ~ ! [L1: list_real,L22: list_o] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_real_o @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ L1 )
% 13.77/7.79 = ( size_size_list_o @ L22 ) )
% 13.77/7.79 => ( ( size_s987546567493390085real_o @ L )
% 13.77/7.79 != ( size_size_list_o @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6551_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P6834414599653733731al_nat] :
% 13.77/7.79 ~ ! [L1: list_real,L22: list_nat] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_real_nat @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_size_list_real @ L1 )
% 13.77/7.79 = ( size_size_list_nat @ L22 ) )
% 13.77/7.79 => ( ( size_s1877336372972134351al_nat @ L )
% 13.77/7.79 != ( size_size_list_nat @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6552_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P7495141550334521929T_VEBT] :
% 13.77/7.79 ~ ! [L1: list_o,L22: list_VEBT_VEBT] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_o_VEBT_VEBT @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_size_list_o @ L1 )
% 13.77/7.79 = ( size_s6755466524823107622T_VEBT @ L22 ) )
% 13.77/7.79 => ( ( size_s4313452262239582901T_VEBT @ L )
% 13.77/7.79 != ( size_s6755466524823107622T_VEBT @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6553_pair__list__split,axiom,
% 13.77/7.79 ! [L: list_P5232166724548748803o_real] :
% 13.77/7.79 ~ ! [L1: list_o,L22: list_real] :
% 13.77/7.79 ( ( L
% 13.77/7.79 = ( zip_o_real @ L1 @ L22 ) )
% 13.77/7.79 => ( ( ( size_size_list_o @ L1 )
% 13.77/7.79 = ( size_size_list_real @ L22 ) )
% 13.77/7.79 => ( ( size_s2624279037499656343o_real @ L )
% 13.77/7.79 != ( size_size_list_real @ L22 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6554_real__arch__simple,axiom,
% 13.77/7.79 ! [X: real] :
% 13.77/7.79 ? [N2: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6555_real__arch__simple,axiom,
% 13.77/7.79 ! [X: rat] :
% 13.77/7.79 ? [N2: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6556_reals__Archimedean2,axiom,
% 13.77/7.79 ! [X: rat] :
% 13.77/7.79 ? [N2: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6557_reals__Archimedean2,axiom,
% 13.77/7.79 ! [X: real] :
% 13.77/7.79 ? [N2: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6558_mult__of__nat__commute,axiom,
% 13.77/7.79 ! [X: nat,Y: uint32] :
% 13.77/7.79 ( ( times_times_uint32 @ ( semiri2565882477558803405uint32 @ X ) @ Y )
% 13.77/7.79 = ( times_times_uint32 @ Y @ ( semiri2565882477558803405uint32 @ X ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6559_mult__of__nat__commute,axiom,
% 13.77/7.79 ! [X: nat,Y: nat] :
% 13.77/7.79 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 13.77/7.79 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6560_mult__of__nat__commute,axiom,
% 13.77/7.79 ! [X: nat,Y: real] :
% 13.77/7.79 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 13.77/7.79 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6561_mult__of__nat__commute,axiom,
% 13.77/7.79 ! [X: nat,Y: int] :
% 13.77/7.79 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 13.77/7.79 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6562_mult__of__nat__commute,axiom,
% 13.77/7.79 ! [X: nat,Y: code_integer] :
% 13.77/7.79 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 13.77/7.79 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6563_lessThan__non__empty,axiom,
% 13.77/7.79 ! [X: int] :
% 13.77/7.79 ( ( set_ord_lessThan_int @ X )
% 13.77/7.79 != bot_bot_set_int ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6564_lessThan__non__empty,axiom,
% 13.77/7.79 ! [X: real] :
% 13.77/7.79 ( ( set_or5984915006950818249n_real @ X )
% 13.77/7.79 != bot_bot_set_real ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6565_infinite__Iio,axiom,
% 13.77/7.79 ! [A: int] :
% 13.77/7.79 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6566_infinite__Iio,axiom,
% 13.77/7.79 ! [A: real] :
% 13.77/7.79 ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6567_sum_OlessThan__Suc__shift,axiom,
% 13.77/7.79 ! [G: nat > rat,N: nat] :
% 13.77/7.79 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.79 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 13.77/7.79 @ ( groups2906978787729119204at_rat
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6568_sum_OlessThan__Suc__shift,axiom,
% 13.77/7.79 ! [G: nat > int,N: nat] :
% 13.77/7.79 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.79 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 13.77/7.79 @ ( groups3539618377306564664at_int
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6569_sum_OlessThan__Suc__shift,axiom,
% 13.77/7.79 ! [G: nat > nat,N: nat] :
% 13.77/7.79 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.79 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 13.77/7.79 @ ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6570_sum_OlessThan__Suc__shift,axiom,
% 13.77/7.79 ! [G: nat > real,N: nat] :
% 13.77/7.79 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.79 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 13.77/7.79 @ ( groups6591440286371151544t_real
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6571_sum__lessThan__telescope,axiom,
% 13.77/7.79 ! [F: nat > uint32,M: nat] :
% 13.77/7.79 ( ( groups833757482993574392uint32
% 13.77/7.79 @ ^ [N6: nat] : ( minus_minus_uint32 @ ( F @ ( suc @ N6 ) ) @ ( F @ N6 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ M ) )
% 13.77/7.79 = ( minus_minus_uint32 @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6572_sum__lessThan__telescope,axiom,
% 13.77/7.79 ! [F: nat > int,M: nat] :
% 13.77/7.79 ( ( groups3539618377306564664at_int
% 13.77/7.79 @ ^ [N6: nat] : ( minus_minus_int @ ( F @ ( suc @ N6 ) ) @ ( F @ N6 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ M ) )
% 13.77/7.79 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6573_sum__lessThan__telescope,axiom,
% 13.77/7.79 ! [F: nat > real,M: nat] :
% 13.77/7.79 ( ( groups6591440286371151544t_real
% 13.77/7.79 @ ^ [N6: nat] : ( minus_minus_real @ ( F @ ( suc @ N6 ) ) @ ( F @ N6 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ M ) )
% 13.77/7.79 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6574_sum__lessThan__telescope_H,axiom,
% 13.77/7.79 ! [F: nat > uint32,M: nat] :
% 13.77/7.79 ( ( groups833757482993574392uint32
% 13.77/7.79 @ ^ [N6: nat] : ( minus_minus_uint32 @ ( F @ N6 ) @ ( F @ ( suc @ N6 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ M ) )
% 13.77/7.79 = ( minus_minus_uint32 @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6575_sum__lessThan__telescope_H,axiom,
% 13.77/7.79 ! [F: nat > int,M: nat] :
% 13.77/7.79 ( ( groups3539618377306564664at_int
% 13.77/7.79 @ ^ [N6: nat] : ( minus_minus_int @ ( F @ N6 ) @ ( F @ ( suc @ N6 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ M ) )
% 13.77/7.79 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6576_sum__lessThan__telescope_H,axiom,
% 13.77/7.79 ! [F: nat > real,M: nat] :
% 13.77/7.79 ( ( groups6591440286371151544t_real
% 13.77/7.79 @ ^ [N6: nat] : ( minus_minus_real @ ( F @ N6 ) @ ( F @ ( suc @ N6 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ M ) )
% 13.77/7.79 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6577_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > uint32,Y: vEBT_VEBT > uint32] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_uint32 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6578_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_real,X: real > uint32,Y: real > uint32] :
% 13.77/7.79 ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_uint32 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6579_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_nat,X: nat > uint32,Y: nat > uint32] :
% 13.77/7.79 ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_uint32 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6580_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_int,X: int > uint32,Y: int > uint32] :
% 13.77/7.79 ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_uint32 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6581_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_complex,X: complex > uint32,Y: complex > uint32] :
% 13.77/7.79 ( ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [I3: complex] :
% 13.77/7.79 ( ( member_complex @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [I3: complex] :
% 13.77/7.79 ( ( member_complex @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [I3: complex] :
% 13.77/7.79 ( ( member_complex @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_uint32 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6582_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_Code_integer,X: code_integer > uint32,Y: code_integer > uint32] :
% 13.77/7.79 ( ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [I3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [I3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_uint32 ) ) ) )
% 13.77/7.79 => ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [I3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_uint32 @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_uint32 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6583_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > real,Y: vEBT_VEBT > real] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6584_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_real,X: real > real,Y: real > real] :
% 13.77/7.79 ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6585_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 13.77/7.79 ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6586_sum_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_int,X: int > real,Y: int > real] :
% 13.77/7.79 ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != zero_zero_real ) ) ) )
% 13.77/7.79 => ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( plus_plus_real @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6587_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > rat,Y: vEBT_VEBT > rat] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_rat ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6588_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_real,X: real > rat,Y: real > rat] :
% 13.77/7.79 ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_rat ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6589_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 13.77/7.79 ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_rat ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6590_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_int,X: int > rat,Y: int > rat] :
% 13.77/7.79 ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_rat ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6591_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_complex,X: complex > rat,Y: complex > rat] :
% 13.77/7.79 ( ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [I3: complex] :
% 13.77/7.79 ( ( member_complex @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [I3: complex] :
% 13.77/7.79 ( ( member_complex @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [I3: complex] :
% 13.77/7.79 ( ( member_complex @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_rat ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6592_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_Code_integer,X: code_integer > rat,Y: code_integer > rat] :
% 13.77/7.79 ( ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [I3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [I3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_rat ) ) ) )
% 13.77/7.79 => ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [I3: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_rat ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6593_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_VEBT_VEBT,X: vEBT_VEBT > assn,Y: vEBT_VEBT > assn] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( finite5795047828879050333T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_assn ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6594_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_real,X: real > assn,Y: real > assn] :
% 13.77/7.79 ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_assn ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6595_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_nat,X: nat > assn,Y: nat > assn] :
% 13.77/7.79 ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] :
% 13.77/7.79 ( ( member_nat @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_assn ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6596_prod_Ofinite__Collect__op,axiom,
% 13.77/7.79 ! [I5: set_int,X: int > assn,Y: int > assn] :
% 13.77/7.79 ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( X @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( Y @ I3 )
% 13.77/7.79 != one_one_assn ) ) ) )
% 13.77/7.79 => ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [I3: int] :
% 13.77/7.79 ( ( member_int @ I3 @ I5 )
% 13.77/7.79 & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 13.77/7.79 != one_one_assn ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6597_filter__preserves__multiset,axiom,
% 13.77/7.79 ! [M7: list_nat > nat,P2: list_nat > $o] :
% 13.77/7.79 ( ( finite8100373058378681591st_nat
% 13.77/7.79 @ ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite8100373058378681591st_nat
% 13.77/7.79 @ ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6598_filter__preserves__multiset,axiom,
% 13.77/7.79 ! [M7: set_nat > nat,P2: set_nat > $o] :
% 13.77/7.79 ( ( finite1152437895449049373et_nat
% 13.77/7.79 @ ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite1152437895449049373et_nat
% 13.77/7.79 @ ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6599_filter__preserves__multiset,axiom,
% 13.77/7.79 ! [M7: nat > nat,P2: nat > $o] :
% 13.77/7.79 ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6600_filter__preserves__multiset,axiom,
% 13.77/7.79 ! [M7: int > nat,P2: int > $o] :
% 13.77/7.79 ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6601_filter__preserves__multiset,axiom,
% 13.77/7.79 ! [M7: complex > nat,P2: complex > $o] :
% 13.77/7.79 ( ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6602_filter__preserves__multiset,axiom,
% 13.77/7.79 ! [M7: code_integer > nat,P2: code_integer > $o] :
% 13.77/7.79 ( ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P2 @ X4 ) @ ( M7 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6603_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > uint32,P2: vEBT_VEBT > $o] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( groups8325533452322294502uint32 @ G
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups8325533452322294502uint32
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6604_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_real,G: real > uint32,P2: real > $o] :
% 13.77/7.79 ( ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( groups5944083974425963860uint32 @ G
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups5944083974425963860uint32
% 13.77/7.79 @ ^ [X4: real] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6605_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_nat,G: nat > uint32,P2: nat > $o] :
% 13.77/7.79 ( ( finite_finite_nat @ A4 )
% 13.77/7.79 => ( ( groups833757482993574392uint32 @ G
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( member_nat @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups833757482993574392uint32
% 13.77/7.79 @ ^ [X4: nat] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6606_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_int,G: int > uint32,P2: int > $o] :
% 13.77/7.79 ( ( finite_finite_int @ A4 )
% 13.77/7.79 => ( ( groups5712668689793887828uint32 @ G
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups5712668689793887828uint32
% 13.77/7.79 @ ^ [X4: int] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6607_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_complex,G: complex > uint32,P2: complex > $o] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.79 => ( ( groups8736914816313324502uint32 @ G
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( member_complex @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups8736914816313324502uint32
% 13.77/7.79 @ ^ [X4: complex] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6608_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_Code_integer,G: code_integer > uint32,P2: code_integer > $o] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.79 => ( ( groups8847630953604152069uint32 @ G
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups8847630953604152069uint32
% 13.77/7.79 @ ^ [X4: code_integer] : ( if_uint32 @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_uint32 )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6609_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > real,P2: vEBT_VEBT > $o] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.79 => ( ( groups2240296850493347238T_real @ G
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups2240296850493347238T_real
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6610_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_real,G: real > real,P2: real > $o] :
% 13.77/7.79 ( ( finite_finite_real @ A4 )
% 13.77/7.79 => ( ( groups8097168146408367636l_real @ G
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups8097168146408367636l_real
% 13.77/7.79 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6611_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_int,G: int > real,P2: int > $o] :
% 13.77/7.79 ( ( finite_finite_int @ A4 )
% 13.77/7.79 => ( ( groups8778361861064173332t_real @ G
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups8778361861064173332t_real
% 13.77/7.79 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6612_sum_Ointer__filter,axiom,
% 13.77/7.79 ! [A4: set_complex,G: complex > real,P2: complex > $o] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.79 => ( ( groups5808333547571424918x_real @ G
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( member_complex @ X4 @ A4 )
% 13.77/7.79 & ( P2 @ X4 ) ) ) )
% 13.77/7.79 = ( groups5808333547571424918x_real
% 13.77/7.79 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( G @ X4 ) @ zero_zero_real )
% 13.77/7.79 @ A4 ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6613_image__constant,axiom,
% 13.77/7.79 ! [X: nat,A4: set_nat,C2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_nat @ X @ A4 )
% 13.77/7.79 => ( ( image_nat_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6614_image__constant,axiom,
% 13.77/7.79 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,C2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.79 => ( ( image_3375948659692109573T_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6615_image__constant,axiom,
% 13.77/7.79 ! [X: real,A4: set_real,C2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_real @ X @ A4 )
% 13.77/7.79 => ( ( image_real_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: real] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6616_image__constant,axiom,
% 13.77/7.79 ! [X: int,A4: set_int,C2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_int @ X @ A4 )
% 13.77/7.79 => ( ( image_int_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6617_image__constant,axiom,
% 13.77/7.79 ! [X: nat,A4: set_nat,C2: nat] :
% 13.77/7.79 ( ( member_nat @ X @ A4 )
% 13.77/7.79 => ( ( image_nat_nat
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6618_image__constant,axiom,
% 13.77/7.79 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,C2: nat] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.79 => ( ( image_VEBT_VEBT_nat
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6619_image__constant,axiom,
% 13.77/7.79 ! [X: real,A4: set_real,C2: nat] :
% 13.77/7.79 ( ( member_real @ X @ A4 )
% 13.77/7.79 => ( ( image_real_nat
% 13.77/7.79 @ ^ [X4: real] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6620_image__constant,axiom,
% 13.77/7.79 ! [X: int,A4: set_int,C2: nat] :
% 13.77/7.79 ( ( member_int @ X @ A4 )
% 13.77/7.79 => ( ( image_int_nat
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6621_image__constant,axiom,
% 13.77/7.79 ! [X: nat,A4: set_nat,C2: int] :
% 13.77/7.79 ( ( member_nat @ X @ A4 )
% 13.77/7.79 => ( ( image_nat_int
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6622_image__constant,axiom,
% 13.77/7.79 ! [X: vEBT_VEBT,A4: set_VEBT_VEBT,C2: int] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X @ A4 )
% 13.77/7.79 => ( ( image_VEBT_VEBT_int
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6623_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_nat,C2: vEBT_VEBT] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bo8194388402131092736T_VEBT ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6624_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_nat,C2: nat] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_nat
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bot_set_nat ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_nat
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6625_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_nat,C2: int] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_int
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bot_set_int ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_int
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6626_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_nat,C2: $o] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_o
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bot_set_o ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_nat )
% 13.77/7.79 => ( ( image_nat_o
% 13.77/7.79 @ ^ [X4: nat] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_o @ C2 @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6627_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_int,C2: vEBT_VEBT] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bo8194388402131092736T_VEBT ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6628_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_int,C2: nat] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_nat
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bot_set_nat ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_nat
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6629_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_int,C2: int] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_int
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bot_set_int ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_int
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_int @ C2 @ bot_bot_set_int ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6630_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_int,C2: $o] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_o
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bot_set_o ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_int )
% 13.77/7.79 => ( ( image_int_o
% 13.77/7.79 @ ^ [X4: int] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_o @ C2 @ bot_bot_set_o ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6631_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_o,C2: vEBT_VEBT] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_o )
% 13.77/7.79 => ( ( image_o_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: $o] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bo8194388402131092736T_VEBT ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_o )
% 13.77/7.79 => ( ( image_o_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: $o] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_VEBT_VEBT @ C2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6632_image__constant__conv,axiom,
% 13.77/7.79 ! [A4: set_o,C2: nat] :
% 13.77/7.79 ( ( ( A4 = bot_bot_set_o )
% 13.77/7.79 => ( ( image_o_nat
% 13.77/7.79 @ ^ [X4: $o] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = bot_bot_set_nat ) )
% 13.77/7.79 & ( ( A4 != bot_bot_set_o )
% 13.77/7.79 => ( ( image_o_nat
% 13.77/7.79 @ ^ [X4: $o] : C2
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( insert_nat @ C2 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6633_foldl__length__aux,axiom,
% 13.77/7.79 ! [A: nat,L: list_VEBT_VEBT] :
% 13.77/7.79 ( ( foldl_nat_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: nat,X4: vEBT_VEBT] : ( suc @ I3 )
% 13.77/7.79 @ A
% 13.77/7.79 @ L )
% 13.77/7.79 = ( plus_plus_nat @ A @ ( size_s6755466524823107622T_VEBT @ L ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6634_foldl__length__aux,axiom,
% 13.77/7.79 ! [A: nat,L: list_real] :
% 13.77/7.79 ( ( foldl_nat_real
% 13.77/7.79 @ ^ [I3: nat,X4: real] : ( suc @ I3 )
% 13.77/7.79 @ A
% 13.77/7.79 @ L )
% 13.77/7.79 = ( plus_plus_nat @ A @ ( size_size_list_real @ L ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6635_foldl__length__aux,axiom,
% 13.77/7.79 ! [A: nat,L: list_o] :
% 13.77/7.79 ( ( foldl_nat_o
% 13.77/7.79 @ ^ [I3: nat,X4: $o] : ( suc @ I3 )
% 13.77/7.79 @ A
% 13.77/7.79 @ L )
% 13.77/7.79 = ( plus_plus_nat @ A @ ( size_size_list_o @ L ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6636_foldl__length__aux,axiom,
% 13.77/7.79 ! [A: nat,L: list_nat] :
% 13.77/7.79 ( ( foldl_nat_nat
% 13.77/7.79 @ ^ [I3: nat,X4: nat] : ( suc @ I3 )
% 13.77/7.79 @ A
% 13.77/7.79 @ L )
% 13.77/7.79 = ( plus_plus_nat @ A @ ( size_size_list_nat @ L ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6637_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_VEBT_VEBT,H2: vEBT_VEBT > nat,G: vEBT_VEBT > nat] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.79 => ( ( groups771621172384141258BT_nat @ H2 @ S3 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups771621172384141258BT_nat @ H2
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_VEBT_VEBT_nat @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6638_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_real,H2: real > nat,G: real > nat] :
% 13.77/7.79 ( ( finite_finite_real @ S3 )
% 13.77/7.79 => ( ( groups1935376822645274424al_nat @ H2 @ S3 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups1935376822645274424al_nat @ H2
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_real_nat @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6639_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_int,H2: int > nat,G: int > nat] :
% 13.77/7.79 ( ( finite_finite_int @ S3 )
% 13.77/7.79 => ( ( groups4541462559716669496nt_nat @ H2 @ S3 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups4541462559716669496nt_nat @ H2
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_int_nat @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6640_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_complex,H2: complex > nat,G: complex > nat] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.79 => ( ( groups5693394587270226106ex_nat @ H2 @ S3 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups5693394587270226106ex_nat @ H2
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] :
% 13.77/7.79 ( ( member_complex @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_complex_nat @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6641_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_Code_integer,H2: code_integer > nat,G: code_integer > nat] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.79 => ( ( groups7237345082560585321er_nat @ H2 @ S3 )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( groups7237345082560585321er_nat @ H2
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_951025933927791156er_nat @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6642_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_VEBT_VEBT,H2: vEBT_VEBT > complex,G: vEBT_VEBT > complex] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.79 => ( ( groups1794756597179926696omplex @ H2 @ S3 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups1794756597179926696omplex @ H2
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_3793382806556112285omplex @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6643_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_real,H2: real > complex,G: real > complex] :
% 13.77/7.79 ( ( finite_finite_real @ S3 )
% 13.77/7.79 => ( ( groups5754745047067104278omplex @ H2 @ S3 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups5754745047067104278omplex @ H2
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_real_complex @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6644_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_nat,H2: nat > complex,G: nat > complex] :
% 13.77/7.79 ( ( finite_finite_nat @ S3 )
% 13.77/7.79 => ( ( groups2073611262835488442omplex @ H2 @ S3 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups2073611262835488442omplex @ H2
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] :
% 13.77/7.79 ( ( member_nat @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_nat_complex @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6645_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_int,H2: int > complex,G: int > complex] :
% 13.77/7.79 ( ( finite_finite_int @ S3 )
% 13.77/7.79 => ( ( groups3049146728041665814omplex @ H2 @ S3 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups3049146728041665814omplex @ H2
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_int_complex @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6646_sum_Oimage__gen,axiom,
% 13.77/7.79 ! [S3: set_Code_integer,H2: code_integer > complex,G: code_integer > complex] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.79 => ( ( groups8024822376189712711omplex @ H2 @ S3 )
% 13.77/7.79 = ( groups7754918857620584856omplex
% 13.77/7.79 @ ^ [Y4: complex] :
% 13.77/7.79 ( groups8024822376189712711omplex @ H2
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) )
% 13.77/7.79 @ ( image_3397630267976458002omplex @ G @ S3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6647_nat__seg__image__imp__finite,axiom,
% 13.77/7.79 ! [A4: set_set_nat,F: nat > set_nat,N: nat] :
% 13.77/7.79 ( ( A4
% 13.77/7.79 = ( image_nat_set_nat @ F
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 13.77/7.79 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6648_nat__seg__image__imp__finite,axiom,
% 13.77/7.79 ! [A4: set_nat,F: nat > nat,N: nat] :
% 13.77/7.79 ( ( A4
% 13.77/7.79 = ( image_nat_nat @ F
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 13.77/7.79 => ( finite_finite_nat @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6649_nat__seg__image__imp__finite,axiom,
% 13.77/7.79 ! [A4: set_int,F: nat > int,N: nat] :
% 13.77/7.79 ( ( A4
% 13.77/7.79 = ( image_nat_int @ F
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 13.77/7.79 => ( finite_finite_int @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6650_nat__seg__image__imp__finite,axiom,
% 13.77/7.79 ! [A4: set_complex,F: nat > complex,N: nat] :
% 13.77/7.79 ( ( A4
% 13.77/7.79 = ( image_nat_complex @ F
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 13.77/7.79 => ( finite3207457112153483333omplex @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6651_nat__seg__image__imp__finite,axiom,
% 13.77/7.79 ! [A4: set_Code_integer,F: nat > code_integer,N: nat] :
% 13.77/7.79 ( ( A4
% 13.77/7.79 = ( image_1215581382706833972nteger @ F
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) ) )
% 13.77/7.79 => ( finite6017078050557962740nteger @ A4 ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6652_finite__conv__nat__seg__image,axiom,
% 13.77/7.79 ( finite1152437895449049373et_nat
% 13.77/7.79 = ( ^ [A6: set_set_nat] :
% 13.77/7.79 ? [N6: nat,F5: nat > set_nat] :
% 13.77/7.79 ( A6
% 13.77/7.79 = ( image_nat_set_nat @ F5
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6653_finite__conv__nat__seg__image,axiom,
% 13.77/7.79 ( finite_finite_nat
% 13.77/7.79 = ( ^ [A6: set_nat] :
% 13.77/7.79 ? [N6: nat,F5: nat > nat] :
% 13.77/7.79 ( A6
% 13.77/7.79 = ( image_nat_nat @ F5
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6654_finite__conv__nat__seg__image,axiom,
% 13.77/7.79 ( finite_finite_int
% 13.77/7.79 = ( ^ [A6: set_int] :
% 13.77/7.79 ? [N6: nat,F5: nat > int] :
% 13.77/7.79 ( A6
% 13.77/7.79 = ( image_nat_int @ F5
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6655_finite__conv__nat__seg__image,axiom,
% 13.77/7.79 ( finite3207457112153483333omplex
% 13.77/7.79 = ( ^ [A6: set_complex] :
% 13.77/7.79 ? [N6: nat,F5: nat > complex] :
% 13.77/7.79 ( A6
% 13.77/7.79 = ( image_nat_complex @ F5
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6656_finite__conv__nat__seg__image,axiom,
% 13.77/7.79 ( finite6017078050557962740nteger
% 13.77/7.79 = ( ^ [A6: set_Code_integer] :
% 13.77/7.79 ? [N6: nat,F5: nat > code_integer] :
% 13.77/7.79 ( A6
% 13.77/7.79 = ( image_1215581382706833972nteger @ F5
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N6 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6657_finite__int__segment,axiom,
% 13.77/7.79 ! [A: real,B: real] :
% 13.77/7.79 ( finite_finite_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ ring_1_Ints_real )
% 13.77/7.79 & ( ord_less_eq_real @ A @ X4 )
% 13.77/7.79 & ( ord_less_eq_real @ X4 @ B ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6658_finite__int__segment,axiom,
% 13.77/7.79 ! [A: rat,B: rat] :
% 13.77/7.79 ( finite_finite_rat
% 13.77/7.79 @ ( collect_rat
% 13.77/7.79 @ ^ [X4: rat] :
% 13.77/7.79 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 13.77/7.79 & ( ord_less_eq_rat @ A @ X4 )
% 13.77/7.79 & ( ord_less_eq_rat @ X4 @ B ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6659_sum_Oshift__bounds__Suc__ivl,axiom,
% 13.77/7.79 ! [G: nat > nat,M: nat,N: nat] :
% 13.77/7.79 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 13.77/7.79 = ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 13.77/7.79 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6660_sum_Oshift__bounds__Suc__ivl,axiom,
% 13.77/7.79 ! [G: nat > real,M: nat,N: nat] :
% 13.77/7.79 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 13.77/7.79 = ( groups6591440286371151544t_real
% 13.77/7.79 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 13.77/7.79 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6661_sum__subtractf__nat,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > nat,F: vEBT_VEBT > nat] :
% 13.77/7.79 ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 13.77/7.79 => ( ( groups771621172384141258BT_nat
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( minus_minus_nat @ ( groups771621172384141258BT_nat @ F @ A4 ) @ ( groups771621172384141258BT_nat @ G @ A4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6662_sum__subtractf__nat,axiom,
% 13.77/7.79 ! [A4: set_real,G: real > nat,F: real > nat] :
% 13.77/7.79 ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 13.77/7.79 => ( ( groups1935376822645274424al_nat
% 13.77/7.79 @ ^ [X4: real] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( groups1935376822645274424al_nat @ G @ A4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6663_sum__subtractf__nat,axiom,
% 13.77/7.79 ! [A4: set_int,G: int > nat,F: int > nat] :
% 13.77/7.79 ( ! [X3: int] :
% 13.77/7.79 ( ( member_int @ X3 @ A4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 13.77/7.79 => ( ( groups4541462559716669496nt_nat
% 13.77/7.79 @ ^ [X4: int] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6664_sum__subtractf__nat,axiom,
% 13.77/7.79 ! [A4: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 13.77/7.79 ( ! [X3: set_nat] :
% 13.77/7.79 ( ( member_set_nat @ X3 @ A4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 13.77/7.79 => ( ( groups8294997508430121362at_nat
% 13.77/7.79 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( groups8294997508430121362at_nat @ G @ A4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6665_sum__subtractf__nat,axiom,
% 13.77/7.79 ! [A4: set_nat,G: nat > nat,F: nat > nat] :
% 13.77/7.79 ( ! [X3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ A4 )
% 13.77/7.79 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 13.77/7.79 => ( ( groups3542108847815614940at_nat
% 13.77/7.79 @ ^ [X4: nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 13.77/7.79 @ A4 )
% 13.77/7.79 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6666_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,T: set_VEBT_VEBT,R2: vEBT_VEBT > vEBT_VEBT > $o,K: vEBT_VEBT > nat] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ( finite5795047828879050333T_VEBT @ T )
% 13.77/7.79 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ T )
% 13.77/7.79 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups771621172384141258BT_nat
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [J3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups771621172384141258BT_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6667_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,T: set_real,R2: vEBT_VEBT > real > $o,K: real > nat] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ( finite_finite_real @ T )
% 13.77/7.79 => ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ T )
% 13.77/7.79 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups771621172384141258BT_nat
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( finite_card_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [J3: real] :
% 13.77/7.79 ( ( member_real @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6668_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_real,T: set_VEBT_VEBT,R2: real > vEBT_VEBT > $o,K: vEBT_VEBT > nat] :
% 13.77/7.79 ( ( finite_finite_real @ S )
% 13.77/7.79 => ( ( finite5795047828879050333T_VEBT @ T )
% 13.77/7.79 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ T )
% 13.77/7.79 => ( ( finite_card_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups1935376822645274424al_nat
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [J3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups771621172384141258BT_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6669_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_real,T: set_real,R2: real > real > $o,K: real > nat] :
% 13.77/7.79 ( ( finite_finite_real @ S )
% 13.77/7.79 => ( ( finite_finite_real @ T )
% 13.77/7.79 => ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ T )
% 13.77/7.79 => ( ( finite_card_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups1935376822645274424al_nat
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( finite_card_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [J3: real] :
% 13.77/7.79 ( ( member_real @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6670_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,T: set_literal,R2: vEBT_VEBT > literal > $o,K: literal > nat] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ( finite5847741373460823677iteral @ T )
% 13.77/7.79 => ( ! [X3: literal] :
% 13.77/7.79 ( ( member_literal @ X3 @ T )
% 13.77/7.79 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups771621172384141258BT_nat
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( finite_card_literal
% 13.77/7.79 @ ( collect_literal
% 13.77/7.79 @ ^ [J3: literal] :
% 13.77/7.79 ( ( member_literal @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups8652099787943017962al_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6671_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_real,T: set_literal,R2: real > literal > $o,K: literal > nat] :
% 13.77/7.79 ( ( finite_finite_real @ S )
% 13.77/7.79 => ( ( finite5847741373460823677iteral @ T )
% 13.77/7.79 => ( ! [X3: literal] :
% 13.77/7.79 ( ( member_literal @ X3 @ T )
% 13.77/7.79 => ( ( finite_card_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( ( member_real @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups1935376822645274424al_nat
% 13.77/7.79 @ ^ [I3: real] :
% 13.77/7.79 ( finite_card_literal
% 13.77/7.79 @ ( collect_literal
% 13.77/7.79 @ ^ [J3: literal] :
% 13.77/7.79 ( ( member_literal @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups8652099787943017962al_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6672_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_literal,T: set_VEBT_VEBT,R2: literal > vEBT_VEBT > $o,K: vEBT_VEBT > nat] :
% 13.77/7.79 ( ( finite5847741373460823677iteral @ S )
% 13.77/7.79 => ( ( finite5795047828879050333T_VEBT @ T )
% 13.77/7.79 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ T )
% 13.77/7.79 => ( ( finite_card_literal
% 13.77/7.79 @ ( collect_literal
% 13.77/7.79 @ ^ [I3: literal] :
% 13.77/7.79 ( ( member_literal @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups8652099787943017962al_nat
% 13.77/7.79 @ ^ [I3: literal] :
% 13.77/7.79 ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [J3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups771621172384141258BT_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6673_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_literal,T: set_real,R2: literal > real > $o,K: real > nat] :
% 13.77/7.79 ( ( finite5847741373460823677iteral @ S )
% 13.77/7.79 => ( ( finite_finite_real @ T )
% 13.77/7.79 => ( ! [X3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ T )
% 13.77/7.79 => ( ( finite_card_literal
% 13.77/7.79 @ ( collect_literal
% 13.77/7.79 @ ^ [I3: literal] :
% 13.77/7.79 ( ( member_literal @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups8652099787943017962al_nat
% 13.77/7.79 @ ^ [I3: literal] :
% 13.77/7.79 ( finite_card_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [J3: real] :
% 13.77/7.79 ( ( member_real @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups1935376822645274424al_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6674_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_literal,T: set_literal,R2: literal > literal > $o,K: literal > nat] :
% 13.77/7.79 ( ( finite5847741373460823677iteral @ S )
% 13.77/7.79 => ( ( finite5847741373460823677iteral @ T )
% 13.77/7.79 => ( ! [X3: literal] :
% 13.77/7.79 ( ( member_literal @ X3 @ T )
% 13.77/7.79 => ( ( finite_card_literal
% 13.77/7.79 @ ( collect_literal
% 13.77/7.79 @ ^ [I3: literal] :
% 13.77/7.79 ( ( member_literal @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups8652099787943017962al_nat
% 13.77/7.79 @ ^ [I3: literal] :
% 13.77/7.79 ( finite_card_literal
% 13.77/7.79 @ ( collect_literal
% 13.77/7.79 @ ^ [J3: literal] :
% 13.77/7.79 ( ( member_literal @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups8652099787943017962al_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6675_sum__multicount__gen,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,T: set_int,R2: vEBT_VEBT > int > $o,K: int > nat] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ( finite_finite_int @ T )
% 13.77/7.79 => ( ! [X3: int] :
% 13.77/7.79 ( ( member_int @ X3 @ T )
% 13.77/7.79 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I3 @ S )
% 13.77/7.79 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.79 = ( K @ X3 ) ) )
% 13.77/7.79 => ( ( groups771621172384141258BT_nat
% 13.77/7.79 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.79 ( finite_card_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [J3: int] :
% 13.77/7.79 ( ( member_int @ J3 @ T )
% 13.77/7.79 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.79 @ S )
% 13.77/7.79 = ( groups4541462559716669496nt_nat @ K @ T ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6676_total__onI,axiom,
% 13.77/7.79 ! [A4: set_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 13.77/7.79 ( ! [X3: vEBT_VEBT,Y3: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X3 @ A4 )
% 13.77/7.79 => ( ( member_VEBT_VEBT @ Y3 @ A4 )
% 13.77/7.79 => ( ( X3 != Y3 )
% 13.77/7.79 => ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X3 @ Y3 ) @ R )
% 13.77/7.79 | ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ Y3 @ X3 ) @ R ) ) ) ) )
% 13.77/7.79 => ( total_on_VEBT_VEBT @ A4 @ R ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6677_total__onI,axiom,
% 13.77/7.79 ! [A4: set_real,R: set_Pr6218003697084177305l_real] :
% 13.77/7.79 ( ! [X3: real,Y3: real] :
% 13.77/7.79 ( ( member_real @ X3 @ A4 )
% 13.77/7.79 => ( ( member_real @ Y3 @ A4 )
% 13.77/7.79 => ( ( X3 != Y3 )
% 13.77/7.79 => ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X3 @ Y3 ) @ R )
% 13.77/7.79 | ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ Y3 @ X3 ) @ R ) ) ) ) )
% 13.77/7.79 => ( total_on_real @ A4 @ R ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6678_total__onI,axiom,
% 13.77/7.79 ! [A4: set_set_nat,R: set_Pr5488025237498180813et_nat] :
% 13.77/7.79 ( ! [X3: set_nat,Y3: set_nat] :
% 13.77/7.79 ( ( member_set_nat @ X3 @ A4 )
% 13.77/7.79 => ( ( member_set_nat @ Y3 @ A4 )
% 13.77/7.79 => ( ( X3 != Y3 )
% 13.77/7.79 => ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X3 @ Y3 ) @ R )
% 13.77/7.79 | ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ Y3 @ X3 ) @ R ) ) ) ) )
% 13.77/7.79 => ( total_on_set_nat @ A4 @ R ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6679_total__onI,axiom,
% 13.77/7.79 ! [A4: set_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.79 ( ! [X3: uint32,Y3: uint32] :
% 13.77/7.79 ( ( member_uint32 @ X3 @ A4 )
% 13.77/7.79 => ( ( member_uint32 @ Y3 @ A4 )
% 13.77/7.79 => ( ( X3 != Y3 )
% 13.77/7.79 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y3 ) @ R )
% 13.77/7.79 | ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y3 @ X3 ) @ R ) ) ) ) )
% 13.77/7.79 => ( total_on_uint32 @ A4 @ R ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6680_total__onI,axiom,
% 13.77/7.79 ! [A4: set_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.79 ( ! [X3: nat,Y3: nat] :
% 13.77/7.79 ( ( member_nat @ X3 @ A4 )
% 13.77/7.79 => ( ( member_nat @ Y3 @ A4 )
% 13.77/7.79 => ( ( X3 != Y3 )
% 13.77/7.79 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 13.77/7.79 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y3 @ X3 ) @ R ) ) ) ) )
% 13.77/7.79 => ( total_on_nat @ A4 @ R ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6681_total__onI,axiom,
% 13.77/7.79 ! [A4: set_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.79 ( ! [X3: int,Y3: int] :
% 13.77/7.79 ( ( member_int @ X3 @ A4 )
% 13.77/7.79 => ( ( member_int @ Y3 @ A4 )
% 13.77/7.79 => ( ( X3 != Y3 )
% 13.77/7.79 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y3 ) @ R )
% 13.77/7.79 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y3 @ X3 ) @ R ) ) ) ) )
% 13.77/7.79 => ( total_on_int @ A4 @ R ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6682_total__on__def,axiom,
% 13.77/7.79 ( total_on_uint32
% 13.77/7.79 = ( ^ [A6: set_uint32,R5: set_Pr1773385645901665561uint32] :
% 13.77/7.79 ! [X4: uint32] :
% 13.77/7.79 ( ( member_uint32 @ X4 @ A6 )
% 13.77/7.79 => ! [Y4: uint32] :
% 13.77/7.79 ( ( member_uint32 @ Y4 @ A6 )
% 13.77/7.79 => ( ( X4 != Y4 )
% 13.77/7.79 => ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X4 @ Y4 ) @ R5 )
% 13.77/7.79 | ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ Y4 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6683_total__on__def,axiom,
% 13.77/7.79 ( total_on_nat
% 13.77/7.79 = ( ^ [A6: set_nat,R5: set_Pr1261947904930325089at_nat] :
% 13.77/7.79 ! [X4: nat] :
% 13.77/7.79 ( ( member_nat @ X4 @ A6 )
% 13.77/7.79 => ! [Y4: nat] :
% 13.77/7.79 ( ( member_nat @ Y4 @ A6 )
% 13.77/7.79 => ( ( X4 != Y4 )
% 13.77/7.79 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R5 )
% 13.77/7.79 | ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y4 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6684_total__on__def,axiom,
% 13.77/7.79 ( total_on_int
% 13.77/7.79 = ( ^ [A6: set_int,R5: set_Pr958786334691620121nt_int] :
% 13.77/7.79 ! [X4: int] :
% 13.77/7.79 ( ( member_int @ X4 @ A6 )
% 13.77/7.79 => ! [Y4: int] :
% 13.77/7.79 ( ( member_int @ Y4 @ A6 )
% 13.77/7.79 => ( ( X4 != Y4 )
% 13.77/7.79 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R5 )
% 13.77/7.79 | ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y4 @ X4 ) @ R5 ) ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6685_finite__if__eq__beyond__finite,axiom,
% 13.77/7.79 ! [S3: set_int,S2: set_int] :
% 13.77/7.79 ( ( finite_finite_int @ S3 )
% 13.77/7.79 => ( finite6197958912794628473et_int
% 13.77/7.79 @ ( collect_set_int
% 13.77/7.79 @ ^ [S8: set_int] :
% 13.77/7.79 ( ( minus_minus_set_int @ S8 @ S3 )
% 13.77/7.79 = ( minus_minus_set_int @ S2 @ S3 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6686_finite__if__eq__beyond__finite,axiom,
% 13.77/7.79 ! [S3: set_complex,S2: set_complex] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.79 => ( finite6551019134538273531omplex
% 13.77/7.79 @ ( collect_set_complex
% 13.77/7.79 @ ^ [S8: set_complex] :
% 13.77/7.79 ( ( minus_811609699411566653omplex @ S8 @ S3 )
% 13.77/7.79 = ( minus_811609699411566653omplex @ S2 @ S3 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6687_finite__if__eq__beyond__finite,axiom,
% 13.77/7.79 ! [S3: set_Code_integer,S2: set_Code_integer] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.79 => ( finite6931041176100689706nteger
% 13.77/7.79 @ ( collec574505750873337192nteger
% 13.77/7.79 @ ^ [S8: set_Code_integer] :
% 13.77/7.79 ( ( minus_2355218937544613996nteger @ S8 @ S3 )
% 13.77/7.79 = ( minus_2355218937544613996nteger @ S2 @ S3 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6688_finite__if__eq__beyond__finite,axiom,
% 13.77/7.79 ! [S3: set_nat,S2: set_nat] :
% 13.77/7.79 ( ( finite_finite_nat @ S3 )
% 13.77/7.79 => ( finite1152437895449049373et_nat
% 13.77/7.79 @ ( collect_set_nat
% 13.77/7.79 @ ^ [S8: set_nat] :
% 13.77/7.79 ( ( minus_minus_set_nat @ S8 @ S3 )
% 13.77/7.79 = ( minus_minus_set_nat @ S2 @ S3 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6689_total__on__empty,axiom,
% 13.77/7.79 ! [R: set_Pr1261947904930325089at_nat] : ( total_on_nat @ bot_bot_set_nat @ R ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6690_total__on__empty,axiom,
% 13.77/7.79 ! [R: set_Pr958786334691620121nt_int] : ( total_on_int @ bot_bot_set_int @ R ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6691_total__on__empty,axiom,
% 13.77/7.79 ! [R: set_Product_prod_o_o] : ( total_on_o @ bot_bot_set_o @ R ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6692_Fpow__def,axiom,
% 13.77/7.79 ( finite_Fpow_nat
% 13.77/7.79 = ( ^ [A6: set_nat] :
% 13.77/7.79 ( collect_set_nat
% 13.77/7.79 @ ^ [X8: set_nat] :
% 13.77/7.79 ( ( ord_less_eq_set_nat @ X8 @ A6 )
% 13.77/7.79 & ( finite_finite_nat @ X8 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6693_Fpow__def,axiom,
% 13.77/7.79 ( finite_Fpow_complex
% 13.77/7.79 = ( ^ [A6: set_complex] :
% 13.77/7.79 ( collect_set_complex
% 13.77/7.79 @ ^ [X8: set_complex] :
% 13.77/7.79 ( ( ord_le211207098394363844omplex @ X8 @ A6 )
% 13.77/7.79 & ( finite3207457112153483333omplex @ X8 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6694_Fpow__def,axiom,
% 13.77/7.79 ( finite1532502677820914807nteger
% 13.77/7.79 = ( ^ [A6: set_Code_integer] :
% 13.77/7.79 ( collec574505750873337192nteger
% 13.77/7.79 @ ^ [X8: set_Code_integer] :
% 13.77/7.79 ( ( ord_le7084787975880047091nteger @ X8 @ A6 )
% 13.77/7.79 & ( finite6017078050557962740nteger @ X8 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6695_Fpow__def,axiom,
% 13.77/7.79 ( finite_Fpow_int
% 13.77/7.79 = ( ^ [A6: set_int] :
% 13.77/7.79 ( collect_set_int
% 13.77/7.79 @ ^ [X8: set_int] :
% 13.77/7.79 ( ( ord_less_eq_set_int @ X8 @ A6 )
% 13.77/7.79 & ( finite_finite_int @ X8 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6696_distinct__finite__set,axiom,
% 13.77/7.79 ! [X: set_VEBT_VEBT] :
% 13.77/7.79 ( finite3004134309566078307T_VEBT
% 13.77/7.79 @ ( collec5608196760682091941T_VEBT
% 13.77/7.79 @ ^ [Ys3: list_VEBT_VEBT] :
% 13.77/7.79 ( ( ( set_VEBT_VEBT2 @ Ys3 )
% 13.77/7.79 = X )
% 13.77/7.79 & ( distinct_VEBT_VEBT @ Ys3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6697_distinct__finite__set,axiom,
% 13.77/7.79 ! [X: set_nat] :
% 13.77/7.79 ( finite8100373058378681591st_nat
% 13.77/7.79 @ ( collect_list_nat
% 13.77/7.79 @ ^ [Ys3: list_nat] :
% 13.77/7.79 ( ( ( set_nat2 @ Ys3 )
% 13.77/7.79 = X )
% 13.77/7.79 & ( distinct_nat @ Ys3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6698_distinct__finite__set,axiom,
% 13.77/7.79 ! [X: set_real] :
% 13.77/7.79 ( finite306553202115118035t_real
% 13.77/7.79 @ ( collect_list_real
% 13.77/7.79 @ ^ [Ys3: list_real] :
% 13.77/7.79 ( ( ( set_real2 @ Ys3 )
% 13.77/7.79 = X )
% 13.77/7.79 & ( distinct_real @ Ys3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6699_distinct__finite__set,axiom,
% 13.77/7.79 ! [X: set_o] :
% 13.77/7.79 ( finite_finite_list_o
% 13.77/7.79 @ ( collect_list_o
% 13.77/7.79 @ ^ [Ys3: list_o] :
% 13.77/7.79 ( ( ( set_o2 @ Ys3 )
% 13.77/7.79 = X )
% 13.77/7.79 & ( distinct_o @ Ys3 ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6700_diff__power__eq__sum,axiom,
% 13.77/7.79 ! [X: complex,N: nat,Y: complex] :
% 13.77/7.79 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 13.77/7.79 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 13.77/7.79 @ ( groups2073611262835488442omplex
% 13.77/7.79 @ ^ [P7: nat] : ( times_times_complex @ ( power_power_complex @ X @ P7 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6701_diff__power__eq__sum,axiom,
% 13.77/7.79 ! [X: uint32,N: nat,Y: uint32] :
% 13.77/7.79 ( ( minus_minus_uint32 @ ( power_power_uint32 @ X @ ( suc @ N ) ) @ ( power_power_uint32 @ Y @ ( suc @ N ) ) )
% 13.77/7.79 = ( times_times_uint32 @ ( minus_minus_uint32 @ X @ Y )
% 13.77/7.79 @ ( groups833757482993574392uint32
% 13.77/7.79 @ ^ [P7: nat] : ( times_times_uint32 @ ( power_power_uint32 @ X @ P7 ) @ ( power_power_uint32 @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6702_diff__power__eq__sum,axiom,
% 13.77/7.79 ! [X: int,N: nat,Y: int] :
% 13.77/7.79 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 13.77/7.79 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 13.77/7.79 @ ( groups3539618377306564664at_int
% 13.77/7.79 @ ^ [P7: nat] : ( times_times_int @ ( power_power_int @ X @ P7 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6703_diff__power__eq__sum,axiom,
% 13.77/7.79 ! [X: real,N: nat,Y: real] :
% 13.77/7.79 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 13.77/7.79 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 13.77/7.79 @ ( groups6591440286371151544t_real
% 13.77/7.79 @ ^ [P7: nat] : ( times_times_real @ ( power_power_real @ X @ P7 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P7 ) ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6704_power__diff__sumr2,axiom,
% 13.77/7.79 ! [X: complex,N: nat,Y: complex] :
% 13.77/7.79 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 13.77/7.79 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 13.77/7.79 @ ( groups2073611262835488442omplex
% 13.77/7.79 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6705_power__diff__sumr2,axiom,
% 13.77/7.79 ! [X: uint32,N: nat,Y: uint32] :
% 13.77/7.79 ( ( minus_minus_uint32 @ ( power_power_uint32 @ X @ N ) @ ( power_power_uint32 @ Y @ N ) )
% 13.77/7.79 = ( times_times_uint32 @ ( minus_minus_uint32 @ X @ Y )
% 13.77/7.79 @ ( groups833757482993574392uint32
% 13.77/7.79 @ ^ [I3: nat] : ( times_times_uint32 @ ( power_power_uint32 @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_uint32 @ X @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6706_power__diff__sumr2,axiom,
% 13.77/7.79 ! [X: int,N: nat,Y: int] :
% 13.77/7.79 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 13.77/7.79 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 13.77/7.79 @ ( groups3539618377306564664at_int
% 13.77/7.79 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6707_power__diff__sumr2,axiom,
% 13.77/7.79 ! [X: real,N: nat,Y: real] :
% 13.77/7.79 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 13.77/7.79 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 13.77/7.79 @ ( groups6591440286371151544t_real
% 13.77/7.79 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_real @ X @ I3 ) )
% 13.77/7.79 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6708_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,B4: real,I: vEBT_VEBT] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups2240296850493347238T_real @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_VEBT_VEBT @ I @ S )
% 13.77/7.79 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6709_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_real,F: real > real,B4: real,I: real] :
% 13.77/7.79 ( ( finite_finite_real @ S )
% 13.77/7.79 => ( ! [I2: real] :
% 13.77/7.79 ( ( member_real @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_real @ I @ S )
% 13.77/7.79 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6710_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_int,F: int > real,B4: real,I: int] :
% 13.77/7.79 ( ( finite_finite_int @ S )
% 13.77/7.79 => ( ! [I2: int] :
% 13.77/7.79 ( ( member_int @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_int @ I @ S )
% 13.77/7.79 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6711_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_complex,F: complex > real,B4: real,I: complex] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ S )
% 13.77/7.79 => ( ! [I2: complex] :
% 13.77/7.79 ( ( member_complex @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_complex @ I @ S )
% 13.77/7.79 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6712_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_Code_integer,F: code_integer > real,B4: real,I: code_integer] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ S )
% 13.77/7.79 => ( ! [I2: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups1270011288395367621r_real @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_Code_integer @ I @ S )
% 13.77/7.79 => ( ord_less_eq_real @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6713_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,B4: rat,I: vEBT_VEBT] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_VEBT_VEBT @ I @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6714_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_real,F: real > rat,B4: rat,I: real] :
% 13.77/7.79 ( ( finite_finite_real @ S )
% 13.77/7.79 => ( ! [I2: real] :
% 13.77/7.79 ( ( member_real @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_real @ I @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6715_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_nat,F: nat > rat,B4: rat,I: nat] :
% 13.77/7.79 ( ( finite_finite_nat @ S )
% 13.77/7.79 => ( ! [I2: nat] :
% 13.77/7.79 ( ( member_nat @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_nat @ I @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6716_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_int,F: int > rat,B4: rat,I: int] :
% 13.77/7.79 ( ( finite_finite_int @ S )
% 13.77/7.79 => ( ! [I2: int] :
% 13.77/7.79 ( ( member_int @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_int @ I @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6717_sum__nonneg__leq__bound,axiom,
% 13.77/7.79 ! [S: set_complex,F: complex > rat,B4: rat,I: complex] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ S )
% 13.77/7.79 => ( ! [I2: complex] :
% 13.77/7.79 ( ( member_complex @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 13.77/7.79 = B4 )
% 13.77/7.79 => ( ( member_complex @ I @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6718_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > real,I: vEBT_VEBT] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups2240296850493347238T_real @ F @ S )
% 13.77/7.79 = zero_zero_real )
% 13.77/7.79 => ( ( member_VEBT_VEBT @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_real ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6719_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_real,F: real > real,I: real] :
% 13.77/7.79 ( ( finite_finite_real @ S )
% 13.77/7.79 => ( ! [I2: real] :
% 13.77/7.79 ( ( member_real @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 13.77/7.79 = zero_zero_real )
% 13.77/7.79 => ( ( member_real @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_real ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6720_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_int,F: int > real,I: int] :
% 13.77/7.79 ( ( finite_finite_int @ S )
% 13.77/7.79 => ( ! [I2: int] :
% 13.77/7.79 ( ( member_int @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 13.77/7.79 = zero_zero_real )
% 13.77/7.79 => ( ( member_int @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_real ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6721_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_complex,F: complex > real,I: complex] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ S )
% 13.77/7.79 => ( ! [I2: complex] :
% 13.77/7.79 ( ( member_complex @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 13.77/7.79 = zero_zero_real )
% 13.77/7.79 => ( ( member_complex @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_real ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6722_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_Code_integer,F: code_integer > real,I: code_integer] :
% 13.77/7.79 ( ( finite6017078050557962740nteger @ S )
% 13.77/7.79 => ( ! [I2: code_integer] :
% 13.77/7.79 ( ( member_Code_integer @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups1270011288395367621r_real @ F @ S )
% 13.77/7.79 = zero_zero_real )
% 13.77/7.79 => ( ( member_Code_integer @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_real ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6723_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_VEBT_VEBT,F: vEBT_VEBT > rat,I: vEBT_VEBT] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S )
% 13.77/7.79 => ( ! [I2: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups136491112297645522BT_rat @ F @ S )
% 13.77/7.79 = zero_zero_rat )
% 13.77/7.79 => ( ( member_VEBT_VEBT @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_rat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6724_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_real,F: real > rat,I: real] :
% 13.77/7.79 ( ( finite_finite_real @ S )
% 13.77/7.79 => ( ! [I2: real] :
% 13.77/7.79 ( ( member_real @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 13.77/7.79 = zero_zero_rat )
% 13.77/7.79 => ( ( member_real @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_rat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6725_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_nat,F: nat > rat,I: nat] :
% 13.77/7.79 ( ( finite_finite_nat @ S )
% 13.77/7.79 => ( ! [I2: nat] :
% 13.77/7.79 ( ( member_nat @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 13.77/7.79 = zero_zero_rat )
% 13.77/7.79 => ( ( member_nat @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_rat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6726_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_int,F: int > rat,I: int] :
% 13.77/7.79 ( ( finite_finite_int @ S )
% 13.77/7.79 => ( ! [I2: int] :
% 13.77/7.79 ( ( member_int @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 13.77/7.79 = zero_zero_rat )
% 13.77/7.79 => ( ( member_int @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_rat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6727_sum__nonneg__0,axiom,
% 13.77/7.79 ! [S: set_complex,F: complex > rat,I: complex] :
% 13.77/7.79 ( ( finite3207457112153483333omplex @ S )
% 13.77/7.79 => ( ! [I2: complex] :
% 13.77/7.79 ( ( member_complex @ I2 @ S )
% 13.77/7.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) ) )
% 13.77/7.79 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 13.77/7.79 = zero_zero_rat )
% 13.77/7.79 => ( ( member_complex @ I @ S )
% 13.77/7.79 => ( ( F @ I )
% 13.77/7.79 = zero_zero_rat ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6728_add__mset__in__multiset,axiom,
% 13.77/7.79 ! [M7: list_nat > nat,A: list_nat] :
% 13.77/7.79 ( ( finite8100373058378681591st_nat
% 13.77/7.79 @ ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite8100373058378681591st_nat
% 13.77/7.79 @ ( collect_list_nat
% 13.77/7.79 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6729_add__mset__in__multiset,axiom,
% 13.77/7.79 ! [M7: set_nat > nat,A: set_nat] :
% 13.77/7.79 ( ( finite1152437895449049373et_nat
% 13.77/7.79 @ ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite1152437895449049373et_nat
% 13.77/7.79 @ ( collect_set_nat
% 13.77/7.79 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6730_add__mset__in__multiset,axiom,
% 13.77/7.79 ! [M7: nat > nat,A: nat] :
% 13.77/7.79 ( ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite_finite_nat
% 13.77/7.79 @ ( collect_nat
% 13.77/7.79 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6731_add__mset__in__multiset,axiom,
% 13.77/7.79 ! [M7: int > nat,A: int] :
% 13.77/7.79 ( ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite_finite_int
% 13.77/7.79 @ ( collect_int
% 13.77/7.79 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6732_add__mset__in__multiset,axiom,
% 13.77/7.79 ! [M7: complex > nat,A: complex] :
% 13.77/7.79 ( ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite3207457112153483333omplex
% 13.77/7.79 @ ( collect_complex
% 13.77/7.79 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6733_add__mset__in__multiset,axiom,
% 13.77/7.79 ! [M7: code_integer > nat,A: code_integer] :
% 13.77/7.79 ( ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.79 => ( finite6017078050557962740nteger
% 13.77/7.79 @ ( collect_Code_integer
% 13.77/7.79 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M7 @ X4 ) ) @ ( M7 @ X4 ) ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6734_sum__fun__comp,axiom,
% 13.77/7.79 ! [S3: set_VEBT_VEBT,R2: set_nat,G: vEBT_VEBT > nat,F: nat > uint32] :
% 13.77/7.79 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.79 => ( ( finite_finite_nat @ R2 )
% 13.77/7.79 => ( ( ord_less_eq_set_nat @ ( image_VEBT_VEBT_nat @ G @ S3 ) @ R2 )
% 13.77/7.79 => ( ( groups8325533452322294502uint32
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ S3 )
% 13.77/7.79 = ( groups833757482993574392uint32
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( times_times_uint32
% 13.77/7.79 @ ( semiri2565882477558803405uint32
% 13.77/7.79 @ ( finite7802652506058667612T_VEBT
% 13.77/7.79 @ ( collect_VEBT_VEBT
% 13.77/7.79 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.79 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) ) )
% 13.77/7.79 @ ( F @ Y4 ) )
% 13.77/7.79 @ R2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6735_sum__fun__comp,axiom,
% 13.77/7.79 ! [S3: set_real,R2: set_nat,G: real > nat,F: nat > uint32] :
% 13.77/7.79 ( ( finite_finite_real @ S3 )
% 13.77/7.79 => ( ( finite_finite_nat @ R2 )
% 13.77/7.79 => ( ( ord_less_eq_set_nat @ ( image_real_nat @ G @ S3 ) @ R2 )
% 13.77/7.79 => ( ( groups5944083974425963860uint32
% 13.77/7.79 @ ^ [X4: real] : ( F @ ( G @ X4 ) )
% 13.77/7.79 @ S3 )
% 13.77/7.79 = ( groups833757482993574392uint32
% 13.77/7.79 @ ^ [Y4: nat] :
% 13.77/7.79 ( times_times_uint32
% 13.77/7.79 @ ( semiri2565882477558803405uint32
% 13.77/7.79 @ ( finite_card_real
% 13.77/7.79 @ ( collect_real
% 13.77/7.79 @ ^ [X4: real] :
% 13.77/7.79 ( ( member_real @ X4 @ S3 )
% 13.77/7.79 & ( ( G @ X4 )
% 13.77/7.79 = Y4 ) ) ) ) )
% 13.77/7.79 @ ( F @ Y4 ) )
% 13.77/7.79 @ R2 ) ) ) ) ) ).
% 13.77/7.79
% 13.77/7.79 thf(fact_6736_sum__fun__comp,axiom,
% 13.77/7.79 ! [S3: set_literal,R2: set_nat,G: literal > nat,F: nat > uint32] :
% 13.77/7.79 ( ( finite5847741373460823677iteral @ S3 )
% 13.77/7.80 => ( ( finite_finite_nat @ R2 )
% 13.77/7.80 => ( ( ord_less_eq_set_nat @ ( image_literal_nat @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups4542640294765070598uint32
% 13.77/7.80 @ ^ [X4: literal] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups833757482993574392uint32
% 13.77/7.80 @ ^ [Y4: nat] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [X4: literal] :
% 13.77/7.80 ( ( member_literal @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6737_sum__fun__comp,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,R2: set_complex,G: vEBT_VEBT > complex,F: complex > uint32] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( finite3207457112153483333omplex @ R2 )
% 13.77/7.80 => ( ( ord_le211207098394363844omplex @ ( image_3793382806556112285omplex @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups8325533452322294502uint32
% 13.77/7.80 @ ^ [X4: vEBT_VEBT] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups8736914816313324502uint32
% 13.77/7.80 @ ^ [Y4: complex] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6738_sum__fun__comp,axiom,
% 13.77/7.80 ! [S3: set_real,R2: set_complex,G: real > complex,F: complex > uint32] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( finite3207457112153483333omplex @ R2 )
% 13.77/7.80 => ( ( ord_le211207098394363844omplex @ ( image_real_complex @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups5944083974425963860uint32
% 13.77/7.80 @ ^ [X4: real] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups8736914816313324502uint32
% 13.77/7.80 @ ^ [Y4: complex] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [X4: real] :
% 13.77/7.80 ( ( member_real @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6739_sum__fun__comp,axiom,
% 13.77/7.80 ! [S3: set_literal,R2: set_complex,G: literal > complex,F: complex > uint32] :
% 13.77/7.80 ( ( finite5847741373460823677iteral @ S3 )
% 13.77/7.80 => ( ( finite3207457112153483333omplex @ R2 )
% 13.77/7.80 => ( ( ord_le211207098394363844omplex @ ( image_5274195009022015549omplex @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups4542640294765070598uint32
% 13.77/7.80 @ ^ [X4: literal] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups8736914816313324502uint32
% 13.77/7.80 @ ^ [Y4: complex] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [X4: literal] :
% 13.77/7.80 ( ( member_literal @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6740_sum__fun__comp,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,R2: set_Code_integer,G: vEBT_VEBT > code_integer,F: code_integer > uint32] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( finite6017078050557962740nteger @ R2 )
% 13.77/7.80 => ( ( ord_le7084787975880047091nteger @ ( image_2092689629700589388nteger @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups8325533452322294502uint32
% 13.77/7.80 @ ^ [X4: vEBT_VEBT] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups8847630953604152069uint32
% 13.77/7.80 @ ^ [Y4: code_integer] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [X4: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6741_sum__fun__comp,axiom,
% 13.77/7.80 ! [S3: set_real,R2: set_Code_integer,G: real > code_integer,F: code_integer > uint32] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( finite6017078050557962740nteger @ R2 )
% 13.77/7.80 => ( ( ord_le7084787975880047091nteger @ ( image_4958697645175560720nteger @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups5944083974425963860uint32
% 13.77/7.80 @ ^ [X4: real] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups8847630953604152069uint32
% 13.77/7.80 @ ^ [Y4: code_integer] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [X4: real] :
% 13.77/7.80 ( ( member_real @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6742_sum__fun__comp,axiom,
% 13.77/7.80 ! [S3: set_literal,R2: set_Code_integer,G: literal > code_integer,F: code_integer > uint32] :
% 13.77/7.80 ( ( finite5847741373460823677iteral @ S3 )
% 13.77/7.80 => ( ( finite6017078050557962740nteger @ R2 )
% 13.77/7.80 => ( ( ord_le7084787975880047091nteger @ ( image_4442872163159017964nteger @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups4542640294765070598uint32
% 13.77/7.80 @ ^ [X4: literal] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups8847630953604152069uint32
% 13.77/7.80 @ ^ [Y4: code_integer] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [X4: literal] :
% 13.77/7.80 ( ( member_literal @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6743_sum__fun__comp,axiom,
% 13.77/7.80 ! [S3: set_nat,R2: set_nat,G: nat > nat,F: nat > uint32] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( finite_finite_nat @ R2 )
% 13.77/7.80 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G @ S3 ) @ R2 )
% 13.77/7.80 => ( ( groups833757482993574392uint32
% 13.77/7.80 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups833757482993574392uint32
% 13.77/7.80 @ ^ [Y4: nat] :
% 13.77/7.80 ( times_times_uint32
% 13.77/7.80 @ ( semiri2565882477558803405uint32
% 13.77/7.80 @ ( finite_card_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) ) )
% 13.77/7.80 @ ( F @ Y4 ) )
% 13.77/7.80 @ R2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6744_diff__preserves__multiset,axiom,
% 13.77/7.80 ! [M7: list_nat > nat,N8: list_nat > nat] :
% 13.77/7.80 ( ( finite8100373058378681591st_nat
% 13.77/7.80 @ ( collect_list_nat
% 13.77/7.80 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.80 => ( finite8100373058378681591st_nat
% 13.77/7.80 @ ( collect_list_nat
% 13.77/7.80 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6745_diff__preserves__multiset,axiom,
% 13.77/7.80 ! [M7: set_nat > nat,N8: set_nat > nat] :
% 13.77/7.80 ( ( finite1152437895449049373et_nat
% 13.77/7.80 @ ( collect_set_nat
% 13.77/7.80 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.80 => ( finite1152437895449049373et_nat
% 13.77/7.80 @ ( collect_set_nat
% 13.77/7.80 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6746_diff__preserves__multiset,axiom,
% 13.77/7.80 ! [M7: nat > nat,N8: nat > nat] :
% 13.77/7.80 ( ( finite_finite_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.80 => ( finite_finite_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6747_diff__preserves__multiset,axiom,
% 13.77/7.80 ! [M7: int > nat,N8: int > nat] :
% 13.77/7.80 ( ( finite_finite_int
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.80 => ( finite_finite_int
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6748_diff__preserves__multiset,axiom,
% 13.77/7.80 ! [M7: complex > nat,N8: complex > nat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.80 => ( finite3207457112153483333omplex
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6749_diff__preserves__multiset,axiom,
% 13.77/7.80 ! [M7: code_integer > nat,N8: code_integer > nat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger
% 13.77/7.80 @ ( collect_Code_integer
% 13.77/7.80 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M7 @ X4 ) ) ) )
% 13.77/7.80 => ( finite6017078050557962740nteger
% 13.77/7.80 @ ( collect_Code_integer
% 13.77/7.80 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M7 @ X4 ) @ ( N8 @ X4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6750_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_nat,T3: set_complex,G: nat > complex,H2: nat > nat] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.80 => ( ( ord_le211207098394363844omplex @ ( image_nat_complex @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups5693394587270226106ex_nat
% 13.77/7.80 @ ^ [Y4: complex] :
% 13.77/7.80 ( groups3542108847815614940at_nat @ H2
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups3542108847815614940at_nat @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6751_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_nat,T3: set_Code_integer,G: nat > code_integer,H2: nat > nat] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.80 => ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups7237345082560585321er_nat
% 13.77/7.80 @ ^ [Y4: code_integer] :
% 13.77/7.80 ( groups3542108847815614940at_nat @ H2
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups3542108847815614940at_nat @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6752_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_nat,T3: set_int,G: nat > int,H2: nat > nat] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( finite_finite_int @ T3 )
% 13.77/7.80 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups4541462559716669496nt_nat
% 13.77/7.80 @ ^ [Y4: int] :
% 13.77/7.80 ( groups3542108847815614940at_nat @ H2
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups3542108847815614940at_nat @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6753_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_complex,T3: set_nat,G: complex > nat,H2: complex > complex] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( finite_finite_nat @ T3 )
% 13.77/7.80 => ( ( ord_less_eq_set_nat @ ( image_complex_nat @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups2073611262835488442omplex
% 13.77/7.80 @ ^ [Y4: nat] :
% 13.77/7.80 ( groups7754918857620584856omplex @ H2
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] :
% 13.77/7.80 ( ( member_complex @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups7754918857620584856omplex @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6754_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_complex,T3: set_Code_integer,G: complex > code_integer,H2: complex > complex] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.80 => ( ( ord_le7084787975880047091nteger @ ( image_1994230757181692690nteger @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups8024822376189712711omplex
% 13.77/7.80 @ ^ [Y4: code_integer] :
% 13.77/7.80 ( groups7754918857620584856omplex @ H2
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] :
% 13.77/7.80 ( ( member_complex @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups7754918857620584856omplex @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6755_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_complex,T3: set_int,G: complex > int,H2: complex > complex] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( finite_finite_int @ T3 )
% 13.77/7.80 => ( ( ord_less_eq_set_int @ ( image_complex_int @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups3049146728041665814omplex
% 13.77/7.80 @ ^ [Y4: int] :
% 13.77/7.80 ( groups7754918857620584856omplex @ H2
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] :
% 13.77/7.80 ( ( member_complex @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups7754918857620584856omplex @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6756_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_nat,T3: set_complex,G: nat > complex,H2: nat > real] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( finite3207457112153483333omplex @ T3 )
% 13.77/7.80 => ( ( ord_le211207098394363844omplex @ ( image_nat_complex @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups5808333547571424918x_real
% 13.77/7.80 @ ^ [Y4: complex] :
% 13.77/7.80 ( groups6591440286371151544t_real @ H2
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups6591440286371151544t_real @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6757_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_nat,T3: set_Code_integer,G: nat > code_integer,H2: nat > real] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( finite6017078050557962740nteger @ T3 )
% 13.77/7.80 => ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups1270011288395367621r_real
% 13.77/7.80 @ ^ [Y4: code_integer] :
% 13.77/7.80 ( groups6591440286371151544t_real @ H2
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups6591440286371151544t_real @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6758_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_nat,T3: set_int,G: nat > int,H2: nat > real] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( finite_finite_int @ T3 )
% 13.77/7.80 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups8778361861064173332t_real
% 13.77/7.80 @ ^ [Y4: int] :
% 13.77/7.80 ( groups6591440286371151544t_real @ H2
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups6591440286371151544t_real @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6759_sum_Ogroup,axiom,
% 13.77/7.80 ! [S3: set_int,T3: set_nat,G: int > nat,H2: int > int] :
% 13.77/7.80 ( ( finite_finite_int @ S3 )
% 13.77/7.80 => ( ( finite_finite_nat @ T3 )
% 13.77/7.80 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ G @ S3 ) @ T3 )
% 13.77/7.80 => ( ( groups3539618377306564664at_int
% 13.77/7.80 @ ^ [Y4: nat] :
% 13.77/7.80 ( groups4538972089207619220nt_int @ H2
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [X4: int] :
% 13.77/7.80 ( ( member_int @ X4 @ S3 )
% 13.77/7.80 & ( ( G @ X4 )
% 13.77/7.80 = Y4 ) ) ) )
% 13.77/7.80 @ T3 )
% 13.77/7.80 = ( groups4538972089207619220nt_int @ H2 @ S3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6760_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_int,G: int > uint32] :
% 13.77/7.80 ( ( finite_finite_int @ A4 )
% 13.77/7.80 => ( ( groups5712668689793887828uint32 @ G
% 13.77/7.80 @ ( minus_minus_set_int @ A4
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [X4: int] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_uint32 ) ) ) )
% 13.77/7.80 = ( groups5712668689793887828uint32 @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6761_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_complex,G: complex > uint32] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.80 => ( ( groups8736914816313324502uint32 @ G
% 13.77/7.80 @ ( minus_811609699411566653omplex @ A4
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_uint32 ) ) ) )
% 13.77/7.80 = ( groups8736914816313324502uint32 @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6762_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_Code_integer,G: code_integer > uint32] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.80 => ( ( groups8847630953604152069uint32 @ G
% 13.77/7.80 @ ( minus_2355218937544613996nteger @ A4
% 13.77/7.80 @ ( collect_Code_integer
% 13.77/7.80 @ ^ [X4: code_integer] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_uint32 ) ) ) )
% 13.77/7.80 = ( groups8847630953604152069uint32 @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6763_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_int,G: int > real] :
% 13.77/7.80 ( ( finite_finite_int @ A4 )
% 13.77/7.80 => ( ( groups8778361861064173332t_real @ G
% 13.77/7.80 @ ( minus_minus_set_int @ A4
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [X4: int] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_real ) ) ) )
% 13.77/7.80 = ( groups8778361861064173332t_real @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6764_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_complex,G: complex > real] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.80 => ( ( groups5808333547571424918x_real @ G
% 13.77/7.80 @ ( minus_811609699411566653omplex @ A4
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_real ) ) ) )
% 13.77/7.80 = ( groups5808333547571424918x_real @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6765_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_Code_integer,G: code_integer > real] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.80 => ( ( groups1270011288395367621r_real @ G
% 13.77/7.80 @ ( minus_2355218937544613996nteger @ A4
% 13.77/7.80 @ ( collect_Code_integer
% 13.77/7.80 @ ^ [X4: code_integer] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_real ) ) ) )
% 13.77/7.80 = ( groups1270011288395367621r_real @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6766_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_int,G: int > rat] :
% 13.77/7.80 ( ( finite_finite_int @ A4 )
% 13.77/7.80 => ( ( groups3906332499630173760nt_rat @ G
% 13.77/7.80 @ ( minus_minus_set_int @ A4
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [X4: int] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_rat ) ) ) )
% 13.77/7.80 = ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6767_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_complex,G: complex > rat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.80 => ( ( groups5058264527183730370ex_rat @ G
% 13.77/7.80 @ ( minus_811609699411566653omplex @ A4
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [X4: complex] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_rat ) ) ) )
% 13.77/7.80 = ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6768_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_Code_integer,G: code_integer > rat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.80 => ( ( groups6602215022474089585er_rat @ G
% 13.77/7.80 @ ( minus_2355218937544613996nteger @ A4
% 13.77/7.80 @ ( collect_Code_integer
% 13.77/7.80 @ ^ [X4: code_integer] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_rat ) ) ) )
% 13.77/7.80 = ( groups6602215022474089585er_rat @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6769_sum_Osetdiff__irrelevant,axiom,
% 13.77/7.80 ! [A4: set_int,G: int > nat] :
% 13.77/7.80 ( ( finite_finite_int @ A4 )
% 13.77/7.80 => ( ( groups4541462559716669496nt_nat @ G
% 13.77/7.80 @ ( minus_minus_set_int @ A4
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [X4: int] :
% 13.77/7.80 ( ( G @ X4 )
% 13.77/7.80 = zero_zero_nat ) ) ) )
% 13.77/7.80 = ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6770_sum__Suc,axiom,
% 13.77/7.80 ! [F: complex > nat,A4: set_complex] :
% 13.77/7.80 ( ( groups5693394587270226106ex_nat
% 13.77/7.80 @ ^ [X4: complex] : ( suc @ ( F @ X4 ) )
% 13.77/7.80 @ A4 )
% 13.77/7.80 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( finite_card_complex @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6771_sum__Suc,axiom,
% 13.77/7.80 ! [F: literal > nat,A4: set_literal] :
% 13.77/7.80 ( ( groups8652099787943017962al_nat
% 13.77/7.80 @ ^ [X4: literal] : ( suc @ ( F @ X4 ) )
% 13.77/7.80 @ A4 )
% 13.77/7.80 = ( plus_plus_nat @ ( groups8652099787943017962al_nat @ F @ A4 ) @ ( finite_card_literal @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6772_sum__Suc,axiom,
% 13.77/7.80 ! [F: list_nat > nat,A4: set_list_nat] :
% 13.77/7.80 ( ( groups4396056296759096172at_nat
% 13.77/7.80 @ ^ [X4: list_nat] : ( suc @ ( F @ X4 ) )
% 13.77/7.80 @ A4 )
% 13.77/7.80 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F @ A4 ) @ ( finite_card_list_nat @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6773_sum__Suc,axiom,
% 13.77/7.80 ! [F: set_nat > nat,A4: set_set_nat] :
% 13.77/7.80 ( ( groups8294997508430121362at_nat
% 13.77/7.80 @ ^ [X4: set_nat] : ( suc @ ( F @ X4 ) )
% 13.77/7.80 @ A4 )
% 13.77/7.80 = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ F @ A4 ) @ ( finite_card_set_nat @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6774_sum__Suc,axiom,
% 13.77/7.80 ! [F: nat > nat,A4: set_nat] :
% 13.77/7.80 ( ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [X4: nat] : ( suc @ ( F @ X4 ) )
% 13.77/7.80 @ A4 )
% 13.77/7.80 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( finite_card_nat @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6775_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,T3: set_VEBT_VEBT,R2: vEBT_VEBT > vEBT_VEBT > $o,K: nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.80 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ X3 @ T3 )
% 13.77/7.80 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups771621172384141258BT_nat
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [J3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite7802652506058667612T_VEBT @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6776_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,T3: set_real,R2: vEBT_VEBT > real > $o,K: nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( finite_finite_real @ T3 )
% 13.77/7.80 => ( ! [X3: real] :
% 13.77/7.80 ( ( member_real @ X3 @ T3 )
% 13.77/7.80 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups771621172384141258BT_nat
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [J3: real] :
% 13.77/7.80 ( ( member_real @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite_card_real @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6777_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_real,T3: set_VEBT_VEBT,R2: real > vEBT_VEBT > $o,K: nat] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.80 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ X3 @ T3 )
% 13.77/7.80 => ( ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [I3: real] :
% 13.77/7.80 ( ( member_real @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups1935376822645274424al_nat
% 13.77/7.80 @ ^ [I3: real] :
% 13.77/7.80 ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [J3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite7802652506058667612T_VEBT @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6778_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_real,T3: set_real,R2: real > real > $o,K: nat] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( finite_finite_real @ T3 )
% 13.77/7.80 => ( ! [X3: real] :
% 13.77/7.80 ( ( member_real @ X3 @ T3 )
% 13.77/7.80 => ( ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [I3: real] :
% 13.77/7.80 ( ( member_real @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups1935376822645274424al_nat
% 13.77/7.80 @ ^ [I3: real] :
% 13.77/7.80 ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [J3: real] :
% 13.77/7.80 ( ( member_real @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite_card_real @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6779_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,T3: set_literal,R2: vEBT_VEBT > literal > $o,K: nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( finite5847741373460823677iteral @ T3 )
% 13.77/7.80 => ( ! [X3: literal] :
% 13.77/7.80 ( ( member_literal @ X3 @ T3 )
% 13.77/7.80 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups771621172384141258BT_nat
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [J3: literal] :
% 13.77/7.80 ( ( member_literal @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite_card_literal @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6780_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_real,T3: set_literal,R2: real > literal > $o,K: nat] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( finite5847741373460823677iteral @ T3 )
% 13.77/7.80 => ( ! [X3: literal] :
% 13.77/7.80 ( ( member_literal @ X3 @ T3 )
% 13.77/7.80 => ( ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [I3: real] :
% 13.77/7.80 ( ( member_real @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups1935376822645274424al_nat
% 13.77/7.80 @ ^ [I3: real] :
% 13.77/7.80 ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [J3: literal] :
% 13.77/7.80 ( ( member_literal @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite_card_literal @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6781_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_literal,T3: set_VEBT_VEBT,R2: literal > vEBT_VEBT > $o,K: nat] :
% 13.77/7.80 ( ( finite5847741373460823677iteral @ S3 )
% 13.77/7.80 => ( ( finite5795047828879050333T_VEBT @ T3 )
% 13.77/7.80 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ X3 @ T3 )
% 13.77/7.80 => ( ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [I3: literal] :
% 13.77/7.80 ( ( member_literal @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups8652099787943017962al_nat
% 13.77/7.80 @ ^ [I3: literal] :
% 13.77/7.80 ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [J3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite7802652506058667612T_VEBT @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6782_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_literal,T3: set_real,R2: literal > real > $o,K: nat] :
% 13.77/7.80 ( ( finite5847741373460823677iteral @ S3 )
% 13.77/7.80 => ( ( finite_finite_real @ T3 )
% 13.77/7.80 => ( ! [X3: real] :
% 13.77/7.80 ( ( member_real @ X3 @ T3 )
% 13.77/7.80 => ( ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [I3: literal] :
% 13.77/7.80 ( ( member_literal @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups8652099787943017962al_nat
% 13.77/7.80 @ ^ [I3: literal] :
% 13.77/7.80 ( finite_card_real
% 13.77/7.80 @ ( collect_real
% 13.77/7.80 @ ^ [J3: real] :
% 13.77/7.80 ( ( member_real @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite_card_real @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6783_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_literal,T3: set_literal,R2: literal > literal > $o,K: nat] :
% 13.77/7.80 ( ( finite5847741373460823677iteral @ S3 )
% 13.77/7.80 => ( ( finite5847741373460823677iteral @ T3 )
% 13.77/7.80 => ( ! [X3: literal] :
% 13.77/7.80 ( ( member_literal @ X3 @ T3 )
% 13.77/7.80 => ( ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [I3: literal] :
% 13.77/7.80 ( ( member_literal @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups8652099787943017962al_nat
% 13.77/7.80 @ ^ [I3: literal] :
% 13.77/7.80 ( finite_card_literal
% 13.77/7.80 @ ( collect_literal
% 13.77/7.80 @ ^ [J3: literal] :
% 13.77/7.80 ( ( member_literal @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite_card_literal @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6784_sum__multicount,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,T3: set_nat,R2: vEBT_VEBT > nat > $o,K: nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( finite_finite_nat @ T3 )
% 13.77/7.80 => ( ! [X3: nat] :
% 13.77/7.80 ( ( member_nat @ X3 @ T3 )
% 13.77/7.80 => ( ( finite7802652506058667612T_VEBT
% 13.77/7.80 @ ( collect_VEBT_VEBT
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I3 @ S3 )
% 13.77/7.80 & ( R2 @ I3 @ X3 ) ) ) )
% 13.77/7.80 = K ) )
% 13.77/7.80 => ( ( groups771621172384141258BT_nat
% 13.77/7.80 @ ^ [I3: vEBT_VEBT] :
% 13.77/7.80 ( finite_card_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [J3: nat] :
% 13.77/7.80 ( ( member_nat @ J3 @ T3 )
% 13.77/7.80 & ( R2 @ I3 @ J3 ) ) ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( times_times_nat @ K @ ( finite_card_nat @ T3 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6785_card__less,axiom,
% 13.77/7.80 ! [M7: set_nat,I: nat] :
% 13.77/7.80 ( ( member_nat @ zero_zero_nat @ M7 )
% 13.77/7.80 => ( ( finite_card_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [K3: nat] :
% 13.77/7.80 ( ( member_nat @ K3 @ M7 )
% 13.77/7.80 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) )
% 13.77/7.80 != zero_zero_nat ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6786_card__less__Suc,axiom,
% 13.77/7.80 ! [M7: set_nat,I: nat] :
% 13.77/7.80 ( ( member_nat @ zero_zero_nat @ M7 )
% 13.77/7.80 => ( ( suc
% 13.77/7.80 @ ( finite_card_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [K3: nat] :
% 13.77/7.80 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 13.77/7.80 & ( ord_less_nat @ K3 @ I ) ) ) ) )
% 13.77/7.80 = ( finite_card_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [K3: nat] :
% 13.77/7.80 ( ( member_nat @ K3 @ M7 )
% 13.77/7.80 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6787_card__less__Suc2,axiom,
% 13.77/7.80 ! [M7: set_nat,I: nat] :
% 13.77/7.80 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 13.77/7.80 => ( ( finite_card_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [K3: nat] :
% 13.77/7.80 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 13.77/7.80 & ( ord_less_nat @ K3 @ I ) ) ) )
% 13.77/7.80 = ( finite_card_nat
% 13.77/7.80 @ ( collect_nat
% 13.77/7.80 @ ^ [K3: nat] :
% 13.77/7.80 ( ( member_nat @ K3 @ M7 )
% 13.77/7.80 & ( ord_less_nat @ K3 @ ( suc @ I ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6788_foldr__length__aux,axiom,
% 13.77/7.80 ! [L: list_VEBT_VEBT,A: nat] :
% 13.77/7.80 ( ( foldr_VEBT_VEBT_nat
% 13.77/7.80 @ ^ [X4: vEBT_VEBT] : suc
% 13.77/7.80 @ L
% 13.77/7.80 @ A )
% 13.77/7.80 = ( plus_plus_nat @ A @ ( size_s6755466524823107622T_VEBT @ L ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6789_foldr__length__aux,axiom,
% 13.77/7.80 ! [L: list_real,A: nat] :
% 13.77/7.80 ( ( foldr_real_nat
% 13.77/7.80 @ ^ [X4: real] : suc
% 13.77/7.80 @ L
% 13.77/7.80 @ A )
% 13.77/7.80 = ( plus_plus_nat @ A @ ( size_size_list_real @ L ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6790_foldr__length__aux,axiom,
% 13.77/7.80 ! [L: list_o,A: nat] :
% 13.77/7.80 ( ( foldr_o_nat
% 13.77/7.80 @ ^ [X4: $o] : suc
% 13.77/7.80 @ L
% 13.77/7.80 @ A )
% 13.77/7.80 = ( plus_plus_nat @ A @ ( size_size_list_o @ L ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6791_foldr__length__aux,axiom,
% 13.77/7.80 ! [L: list_nat,A: nat] :
% 13.77/7.80 ( ( foldr_nat_nat
% 13.77/7.80 @ ^ [X4: nat] : suc
% 13.77/7.80 @ L
% 13.77/7.80 @ A )
% 13.77/7.80 = ( plus_plus_nat @ A @ ( size_size_list_nat @ L ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6792_bot_Oordering__top__axioms,axiom,
% 13.77/7.80 ( ordering_top_set_nat
% 13.77/7.80 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 13.77/7.80 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 )
% 13.77/7.80 @ bot_bot_set_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6793_bot_Oordering__top__axioms,axiom,
% 13.77/7.80 ( ordering_top_assn
% 13.77/7.80 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 13.77/7.80 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 )
% 13.77/7.80 @ bot_bot_assn ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6794_bot_Oordering__top__axioms,axiom,
% 13.77/7.80 ( ordering_top_set_o
% 13.77/7.80 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_eq_set_o @ Y4 @ X4 )
% 13.77/7.80 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_set_o @ Y4 @ X4 )
% 13.77/7.80 @ bot_bot_set_o ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6795_bot_Oordering__top__axioms,axiom,
% 13.77/7.80 ( ordering_top_set_int
% 13.77/7.80 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 13.77/7.80 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 )
% 13.77/7.80 @ bot_bot_set_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6796_bot_Oordering__top__axioms,axiom,
% 13.77/7.80 ( ordering_top_nat
% 13.77/7.80 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 13.77/7.80 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 13.77/7.80 @ bot_bot_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6797_card__sum__le__nat__sum,axiom,
% 13.77/7.80 ! [S3: set_nat] :
% 13.77/7.80 ( ord_less_eq_nat
% 13.77/7.80 @ ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [X4: nat] : X4
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 13.77/7.80 @ ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [X4: nat] : X4
% 13.77/7.80 @ S3 ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6798_set__zip__rightD,axiom,
% 13.77/7.80 ! [X: $o,Y: $o,Xs: list_o,Ys: list_o] :
% 13.77/7.80 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( set_Product_prod_o_o2 @ ( zip_o_o @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_o @ Y @ ( set_o2 @ Ys ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6799_set__zip__rightD,axiom,
% 13.77/7.80 ! [X: uint32,Y: uint32,Xs: list_uint32,Ys: list_uint32] :
% 13.77/7.80 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_uint32 @ Y @ ( set_uint322 @ Ys ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6800_set__zip__rightD,axiom,
% 13.77/7.80 ! [X: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 13.77/7.80 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6801_set__zip__rightD,axiom,
% 13.77/7.80 ! [X: int,Y: int,Xs: list_int,Ys: list_int] :
% 13.77/7.80 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6802_set__zip__rightD,axiom,
% 13.77/7.80 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 13.77/7.80 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( set_Pr364071364088684201et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member6260224972018164377et_nat @ Y @ ( set_Pr3864771053587467565et_nat @ Ys ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6803_set__zip__rightD,axiom,
% 13.77/7.80 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 13.77/7.80 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( set_Pr7458301993993767461et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member1996754912294343701et_nat @ Y @ ( set_Pr364071364088684201et_nat @ Ys ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6804_set__zip__leftD,axiom,
% 13.77/7.80 ! [X: $o,Y: $o,Xs: list_o,Ys: list_o] :
% 13.77/7.80 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ ( set_Product_prod_o_o2 @ ( zip_o_o @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_o @ X @ ( set_o2 @ Xs ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6805_set__zip__leftD,axiom,
% 13.77/7.80 ! [X: uint32,Y: uint32,Xs: list_uint32,Ys: list_uint32] :
% 13.77/7.80 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_uint32 @ X @ ( set_uint322 @ Xs ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6806_set__zip__leftD,axiom,
% 13.77/7.80 ! [X: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 13.77/7.80 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_nat @ X @ ( set_nat2 @ Xs ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6807_set__zip__leftD,axiom,
% 13.77/7.80 ! [X: int,Y: int,Xs: list_int,Ys: list_int] :
% 13.77/7.80 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member_int @ X @ ( set_int2 @ Xs ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6808_set__zip__leftD,axiom,
% 13.77/7.80 ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P9062070895058802706et_nat] :
% 13.77/7.80 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X @ Y ) @ ( set_Pr364071364088684201et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6809_set__zip__leftD,axiom,
% 13.77/7.80 ! [X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat,Xs: list_P7985473006766602707_nat_o,Ys: list_P2321686559999237006et_nat] :
% 13.77/7.80 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X @ Y ) @ ( set_Pr7458301993993767461et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ( member6576561426505652726_nat_o @ X @ ( set_Pr400311997697478754_nat_o @ Xs ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6810_in__set__zipE,axiom,
% 13.77/7.80 ! [X: int,Y: vEBT_VEBT,Xs: list_int,Ys: list_VEBT_VEBT] :
% 13.77/7.80 ( ( member2056185340421749780T_VEBT @ ( produc3329399203697025711T_VEBT @ X @ Y ) @ ( set_Pr8714266321650254504T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6811_in__set__zipE,axiom,
% 13.77/7.80 ! [X: int,Y: nat,Xs: list_int,Ys: list_nat] :
% 13.77/7.80 ( ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X @ Y ) @ ( set_Pr6647972299459129970nt_nat @ ( zip_int_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6812_in__set__zipE,axiom,
% 13.77/7.80 ! [X: int,Y: real,Xs: list_int,Ys: list_real] :
% 13.77/7.80 ( ( member2744130022092475746t_real @ ( produc801115645435158769t_real @ X @ Y ) @ ( set_Pr112895574167722958t_real @ ( zip_int_real @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6813_in__set__zipE,axiom,
% 13.77/7.80 ! [X: int,Y: $o,Xs: list_int,Ys: list_o] :
% 13.77/7.80 ( ( member4489920277610959864_int_o @ ( product_Pair_int_o @ X @ Y ) @ ( set_Pr8694291782656941196_int_o @ ( zip_int_o @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ( member_o @ Y @ ( set_o2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6814_in__set__zipE,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: int,Xs: list_VEBT_VEBT,Ys: list_int] :
% 13.77/7.80 ( ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ X @ Y ) @ ( set_Pr2853735649769556538BT_int @ ( zip_VEBT_VEBT_int @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6815_in__set__zipE,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 13.77/7.80 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6816_in__set__zipE,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 13.77/7.80 ( ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X @ Y ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6817_in__set__zipE,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: real,Xs: list_VEBT_VEBT,Ys: list_real] :
% 13.77/7.80 ( ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X @ Y ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6818_in__set__zipE,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: $o,Xs: list_VEBT_VEBT,Ys: list_o] :
% 13.77/7.80 ( ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X @ Y ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ( member_o @ Y @ ( set_o2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6819_in__set__zipE,axiom,
% 13.77/7.80 ! [X: nat,Y: int,Xs: list_nat,Ys: list_int] :
% 13.77/7.80 ( ( member4262671552274231302at_int @ ( product_Pair_nat_int @ X @ Y ) @ ( set_Pr1470767568048878706at_int @ ( zip_nat_int @ Xs @ Ys ) ) )
% 13.77/7.80 => ~ ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 13.77/7.80 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6820_zip__same,axiom,
% 13.77/7.80 ! [A: set_nat,B: set_nat,Xs: list_set_nat] :
% 13.77/7.80 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ B ) @ ( set_Pr9040384385603167362et_nat @ ( zip_set_nat_set_nat @ Xs @ Xs ) ) )
% 13.77/7.80 = ( ( member_set_nat @ A @ ( set_set_nat2 @ Xs ) )
% 13.77/7.80 & ( A = B ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6821_zip__same,axiom,
% 13.77/7.80 ! [A: vEBT_VEBT,B: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 13.77/7.80 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ A @ B ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Xs ) ) )
% 13.77/7.80 = ( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 & ( A = B ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6822_zip__same,axiom,
% 13.77/7.80 ! [A: real,B: real,Xs: list_real] :
% 13.77/7.80 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ A @ B ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs @ Xs ) ) )
% 13.77/7.80 = ( ( member_real @ A @ ( set_real2 @ Xs ) )
% 13.77/7.80 & ( A = B ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6823_zip__same,axiom,
% 13.77/7.80 ! [A: $o,B: $o,Xs: list_o] :
% 13.77/7.80 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ A @ B ) @ ( set_Product_prod_o_o2 @ ( zip_o_o @ Xs @ Xs ) ) )
% 13.77/7.80 = ( ( member_o @ A @ ( set_o2 @ Xs ) )
% 13.77/7.80 & ( A = B ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6824_zip__same,axiom,
% 13.77/7.80 ! [A: uint32,B: uint32,Xs: list_uint32] :
% 13.77/7.80 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ A @ B ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Xs ) ) )
% 13.77/7.80 = ( ( member_uint32 @ A @ ( set_uint322 @ Xs ) )
% 13.77/7.80 & ( A = B ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6825_zip__same,axiom,
% 13.77/7.80 ! [A: nat,B: nat,Xs: list_nat] :
% 13.77/7.80 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs @ Xs ) ) )
% 13.77/7.80 = ( ( member_nat @ A @ ( set_nat2 @ Xs ) )
% 13.77/7.80 & ( A = B ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6826_zip__same,axiom,
% 13.77/7.80 ! [A: int,B: int,Xs: list_int] :
% 13.77/7.80 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Xs ) ) )
% 13.77/7.80 = ( ( member_int @ A @ ( set_int2 @ Xs ) )
% 13.77/7.80 & ( A = B ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6827_of__nat__0__le__iff,axiom,
% 13.77/7.80 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6828_of__nat__0__le__iff,axiom,
% 13.77/7.80 ! [N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6829_of__nat__0__le__iff,axiom,
% 13.77/7.80 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6830_of__nat__0__le__iff,axiom,
% 13.77/7.80 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6831_of__nat__0__le__iff,axiom,
% 13.77/7.80 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6832_of__nat__less__0__iff,axiom,
% 13.77/7.80 ! [M: nat] :
% 13.77/7.80 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6833_of__nat__less__0__iff,axiom,
% 13.77/7.80 ! [M: nat] :
% 13.77/7.80 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6834_of__nat__less__0__iff,axiom,
% 13.77/7.80 ! [M: nat] :
% 13.77/7.80 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6835_of__nat__less__0__iff,axiom,
% 13.77/7.80 ! [M: nat] :
% 13.77/7.80 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6836_of__nat__less__0__iff,axiom,
% 13.77/7.80 ! [M: nat] :
% 13.77/7.80 ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6837_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_o,I: nat,X: $o,Ys: list_o,Y: $o] :
% 13.77/7.80 ( ( zip_o_o @ ( list_update_o @ Xs @ I @ X ) @ ( list_update_o @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u1537252308907898773od_o_o @ ( zip_o_o @ Xs @ Ys ) @ I @ ( product_Pair_o_o @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6838_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi,Ys: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 13.77/7.80 ( ( zip_VE793581609497812771_VEBTi @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u30558089781959097_VEBTi @ ( zip_VE793581609497812771_VEBTi @ Xs @ Ys ) @ I @ ( produc436343169921013763_VEBTi @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6839_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBTi,I: nat,X: vEBT_VEBTi,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.80 ( ( zip_VE7413257051550508102T_VEBT @ ( list_u6098035379799741383_VEBTi @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u9044509791230035014T_VEBT @ ( zip_VE7413257051550508102T_VEBT @ Xs @ Ys ) @ I @ ( produc7053807326796202854T_VEBT @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6840_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Ys: list_VEBT_VEBTi,Y: vEBT_VEBTi] :
% 13.77/7.80 ( ( zip_VE6444338338598820466_VEBTi @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u6098035379799741383_VEBTi @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u636002643828906794_VEBTi @ ( zip_VE6444338338598820466_VEBTi @ Xs @ Ys ) @ I @ ( produc6084888613844515218_VEBTi @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6841_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.80 ( ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ ( list_u1324408373059187874T_VEBT @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) @ I @ ( produc537772716801021591T_VEBT @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6842_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_uint32,I: nat,X: uint32,Ys: list_uint32,Y: uint32] :
% 13.77/7.80 ( ( zip_uint32_uint32 @ ( list_update_uint32 @ Xs @ I @ X ) @ ( list_update_uint32 @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u2546161786664092711uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) @ I @ ( produc1400373151660368625uint32 @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6843_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_nat,I: nat,X: nat,Ys: list_nat,Y: nat] :
% 13.77/7.80 ( ( zip_nat_nat @ ( list_update_nat @ Xs @ I @ X ) @ ( list_update_nat @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u6180841689913720943at_nat @ ( zip_nat_nat @ Xs @ Ys ) @ I @ ( product_Pair_nat_nat @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6844_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_int,I: nat,X: int,Ys: list_int,Y: int] :
% 13.77/7.80 ( ( zip_int_int @ ( list_update_int @ Xs @ I @ X ) @ ( list_update_int @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u3002344382305578791nt_int @ ( zip_int_int @ Xs @ Ys ) @ I @ ( product_Pair_int_int @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6845_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_P7985473006766602707_nat_o,I: nat,X: produc3658429121746597890et_nat > $o,Ys: list_P9062070895058802706et_nat,Y: produc3658429121746597890et_nat] :
% 13.77/7.80 ( ( zip_Pr7134870689397686104et_nat @ ( list_u6943956310655620667_nat_o @ Xs @ I @ X ) @ ( list_u9060326803697358356et_nat @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u1866171116859985808et_nat @ ( zip_Pr7134870689397686104et_nat @ Xs @ Ys ) @ I @ ( produc5001842942810119800et_nat @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6846_zip__update,axiom,
% 13.77/7.80 ! [Xs: list_P7985473006766602707_nat_o,I: nat,X: produc3658429121746597890et_nat > $o,Ys: list_P2321686559999237006et_nat,Y: produc3925858234332021118et_nat] :
% 13.77/7.80 ( ( zip_Pr8136144321567152340et_nat @ ( list_u6943956310655620667_nat_o @ Xs @ I @ X ) @ ( list_u1866171116859985808et_nat @ Ys @ I @ Y ) )
% 13.77/7.80 = ( list_u1913845194572276492et_nat @ ( zip_Pr8136144321567152340et_nat @ Xs @ Ys ) @ I @ ( produc2245416461498447860et_nat @ X @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6847_one__diff__power__eq_H,axiom,
% 13.77/7.80 ! [X: rat,N: nat] :
% 13.77/7.80 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 13.77/7.80 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 13.77/7.80 @ ( groups2906978787729119204at_rat
% 13.77/7.80 @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 13.77/7.80 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6848_one__diff__power__eq_H,axiom,
% 13.77/7.80 ! [X: complex,N: nat] :
% 13.77/7.80 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 13.77/7.80 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 13.77/7.80 @ ( groups2073611262835488442omplex
% 13.77/7.80 @ ^ [I3: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 13.77/7.80 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6849_one__diff__power__eq_H,axiom,
% 13.77/7.80 ! [X: uint32,N: nat] :
% 13.77/7.80 ( ( minus_minus_uint32 @ one_one_uint32 @ ( power_power_uint32 @ X @ N ) )
% 13.77/7.80 = ( times_times_uint32 @ ( minus_minus_uint32 @ one_one_uint32 @ X )
% 13.77/7.80 @ ( groups833757482993574392uint32
% 13.77/7.80 @ ^ [I3: nat] : ( power_power_uint32 @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 13.77/7.80 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6850_one__diff__power__eq_H,axiom,
% 13.77/7.80 ! [X: int,N: nat] :
% 13.77/7.80 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 13.77/7.80 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 13.77/7.80 @ ( groups3539618377306564664at_int
% 13.77/7.80 @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 13.77/7.80 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6851_one__diff__power__eq_H,axiom,
% 13.77/7.80 ! [X: real,N: nat] :
% 13.77/7.80 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 13.77/7.80 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 13.77/7.80 @ ( groups6591440286371151544t_real
% 13.77/7.80 @ ^ [I3: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 13.77/7.80 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6852_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 13.77/7.80 != zero_zero_rat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6853_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 13.77/7.80 != zero_zero_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6854_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 13.77/7.80 != zero_zero_real ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6855_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 13.77/7.80 != zero_zero_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6856_semiring__char__0__class_Oof__nat__neq__0,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( semiri4939895301339042750nteger @ ( suc @ N ) )
% 13.77/7.80 != zero_z3403309356797280102nteger ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6857_of__nat__less__imp__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 13.77/7.80 => ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6858_of__nat__less__imp__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 13.77/7.80 => ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6859_of__nat__less__imp__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.80 => ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6860_of__nat__less__imp__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.80 => ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6861_of__nat__less__imp__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.80 => ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6862_less__imp__of__nat__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ M @ N )
% 13.77/7.80 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6863_less__imp__of__nat__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ M @ N )
% 13.77/7.80 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6864_less__imp__of__nat__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ M @ N )
% 13.77/7.80 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6865_less__imp__of__nat__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ M @ N )
% 13.77/7.80 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6866_less__imp__of__nat__less,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ M @ N )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6867_of__nat__mono,axiom,
% 13.77/7.80 ! [I: nat,J: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.80 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6868_of__nat__mono,axiom,
% 13.77/7.80 ! [I: nat,J: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6869_of__nat__mono,axiom,
% 13.77/7.80 ! [I: nat,J: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.80 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6870_of__nat__mono,axiom,
% 13.77/7.80 ! [I: nat,J: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.80 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6871_of__nat__mono,axiom,
% 13.77/7.80 ! [I: nat,J: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.80 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6872_Iio__eq__empty__iff,axiom,
% 13.77/7.80 ! [N: $o] :
% 13.77/7.80 ( ( ( set_ord_lessThan_o @ N )
% 13.77/7.80 = bot_bot_set_o )
% 13.77/7.80 = ( N = bot_bot_o ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6873_Iio__eq__empty__iff,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( ( set_ord_lessThan_nat @ N )
% 13.77/7.80 = bot_bot_set_nat )
% 13.77/7.80 = ( N = bot_bot_nat ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6874_lessThan__atLeast0,axiom,
% 13.77/7.80 ( set_ord_lessThan_nat
% 13.77/7.80 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6875_lessThan__strict__subset__iff,axiom,
% 13.77/7.80 ! [M: rat,N: rat] :
% 13.77/7.80 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 13.77/7.80 = ( ord_less_rat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6876_lessThan__strict__subset__iff,axiom,
% 13.77/7.80 ! [M: num,N: num] :
% 13.77/7.80 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 13.77/7.80 = ( ord_less_num @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6877_lessThan__strict__subset__iff,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.80 = ( ord_less_nat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6878_lessThan__strict__subset__iff,axiom,
% 13.77/7.80 ! [M: int,N: int] :
% 13.77/7.80 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 13.77/7.80 = ( ord_less_int @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6879_lessThan__strict__subset__iff,axiom,
% 13.77/7.80 ! [M: real,N: real] :
% 13.77/7.80 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 13.77/7.80 = ( ord_less_real @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6880_lessThan__empty__iff,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( ( set_ord_lessThan_nat @ N )
% 13.77/7.80 = bot_bot_set_nat )
% 13.77/7.80 = ( N = zero_zero_nat ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6881_lessThan__Suc,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 13.77/7.80 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6882_sum__Suc__diff_H,axiom,
% 13.77/7.80 ! [M: nat,N: nat,F: nat > uint32] :
% 13.77/7.80 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.80 => ( ( groups833757482993574392uint32
% 13.77/7.80 @ ^ [I3: nat] : ( minus_minus_uint32 @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.80 = ( minus_minus_uint32 @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6883_sum__Suc__diff_H,axiom,
% 13.77/7.80 ! [M: nat,N: nat,F: nat > int] :
% 13.77/7.80 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.80 => ( ( groups3539618377306564664at_int
% 13.77/7.80 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.80 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6884_sum__Suc__diff_H,axiom,
% 13.77/7.80 ! [M: nat,N: nat,F: nat > real] :
% 13.77/7.80 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.80 => ( ( groups6591440286371151544t_real
% 13.77/7.80 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 13.77/7.80 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6885_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_complex,F: complex > real,K: real] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_complex )
% 13.77/7.80 => ( ( lattic4275903605611617917x_real
% 13.77/7.80 @ ( image_complex_real
% 13.77/7.80 @ ^ [X4: complex] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_complex_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6886_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,F: code_integer > real,K: real] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.80 => ( ( lattic4275903605611617917x_real
% 13.77/7.80 @ ( image_7738145705984076560r_real
% 13.77/7.80 @ ^ [X4: code_integer] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_7738145705984076560r_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6887_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_complex,F: complex > rat,K: rat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_complex )
% 13.77/7.80 => ( ( lattic7630753665789217321ax_rat
% 13.77/7.80 @ ( image_complex_rat
% 13.77/7.80 @ ^ [X4: complex] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_rat @ ( lattic7630753665789217321ax_rat @ ( image_complex_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6888_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,F: code_integer > rat,K: rat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.80 => ( ( lattic7630753665789217321ax_rat
% 13.77/7.80 @ ( image_315895873841295420er_rat
% 13.77/7.80 @ ^ [X4: code_integer] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_rat @ ( lattic7630753665789217321ax_rat @ ( image_315895873841295420er_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6889_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_complex,F: complex > int,K: int] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_complex )
% 13.77/7.80 => ( ( lattic8263393255366662781ax_int
% 13.77/7.80 @ ( image_complex_int
% 13.77/7.80 @ ^ [X4: complex] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_int @ ( lattic8263393255366662781ax_int @ ( image_complex_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6890_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,F: code_integer > int,K: int] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.80 => ( ( lattic8263393255366662781ax_int
% 13.77/7.80 @ ( image_948535463418740880er_int
% 13.77/7.80 @ ^ [X4: code_integer] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_int @ ( lattic8263393255366662781ax_int @ ( image_948535463418740880er_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6891_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_nat,F: nat > real,K: real] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_nat )
% 13.77/7.80 => ( ( lattic4275903605611617917x_real
% 13.77/7.80 @ ( image_nat_real
% 13.77/7.80 @ ^ [X4: nat] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_nat_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6892_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_nat,F: nat > rat,K: rat] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_nat )
% 13.77/7.80 => ( ( lattic7630753665789217321ax_rat
% 13.77/7.80 @ ( image_nat_rat
% 13.77/7.80 @ ^ [X4: nat] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_rat @ ( lattic7630753665789217321ax_rat @ ( image_nat_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6893_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_nat,F: nat > int,K: int] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_nat )
% 13.77/7.80 => ( ( lattic8263393255366662781ax_int
% 13.77/7.80 @ ( image_nat_int
% 13.77/7.80 @ ^ [X4: nat] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_int @ ( lattic8263393255366662781ax_int @ ( image_nat_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6894_Max__add__commute,axiom,
% 13.77/7.80 ! [S3: set_int,F: int > real,K: real] :
% 13.77/7.80 ( ( finite_finite_int @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_int )
% 13.77/7.80 => ( ( lattic4275903605611617917x_real
% 13.77/7.80 @ ( image_int_real
% 13.77/7.80 @ ^ [X4: int] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic4275903605611617917x_real @ ( image_int_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6895_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_complex,F: complex > real,K: real] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_complex )
% 13.77/7.80 => ( ( lattic3629708407755379051n_real
% 13.77/7.80 @ ( image_complex_real
% 13.77/7.80 @ ^ [X4: complex] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_complex_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6896_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,F: code_integer > real,K: real] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.80 => ( ( lattic3629708407755379051n_real
% 13.77/7.80 @ ( image_7738145705984076560r_real
% 13.77/7.80 @ ^ [X4: code_integer] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_7738145705984076560r_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6897_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_complex,F: complex > rat,K: rat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_complex )
% 13.77/7.80 => ( ( lattic8086005427650270231in_rat
% 13.77/7.80 @ ( image_complex_rat
% 13.77/7.80 @ ^ [X4: complex] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_rat @ ( lattic8086005427650270231in_rat @ ( image_complex_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6898_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,F: code_integer > rat,K: rat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.80 => ( ( lattic8086005427650270231in_rat
% 13.77/7.80 @ ( image_315895873841295420er_rat
% 13.77/7.80 @ ^ [X4: code_integer] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_rat @ ( lattic8086005427650270231in_rat @ ( image_315895873841295420er_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6899_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_complex,F: complex > int,K: int] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_complex )
% 13.77/7.80 => ( ( lattic8718645017227715691in_int
% 13.77/7.80 @ ( image_complex_int
% 13.77/7.80 @ ^ [X4: complex] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_int @ ( lattic8718645017227715691in_int @ ( image_complex_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6900_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,F: code_integer > int,K: int] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bo3990330152332043303nteger )
% 13.77/7.80 => ( ( lattic8718645017227715691in_int
% 13.77/7.80 @ ( image_948535463418740880er_int
% 13.77/7.80 @ ^ [X4: code_integer] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_int @ ( lattic8718645017227715691in_int @ ( image_948535463418740880er_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6901_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_nat,F: nat > real,K: real] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_nat )
% 13.77/7.80 => ( ( lattic3629708407755379051n_real
% 13.77/7.80 @ ( image_nat_real
% 13.77/7.80 @ ^ [X4: nat] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_nat_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6902_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_nat,F: nat > rat,K: rat] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_nat )
% 13.77/7.80 => ( ( lattic8086005427650270231in_rat
% 13.77/7.80 @ ( image_nat_rat
% 13.77/7.80 @ ^ [X4: nat] : ( plus_plus_rat @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_rat @ ( lattic8086005427650270231in_rat @ ( image_nat_rat @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6903_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_nat,F: nat > int,K: int] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_nat )
% 13.77/7.80 => ( ( lattic8718645017227715691in_int
% 13.77/7.80 @ ( image_nat_int
% 13.77/7.80 @ ^ [X4: nat] : ( plus_plus_int @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_int @ ( lattic8718645017227715691in_int @ ( image_nat_int @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6904_Min__add__commute,axiom,
% 13.77/7.80 ! [S3: set_int,F: int > real,K: real] :
% 13.77/7.80 ( ( finite_finite_int @ S3 )
% 13.77/7.80 => ( ( S3 != bot_bot_set_int )
% 13.77/7.80 => ( ( lattic3629708407755379051n_real
% 13.77/7.80 @ ( image_int_real
% 13.77/7.80 @ ^ [X4: int] : ( plus_plus_real @ ( F @ X4 ) @ K )
% 13.77/7.80 @ S3 ) )
% 13.77/7.80 = ( plus_plus_real @ ( lattic3629708407755379051n_real @ ( image_int_real @ F @ S3 ) ) @ K ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6905_sum_OatLeastLessThan__rev,axiom,
% 13.77/7.80 ! [G: nat > nat,N: nat,M: nat] :
% 13.77/7.80 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 13.77/7.80 = ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6906_sum_OatLeastLessThan__rev,axiom,
% 13.77/7.80 ! [G: nat > real,N: nat,M: nat] :
% 13.77/7.80 ( ( groups6591440286371151544t_real @ G @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 13.77/7.80 = ( groups6591440286371151544t_real
% 13.77/7.80 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6907_of__nat__max,axiom,
% 13.77/7.80 ! [X: nat,Y: nat] :
% 13.77/7.80 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 13.77/7.80 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6908_of__nat__max,axiom,
% 13.77/7.80 ! [X: nat,Y: nat] :
% 13.77/7.80 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 13.77/7.80 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6909_of__nat__max,axiom,
% 13.77/7.80 ! [X: nat,Y: nat] :
% 13.77/7.80 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 13.77/7.80 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6910_of__nat__max,axiom,
% 13.77/7.80 ! [X: nat,Y: nat] :
% 13.77/7.80 ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 13.77/7.80 = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6911_finite__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_complex,N: nat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.80 => ( finite8712137658972009173omplex
% 13.77/7.80 @ ( collect_list_complex
% 13.77/7.80 @ ^ [Xs2: list_complex] :
% 13.77/7.80 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 13.77/7.80 = N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6912_finite__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_Code_integer,N: nat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.80 => ( finite1283093830868386564nteger
% 13.77/7.80 @ ( collec3483841146883906114nteger
% 13.77/7.80 @ ^ [Xs2: list_Code_integer] :
% 13.77/7.80 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 13.77/7.80 = N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6913_finite__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,N: nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.80 => ( finite3004134309566078307T_VEBT
% 13.77/7.80 @ ( collec5608196760682091941T_VEBT
% 13.77/7.80 @ ^ [Xs2: list_VEBT_VEBT] :
% 13.77/7.80 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 13.77/7.80 = N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6914_finite__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_real,N: nat] :
% 13.77/7.80 ( ( finite_finite_real @ A4 )
% 13.77/7.80 => ( finite306553202115118035t_real
% 13.77/7.80 @ ( collect_list_real
% 13.77/7.80 @ ^ [Xs2: list_real] :
% 13.77/7.80 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_real @ Xs2 )
% 13.77/7.80 = N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6915_finite__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_o,N: nat] :
% 13.77/7.80 ( ( finite_finite_o @ A4 )
% 13.77/7.80 => ( finite_finite_list_o
% 13.77/7.80 @ ( collect_list_o
% 13.77/7.80 @ ^ [Xs2: list_o] :
% 13.77/7.80 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_o @ Xs2 )
% 13.77/7.80 = N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6916_finite__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_nat,N: nat] :
% 13.77/7.80 ( ( finite_finite_nat @ A4 )
% 13.77/7.80 => ( finite8100373058378681591st_nat
% 13.77/7.80 @ ( collect_list_nat
% 13.77/7.80 @ ^ [Xs2: list_nat] :
% 13.77/7.80 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_nat @ Xs2 )
% 13.77/7.80 = N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6917_finite__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_int,N: nat] :
% 13.77/7.80 ( ( finite_finite_int @ A4 )
% 13.77/7.80 => ( finite3922522038869484883st_int
% 13.77/7.80 @ ( collect_list_int
% 13.77/7.80 @ ^ [Xs2: list_int] :
% 13.77/7.80 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_int @ Xs2 )
% 13.77/7.80 = N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6918_distinct__finite__subset,axiom,
% 13.77/7.80 ! [X: set_VEBT_VEBT] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ X )
% 13.77/7.80 => ( finite3004134309566078307T_VEBT
% 13.77/7.80 @ ( collec5608196760682091941T_VEBT
% 13.77/7.80 @ ^ [Ys3: list_VEBT_VEBT] :
% 13.77/7.80 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Ys3 ) @ X )
% 13.77/7.80 & ( distinct_VEBT_VEBT @ Ys3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6919_distinct__finite__subset,axiom,
% 13.77/7.80 ! [X: set_real] :
% 13.77/7.80 ( ( finite_finite_real @ X )
% 13.77/7.80 => ( finite306553202115118035t_real
% 13.77/7.80 @ ( collect_list_real
% 13.77/7.80 @ ^ [Ys3: list_real] :
% 13.77/7.80 ( ( ord_less_eq_set_real @ ( set_real2 @ Ys3 ) @ X )
% 13.77/7.80 & ( distinct_real @ Ys3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6920_distinct__finite__subset,axiom,
% 13.77/7.80 ! [X: set_o] :
% 13.77/7.80 ( ( finite_finite_o @ X )
% 13.77/7.80 => ( finite_finite_list_o
% 13.77/7.80 @ ( collect_list_o
% 13.77/7.80 @ ^ [Ys3: list_o] :
% 13.77/7.80 ( ( ord_less_eq_set_o @ ( set_o2 @ Ys3 ) @ X )
% 13.77/7.80 & ( distinct_o @ Ys3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6921_distinct__finite__subset,axiom,
% 13.77/7.80 ! [X: set_nat] :
% 13.77/7.80 ( ( finite_finite_nat @ X )
% 13.77/7.80 => ( finite8100373058378681591st_nat
% 13.77/7.80 @ ( collect_list_nat
% 13.77/7.80 @ ^ [Ys3: list_nat] :
% 13.77/7.80 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Ys3 ) @ X )
% 13.77/7.80 & ( distinct_nat @ Ys3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6922_distinct__finite__subset,axiom,
% 13.77/7.80 ! [X: set_complex] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ X )
% 13.77/7.80 => ( finite8712137658972009173omplex
% 13.77/7.80 @ ( collect_list_complex
% 13.77/7.80 @ ^ [Ys3: list_complex] :
% 13.77/7.80 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Ys3 ) @ X )
% 13.77/7.80 & ( distinct_complex @ Ys3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6923_distinct__finite__subset,axiom,
% 13.77/7.80 ! [X: set_Code_integer] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ X )
% 13.77/7.80 => ( finite1283093830868386564nteger
% 13.77/7.80 @ ( collec3483841146883906114nteger
% 13.77/7.80 @ ^ [Ys3: list_Code_integer] :
% 13.77/7.80 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Ys3 ) @ X )
% 13.77/7.80 & ( distin1543349897113766820nteger @ Ys3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6924_distinct__finite__subset,axiom,
% 13.77/7.80 ! [X: set_int] :
% 13.77/7.80 ( ( finite_finite_int @ X )
% 13.77/7.80 => ( finite3922522038869484883st_int
% 13.77/7.80 @ ( collect_list_int
% 13.77/7.80 @ ^ [Ys3: list_int] :
% 13.77/7.80 ( ( ord_less_eq_set_int @ ( set_int2 @ Ys3 ) @ X )
% 13.77/7.80 & ( distinct_int @ Ys3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6925_finite__nat__bounded,axiom,
% 13.77/7.80 ! [S3: set_nat] :
% 13.77/7.80 ( ( finite_finite_nat @ S3 )
% 13.77/7.80 => ? [K2: nat] : ( ord_less_eq_set_nat @ S3 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6926_finite__nat__iff__bounded,axiom,
% 13.77/7.80 ( finite_finite_nat
% 13.77/7.80 = ( ^ [S6: set_nat] :
% 13.77/7.80 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6927_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C2: vEBT_VEBT > real] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.80 => ( ( groups2240296850493347238T_real
% 13.77/7.80 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.80 => ( ( groups2240296850493347238T_real
% 13.77/7.80 @ ^ [K3: vEBT_VEBT] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups2240296850493347238T_real @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6928_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_real,A: real,B: real > real,C2: real > real] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( ( member_real @ A @ S3 )
% 13.77/7.80 => ( ( groups8097168146408367636l_real
% 13.77/7.80 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_real @ A @ S3 )
% 13.77/7.80 => ( ( groups8097168146408367636l_real
% 13.77/7.80 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups8097168146408367636l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6929_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_complex,A: complex,B: complex > real,C2: complex > real] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( ( member_complex @ A @ S3 )
% 13.77/7.80 => ( ( groups5808333547571424918x_real
% 13.77/7.80 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_complex @ A @ S3 )
% 13.77/7.80 => ( ( groups5808333547571424918x_real
% 13.77/7.80 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups5808333547571424918x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6930_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,A: code_integer,B: code_integer > real,C2: code_integer > real] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( ( member_Code_integer @ A @ S3 )
% 13.77/7.80 => ( ( groups1270011288395367621r_real
% 13.77/7.80 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_real @ ( B @ A ) @ ( groups1270011288395367621r_real @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_Code_integer @ A @ S3 )
% 13.77/7.80 => ( ( groups1270011288395367621r_real
% 13.77/7.80 @ ^ [K3: code_integer] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups1270011288395367621r_real @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6931_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C2: vEBT_VEBT > rat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.80 => ( ( groups136491112297645522BT_rat
% 13.77/7.80 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.80 => ( ( groups136491112297645522BT_rat
% 13.77/7.80 @ ^ [K3: vEBT_VEBT] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups136491112297645522BT_rat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6932_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_real,A: real,B: real > rat,C2: real > rat] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( ( member_real @ A @ S3 )
% 13.77/7.80 => ( ( groups1300246762558778688al_rat
% 13.77/7.80 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_real @ A @ S3 )
% 13.77/7.80 => ( ( groups1300246762558778688al_rat
% 13.77/7.80 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups1300246762558778688al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6933_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_complex,A: complex,B: complex > rat,C2: complex > rat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ S3 )
% 13.77/7.80 => ( ( ( member_complex @ A @ S3 )
% 13.77/7.80 => ( ( groups5058264527183730370ex_rat
% 13.77/7.80 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_complex @ A @ S3 )
% 13.77/7.80 => ( ( groups5058264527183730370ex_rat
% 13.77/7.80 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups5058264527183730370ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6934_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_Code_integer,A: code_integer,B: code_integer > rat,C2: code_integer > rat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ S3 )
% 13.77/7.80 => ( ( ( member_Code_integer @ A @ S3 )
% 13.77/7.80 => ( ( groups6602215022474089585er_rat
% 13.77/7.80 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_rat @ ( B @ A ) @ ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_Code_integer @ A @ S3 )
% 13.77/7.80 => ( ( groups6602215022474089585er_rat
% 13.77/7.80 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups6602215022474089585er_rat @ C2 @ ( minus_2355218937544613996nteger @ S3 @ ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6935_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C2: vEBT_VEBT > nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ S3 )
% 13.77/7.80 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.80 => ( ( groups771621172384141258BT_nat
% 13.77/7.80 @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 13.77/7.80 => ( ( groups771621172384141258BT_nat
% 13.77/7.80 @ ^ [K3: vEBT_VEBT] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups771621172384141258BT_nat @ C2 @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6936_sum_Odelta__remove,axiom,
% 13.77/7.80 ! [S3: set_real,A: real,B: real > nat,C2: real > nat] :
% 13.77/7.80 ( ( finite_finite_real @ S3 )
% 13.77/7.80 => ( ( ( member_real @ A @ S3 )
% 13.77/7.80 => ( ( groups1935376822645274424al_nat
% 13.77/7.80 @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( plus_plus_nat @ ( B @ A ) @ ( groups1935376822645274424al_nat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 13.77/7.80 & ( ~ ( member_real @ A @ S3 )
% 13.77/7.80 => ( ( groups1935376822645274424al_nat
% 13.77/7.80 @ ^ [K3: real] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 13.77/7.80 @ S3 )
% 13.77/7.80 = ( groups1935376822645274424al_nat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6937_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_literal,N: nat] :
% 13.77/7.80 ( ( finite5847741373460823677iteral @ A4 )
% 13.77/7.80 => ( ( finite7554361855635516162iteral
% 13.77/7.80 @ ( collect_list_literal
% 13.77/7.80 @ ^ [Xs2: list_literal] :
% 13.77/7.80 ( ( ord_le7307670543136651348iteral @ ( set_literal2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s2501651207091587910iteral @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_literal @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6938_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_list_nat,N: nat] :
% 13.77/7.80 ( ( finite8100373058378681591st_nat @ A4 )
% 13.77/7.80 => ( ( finite7325466520557071688st_nat
% 13.77/7.80 @ ( collec5989764272469232197st_nat
% 13.77/7.80 @ ^ [Xs2: list_list_nat] :
% 13.77/7.80 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s3023201423986296836st_nat @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_list_nat @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6939_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_set_nat,N: nat] :
% 13.77/7.80 ( ( finite1152437895449049373et_nat @ A4 )
% 13.77/7.80 => ( ( finite5631907774883551598et_nat
% 13.77/7.80 @ ( collect_list_set_nat
% 13.77/7.80 @ ^ [Xs2: list_set_nat] :
% 13.77/7.80 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s3254054031482475050et_nat @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_set_nat @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6940_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_complex,N: nat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.80 => ( ( finite5120063068150530198omplex
% 13.77/7.80 @ ( collect_list_complex
% 13.77/7.80 @ ^ [Xs2: list_complex] :
% 13.77/7.80 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_complex @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6941_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_Code_integer,N: nat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.80 => ( ( finite5823187341872139973nteger
% 13.77/7.80 @ ( collec3483841146883906114nteger
% 13.77/7.80 @ ^ [Xs2: list_Code_integer] :
% 13.77/7.80 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite4902975817058060853nteger @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6942_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,N: nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.80 => ( ( finite5915292604075114978T_VEBT
% 13.77/7.80 @ ( collec5608196760682091941T_VEBT
% 13.77/7.80 @ ^ [Xs2: list_VEBT_VEBT] :
% 13.77/7.80 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6943_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_real,N: nat] :
% 13.77/7.80 ( ( finite_finite_real @ A4 )
% 13.77/7.80 => ( ( finite4141703471298347796t_real
% 13.77/7.80 @ ( collect_list_real
% 13.77/7.80 @ ^ [Xs2: list_real] :
% 13.77/7.80 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_real @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_real @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6944_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_o,N: nat] :
% 13.77/7.80 ( ( finite_finite_o @ A4 )
% 13.77/7.80 => ( ( finite_card_list_o
% 13.77/7.80 @ ( collect_list_o
% 13.77/7.80 @ ^ [Xs2: list_o] :
% 13.77/7.80 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_o @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_o @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6945_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_nat,N: nat] :
% 13.77/7.80 ( ( finite_finite_nat @ A4 )
% 13.77/7.80 => ( ( finite_card_list_nat
% 13.77/7.80 @ ( collect_list_nat
% 13.77/7.80 @ ^ [Xs2: list_nat] :
% 13.77/7.80 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_nat @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_nat @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6946_card__lists__length__eq,axiom,
% 13.77/7.80 ! [A4: set_int,N: nat] :
% 13.77/7.80 ( ( finite_finite_int @ A4 )
% 13.77/7.80 => ( ( finite_card_list_int
% 13.77/7.80 @ ( collect_list_int
% 13.77/7.80 @ ^ [Xs2: list_int] :
% 13.77/7.80 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ( size_size_list_int @ Xs2 )
% 13.77/7.80 = N ) ) ) )
% 13.77/7.80 = ( power_power_nat @ ( finite_card_int @ A4 ) @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6947_finite__lists__length__le,axiom,
% 13.77/7.80 ! [A4: set_complex,N: nat] :
% 13.77/7.80 ( ( finite3207457112153483333omplex @ A4 )
% 13.77/7.80 => ( finite8712137658972009173omplex
% 13.77/7.80 @ ( collect_list_complex
% 13.77/7.80 @ ^ [Xs2: list_complex] :
% 13.77/7.80 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6948_finite__lists__length__le,axiom,
% 13.77/7.80 ! [A4: set_Code_integer,N: nat] :
% 13.77/7.80 ( ( finite6017078050557962740nteger @ A4 )
% 13.77/7.80 => ( finite1283093830868386564nteger
% 13.77/7.80 @ ( collec3483841146883906114nteger
% 13.77/7.80 @ ^ [Xs2: list_Code_integer] :
% 13.77/7.80 ( ( ord_le7084787975880047091nteger @ ( set_Code_integer2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ord_less_eq_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6949_finite__lists__length__le,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,N: nat] :
% 13.77/7.80 ( ( finite5795047828879050333T_VEBT @ A4 )
% 13.77/7.80 => ( finite3004134309566078307T_VEBT
% 13.77/7.80 @ ( collec5608196760682091941T_VEBT
% 13.77/7.80 @ ^ [Xs2: list_VEBT_VEBT] :
% 13.77/7.80 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6950_finite__lists__length__le,axiom,
% 13.77/7.80 ! [A4: set_real,N: nat] :
% 13.77/7.80 ( ( finite_finite_real @ A4 )
% 13.77/7.80 => ( finite306553202115118035t_real
% 13.77/7.80 @ ( collect_list_real
% 13.77/7.80 @ ^ [Xs2: list_real] :
% 13.77/7.80 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ord_less_eq_nat @ ( size_size_list_real @ Xs2 ) @ N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6951_finite__lists__length__le,axiom,
% 13.77/7.80 ! [A4: set_o,N: nat] :
% 13.77/7.80 ( ( finite_finite_o @ A4 )
% 13.77/7.80 => ( finite_finite_list_o
% 13.77/7.80 @ ( collect_list_o
% 13.77/7.80 @ ^ [Xs2: list_o] :
% 13.77/7.80 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6952_finite__lists__length__le,axiom,
% 13.77/7.80 ! [A4: set_nat,N: nat] :
% 13.77/7.80 ( ( finite_finite_nat @ A4 )
% 13.77/7.80 => ( finite8100373058378681591st_nat
% 13.77/7.80 @ ( collect_list_nat
% 13.77/7.80 @ ^ [Xs2: list_nat] :
% 13.77/7.80 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6953_finite__lists__length__le,axiom,
% 13.77/7.80 ! [A4: set_int,N: nat] :
% 13.77/7.80 ( ( finite_finite_int @ A4 )
% 13.77/7.80 => ( finite3922522038869484883st_int
% 13.77/7.80 @ ( collect_list_int
% 13.77/7.80 @ ^ [Xs2: list_int] :
% 13.77/7.80 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 )
% 13.77/7.80 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6954_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_uint32,Ys: list_uint32,Y: uint32] :
% 13.77/7.80 ( ( ( size_s4844771616002835472uint32 @ Xs )
% 13.77/7.80 = ( size_s4844771616002835472uint32 @ Ys ) )
% 13.77/7.80 => ( ( member_uint32 @ Y @ ( set_uint322 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: uint32] :
% 13.77/7.80 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6955_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_int,Y: int] :
% 13.77/7.80 ( ( ( size_size_list_int @ Xs )
% 13.77/7.80 = ( size_size_list_int @ Ys ) )
% 13.77/7.80 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: int] :
% 13.77/7.80 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6956_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_int,Y: int] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_size_list_int @ Ys ) )
% 13.77/7.80 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.80 ~ ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ X3 @ Y ) @ ( set_Pr2853735649769556538BT_int @ ( zip_VEBT_VEBT_int @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6957_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.80 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.80 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X3 @ Y ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6958_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_real,Y: real] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_size_list_real @ Ys ) )
% 13.77/7.80 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.80 ~ ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X3 @ Y ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6959_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_o,Y: $o] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_size_list_o @ Ys ) )
% 13.77/7.80 => ( ( member_o @ Y @ ( set_o2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.80 ~ ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X3 @ Y ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6960_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_nat,Y: nat] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_size_list_nat @ Ys ) )
% 13.77/7.80 => ( ( member_nat @ Y @ ( set_nat2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: vEBT_VEBT] :
% 13.77/7.80 ~ ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X3 @ Y ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6961_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_real,Ys: list_int,Y: int] :
% 13.77/7.80 ( ( ( size_size_list_real @ Xs )
% 13.77/7.80 = ( size_size_list_int @ Ys ) )
% 13.77/7.80 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: real] :
% 13.77/7.80 ~ ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X3 @ Y ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6962_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_real,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.80 ( ( ( size_size_list_real @ Xs )
% 13.77/7.80 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.80 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: real] :
% 13.77/7.80 ~ ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X3 @ Y ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6963_in__set__impl__in__set__zip2,axiom,
% 13.77/7.80 ! [Xs: list_real,Ys: list_real,Y: real] :
% 13.77/7.80 ( ( ( size_size_list_real @ Xs )
% 13.77/7.80 = ( size_size_list_real @ Ys ) )
% 13.77/7.80 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 13.77/7.80 => ~ ! [X3: real] :
% 13.77/7.80 ~ ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X3 @ Y ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6964_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_uint32,Ys: list_uint32,X: uint32] :
% 13.77/7.80 ( ( ( size_s4844771616002835472uint32 @ Xs )
% 13.77/7.80 = ( size_s4844771616002835472uint32 @ Ys ) )
% 13.77/7.80 => ( ( member_uint32 @ X @ ( set_uint322 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: uint32] :
% 13.77/7.80 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y3 ) @ ( set_Pr2418681094996576974uint32 @ ( zip_uint32_uint32 @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6965_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_int,X: int] :
% 13.77/7.80 ( ( ( size_size_list_int @ Xs )
% 13.77/7.80 = ( size_size_list_int @ Ys ) )
% 13.77/7.80 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: int] :
% 13.77/7.80 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y3 ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6966_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_VEBT_VEBT,X: int] :
% 13.77/7.80 ( ( ( size_size_list_int @ Xs )
% 13.77/7.80 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.80 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: vEBT_VEBT] :
% 13.77/7.80 ~ ( member2056185340421749780T_VEBT @ ( produc3329399203697025711T_VEBT @ X @ Y3 ) @ ( set_Pr8714266321650254504T_VEBT @ ( zip_int_VEBT_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6967_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_real,X: int] :
% 13.77/7.80 ( ( ( size_size_list_int @ Xs )
% 13.77/7.80 = ( size_size_list_real @ Ys ) )
% 13.77/7.80 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: real] :
% 13.77/7.80 ~ ( member2744130022092475746t_real @ ( produc801115645435158769t_real @ X @ Y3 ) @ ( set_Pr112895574167722958t_real @ ( zip_int_real @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6968_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_o,X: int] :
% 13.77/7.80 ( ( ( size_size_list_int @ Xs )
% 13.77/7.80 = ( size_size_list_o @ Ys ) )
% 13.77/7.80 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: $o] :
% 13.77/7.80 ~ ( member4489920277610959864_int_o @ ( product_Pair_int_o @ X @ Y3 ) @ ( set_Pr8694291782656941196_int_o @ ( zip_int_o @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6969_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_nat,X: int] :
% 13.77/7.80 ( ( ( size_size_list_int @ Xs )
% 13.77/7.80 = ( size_size_list_nat @ Ys ) )
% 13.77/7.80 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: nat] :
% 13.77/7.80 ~ ( member216504246829706758nt_nat @ ( product_Pair_int_nat @ X @ Y3 ) @ ( set_Pr6647972299459129970nt_nat @ ( zip_int_nat @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6970_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 13.77/7.80 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: vEBT_VEBT] :
% 13.77/7.80 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y3 ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6971_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_real,X: vEBT_VEBT] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_size_list_real @ Ys ) )
% 13.77/7.80 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: real] :
% 13.77/7.80 ~ ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X @ Y3 ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6972_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_o,X: vEBT_VEBT] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_size_list_o @ Ys ) )
% 13.77/7.80 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: $o] :
% 13.77/7.80 ~ ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X @ Y3 ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6973_in__set__impl__in__set__zip1,axiom,
% 13.77/7.80 ! [Xs: list_VEBT_VEBT,Ys: list_nat,X: vEBT_VEBT] :
% 13.77/7.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 13.77/7.80 = ( size_size_list_nat @ Ys ) )
% 13.77/7.80 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 13.77/7.80 => ~ ! [Y3: nat] :
% 13.77/7.80 ~ ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X @ Y3 ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs @ Ys ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6974_ex__less__of__nat__mult,axiom,
% 13.77/7.80 ! [X: rat,Y: rat] :
% 13.77/7.80 ( ( ord_less_rat @ zero_zero_rat @ X )
% 13.77/7.80 => ? [N2: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ X ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6975_ex__less__of__nat__mult,axiom,
% 13.77/7.80 ! [X: real,Y: real] :
% 13.77/7.80 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.80 => ? [N2: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6976_of__nat__gt__0,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( ( semiri2565882477558803405uint32 @ K )
% 13.77/7.80 != zero_zero_uint32 )
% 13.77/7.80 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6977_of__nat__gt__0,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( ( semiri681578069525770553at_rat @ K )
% 13.77/7.80 != zero_zero_rat )
% 13.77/7.80 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6978_of__nat__gt__0,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( ( semiri1316708129612266289at_nat @ K )
% 13.77/7.80 != zero_zero_nat )
% 13.77/7.80 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6979_of__nat__gt__0,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( ( semiri5074537144036343181t_real @ K )
% 13.77/7.80 != zero_zero_real )
% 13.77/7.80 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6980_of__nat__gt__0,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( ( semiri1314217659103216013at_int @ K )
% 13.77/7.80 != zero_zero_int )
% 13.77/7.80 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6981_of__nat__gt__0,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( ( semiri4939895301339042750nteger @ K )
% 13.77/7.80 != zero_z3403309356797280102nteger )
% 13.77/7.80 => ( ord_less_nat @ zero_zero_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6982_of__nat__diff,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.80 => ( ( semiri2565882477558803405uint32 @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.80 = ( minus_minus_uint32 @ ( semiri2565882477558803405uint32 @ M ) @ ( semiri2565882477558803405uint32 @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6983_of__nat__diff,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.80 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.80 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6984_of__nat__diff,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.80 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.80 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6985_of__nat__diff,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.80 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.80 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6986_of__nat__diff,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.80 => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.80 = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6987_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_nat,Xy: product_prod_int_nat,Xys: list_P8198026277950538467nt_nat] :
% 13.77/7.80 ( ( ( zip_int_nat @ Xs @ Ys )
% 13.77/7.80 = ( cons_P7512249878480867347nt_nat @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: int,Xs5: list_int] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_int @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: nat,Ys4: list_nat] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_nat @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_int_nat @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_int_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6988_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_o,Xy: product_prod_int_o,Xys: list_P5087981734274514673_int_o] :
% 13.77/7.80 ( ( ( zip_int_o @ Xs @ Ys )
% 13.77/7.80 = ( cons_P7321330006258091179_int_o @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: int,Xs5: list_int] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_int @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: $o,Ys4: list_o] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_o @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_int_o @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_int_o @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6989_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_nat,Ys: list_int,Xy: product_prod_nat_int,Xys: list_P3521021558325789923at_int] :
% 13.77/7.80 ( ( ( zip_nat_int @ Xs @ Ys )
% 13.77/7.80 = ( cons_P2335045147070616083at_int @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: nat,Xs5: list_nat] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_nat @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: int,Ys4: list_int] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_int @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_nat_int @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_nat_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6990_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_nat,Ys: list_o,Xy: product_prod_nat_o,Xys: list_P7333126701944960589_nat_o] :
% 13.77/7.80 ( ( ( zip_nat_o @ Xs @ Ys )
% 13.77/7.80 = ( cons_P9142372351690779143_nat_o @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: nat,Xs5: list_nat] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_nat @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: $o,Ys4: list_o] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_o @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_nat_o @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_nat_o @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6991_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_o,Ys: list_int,Xy: product_prod_o_int,Xys: list_P3795440434834930179_o_int] :
% 13.77/7.80 ( ( ( zip_o_int @ Xs @ Ys )
% 13.77/7.80 = ( cons_P1455986808126089405_o_int @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: $o,Xs5: list_o] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_o @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: int,Ys4: list_int] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_int @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_o_int @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_o_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6992_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_o,Ys: list_nat,Xy: product_prod_o_nat,Xys: list_P6285523579766656935_o_nat] :
% 13.77/7.80 ( ( ( zip_o_nat @ Xs @ Ys )
% 13.77/7.80 = ( cons_P5633837827635286113_o_nat @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: $o,Xs5: list_o] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_o @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: nat,Ys4: list_nat] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_nat @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_o_nat @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_o_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6993_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_o,Ys: list_o,Xy: product_prod_o_o,Xys: list_P4002435161011370285od_o_o] :
% 13.77/7.80 ( ( ( zip_o_o @ Xs @ Ys )
% 13.77/7.80 = ( cons_P8766293264717362397od_o_o @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: $o,Xs5: list_o] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_o @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: $o,Ys4: list_o] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_o @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_o_o @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_o_o @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6994_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_uint32,Ys: list_uint32,Xy: produc827990862158126777uint32,Xys: list_P3069071885182933823uint32] :
% 13.77/7.80 ( ( ( zip_uint32_uint32 @ Xs @ Ys )
% 13.77/7.80 = ( cons_P3149448846263281007uint32 @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: uint32,Xs5: list_uint32] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_uint32 @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: uint32,Ys4: list_uint32] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_uint32 @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( produc1400373151660368625uint32 @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_uint32_uint32 @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6995_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_nat,Ys: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 13.77/7.80 ( ( ( zip_nat_nat @ Xs @ Ys )
% 13.77/7.80 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: nat,Xs5: list_nat] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_nat @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: nat,Ys4: list_nat] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_nat @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_nat_nat @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6996_zip__eq__ConsE,axiom,
% 13.77/7.80 ! [Xs: list_int,Ys: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 13.77/7.80 ( ( ( zip_int_int @ Xs @ Ys )
% 13.77/7.80 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 13.77/7.80 => ~ ! [X3: int,Xs5: list_int] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_int @ X3 @ Xs5 ) )
% 13.77/7.80 => ! [Y3: int,Ys4: list_int] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_int @ Y3 @ Ys4 ) )
% 13.77/7.80 => ( ( Xy
% 13.77/7.80 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 13.77/7.80 => ( Xys
% 13.77/7.80 != ( zip_int_int @ Xs5 @ Ys4 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6997_lenlex__irreflexive,axiom,
% 13.77/7.80 ! [R: set_Pr1773385645901665561uint32,Xs: list_uint32] :
% 13.77/7.80 ( ! [X3: uint32] :
% 13.77/7.80 ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ X3 ) @ R )
% 13.77/7.80 => ~ ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Xs ) @ ( lenlex_uint32 @ R ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6998_lenlex__irreflexive,axiom,
% 13.77/7.80 ! [R: set_Pr1261947904930325089at_nat,Xs: list_nat] :
% 13.77/7.80 ( ! [X3: nat] :
% 13.77/7.80 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R )
% 13.77/7.80 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Xs ) @ ( lenlex_nat @ R ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_6999_lenlex__irreflexive,axiom,
% 13.77/7.80 ! [R: set_Pr958786334691620121nt_int,Xs: list_int] :
% 13.77/7.80 ( ! [X3: int] :
% 13.77/7.80 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ R )
% 13.77/7.80 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Xs ) @ ( lenlex_int @ R ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7000_reals__Archimedean3,axiom,
% 13.77/7.80 ! [X: real] :
% 13.77/7.80 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.80 => ! [Y5: real] :
% 13.77/7.80 ? [N2: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7001_image__minus__const__atLeastLessThan__nat,axiom,
% 13.77/7.80 ! [C2: nat,Y: nat,X: nat] :
% 13.77/7.80 ( ( ( ord_less_nat @ C2 @ Y )
% 13.77/7.80 => ( ( image_nat_nat
% 13.77/7.80 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C2 )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 13.77/7.80 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C2 ) @ ( minus_minus_nat @ Y @ C2 ) ) ) )
% 13.77/7.80 & ( ~ ( ord_less_nat @ C2 @ Y )
% 13.77/7.80 => ( ( ( ord_less_nat @ X @ Y )
% 13.77/7.80 => ( ( image_nat_nat
% 13.77/7.80 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C2 )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 13.77/7.80 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 13.77/7.80 & ( ~ ( ord_less_nat @ X @ Y )
% 13.77/7.80 => ( ( image_nat_nat
% 13.77/7.80 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C2 )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 13.77/7.80 = bot_bot_set_nat ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7002_listrel1I1,axiom,
% 13.77/7.80 ! [X: $o,Y: $o,R: set_Product_prod_o_o,Xs: list_o] :
% 13.77/7.80 ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R )
% 13.77/7.80 => ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ ( cons_o @ Y @ Xs ) ) @ ( listrel1_o @ R ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7003_listrel1I1,axiom,
% 13.77/7.80 ! [X: uint32,Y: uint32,R: set_Pr1773385645901665561uint32,Xs: list_uint32] :
% 13.77/7.80 ( ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y ) @ R )
% 13.77/7.80 => ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ ( cons_uint32 @ Y @ Xs ) ) @ ( listrel1_uint32 @ R ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7004_listrel1I1,axiom,
% 13.77/7.80 ! [X: nat,Y: nat,R: set_Pr1261947904930325089at_nat,Xs: list_nat] :
% 13.77/7.80 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 13.77/7.80 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ ( cons_nat @ Y @ Xs ) ) @ ( listrel1_nat @ R ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7005_listrel1I1,axiom,
% 13.77/7.80 ! [X: int,Y: int,R: set_Pr958786334691620121nt_int,Xs: list_int] :
% 13.77/7.80 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 13.77/7.80 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ ( cons_int @ Y @ Xs ) ) @ ( listrel1_int @ R ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7006_Cons__listrel1E1,axiom,
% 13.77/7.80 ! [X: $o,Xs: list_o,Ys: list_o,R: set_Product_prod_o_o] :
% 13.77/7.80 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs ) @ Ys ) @ ( listrel1_o @ R ) )
% 13.77/7.80 => ( ! [Y3: $o] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_o @ Y3 @ Xs ) )
% 13.77/7.80 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y3 ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_o] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_o @ X @ Zs2 ) )
% 13.77/7.80 => ~ ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ Zs2 ) @ ( listrel1_o @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7007_Cons__listrel1E1,axiom,
% 13.77/7.80 ! [X: uint32,Xs: list_uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.80 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ ( cons_uint32 @ X @ Xs ) @ Ys ) @ ( listrel1_uint32 @ R ) )
% 13.77/7.80 => ( ! [Y3: uint32] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_uint32 @ Y3 @ Xs ) )
% 13.77/7.80 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X @ Y3 ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_uint32] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_uint32 @ X @ Zs2 ) )
% 13.77/7.80 => ~ ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ Zs2 ) @ ( listrel1_uint32 @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7008_Cons__listrel1E1,axiom,
% 13.77/7.80 ! [X: nat,Xs: list_nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.80 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs ) @ Ys ) @ ( listrel1_nat @ R ) )
% 13.77/7.80 => ( ! [Y3: nat] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_nat @ Y3 @ Xs ) )
% 13.77/7.80 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y3 ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_nat] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_nat @ X @ Zs2 ) )
% 13.77/7.80 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ Zs2 ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7009_Cons__listrel1E1,axiom,
% 13.77/7.80 ! [X: int,Xs: list_int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.80 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs ) @ Ys ) @ ( listrel1_int @ R ) )
% 13.77/7.80 => ( ! [Y3: int] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_int @ Y3 @ Xs ) )
% 13.77/7.80 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y3 ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_int] :
% 13.77/7.80 ( ( Ys
% 13.77/7.80 = ( cons_int @ X @ Zs2 ) )
% 13.77/7.80 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ Zs2 ) @ ( listrel1_int @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7010_Cons__listrel1E2,axiom,
% 13.77/7.80 ! [Xs: list_o,Y: $o,Ys: list_o,R: set_Product_prod_o_o] :
% 13.77/7.80 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs @ ( cons_o @ Y @ Ys ) ) @ ( listrel1_o @ R ) )
% 13.77/7.80 => ( ! [X3: $o] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_o @ X3 @ Ys ) )
% 13.77/7.80 => ~ ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X3 @ Y ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_o] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_o @ Y @ Zs2 ) )
% 13.77/7.80 => ~ ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Zs2 @ Ys ) @ ( listrel1_o @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7011_Cons__listrel1E2,axiom,
% 13.77/7.80 ! [Xs: list_uint32,Y: uint32,Ys: list_uint32,R: set_Pr1773385645901665561uint32] :
% 13.77/7.80 ( ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Xs @ ( cons_uint32 @ Y @ Ys ) ) @ ( listrel1_uint32 @ R ) )
% 13.77/7.80 => ( ! [X3: uint32] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_uint32 @ X3 @ Ys ) )
% 13.77/7.80 => ~ ( member8027108493173000802uint32 @ ( produc1400373151660368625uint32 @ X3 @ Y ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_uint32] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_uint32 @ Y @ Zs2 ) )
% 13.77/7.80 => ~ ( member2333554998283850498uint32 @ ( produc7487160679990061969uint32 @ Zs2 @ Ys ) @ ( listrel1_uint32 @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7012_Cons__listrel1E2,axiom,
% 13.77/7.80 ! [Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.80 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 13.77/7.80 => ( ! [X3: nat] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_nat @ X3 @ Ys ) )
% 13.77/7.80 => ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_nat] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_nat @ Y @ Zs2 ) )
% 13.77/7.80 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Zs2 @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7013_Cons__listrel1E2,axiom,
% 13.77/7.80 ! [Xs: list_int,Y: int,Ys: list_int,R: set_Pr958786334691620121nt_int] :
% 13.77/7.80 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs @ ( cons_int @ Y @ Ys ) ) @ ( listrel1_int @ R ) )
% 13.77/7.80 => ( ! [X3: int] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_int @ X3 @ Ys ) )
% 13.77/7.80 => ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ R ) )
% 13.77/7.80 => ~ ! [Zs2: list_int] :
% 13.77/7.80 ( ( Xs
% 13.77/7.80 = ( cons_int @ Y @ Zs2 ) )
% 13.77/7.80 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Zs2 @ Ys ) @ ( listrel1_int @ R ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7014_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,K4: real,F: vEBT_VEBT > real] :
% 13.77/7.80 ( ! [I2: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) @ ( groups2240296850493347238T_real @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7015_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_real,K4: real,F: real > real] :
% 13.77/7.80 ( ! [I2: real] :
% 13.77/7.80 ( ( member_real @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K4 ) @ ( groups8097168146408367636l_real @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7016_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_int,K4: real,F: int > real] :
% 13.77/7.80 ( ! [I2: int] :
% 13.77/7.80 ( ( member_int @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K4 ) @ ( groups8778361861064173332t_real @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7017_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_complex,K4: real,F: complex > real] :
% 13.77/7.80 ( ! [I2: complex] :
% 13.77/7.80 ( ( member_complex @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K4 ) @ ( groups5808333547571424918x_real @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7018_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_literal,K4: real,F: literal > real] :
% 13.77/7.80 ( ! [I2: literal] :
% 13.77/7.80 ( ( member_literal @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_literal @ A4 ) ) @ K4 ) @ ( groups2795228986978005958l_real @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7019_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,K4: code_integer,F: vEBT_VEBT > code_integer] :
% 13.77/7.80 ( ! [I2: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) @ ( groups5748017345553531991nteger @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7020_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_real,K4: code_integer,F: real > code_integer] :
% 13.77/7.80 ( ! [I2: real] :
% 13.77/7.80 ( ( member_real @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_real @ A4 ) ) @ K4 ) @ ( groups7713935264441627589nteger @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7021_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_int,K4: code_integer,F: int > code_integer] :
% 13.77/7.80 ( ! [I2: int] :
% 13.77/7.80 ( ( member_int @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A4 ) ) @ K4 ) @ ( groups7873554091576472773nteger @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7022_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_complex,K4: code_integer,F: complex > code_integer] :
% 13.77/7.80 ( ! [I2: complex] :
% 13.77/7.80 ( ( member_complex @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_complex @ A4 ) ) @ K4 ) @ ( groups6621422865394947399nteger @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7023_sum__bounded__below,axiom,
% 13.77/7.80 ! [A4: set_literal,K4: code_integer,F: literal > code_integer] :
% 13.77/7.80 ( ! [I2: literal] :
% 13.77/7.80 ( ( member_literal @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ K4 @ ( F @ I2 ) ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_literal @ A4 ) ) @ K4 ) @ ( groups8556826181031883383nteger @ F @ A4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7024_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > real,K4: real] :
% 13.77/7.80 ( ! [I2: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( groups2240296850493347238T_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7025_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_real,F: real > real,K4: real] :
% 13.77/7.80 ( ! [I2: real] :
% 13.77/7.80 ( ( member_real @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7026_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_int,F: int > real,K4: real] :
% 13.77/7.80 ( ! [I2: int] :
% 13.77/7.80 ( ( member_int @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7027_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_complex,F: complex > real,K4: real] :
% 13.77/7.80 ( ! [I2: complex] :
% 13.77/7.80 ( ( member_complex @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7028_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_literal,F: literal > real,K4: real] :
% 13.77/7.80 ( ! [I2: literal] :
% 13.77/7.80 ( ( member_literal @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_eq_real @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_less_eq_real @ ( groups2795228986978005958l_real @ F @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7029_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( groups5748017345553531991nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7030_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_real,F: real > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: real] :
% 13.77/7.80 ( ( member_real @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( groups7713935264441627589nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7031_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_int,F: int > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: int] :
% 13.77/7.80 ( ( member_int @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7032_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_complex,F: complex > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: complex] :
% 13.77/7.80 ( ( member_complex @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( groups6621422865394947399nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7033_sum__bounded__above,axiom,
% 13.77/7.80 ! [A4: set_literal,F: literal > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: literal] :
% 13.77/7.80 ( ( member_literal @ I2 @ A4 )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ord_le3102999989581377725nteger @ ( groups8556826181031883383nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7034_nat__less__real__le,axiom,
% 13.77/7.80 ( ord_less_nat
% 13.77/7.80 = ( ^ [N6: nat,M5: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N6 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M5 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7035_nat__le__real__less,axiom,
% 13.77/7.80 ( ord_less_eq_nat
% 13.77/7.80 = ( ^ [N6: nat,M5: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N6 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M5 ) @ one_one_real ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7036_lessThan__Suc__eq__insert__0,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 13.77/7.80 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7037_lenlex__length,axiom,
% 13.77/7.80 ! [Ms: list_VEBT_VEBT,Ns: list_VEBT_VEBT,R: set_Pr6192946355708809607T_VEBT] :
% 13.77/7.80 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R ) )
% 13.77/7.80 => ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7038_lenlex__length,axiom,
% 13.77/7.80 ! [Ms: list_real,Ns: list_real,R: set_Pr6218003697084177305l_real] :
% 13.77/7.80 ( ( member6584958104391596930t_real @ ( produc1408950526243324945t_real @ Ms @ Ns ) @ ( lenlex_real @ R ) )
% 13.77/7.80 => ( ord_less_eq_nat @ ( size_size_list_real @ Ms ) @ ( size_size_list_real @ Ns ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7039_lenlex__length,axiom,
% 13.77/7.80 ! [Ms: list_o,Ns: list_o,R: set_Product_prod_o_o] :
% 13.77/7.80 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R ) )
% 13.77/7.80 => ( ord_less_eq_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7040_lenlex__length,axiom,
% 13.77/7.80 ! [Ms: list_nat,Ns: list_nat,R: set_Pr1261947904930325089at_nat] :
% 13.77/7.80 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R ) )
% 13.77/7.80 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7041_real__archimedian__rdiv__eq__0,axiom,
% 13.77/7.80 ! [X: real,C2: real] :
% 13.77/7.80 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.80 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 13.77/7.80 => ( ! [M3: nat] :
% 13.77/7.80 ( ( ord_less_nat @ zero_zero_nat @ M3 )
% 13.77/7.80 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ X ) @ C2 ) )
% 13.77/7.80 => ( X = zero_zero_real ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7042_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > int,K4: int] :
% 13.77/7.80 ( ! [I2: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 13.77/7.80 => ( ord_less_int @ ( groups769130701875090982BT_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7043_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_real,F: real > int,K4: int] :
% 13.77/7.80 ( ! [I2: real] :
% 13.77/7.80 ( ( member_real @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 13.77/7.80 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7044_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_complex,F: complex > int,K4: int] :
% 13.77/7.80 ( ! [I2: complex] :
% 13.77/7.80 ( ( member_complex @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 13.77/7.80 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7045_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_literal,F: literal > int,K4: int] :
% 13.77/7.80 ( ! [I2: literal] :
% 13.77/7.80 ( ( member_literal @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 13.77/7.80 => ( ord_less_int @ ( groups8649609317433967686al_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7046_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_nat,F: nat > int,K4: int] :
% 13.77/7.80 ( ! [I2: nat] :
% 13.77/7.80 ( ( member_nat @ I2 @ A4 )
% 13.77/7.80 => ( ord_less_int @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 13.77/7.80 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7047_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_VEBT_VEBT,F: vEBT_VEBT > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: vEBT_VEBT] :
% 13.77/7.80 ( ( member_VEBT_VEBT @ I2 @ A4 )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( groups5748017345553531991nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7048_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_real,F: real > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: real] :
% 13.77/7.80 ( ( member_real @ I2 @ A4 )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( groups7713935264441627589nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_real @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7049_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_int,F: int > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: int] :
% 13.77/7.80 ( ( member_int @ I2 @ A4 )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( groups7873554091576472773nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7050_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_complex,F: complex > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: complex] :
% 13.77/7.80 ( ( member_complex @ I2 @ A4 )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( groups6621422865394947399nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_complex @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7051_sum__bounded__above__strict,axiom,
% 13.77/7.80 ! [A4: set_literal,F: literal > code_integer,K4: code_integer] :
% 13.77/7.80 ( ! [I2: literal] :
% 13.77/7.80 ( ( member_literal @ I2 @ A4 )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( F @ I2 ) @ K4 ) )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_literal @ A4 ) )
% 13.77/7.80 => ( ord_le6747313008572928689nteger @ ( groups8556826181031883383nteger @ F @ A4 ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_literal @ A4 ) ) @ K4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7052_linear__plus__1__le__power,axiom,
% 13.77/7.80 ! [X: real,N: nat] :
% 13.77/7.80 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.80 => ( 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 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7053_cnt__cnt__eq,axiom,
% 13.77/7.80 ( vEBT_VEBT_cnt
% 13.77/7.80 = ( ^ [T2: vEBT_VEBT] : ( semiri5074537144036343181t_real @ ( vEBT_VEBT_cnt2 @ T2 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7054_minNulli__rule,axiom,
% 13.77/7.80 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 13.77/7.80 ( hoare_hoare_triple_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_minNulli @ Ti )
% 13.77/7.80 @ ^ [R5: $o] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_VEBT_minNull @ T ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7055_builupi_Hcorr,axiom,
% 13.77/7.80 ! [N: nat] : ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7056_builupicorr,axiom,
% 13.77/7.80 ! [N: nat] : ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7057_vebt__maxtilist,axiom,
% 13.77/7.80 ! [I: nat,Ts2: list_VEBT_VEBT,Tsi: list_VEBT_VEBTi] :
% 13.77/7.80 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ts2 ) )
% 13.77/7.80 => ( hoare_7629718768684598413on_nat @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) @ ( vEBT_vebt_maxti @ ( nth_VEBT_VEBTi @ Tsi @ I ) )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Ts2 @ I ) ) ) )
% 13.77/7.80 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7058_vebt__mintilist,axiom,
% 13.77/7.80 ! [I: nat,Ts2: list_VEBT_VEBT,Tsi: list_VEBT_VEBTi] :
% 13.77/7.80 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Ts2 ) )
% 13.77/7.80 => ( hoare_7629718768684598413on_nat @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) @ ( vEBT_vebt_minti @ ( nth_VEBT_VEBTi @ Tsi @ I ) )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ Ts2 @ I ) ) ) )
% 13.77/7.80 @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Ts2 @ Tsi ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7059_negative__zless,axiom,
% 13.77/7.80 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7060_negative__eq__positive,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.80 = ( semiri1314217659103216013at_int @ M ) )
% 13.77/7.80 = ( ( N = zero_zero_nat )
% 13.77/7.80 & ( M = zero_zero_nat ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7061_vebt__minti__h,axiom,
% 13.77/7.80 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 13.77/7.80 ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_vebt_mint @ T ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7062_vebt__maxti__h,axiom,
% 13.77/7.80 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 13.77/7.80 ( hoare_7629718768684598413on_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_vebt_maxt @ T ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7063_zless__iff__Suc__zadd,axiom,
% 13.77/7.80 ( ord_less_int
% 13.77/7.80 = ( ^ [W3: int,Z2: int] :
% 13.77/7.80 ? [N6: nat] :
% 13.77/7.80 ( Z2
% 13.77/7.80 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N6 ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7064_int__Suc,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 13.77/7.80 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7065_int__ops_I4_J,axiom,
% 13.77/7.80 ! [A: nat] :
% 13.77/7.80 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 13.77/7.80 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7066_negative__zless__0,axiom,
% 13.77/7.80 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7067_negD,axiom,
% 13.77/7.80 ! [X: int] :
% 13.77/7.80 ( ( ord_less_int @ X @ zero_zero_int )
% 13.77/7.80 => ? [N2: nat] :
% 13.77/7.80 ( X
% 13.77/7.80 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7068_not__zle__0__negative,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7069_int__cases,axiom,
% 13.77/7.80 ! [Z: int] :
% 13.77/7.80 ( ! [N2: nat] :
% 13.77/7.80 ( Z
% 13.77/7.80 != ( semiri1314217659103216013at_int @ N2 ) )
% 13.77/7.80 => ~ ! [N2: nat] :
% 13.77/7.80 ( Z
% 13.77/7.80 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7070_int__of__nat__induct,axiom,
% 13.77/7.80 ! [P2: int > $o,Z: int] :
% 13.77/7.80 ( ! [N2: nat] : ( P2 @ ( semiri1314217659103216013at_int @ N2 ) )
% 13.77/7.80 => ( ! [N2: nat] : ( P2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) )
% 13.77/7.80 => ( P2 @ Z ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7071_int__ops_I1_J,axiom,
% 13.77/7.80 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 13.77/7.80 = zero_zero_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7072_int__zle__neg,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 13.77/7.80 = ( ( N = zero_zero_nat )
% 13.77/7.80 & ( M = zero_zero_nat ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7073_nat__int__comparison_I2_J,axiom,
% 13.77/7.80 ( ord_less_nat
% 13.77/7.80 = ( ^ [A7: nat,B7: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7074_zle__int,axiom,
% 13.77/7.80 ! [M: nat,N: nat] :
% 13.77/7.80 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.80 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7075_nat__int__comparison_I3_J,axiom,
% 13.77/7.80 ( ord_less_eq_nat
% 13.77/7.80 = ( ^ [A7: nat,B7: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7076_int__ops_I6_J,axiom,
% 13.77/7.80 ! [A: nat,B: nat] :
% 13.77/7.80 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 13.77/7.80 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 13.77/7.80 = zero_zero_int ) )
% 13.77/7.80 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 13.77/7.80 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 13.77/7.80 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7077_nat__less__as__int,axiom,
% 13.77/7.80 ( ord_less_nat
% 13.77/7.80 = ( ^ [A7: nat,B7: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7078_nat__leq__as__int,axiom,
% 13.77/7.80 ( ord_less_eq_nat
% 13.77/7.80 = ( ^ [A7: nat,B7: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A7 ) @ ( semiri1314217659103216013at_int @ B7 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7079_zmult__zless__mono2__lemma,axiom,
% 13.77/7.80 ! [I: int,J: int,K: nat] :
% 13.77/7.80 ( ( ord_less_int @ I @ J )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.80 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7080_zero__less__imp__eq__int,axiom,
% 13.77/7.80 ! [K: int] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.80 => ? [N2: nat] :
% 13.77/7.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 13.77/7.80 & ( K
% 13.77/7.80 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7081_pos__int__cases,axiom,
% 13.77/7.80 ! [K: int] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.80 => ~ ! [N2: nat] :
% 13.77/7.80 ( ( K
% 13.77/7.80 = ( semiri1314217659103216013at_int @ N2 ) )
% 13.77/7.80 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7082_int__cases4,axiom,
% 13.77/7.80 ! [M: int] :
% 13.77/7.80 ( ! [N2: nat] :
% 13.77/7.80 ( M
% 13.77/7.80 != ( semiri1314217659103216013at_int @ N2 ) )
% 13.77/7.80 => ~ ! [N2: nat] :
% 13.77/7.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 13.77/7.80 => ( M
% 13.77/7.80 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7083_int__cases3,axiom,
% 13.77/7.80 ! [K: int] :
% 13.77/7.80 ( ( K != zero_zero_int )
% 13.77/7.80 => ( ! [N2: nat] :
% 13.77/7.80 ( ( K
% 13.77/7.80 = ( semiri1314217659103216013at_int @ N2 ) )
% 13.77/7.80 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 13.77/7.80 => ~ ! [N2: nat] :
% 13.77/7.80 ( ( K
% 13.77/7.80 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 13.77/7.80 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7084_neg__int__cases,axiom,
% 13.77/7.80 ! [K: int] :
% 13.77/7.80 ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.80 => ~ ! [N2: nat] :
% 13.77/7.80 ( ( K
% 13.77/7.80 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 13.77/7.80 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7085_zdiff__int__split,axiom,
% 13.77/7.80 ! [P2: int > $o,X: nat,Y: nat] :
% 13.77/7.80 ( ( P2 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 13.77/7.80 = ( ( ( ord_less_eq_nat @ Y @ X )
% 13.77/7.80 => ( P2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 13.77/7.80 & ( ( ord_less_nat @ X @ Y )
% 13.77/7.80 => ( P2 @ zero_zero_int ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7086_VEBT__internal_Ocnt_H_Osimps_I1_J,axiom,
% 13.77/7.80 ! [A: $o,B: $o] :
% 13.77/7.80 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.80 = one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7087_bot__nat__0_Oordering__top__axioms,axiom,
% 13.77/7.80 ( ordering_top_nat
% 13.77/7.80 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 13.77/7.80 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 13.77/7.80 @ zero_zero_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7088_Chebyshev__sum__upper__nat,axiom,
% 13.77/7.80 ! [N: nat,A: nat > nat,B: nat > nat] :
% 13.77/7.80 ( ! [I2: nat,J2: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ I2 @ J2 )
% 13.77/7.80 => ( ( ord_less_nat @ J2 @ N )
% 13.77/7.80 => ( ord_less_eq_nat @ ( A @ I2 ) @ ( A @ J2 ) ) ) )
% 13.77/7.80 => ( ! [I2: nat,J2: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ I2 @ J2 )
% 13.77/7.80 => ( ( ord_less_nat @ J2 @ N )
% 13.77/7.80 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I2 ) ) ) )
% 13.77/7.80 => ( ord_less_eq_nat
% 13.77/7.80 @ ( times_times_nat @ N
% 13.77/7.80 @ ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 13.77/7.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 13.77/7.80 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7089_minNrulli__ruleT,axiom,
% 13.77/7.80 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 13.77/7.80 ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_VEBT_minNulli @ Ti )
% 13.77/7.80 @ ^ [R5: $o] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_VEBT_minNull @ T ) ) ) )
% 13.77/7.80 @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7090_T__vebt__buildupi,axiom,
% 13.77/7.80 ! [N: nat,H2: heap_e7401611519738050253t_unit] : ( ord_less_eq_nat @ ( time_time_VEBT_VEBTi @ ( vEBT_V739175172307565963ildupi @ N ) @ H2 ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7091_vebt__maxti__hT,axiom,
% 13.77/7.80 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 13.77/7.80 ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_vebt_maxt @ T ) ) ) )
% 13.77/7.80 @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7092_vebt__minti__hT,axiom,
% 13.77/7.80 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi] :
% 13.77/7.80 ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( R5
% 13.77/7.80 = ( vEBT_vebt_mint @ T ) ) ) )
% 13.77/7.80 @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7093_htt__vebt__buildupi_H,axiom,
% 13.77/7.80 ! [N: nat] : ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7094_htt__vebt__buildupi,axiom,
% 13.77/7.80 ! [N: nat] : ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7095_finite__interval__int1,axiom,
% 13.77/7.80 ! [A: int,B: int] :
% 13.77/7.80 ( finite_finite_int
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [I3: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ A @ I3 )
% 13.77/7.80 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7096_finite__interval__int4,axiom,
% 13.77/7.80 ! [A: int,B: int] :
% 13.77/7.80 ( finite_finite_int
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [I3: int] :
% 13.77/7.80 ( ( ord_less_int @ A @ I3 )
% 13.77/7.80 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7097_finite__interval__int3,axiom,
% 13.77/7.80 ! [A: int,B: int] :
% 13.77/7.80 ( finite_finite_int
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [I3: int] :
% 13.77/7.80 ( ( ord_less_int @ A @ I3 )
% 13.77/7.80 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7098_finite__interval__int2,axiom,
% 13.77/7.80 ! [A: int,B: int] :
% 13.77/7.80 ( finite_finite_int
% 13.77/7.80 @ ( collect_int
% 13.77/7.80 @ ^ [I3: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ A @ I3 )
% 13.77/7.80 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7099_negative__zle,axiom,
% 13.77/7.80 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7100_zle__add1__eq__le,axiom,
% 13.77/7.80 ! [W2: int,Z: int] :
% 13.77/7.80 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 13.77/7.80 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7101_zle__diff1__eq,axiom,
% 13.77/7.80 ! [W2: int,Z: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z @ one_one_int ) )
% 13.77/7.80 = ( ord_less_int @ W2 @ Z ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7102_nonpos__int__cases,axiom,
% 13.77/7.80 ! [K: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 13.77/7.80 => ~ ! [N2: nat] :
% 13.77/7.80 ( K
% 13.77/7.80 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7103_negative__zle__0,axiom,
% 13.77/7.80 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7104_zero__le__imp__eq__int,axiom,
% 13.77/7.80 ! [K: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.80 => ? [N2: nat] :
% 13.77/7.80 ( K
% 13.77/7.80 = ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7105_nonneg__int__cases,axiom,
% 13.77/7.80 ! [K: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.80 => ~ ! [N2: nat] :
% 13.77/7.80 ( K
% 13.77/7.80 != ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7106_zle__iff__zadd,axiom,
% 13.77/7.80 ( ord_less_eq_int
% 13.77/7.80 = ( ^ [W3: int,Z2: int] :
% 13.77/7.80 ? [N6: nat] :
% 13.77/7.80 ( Z2
% 13.77/7.80 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N6 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7107_not__int__zless__negative,axiom,
% 13.77/7.80 ! [N: nat,M: nat] :
% 13.77/7.80 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7108_pos__zmult__eq__1__iff,axiom,
% 13.77/7.80 ! [M: int,N: int] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ M )
% 13.77/7.80 => ( ( ( times_times_int @ M @ N )
% 13.77/7.80 = one_one_int )
% 13.77/7.80 = ( ( M = one_one_int )
% 13.77/7.80 & ( N = one_one_int ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7109_zmult__zless__mono2,axiom,
% 13.77/7.80 ! [I: int,J: int,K: int] :
% 13.77/7.80 ( ( ord_less_int @ I @ J )
% 13.77/7.80 => ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.80 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7110_less__int__code_I1_J,axiom,
% 13.77/7.80 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7111_zless__add1__eq,axiom,
% 13.77/7.80 ! [W2: int,Z: int] :
% 13.77/7.80 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 13.77/7.80 = ( ( ord_less_int @ W2 @ Z )
% 13.77/7.80 | ( W2 = Z ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7112_int__gr__induct,axiom,
% 13.77/7.80 ! [K: int,I: int,P2: int > $o] :
% 13.77/7.80 ( ( ord_less_int @ K @ I )
% 13.77/7.80 => ( ( P2 @ ( plus_plus_int @ K @ one_one_int ) )
% 13.77/7.80 => ( ! [I2: int] :
% 13.77/7.80 ( ( ord_less_int @ K @ I2 )
% 13.77/7.80 => ( ( P2 @ I2 )
% 13.77/7.80 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 13.77/7.80 => ( P2 @ I ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7113_int__less__induct,axiom,
% 13.77/7.80 ! [I: int,K: int,P2: int > $o] :
% 13.77/7.80 ( ( ord_less_int @ I @ K )
% 13.77/7.80 => ( ( P2 @ ( minus_minus_int @ K @ one_one_int ) )
% 13.77/7.80 => ( ! [I2: int] :
% 13.77/7.80 ( ( ord_less_int @ I2 @ K )
% 13.77/7.80 => ( ( P2 @ I2 )
% 13.77/7.80 => ( P2 @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 13.77/7.80 => ( P2 @ I ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7114_odd__less__0__iff,axiom,
% 13.77/7.80 ! [Z: int] :
% 13.77/7.80 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 13.77/7.80 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7115_plusinfinity,axiom,
% 13.77/7.80 ! [D: int,P6: int > $o,P2: int > $o] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ D )
% 13.77/7.80 => ( ! [X3: int,K2: int] :
% 13.77/7.80 ( ( P6 @ X3 )
% 13.77/7.80 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 13.77/7.80 => ( ? [Z5: int] :
% 13.77/7.80 ! [X3: int] :
% 13.77/7.80 ( ( ord_less_int @ Z5 @ X3 )
% 13.77/7.80 => ( ( P2 @ X3 )
% 13.77/7.80 = ( P6 @ X3 ) ) )
% 13.77/7.80 => ( ? [X_12: int] : ( P6 @ X_12 )
% 13.77/7.80 => ? [X_1: int] : ( P2 @ X_1 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7116_minusinfinity,axiom,
% 13.77/7.80 ! [D: int,P1: int > $o,P2: int > $o] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ D )
% 13.77/7.80 => ( ! [X3: int,K2: int] :
% 13.77/7.80 ( ( P1 @ X3 )
% 13.77/7.80 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 13.77/7.80 => ( ? [Z5: int] :
% 13.77/7.80 ! [X3: int] :
% 13.77/7.80 ( ( ord_less_int @ X3 @ Z5 )
% 13.77/7.80 => ( ( P2 @ X3 )
% 13.77/7.80 = ( P1 @ X3 ) ) )
% 13.77/7.80 => ( ? [X_12: int] : ( P1 @ X_12 )
% 13.77/7.80 => ? [X_1: int] : ( P2 @ X_1 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7117_verit__la__generic,axiom,
% 13.77/7.80 ! [A: int,X: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ A @ X )
% 13.77/7.80 | ( A = X )
% 13.77/7.80 | ( ord_less_eq_int @ X @ A ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7118_zless__imp__add1__zle,axiom,
% 13.77/7.80 ! [W2: int,Z: int] :
% 13.77/7.80 ( ( ord_less_int @ W2 @ Z )
% 13.77/7.80 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7119_add1__zle__eq,axiom,
% 13.77/7.80 ! [W2: int,Z: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z )
% 13.77/7.80 = ( ord_less_int @ W2 @ Z ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7120_int__ge__induct,axiom,
% 13.77/7.80 ! [K: int,I: int,P2: int > $o] :
% 13.77/7.80 ( ( ord_less_eq_int @ K @ I )
% 13.77/7.80 => ( ( P2 @ K )
% 13.77/7.80 => ( ! [I2: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ K @ I2 )
% 13.77/7.80 => ( ( P2 @ I2 )
% 13.77/7.80 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 13.77/7.80 => ( P2 @ I ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7121_int__le__induct,axiom,
% 13.77/7.80 ! [I: int,K: int,P2: int > $o] :
% 13.77/7.80 ( ( ord_less_eq_int @ I @ K )
% 13.77/7.80 => ( ( P2 @ K )
% 13.77/7.80 => ( ! [I2: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ I2 @ K )
% 13.77/7.80 => ( ( P2 @ I2 )
% 13.77/7.80 => ( P2 @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 13.77/7.80 => ( P2 @ I ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7122_int__induct,axiom,
% 13.77/7.80 ! [P2: int > $o,K: int,I: int] :
% 13.77/7.80 ( ( P2 @ K )
% 13.77/7.80 => ( ! [I2: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ K @ I2 )
% 13.77/7.80 => ( ( P2 @ I2 )
% 13.77/7.80 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 13.77/7.80 => ( ! [I2: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ I2 @ K )
% 13.77/7.80 => ( ( P2 @ I2 )
% 13.77/7.80 => ( P2 @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 13.77/7.80 => ( P2 @ I ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7123_unique__quotient__lemma__neg,axiom,
% 13.77/7.80 ! [B: int,Q7: int,R6: int,Q3: int,R: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 13.77/7.80 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 13.77/7.80 => ( ( ord_less_int @ B @ R )
% 13.77/7.80 => ( ( ord_less_int @ B @ R6 )
% 13.77/7.80 => ( ord_less_eq_int @ Q3 @ Q7 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7124_unique__quotient__lemma,axiom,
% 13.77/7.80 ! [B: int,Q7: int,R6: int,Q3: int,R: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q7 ) @ R6 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 13.77/7.80 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 13.77/7.80 => ( ( ord_less_int @ R6 @ B )
% 13.77/7.80 => ( ( ord_less_int @ R @ B )
% 13.77/7.80 => ( ord_less_eq_int @ Q7 @ Q3 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7125_zdiv__mono2__neg__lemma,axiom,
% 13.77/7.80 ! [B: int,Q3: int,R: int,B2: int,Q7: int,R6: int] :
% 13.77/7.80 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R )
% 13.77/7.80 = ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 13.77/7.80 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) @ zero_zero_int )
% 13.77/7.80 => ( ( ord_less_int @ R @ B )
% 13.77/7.80 => ( ( ord_less_eq_int @ zero_zero_int @ R6 )
% 13.77/7.80 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 13.77/7.80 => ( ( ord_less_eq_int @ B2 @ B )
% 13.77/7.80 => ( ord_less_eq_int @ Q7 @ Q3 ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7126_zdiv__mono2__lemma,axiom,
% 13.77/7.80 ! [B: int,Q3: int,R: int,B2: int,Q7: int,R6: int] :
% 13.77/7.80 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R )
% 13.77/7.80 = ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 13.77/7.80 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 13.77/7.80 => ( ( ord_less_int @ R6 @ B2 )
% 13.77/7.80 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 13.77/7.80 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 13.77/7.80 => ( ( ord_less_eq_int @ B2 @ B )
% 13.77/7.80 => ( ord_less_eq_int @ Q3 @ Q7 ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7127_q__pos__lemma,axiom,
% 13.77/7.80 ! [B2: int,Q7: int,R6: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q7 ) @ R6 ) )
% 13.77/7.80 => ( ( ord_less_int @ R6 @ B2 )
% 13.77/7.80 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 13.77/7.80 => ( ord_less_eq_int @ zero_zero_int @ Q7 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7128_incr__mult__lemma,axiom,
% 13.77/7.80 ! [D: int,P2: int > $o,K: int] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ D )
% 13.77/7.80 => ( ! [X3: int] :
% 13.77/7.80 ( ( P2 @ X3 )
% 13.77/7.80 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) )
% 13.77/7.80 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.80 => ! [X5: int] :
% 13.77/7.80 ( ( P2 @ X5 )
% 13.77/7.80 => ( P2 @ ( plus_plus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7129_pos__mult__pos__ge,axiom,
% 13.77/7.80 ! [X: int,N: int] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ X )
% 13.77/7.80 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 13.77/7.80 => ( ord_less_eq_int @ ( times_times_int @ N @ one_one_int ) @ ( times_times_int @ N @ X ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7130_decr__mult__lemma,axiom,
% 13.77/7.80 ! [D: int,P2: int > $o,K: int] :
% 13.77/7.80 ( ( ord_less_int @ zero_zero_int @ D )
% 13.77/7.80 => ( ! [X3: int] :
% 13.77/7.80 ( ( P2 @ X3 )
% 13.77/7.80 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) )
% 13.77/7.80 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.80 => ! [X5: int] :
% 13.77/7.80 ( ( P2 @ X5 )
% 13.77/7.80 => ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7131_le__imp__0__less,axiom,
% 13.77/7.80 ! [Z: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.80 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7132_less__1__helper,axiom,
% 13.77/7.80 ! [N: int,M: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ N @ M )
% 13.77/7.80 => ( ord_less_int @ ( minus_minus_int @ N @ one_one_int ) @ M ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7133_imp__le__cong,axiom,
% 13.77/7.80 ! [X: int,X9: int,P2: $o,P6: $o] :
% 13.77/7.80 ( ( X = X9 )
% 13.77/7.80 => ( ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 13.77/7.80 => ( P2 = P6 ) )
% 13.77/7.80 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.80 => P2 )
% 13.77/7.80 = ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 13.77/7.80 => P6 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7134_conj__le__cong,axiom,
% 13.77/7.80 ! [X: int,X9: int,P2: $o,P6: $o] :
% 13.77/7.80 ( ( X = X9 )
% 13.77/7.80 => ( ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 13.77/7.80 => ( P2 = P6 ) )
% 13.77/7.80 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.80 & P2 )
% 13.77/7.80 = ( ( ord_less_eq_int @ zero_zero_int @ X9 )
% 13.77/7.80 & P6 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7135_less__eq__int__code_I1_J,axiom,
% 13.77/7.80 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7136_int__one__le__iff__zero__less,axiom,
% 13.77/7.80 ! [Z: int] :
% 13.77/7.80 ( ( ord_less_eq_int @ one_one_int @ Z )
% 13.77/7.80 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7137_Gcd__int__greater__eq__0,axiom,
% 13.77/7.80 ! [K4: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K4 ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7138_one__integer_Orsp,axiom,
% 13.77/7.80 one_one_int = one_one_int ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7139_Tbuildupi__buildupi_H,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( semiri1314217659103216013at_int @ ( vEBT_V441764108873111860ildupi @ N ) )
% 13.77/7.80 = ( vEBT_V9176841429113362141ildupi @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7140_VEBT__internal_OT__vebt__buildupi_H_Osimps_I1_J,axiom,
% 13.77/7.80 ( ( vEBT_V9176841429113362141ildupi @ zero_zero_nat )
% 13.77/7.80 = one_one_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7141_VEBT__internal_OT__vebt__buildupi_H_Osimps_I2_J,axiom,
% 13.77/7.80 ( ( vEBT_V9176841429113362141ildupi @ ( suc @ zero_zero_nat ) )
% 13.77/7.80 = one_one_int ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7142_finite__nth__roots,axiom,
% 13.77/7.80 ! [N: nat,C2: complex] :
% 13.77/7.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.80 => ( finite3207457112153483333omplex
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [Z2: complex] :
% 13.77/7.80 ( ( power_power_complex @ Z2 @ N )
% 13.77/7.80 = C2 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7143_foldr__same,axiom,
% 13.77/7.80 ! [Xs: list_real,Y: real] :
% 13.77/7.80 ( ! [X3: real,Y3: real] :
% 13.77/7.80 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 13.77/7.80 => ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 13.77/7.80 => ( X3 = Y3 ) ) )
% 13.77/7.80 => ( ! [X3: real] :
% 13.77/7.80 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 13.77/7.80 => ( X3 = Y ) )
% 13.77/7.80 => ( ( foldr_real_real @ plus_plus_real @ Xs @ zero_zero_real )
% 13.77/7.80 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( size_size_list_real @ Xs ) ) @ Y ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7144_vebt__maxti__rule,axiom,
% 13.77/7.80 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,Y: nat] :
% 13.77/7.80 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_maxti @ Ti )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( ( R5
% 13.77/7.80 = ( some_nat @ Y ) )
% 13.77/7.80 = ( vEBT_VEBT_max_in_set @ S @ Y ) ) ) )
% 13.77/7.80 @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7145_foldr0,axiom,
% 13.77/7.80 ! [Xs: list_real,C2: real,D: real] :
% 13.77/7.80 ( ( foldr_real_real @ plus_plus_real @ Xs @ ( plus_plus_real @ C2 @ D ) )
% 13.77/7.80 = ( plus_plus_real @ ( foldr_real_real @ plus_plus_real @ Xs @ D ) @ C2 ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7146_VEBT__internal_Ocnt_H_Osimps_I2_J,axiom,
% 13.77/7.80 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.80 ( ( vEBT_VEBT_cnt2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 13.77/7.80 = ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList ) @ zero_zero_nat ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7147_VEBT__internal_Ocnt_H_Oelims,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.80 ( ( ( vEBT_VEBT_cnt2 @ X )
% 13.77/7.80 = Y )
% 13.77/7.80 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.80 ( X
% 13.77/7.80 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.80 => ( Y != one_one_nat ) )
% 13.77/7.80 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.80 ( ( X
% 13.77/7.80 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.80 => ( Y
% 13.77/7.80 != ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7148_card__nth__roots,axiom,
% 13.77/7.80 ! [C2: complex,N: nat] :
% 13.77/7.80 ( ( C2 != zero_zero_complex )
% 13.77/7.80 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.80 => ( ( finite_card_complex
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [Z2: complex] :
% 13.77/7.80 ( ( power_power_complex @ Z2 @ N )
% 13.77/7.80 = C2 ) ) )
% 13.77/7.80 = N ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7149_card__roots__unity__eq,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.80 => ( ( finite_card_complex
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [Z2: complex] :
% 13.77/7.80 ( ( power_power_complex @ Z2 @ N )
% 13.77/7.80 = one_one_complex ) ) )
% 13.77/7.80 = N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7150_sum__roots__unity,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ one_one_nat @ N )
% 13.77/7.80 => ( ( groups7754918857620584856omplex
% 13.77/7.80 @ ^ [X4: complex] : X4
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [Z2: complex] :
% 13.77/7.80 ( ( power_power_complex @ Z2 @ N )
% 13.77/7.80 = one_one_complex ) ) )
% 13.77/7.80 = zero_zero_complex ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7151_sum__nth__roots,axiom,
% 13.77/7.80 ! [N: nat,C2: complex] :
% 13.77/7.80 ( ( ord_less_nat @ one_one_nat @ N )
% 13.77/7.80 => ( ( groups7754918857620584856omplex
% 13.77/7.80 @ ^ [X4: complex] : X4
% 13.77/7.80 @ ( collect_complex
% 13.77/7.80 @ ^ [Z2: complex] :
% 13.77/7.80 ( ( power_power_complex @ Z2 @ N )
% 13.77/7.80 = C2 ) ) )
% 13.77/7.80 = zero_zero_complex ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7152_vebt__buildupi__rule__basic,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.80 => ( hoare_1429296392585015714_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_Intf_vebt_assn @ N @ bot_bot_set_nat ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7153_vebt__minti__rule,axiom,
% 13.77/7.80 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,Y: nat] :
% 13.77/7.80 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_minti @ Ti )
% 13.77/7.80 @ ^ [R5: option_nat] :
% 13.77/7.80 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 13.77/7.80 @ ( pure_assn
% 13.77/7.80 @ ( ( R5
% 13.77/7.80 = ( some_nat @ Y ) )
% 13.77/7.80 = ( vEBT_VEBT_min_in_set @ S @ Y ) ) ) )
% 13.77/7.80 @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7154_VEBT__internal_Ocnt_H_Opelims,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.80 ( ( ( vEBT_VEBT_cnt2 @ X )
% 13.77/7.80 = Y )
% 13.77/7.80 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ X )
% 13.77/7.80 => ( ! [A3: $o,B3: $o] :
% 13.77/7.80 ( ( X
% 13.77/7.80 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.80 => ( ( Y = one_one_nat )
% 13.77/7.80 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.80 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.80 ( ( X
% 13.77/7.80 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.80 => ( ( Y
% 13.77/7.80 = ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_cnt2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_cnt2 @ TreeList2 ) @ zero_zero_nat ) ) )
% 13.77/7.80 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7155_VEBT__internal_Ocnt_Osimps_I2_J,axiom,
% 13.77/7.80 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.80 ( ( vEBT_VEBT_cnt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 13.77/7.80 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList ) @ zero_zero_real ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7156_VEBT__internal_Ocnt_Oelims,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: real] :
% 13.77/7.80 ( ( ( vEBT_VEBT_cnt @ X )
% 13.77/7.80 = Y )
% 13.77/7.80 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.80 ( X
% 13.77/7.80 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.80 => ( Y != one_one_real ) )
% 13.77/7.80 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.80 ( ( X
% 13.77/7.80 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.80 => ( Y
% 13.77/7.80 != ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7157_VEBT__internal_Ocnt_Opelims,axiom,
% 13.77/7.80 ! [X: vEBT_VEBT,Y: real] :
% 13.77/7.80 ( ( ( vEBT_VEBT_cnt @ X )
% 13.77/7.80 = Y )
% 13.77/7.80 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ X )
% 13.77/7.80 => ( ! [A3: $o,B3: $o] :
% 13.77/7.80 ( ( X
% 13.77/7.80 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.80 => ( ( Y = one_one_real )
% 13.77/7.80 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.80 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.80 ( ( X
% 13.77/7.80 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.80 => ( ( Y
% 13.77/7.80 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( vEBT_VEBT_cnt @ Summary2 ) ) @ ( foldr_real_real @ plus_plus_real @ ( map_VEBT_VEBT_real @ vEBT_VEBT_cnt @ TreeList2 ) @ zero_zero_real ) ) )
% 13.77/7.80 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_cnt_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7158_prod__decode__aux_Opelims,axiom,
% 13.77/7.80 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 13.77/7.80 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 13.77/7.80 = Y )
% 13.77/7.80 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 13.77/7.80 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 13.77/7.80 => ( Y
% 13.77/7.80 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 13.77/7.80 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 13.77/7.80 => ( Y
% 13.77/7.80 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 13.77/7.80 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7159_vebt__buildupi__refines,axiom,
% 13.77/7.80 ! [N: nat] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_V739175172307565963ildupi @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7160_vebt__deletei__refines,axiom,
% 13.77/7.80 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_deletei @ Ti @ X ) @ ( vEBT_V1365221501068881998eletei @ T @ Ti @ X ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7161_vebt__inserti__refines,axiom,
% 13.77/7.80 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine5565527176597971370_VEBTi @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7162_VEBTi_Osize_I3_J,axiom,
% 13.77/7.80 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 13.77/7.80 ( ( size_size_VEBT_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 13.77/7.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ size_size_VEBT_VEBTi @ X13 ) @ ( size_size_VEBT_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7163_vebt__succi__refines,axiom,
% 13.77/7.80 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine7594492741263601813on_nat @ ( vEBT_vebt_succi @ Ti @ X ) @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7164_vebt__predi__refines,axiom,
% 13.77/7.80 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine7594492741263601813on_nat @ ( vEBT_vebt_predi @ Ti @ X ) @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7165_vebt__memberi__refines,axiom,
% 13.77/7.80 ! [Ti: vEBT_VEBTi,X: nat,T: vEBT_VEBT] : ( refine_Imp_refines_o @ ( vEBT_vebt_memberi @ Ti @ X ) @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7166_VEBTi_Osize__gen_I1_J,axiom,
% 13.77/7.80 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi] :
% 13.77/7.80 ( ( vEBT_size_VEBTi @ ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 ) )
% 13.77/7.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_a6397454172108246045_VEBTi @ vEBT_size_VEBTi @ X13 ) @ ( vEBT_size_VEBTi @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7167_TBOUND__minNull,axiom,
% 13.77/7.80 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.80 ( ( vEBT_VEBT_minNull @ T )
% 13.77/7.80 => ( time_T5737551269749752165_VEBTi @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) @ one_one_nat ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7168_TBOUND__vebt__buildupi,axiom,
% 13.77/7.80 ! [N: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_V441764108873111860ildupi @ N ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7169_finite__atMost,axiom,
% 13.77/7.80 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7170_card__atMost,axiom,
% 13.77/7.80 ! [U: nat] :
% 13.77/7.80 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 13.77/7.80 = ( suc @ U ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7171_atMost__0,axiom,
% 13.77/7.80 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 13.77/7.80 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7172_lessThan__Suc__atMost,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 13.77/7.80 = ( set_ord_atMost_nat @ K ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7173_atMost__Suc,axiom,
% 13.77/7.80 ! [K: nat] :
% 13.77/7.80 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 13.77/7.80 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7174_finite__nat__iff__bounded__le,axiom,
% 13.77/7.80 ( finite_finite_nat
% 13.77/7.80 = ( ^ [S6: set_nat] :
% 13.77/7.80 ? [K3: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7175_atMost__Suc__eq__insert__0,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 13.77/7.80 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7176_polynomial__product__nat,axiom,
% 13.77/7.80 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 13.77/7.80 ( ! [I2: nat] :
% 13.77/7.80 ( ( ord_less_nat @ M @ I2 )
% 13.77/7.80 => ( ( A @ I2 )
% 13.77/7.80 = zero_zero_nat ) )
% 13.77/7.80 => ( ! [J2: nat] :
% 13.77/7.80 ( ( ord_less_nat @ N @ J2 )
% 13.77/7.80 => ( ( B @ J2 )
% 13.77/7.80 = zero_zero_nat ) )
% 13.77/7.80 => ( ( times_times_nat
% 13.77/7.80 @ ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X @ I3 ) )
% 13.77/7.80 @ ( set_ord_atMost_nat @ M ) )
% 13.77/7.80 @ ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 13.77/7.80 @ ( set_ord_atMost_nat @ N ) ) )
% 13.77/7.80 = ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [R5: nat] :
% 13.77/7.80 ( times_times_nat
% 13.77/7.80 @ ( groups3542108847815614940at_nat
% 13.77/7.80 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 13.77/7.80 @ ( set_ord_atMost_nat @ R5 ) )
% 13.77/7.80 @ ( power_power_nat @ X @ R5 ) )
% 13.77/7.80 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7177_TBOUND__vebt__minti,axiom,
% 13.77/7.80 ! [T: vEBT_VEBTi] : ( time_T8353473612707095248on_nat @ ( vEBT_vebt_minti @ T ) @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7178_TBOUND__vebt__maxti,axiom,
% 13.77/7.80 ! [T: vEBT_VEBTi] : ( time_T8353473612707095248on_nat @ ( vEBT_vebt_maxti @ T ) @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7179_TBOUND__minNulli,axiom,
% 13.77/7.80 ! [T: vEBT_VEBTi] : ( time_TBOUND_o @ ( vEBT_VEBT_minNulli @ T ) @ one_one_nat ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7180_finite__atLeastAtMost,axiom,
% 13.77/7.80 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7181_image__Suc__atLeastAtMost,axiom,
% 13.77/7.80 ! [I: nat,J: nat] :
% 13.77/7.80 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 13.77/7.80 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7182_card__atLeastAtMost,axiom,
% 13.77/7.80 ! [L: nat,U: nat] :
% 13.77/7.80 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 13.77/7.80 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7183_all__nat__less,axiom,
% 13.77/7.80 ! [N: nat,P2: nat > $o] :
% 13.77/7.80 ( ( ! [M5: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ M5 @ N )
% 13.77/7.80 => ( P2 @ M5 ) ) )
% 13.77/7.80 = ( ! [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 13.77/7.80 => ( P2 @ X4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7184_ex__nat__less,axiom,
% 13.77/7.80 ! [N: nat,P2: nat > $o] :
% 13.77/7.80 ( ( ? [M5: nat] :
% 13.77/7.80 ( ( ord_less_eq_nat @ M5 @ N )
% 13.77/7.80 & ( P2 @ M5 ) ) )
% 13.77/7.80 = ( ? [X4: nat] :
% 13.77/7.80 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 13.77/7.80 & ( P2 @ X4 ) ) ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7185_atLeastLessThanSuc__atLeastAtMost,axiom,
% 13.77/7.80 ! [L: nat,U: nat] :
% 13.77/7.80 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 13.77/7.80 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7186_atMost__atLeast0,axiom,
% 13.77/7.80 ( set_ord_atMost_nat
% 13.77/7.80 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7187_complex__mod__minus__le__complex__mod,axiom,
% 13.77/7.80 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7188_complex__mod__triangle__ineq2,axiom,
% 13.77/7.80 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 13.77/7.80
% 13.77/7.80 thf(fact_7189_atLeast0__atMost__Suc,axiom,
% 13.77/7.80 ! [N: nat] :
% 13.77/7.80 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 13.77/7.80 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7190_Icc__eq__insert__lb__nat,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 13.77/7.81 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7191_atLeastAtMostSuc__conv,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 13.77/7.81 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 13.77/7.81 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7192_atLeastAtMost__insertL,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 13.77/7.81 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7193_subset__eq__atLeast0__atMost__finite,axiom,
% 13.77/7.81 ! [N8: set_nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_set_nat @ N8 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 13.77/7.81 => ( finite_finite_nat @ N8 ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7194_image__Suc__lessThan,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.81 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7195_image__Suc__atMost,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 13.77/7.81 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7196_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 13.77/7.81 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7197_atLeast1__atMost__eq__remove0,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.81 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7198_atLeastAtMostPlus1__int__conv,axiom,
% 13.77/7.81 ! [M: int,N: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 13.77/7.81 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 13.77/7.81 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7199_simp__from__to,axiom,
% 13.77/7.81 ( set_or1266510415728281911st_int
% 13.77/7.81 = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7200_aset_I7_J,axiom,
% 13.77/7.81 ! [D4: int,A4: set_int,T: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ A4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_int @ T @ X5 )
% 13.77/7.81 => ( ord_less_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7201_aset_I5_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,A4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ T @ A4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ A4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_int @ X5 @ T )
% 13.77/7.81 => ( ord_less_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7202_aset_I4_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,A4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ T @ A4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ A4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( X5 != T )
% 13.77/7.81 => ( ( plus_plus_int @ X5 @ D4 )
% 13.77/7.81 != T ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7203_aset_I3_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,A4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ A4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( X5 = T )
% 13.77/7.81 => ( ( plus_plus_int @ X5 @ D4 )
% 13.77/7.81 = T ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7204_bset_I7_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,B4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ T @ B4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ B4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_int @ T @ X5 )
% 13.77/7.81 => ( ord_less_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7205_bset_I5_J,axiom,
% 13.77/7.81 ! [D4: int,B4: set_int,T: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ B4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_int @ X5 @ T )
% 13.77/7.81 => ( ord_less_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7206_bset_I4_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,B4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ T @ B4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ B4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( X5 != T )
% 13.77/7.81 => ( ( minus_minus_int @ X5 @ D4 )
% 13.77/7.81 != T ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7207_bset_I3_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,B4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ B4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( X5 = T )
% 13.77/7.81 => ( ( minus_minus_int @ X5 @ D4 )
% 13.77/7.81 = T ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7208_periodic__finite__ex,axiom,
% 13.77/7.81 ! [D: int,P2: int > $o] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D )
% 13.77/7.81 => ( ! [X3: int,K2: int] :
% 13.77/7.81 ( ( P2 @ X3 )
% 13.77/7.81 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D ) ) ) )
% 13.77/7.81 => ( ( ? [X8: int] : ( P2 @ X8 ) )
% 13.77/7.81 = ( ? [X4: int] :
% 13.77/7.81 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 13.77/7.81 & ( P2 @ X4 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7209_aset_I8_J,axiom,
% 13.77/7.81 ! [D4: int,A4: set_int,T: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ A4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ T @ X5 )
% 13.77/7.81 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X5 @ D4 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7210_aset_I6_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,A4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ A4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ X5 @ T )
% 13.77/7.81 => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D4 ) @ T ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7211_bset_I8_J,axiom,
% 13.77/7.81 ! [D4: int,T: int,B4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ B4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ T @ X5 )
% 13.77/7.81 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X5 @ D4 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7212_bset_I6_J,axiom,
% 13.77/7.81 ! [D4: int,B4: set_int,T: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ! [X5: int] :
% 13.77/7.81 ( ! [Xa3: int] :
% 13.77/7.81 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb2: int] :
% 13.77/7.81 ( ( member_int @ Xb2 @ B4 )
% 13.77/7.81 => ( X5
% 13.77/7.81 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ X5 @ T )
% 13.77/7.81 => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D4 ) @ T ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7213_cpmi,axiom,
% 13.77/7.81 ! [D4: int,P2: int > $o,P6: int > $o,B4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ? [Z5: int] :
% 13.77/7.81 ! [X3: int] :
% 13.77/7.81 ( ( ord_less_int @ X3 @ Z5 )
% 13.77/7.81 => ( ( P2 @ X3 )
% 13.77/7.81 = ( P6 @ X3 ) ) )
% 13.77/7.81 => ( ! [X3: int] :
% 13.77/7.81 ( ! [Xa: int] :
% 13.77/7.81 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb3: int] :
% 13.77/7.81 ( ( member_int @ Xb3 @ B4 )
% 13.77/7.81 => ( X3
% 13.77/7.81 != ( plus_plus_int @ Xb3 @ Xa ) ) ) )
% 13.77/7.81 => ( ( P2 @ X3 )
% 13.77/7.81 => ( P2 @ ( minus_minus_int @ X3 @ D4 ) ) ) )
% 13.77/7.81 => ( ! [X3: int,K2: int] :
% 13.77/7.81 ( ( P6 @ X3 )
% 13.77/7.81 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 13.77/7.81 => ( ( ? [X8: int] : ( P2 @ X8 ) )
% 13.77/7.81 = ( ? [X4: int] :
% 13.77/7.81 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 & ( P6 @ X4 ) )
% 13.77/7.81 | ? [X4: int] :
% 13.77/7.81 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 & ? [Y4: int] :
% 13.77/7.81 ( ( member_int @ Y4 @ B4 )
% 13.77/7.81 & ( P2 @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7214_cppi,axiom,
% 13.77/7.81 ! [D4: int,P2: int > $o,P6: int > $o,A4: set_int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D4 )
% 13.77/7.81 => ( ? [Z5: int] :
% 13.77/7.81 ! [X3: int] :
% 13.77/7.81 ( ( ord_less_int @ Z5 @ X3 )
% 13.77/7.81 => ( ( P2 @ X3 )
% 13.77/7.81 = ( P6 @ X3 ) ) )
% 13.77/7.81 => ( ! [X3: int] :
% 13.77/7.81 ( ! [Xa: int] :
% 13.77/7.81 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 => ! [Xb3: int] :
% 13.77/7.81 ( ( member_int @ Xb3 @ A4 )
% 13.77/7.81 => ( X3
% 13.77/7.81 != ( minus_minus_int @ Xb3 @ Xa ) ) ) )
% 13.77/7.81 => ( ( P2 @ X3 )
% 13.77/7.81 => ( P2 @ ( plus_plus_int @ X3 @ D4 ) ) ) )
% 13.77/7.81 => ( ! [X3: int,K2: int] :
% 13.77/7.81 ( ( P6 @ X3 )
% 13.77/7.81 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 13.77/7.81 => ( ( ? [X8: int] : ( P2 @ X8 ) )
% 13.77/7.81 = ( ? [X4: int] :
% 13.77/7.81 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 & ( P6 @ X4 ) )
% 13.77/7.81 | ? [X4: int] :
% 13.77/7.81 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 13.77/7.81 & ? [Y4: int] :
% 13.77/7.81 ( ( member_int @ Y4 @ A4 )
% 13.77/7.81 & ( P2 @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7215_nat__mult__div__cancel__disj,axiom,
% 13.77/7.81 ! [K: nat,M: nat,N: nat] :
% 13.77/7.81 ( ( ( K = zero_zero_nat )
% 13.77/7.81 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.81 = zero_zero_nat ) )
% 13.77/7.81 & ( ( K != zero_zero_nat )
% 13.77/7.81 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.81 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7216_zdiv__int,axiom,
% 13.77/7.81 ! [A: nat,B: nat] :
% 13.77/7.81 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 13.77/7.81 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7217_real__of__nat__div4,axiom,
% 13.77/7.81 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7218_real__of__nat__div2,axiom,
% 13.77/7.81 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7219_real__of__nat__div3,axiom,
% 13.77/7.81 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7220_pos__imp__zdiv__neg__iff,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 13.77/7.81 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7221_neg__imp__zdiv__neg__iff,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 13.77/7.81 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7222_div__neg__pos__less0,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7223_nat__mult__div__cancel1,axiom,
% 13.77/7.81 ! [K: nat,M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.81 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.81 = ( divide_divide_nat @ M @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7224_nonneg1__imp__zdiv__pos__iff,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 13.77/7.81 = ( ( ord_less_eq_int @ B @ A )
% 13.77/7.81 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7225_pos__imp__zdiv__nonneg__iff,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 13.77/7.81 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7226_neg__imp__zdiv__nonneg__iff,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 13.77/7.81 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7227_pos__imp__zdiv__pos__iff,axiom,
% 13.77/7.81 ! [K: int,I: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 13.77/7.81 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7228_div__nonpos__pos__le0,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7229_div__nonneg__neg__le0,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.81 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7230_div__positive__int,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ L @ K )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7231_div__int__pos__iff,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 13.77/7.81 = ( ( K = zero_zero_int )
% 13.77/7.81 | ( L = zero_zero_int )
% 13.77/7.81 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.81 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 13.77/7.81 | ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.81 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7232_zdiv__mono2__neg,axiom,
% 13.77/7.81 ! [A: int,B2: int,B: int] :
% 13.77/7.81 ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 13.77/7.81 => ( ( ord_less_eq_int @ B2 @ B )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7233_zdiv__mono1__neg,axiom,
% 13.77/7.81 ! [A: int,A2: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ A @ A2 )
% 13.77/7.81 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7234_zdiv__eq__0__iff,axiom,
% 13.77/7.81 ! [I: int,K: int] :
% 13.77/7.81 ( ( ( divide_divide_int @ I @ K )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 = ( ( K = zero_zero_int )
% 13.77/7.81 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 13.77/7.81 & ( ord_less_int @ I @ K ) )
% 13.77/7.81 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 13.77/7.81 & ( ord_less_int @ K @ I ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7235_zdiv__mono2,axiom,
% 13.77/7.81 ! [A: int,B2: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 13.77/7.81 => ( ( ord_less_eq_int @ B2 @ B )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7236_zdiv__mono1,axiom,
% 13.77/7.81 ! [A: int,A2: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ A @ A2 )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7237_int__div__less__self,axiom,
% 13.77/7.81 ! [X: int,K: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ X )
% 13.77/7.81 => ( ( ord_less_int @ one_one_int @ K )
% 13.77/7.81 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7238_div__geq,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ~ ( ord_less_nat @ M @ N )
% 13.77/7.81 => ( ( divide_divide_nat @ M @ N )
% 13.77/7.81 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7239_msrevs_I1_J,axiom,
% 13.77/7.81 ! [N: nat,K: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) @ N )
% 13.77/7.81 = ( plus_plus_nat @ ( divide_divide_nat @ M @ N ) @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7240_verit__less__mono__div__int2,axiom,
% 13.77/7.81 ! [A4: int,B4: int,N: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ A4 @ B4 )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A4 @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7241_div__eq__minus1,axiom,
% 13.77/7.81 ! [B: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 13.77/7.81 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7242_int__div__pos__eq,axiom,
% 13.77/7.81 ! [A: int,B: int,Q3: int,R: int] :
% 13.77/7.81 ( ( A
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 13.77/7.81 => ( ( ord_less_int @ R @ B )
% 13.77/7.81 => ( ( divide_divide_int @ A @ B )
% 13.77/7.81 = Q3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7243_int__div__neg__eq,axiom,
% 13.77/7.81 ! [A: int,B: int,Q3: int,R: int] :
% 13.77/7.81 ( ( A
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ B @ R )
% 13.77/7.81 => ( ( divide_divide_int @ A @ B )
% 13.77/7.81 = Q3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7244_split__zdiv,axiom,
% 13.77/7.81 ! [P2: int > $o,N: int,K: int] :
% 13.77/7.81 ( ( P2 @ ( divide_divide_int @ N @ K ) )
% 13.77/7.81 = ( ( ( K = zero_zero_int )
% 13.77/7.81 => ( P2 @ zero_zero_int ) )
% 13.77/7.81 & ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.81 => ! [I3: int,J3: int] :
% 13.77/7.81 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 13.77/7.81 & ( ord_less_int @ J3 @ K )
% 13.77/7.81 & ( N
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 13.77/7.81 => ( P2 @ I3 ) ) )
% 13.77/7.81 & ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.81 => ! [I3: int,J3: int] :
% 13.77/7.81 ( ( ( ord_less_int @ K @ J3 )
% 13.77/7.81 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 13.77/7.81 & ( N
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 13.77/7.81 => ( P2 @ I3 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7245_int__power__div__base,axiom,
% 13.77/7.81 ! [M: nat,K: int] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 13.77/7.81 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7246_div__pos__geq,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ( ord_less_eq_int @ L @ K )
% 13.77/7.81 => ( ( divide_divide_int @ K @ L )
% 13.77/7.81 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7247_int__div__minus__is__minus1,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_int @ A @ zero_zero_int )
% 13.77/7.81 => ( ( ( divide_divide_int @ A @ B )
% 13.77/7.81 = ( uminus_uminus_int @ A ) )
% 13.77/7.81 = ( B
% 13.77/7.81 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7248_int__div__same__is__1,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.81 => ( ( ( divide_divide_int @ A @ B )
% 13.77/7.81 = A )
% 13.77/7.81 = ( B = one_one_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7249_div__by__Suc__0,axiom,
% 13.77/7.81 ! [M: nat] :
% 13.77/7.81 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 13.77/7.81 = M ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7250_div__less,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ M @ N )
% 13.77/7.81 => ( ( divide_divide_nat @ M @ N )
% 13.77/7.81 = zero_zero_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7251_div__eq__dividend__iff,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.81 => ( ( ( divide_divide_nat @ M @ N )
% 13.77/7.81 = M )
% 13.77/7.81 = ( N = one_one_nat ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7252_div__mult__self1__is__m,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 13.77/7.81 = M ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7253_div__mult__self__is__m,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 13.77/7.81 = M ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7254_div__neg__neg__trivial,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ L @ K )
% 13.77/7.81 => ( ( divide_divide_int @ K @ L )
% 13.77/7.81 = zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7255_div__pos__pos__trivial,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( ord_less_int @ K @ L )
% 13.77/7.81 => ( ( divide_divide_int @ K @ L )
% 13.77/7.81 = zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7256_div__le__mono,axiom,
% 13.77/7.81 ! [M: nat,N: nat,K: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7257_div__le__dividend,axiom,
% 13.77/7.81 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7258_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ( divide_divide_nat @ M @ N )
% 13.77/7.81 = zero_zero_nat )
% 13.77/7.81 = ( ( ord_less_nat @ M @ N )
% 13.77/7.81 | ( N = zero_zero_nat ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7259_Suc__div__le__mono,axiom,
% 13.77/7.81 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7260_less__mult__imp__div__less,axiom,
% 13.77/7.81 ! [M: nat,I: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 13.77/7.81 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7261_times__div__less__eq__dividend,axiom,
% 13.77/7.81 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7262_div__times__less__eq__dividend,axiom,
% 13.77/7.81 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7263_div__mult__le,axiom,
% 13.77/7.81 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ A ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7264_div__greater__zero__iff,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 13.77/7.81 = ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.81 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7265_div__le__mono2,axiom,
% 13.77/7.81 ! [M: nat,N: nat,K: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.81 => ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7266_div__less__dividend,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ one_one_nat @ N )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.81 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7267_div__less__iff__less__mult,axiom,
% 13.77/7.81 ! [Q3: nat,M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 13.77/7.81 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 13.77/7.81 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7268_td__gal__lt,axiom,
% 13.77/7.81 ! [C2: nat,A: nat,B: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.81 => ( ( ord_less_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 13.77/7.81 = ( ord_less_nat @ ( divide_divide_nat @ A @ C2 ) @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7269_zdiv__le__dividend,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ A ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7270_zdiv__zmult2__eq,axiom,
% 13.77/7.81 ! [C2: int,A: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 13.77/7.81 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7271_div__if,axiom,
% 13.77/7.81 ( divide_divide_nat
% 13.77/7.81 = ( ^ [M5: nat,N6: nat] :
% 13.77/7.81 ( if_nat
% 13.77/7.81 @ ( ( ord_less_nat @ M5 @ N6 )
% 13.77/7.81 | ( N6 = zero_zero_nat ) )
% 13.77/7.81 @ zero_zero_nat
% 13.77/7.81 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M5 @ N6 ) @ N6 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7272_div__nat__eqI,axiom,
% 13.77/7.81 ! [N: nat,Q3: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 13.77/7.81 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 13.77/7.81 => ( ( divide_divide_nat @ M @ N )
% 13.77/7.81 = Q3 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7273_split__div,axiom,
% 13.77/7.81 ! [P2: nat > $o,M: nat,N: nat] :
% 13.77/7.81 ( ( P2 @ ( divide_divide_nat @ M @ N ) )
% 13.77/7.81 = ( ( ( N = zero_zero_nat )
% 13.77/7.81 => ( P2 @ zero_zero_nat ) )
% 13.77/7.81 & ( ( N != zero_zero_nat )
% 13.77/7.81 => ! [I3: nat,J3: nat] :
% 13.77/7.81 ( ( ord_less_nat @ J3 @ N )
% 13.77/7.81 => ( ( M
% 13.77/7.81 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 13.77/7.81 => ( P2 @ I3 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7274_dividend__less__div__times,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7275_dividend__less__times__div,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7276_less__eq__div__iff__mult__less__eq,axiom,
% 13.77/7.81 ! [Q3: nat,M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 13.77/7.81 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 13.77/7.81 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7277_td__gal,axiom,
% 13.77/7.81 ! [C2: nat,B: nat,A: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.81 => ( ( ord_less_eq_nat @ ( times_times_nat @ B @ C2 ) @ A )
% 13.77/7.81 = ( ord_less_eq_nat @ B @ ( divide_divide_nat @ A @ C2 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7278_divide__nat__def,axiom,
% 13.77/7.81 ( divide_divide_nat
% 13.77/7.81 = ( ^ [M5: nat,N6: nat] :
% 13.77/7.81 ( if_nat @ ( N6 = zero_zero_nat ) @ zero_zero_nat
% 13.77/7.81 @ ( lattic8265883725875713057ax_nat
% 13.77/7.81 @ ( collect_nat
% 13.77/7.81 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N6 ) @ M5 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7279_le__div__geq,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.81 => ( ( divide_divide_nat @ M @ N )
% 13.77/7.81 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7280_split__div_H,axiom,
% 13.77/7.81 ! [P2: nat > $o,M: nat,N: nat] :
% 13.77/7.81 ( ( P2 @ ( divide_divide_nat @ M @ N ) )
% 13.77/7.81 = ( ( ( N = zero_zero_nat )
% 13.77/7.81 & ( P2 @ zero_zero_nat ) )
% 13.77/7.81 | ? [Q8: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q8 ) @ M )
% 13.77/7.81 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q8 ) ) )
% 13.77/7.81 & ( P2 @ Q8 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7281_power__sub,axiom,
% 13.77/7.81 ! [N: nat,M: nat,A: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 13.77/7.81 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.81 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7282_div__pos__neg__trivial,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 13.77/7.81 => ( ( divide_divide_int @ K @ L )
% 13.77/7.81 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7283_nat__mod__eq_H,axiom,
% 13.77/7.81 ! [A: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ A @ N )
% 13.77/7.81 => ( ( modulo_modulo_nat @ A @ N )
% 13.77/7.81 = A ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7284_mod__less,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ M @ N )
% 13.77/7.81 => ( ( modulo_modulo_nat @ M @ N )
% 13.77/7.81 = M ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7285_binomial__Suc__n,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( binomial @ ( suc @ N ) @ N )
% 13.77/7.81 = ( suc @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7286_mod__by__Suc__0,axiom,
% 13.77/7.81 ! [M: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 13.77/7.81 = zero_zero_nat ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7287_binomial__1,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 13.77/7.81 = N ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7288_binomial__0__Suc,axiom,
% 13.77/7.81 ! [K: nat] :
% 13.77/7.81 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 13.77/7.81 = zero_zero_nat ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7289_binomial__eq__0__iff,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( ( binomial @ N @ K )
% 13.77/7.81 = zero_zero_nat )
% 13.77/7.81 = ( ord_less_nat @ N @ K ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7290_binomial__Suc__Suc,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 13.77/7.81 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7291_binomial__n__0,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( binomial @ N @ zero_zero_nat )
% 13.77/7.81 = one_one_nat ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7292_Suc__mod__mult__self1,axiom,
% 13.77/7.81 ! [M: nat,K: nat,N: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7293_Suc__mod__mult__self2,axiom,
% 13.77/7.81 ! [M: nat,N: nat,K: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7294_Suc__mod__mult__self3,axiom,
% 13.77/7.81 ! [K: nat,N: nat,M: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7295_Suc__mod__mult__self4,axiom,
% 13.77/7.81 ! [N: nat,K: nat,M: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7296_zero__less__binomial__iff,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 13.77/7.81 = ( ord_less_eq_nat @ K @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7297_mod__Suc__eq,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7298_mod__Suc__Suc__eq,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7299_nat__mod__eq,axiom,
% 13.77/7.81 ! [B: nat,N: nat,A: nat] :
% 13.77/7.81 ( ( ord_less_nat @ B @ N )
% 13.77/7.81 => ( ( ( modulo_modulo_nat @ A @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ B @ N ) )
% 13.77/7.81 => ( ( modulo_modulo_nat @ A @ N )
% 13.77/7.81 = B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7300_mod__less__eq__dividend,axiom,
% 13.77/7.81 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7301_binomial__eq__0,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( ord_less_nat @ N @ K )
% 13.77/7.81 => ( ( binomial @ N @ K )
% 13.77/7.81 = zero_zero_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7302_Suc__times__binomial,axiom,
% 13.77/7.81 ! [K: nat,N: nat] :
% 13.77/7.81 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 13.77/7.81 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7303_Suc__times__binomial__eq,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 13.77/7.81 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7304_binomial__symmetric,axiom,
% 13.77/7.81 ! [K: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.81 => ( ( binomial @ N @ K )
% 13.77/7.81 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7305_binomial__le__pow,axiom,
% 13.77/7.81 ! [R: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ R @ N )
% 13.77/7.81 => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7306_mod__Suc,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 13.77/7.81 = N )
% 13.77/7.81 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 13.77/7.81 = zero_zero_nat ) )
% 13.77/7.81 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 13.77/7.81 != N )
% 13.77/7.81 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 13.77/7.81 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7307_mod__induct,axiom,
% 13.77/7.81 ! [P2: nat > $o,N: nat,P3: nat,M: nat] :
% 13.77/7.81 ( ( P2 @ N )
% 13.77/7.81 => ( ( ord_less_nat @ N @ P3 )
% 13.77/7.81 => ( ( ord_less_nat @ M @ P3 )
% 13.77/7.81 => ( ! [N2: nat] :
% 13.77/7.81 ( ( ord_less_nat @ N2 @ P3 )
% 13.77/7.81 => ( ( P2 @ N2 )
% 13.77/7.81 => ( P2 @ ( modulo_modulo_nat @ ( suc @ N2 ) @ P3 ) ) ) )
% 13.77/7.81 => ( P2 @ M ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7308_gcd__nat__induct,axiom,
% 13.77/7.81 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 13.77/7.81 ( ! [M3: nat] : ( P2 @ M3 @ zero_zero_nat )
% 13.77/7.81 => ( ! [M3: nat,N2: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 13.77/7.81 => ( ( P2 @ N2 @ ( modulo_modulo_nat @ M3 @ N2 ) )
% 13.77/7.81 => ( P2 @ M3 @ N2 ) ) )
% 13.77/7.81 => ( P2 @ M @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7309_nat__mod__lem,axiom,
% 13.77/7.81 ! [N: nat,B: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_nat @ B @ N )
% 13.77/7.81 = ( ( modulo_modulo_nat @ B @ N )
% 13.77/7.81 = B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7310_mod__less__divisor,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7311_mod__Suc__le__divisor,axiom,
% 13.77/7.81 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7312_word__rot__lem,axiom,
% 13.77/7.81 ! [L: nat,K: nat,D: nat,N: nat] :
% 13.77/7.81 ( ( ( plus_plus_nat @ L @ K )
% 13.77/7.81 = ( plus_plus_nat @ D @ ( modulo_modulo_nat @ K @ L ) ) )
% 13.77/7.81 => ( ( ord_less_nat @ N @ L )
% 13.77/7.81 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ D @ N ) @ L )
% 13.77/7.81 = N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7313_nat__minus__mod,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( modulo_modulo_nat @ ( minus_minus_nat @ N @ ( modulo_modulo_nat @ N @ M ) ) @ M )
% 13.77/7.81 = zero_zero_nat ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7314_mod__geq,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ~ ( ord_less_nat @ M @ N )
% 13.77/7.81 => ( ( modulo_modulo_nat @ M @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7315_mod__if,axiom,
% 13.77/7.81 ( modulo_modulo_nat
% 13.77/7.81 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( ord_less_nat @ M5 @ N6 ) @ M5 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M5 @ N6 ) @ N6 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7316_mod__nat__sub,axiom,
% 13.77/7.81 ! [X: nat,Z: nat,Y: nat] :
% 13.77/7.81 ( ( ord_less_nat @ X @ Z )
% 13.77/7.81 => ( ( modulo_modulo_nat @ ( minus_minus_nat @ X @ Y ) @ Z )
% 13.77/7.81 = ( minus_minus_nat @ X @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7317_mod__eq__0D,axiom,
% 13.77/7.81 ! [M: nat,D: nat] :
% 13.77/7.81 ( ( ( modulo_modulo_nat @ M @ D )
% 13.77/7.81 = zero_zero_nat )
% 13.77/7.81 => ? [Q5: nat] :
% 13.77/7.81 ( M
% 13.77/7.81 = ( times_times_nat @ D @ Q5 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7318_le__mod__geq,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.81 => ( ( modulo_modulo_nat @ M @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7319_nat__mod__eq__iff,axiom,
% 13.77/7.81 ! [X: nat,N: nat,Y: nat] :
% 13.77/7.81 ( ( ( modulo_modulo_nat @ X @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ Y @ N ) )
% 13.77/7.81 = ( ? [Q1: nat,Q22: nat] :
% 13.77/7.81 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 13.77/7.81 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7320_zero__less__binomial,axiom,
% 13.77/7.81 ! [K: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.81 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7321_Suc__times__binomial__add,axiom,
% 13.77/7.81 ! [A: nat,B: nat] :
% 13.77/7.81 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 13.77/7.81 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7322_binomial__Suc__Suc__eq__times,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 13.77/7.81 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7323_choose__mult,axiom,
% 13.77/7.81 ! [K: nat,M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ K @ M )
% 13.77/7.81 => ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 13.77/7.81 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7324_mod__le__divisor,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7325_div__less__mono,axiom,
% 13.77/7.81 ! [A4: nat,B4: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ A4 @ B4 )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ( modulo_modulo_nat @ A4 @ N )
% 13.77/7.81 = zero_zero_nat )
% 13.77/7.81 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 13.77/7.81 = zero_zero_nat )
% 13.77/7.81 => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7326_mod__nat__add,axiom,
% 13.77/7.81 ! [X: nat,Z: nat,Y: nat] :
% 13.77/7.81 ( ( ord_less_nat @ X @ Z )
% 13.77/7.81 => ( ( ord_less_nat @ Y @ Z )
% 13.77/7.81 => ( ( ( ord_less_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 13.77/7.81 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 13.77/7.81 = ( plus_plus_nat @ X @ Y ) ) )
% 13.77/7.81 & ( ~ ( ord_less_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 13.77/7.81 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ X @ Y ) @ Z )
% 13.77/7.81 = ( minus_minus_nat @ ( plus_plus_nat @ X @ Y ) @ Z ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7327_nat__mod__eq__lemma,axiom,
% 13.77/7.81 ! [X: nat,N: nat,Y: nat] :
% 13.77/7.81 ( ( ( modulo_modulo_nat @ X @ N )
% 13.77/7.81 = ( modulo_modulo_nat @ Y @ N ) )
% 13.77/7.81 => ( ( ord_less_eq_nat @ Y @ X )
% 13.77/7.81 => ? [Q5: nat] :
% 13.77/7.81 ( X
% 13.77/7.81 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q5 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7328_mod__eq__nat2E,axiom,
% 13.77/7.81 ! [M: nat,Q3: nat,N: nat] :
% 13.77/7.81 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 13.77/7.81 = ( modulo_modulo_nat @ N @ Q3 ) )
% 13.77/7.81 => ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ~ ! [S4: nat] :
% 13.77/7.81 ( N
% 13.77/7.81 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S4 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7329_mod__eq__nat1E,axiom,
% 13.77/7.81 ! [M: nat,Q3: nat,N: nat] :
% 13.77/7.81 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 13.77/7.81 = ( modulo_modulo_nat @ N @ Q3 ) )
% 13.77/7.81 => ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.81 => ~ ! [S4: nat] :
% 13.77/7.81 ( M
% 13.77/7.81 != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S4 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7330_sum__choose__upper,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( groups3542108847815614940at_nat
% 13.77/7.81 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 13.77/7.81 @ ( set_ord_atMost_nat @ N ) )
% 13.77/7.81 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7331_binomial__absorption,axiom,
% 13.77/7.81 ! [K: nat,N: nat] :
% 13.77/7.81 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 13.77/7.81 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7332_split__mod,axiom,
% 13.77/7.81 ! [P2: nat > $o,M: nat,N: nat] :
% 13.77/7.81 ( ( P2 @ ( modulo_modulo_nat @ M @ N ) )
% 13.77/7.81 = ( ( ( N = zero_zero_nat )
% 13.77/7.81 => ( P2 @ M ) )
% 13.77/7.81 & ( ( N != zero_zero_nat )
% 13.77/7.81 => ! [I3: nat,J3: nat] :
% 13.77/7.81 ( ( ord_less_nat @ J3 @ N )
% 13.77/7.81 => ( ( M
% 13.77/7.81 = ( plus_plus_nat @ ( times_times_nat @ N @ I3 ) @ J3 ) )
% 13.77/7.81 => ( P2 @ J3 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7333_mod__lemma,axiom,
% 13.77/7.81 ! [C2: nat,R: nat,B: nat,Q3: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.81 => ( ( ord_less_nat @ R @ B )
% 13.77/7.81 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ Q3 @ C2 ) ) @ R ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7334_sum__choose__lower,axiom,
% 13.77/7.81 ! [R: nat,N: nat] :
% 13.77/7.81 ( ( groups3542108847815614940at_nat
% 13.77/7.81 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R @ K3 ) @ K3 )
% 13.77/7.81 @ ( set_ord_atMost_nat @ N ) )
% 13.77/7.81 = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7335_choose__reduce__nat,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.81 => ( ( binomial @ N @ K )
% 13.77/7.81 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7336_times__binomial__minus1__eq,axiom,
% 13.77/7.81 ! [K: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.81 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 13.77/7.81 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7337_Suc__times__mod__eq,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 13.77/7.81 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 13.77/7.81 = one_one_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7338_sum__choose__diagonal,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ( groups3542108847815614940at_nat
% 13.77/7.81 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 13.77/7.81 @ ( set_ord_atMost_nat @ M ) )
% 13.77/7.81 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7339_binomial__addition__formula,axiom,
% 13.77/7.81 ! [N: nat,K: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( binomial @ N @ ( suc @ K ) )
% 13.77/7.81 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7340_verit__le__mono__div,axiom,
% 13.77/7.81 ! [A4: nat,B4: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ A4 @ B4 )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ord_less_eq_nat
% 13.77/7.81 @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 13.77/7.81 @ ( if_nat
% 13.77/7.81 @ ( ( modulo_modulo_nat @ B4 @ N )
% 13.77/7.81 = zero_zero_nat )
% 13.77/7.81 @ one_one_nat
% 13.77/7.81 @ zero_zero_nat ) )
% 13.77/7.81 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7341_vebt__assn__raw_Osimps_I2_J,axiom,
% 13.77/7.81 ! [Mmo: option4927543243414619207at_nat,Deg: nat,Tree_list: list_VEBT_VEBT,Summary: vEBT_VEBT,Mmoi: option4927543243414619207at_nat,Degi: nat,Tree_array: array_VEBT_VEBTi,Summaryi: vEBT_VEBTi] :
% 13.77/7.81 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ Mmo @ Deg @ Tree_list @ Summary ) @ ( vEBT_Nodei @ Mmoi @ Degi @ Tree_array @ Summaryi ) )
% 13.77/7.81 = ( times_times_assn
% 13.77/7.81 @ ( times_times_assn
% 13.77/7.81 @ ( pure_assn
% 13.77/7.81 @ ( ( Mmoi = Mmo )
% 13.77/7.81 & ( Degi = Deg ) ) )
% 13.77/7.81 @ ( vEBT_vebt_assn_raw @ Summary @ Summaryi ) )
% 13.77/7.81 @ ( ex_ass463751140784270563_VEBTi
% 13.77/7.81 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list @ Tree_is2 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7342_upto__aux__rec,axiom,
% 13.77/7.81 ( upto_aux
% 13.77/7.81 = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7343_mod__neg__neg__trivial,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ L @ K )
% 13.77/7.81 => ( ( modulo_modulo_int @ K @ L )
% 13.77/7.81 = K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7344_mod__pos__pos__trivial,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( ord_less_int @ K @ L )
% 13.77/7.81 => ( ( modulo_modulo_int @ K @ L )
% 13.77/7.81 = K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7345_zmod__le__nonneg__dividend,axiom,
% 13.77/7.81 ! [M: int,K: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 13.77/7.81 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7346_neg__mod__bound,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_int @ L @ zero_zero_int )
% 13.77/7.81 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7347_Euclidean__Division_Opos__mod__bound,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7348_zmod__zminus2__not__zero,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 13.77/7.81 != zero_zero_int )
% 13.77/7.81 => ( ( modulo_modulo_int @ K @ L )
% 13.77/7.81 != zero_zero_int ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7349_zmod__zminus1__not__zero,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 13.77/7.81 != zero_zero_int )
% 13.77/7.81 => ( ( modulo_modulo_int @ K @ L )
% 13.77/7.81 != zero_zero_int ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7350_zmod__eq__0__iff,axiom,
% 13.77/7.81 ! [M: int,D: int] :
% 13.77/7.81 ( ( ( modulo_modulo_int @ M @ D )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 = ( ? [Q8: int] :
% 13.77/7.81 ( M
% 13.77/7.81 = ( times_times_int @ D @ Q8 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7351_zmod__eq__0D,axiom,
% 13.77/7.81 ! [M: int,D: int] :
% 13.77/7.81 ( ( ( modulo_modulo_int @ M @ D )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 => ? [Q5: int] :
% 13.77/7.81 ( M
% 13.77/7.81 = ( times_times_int @ D @ Q5 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7352_zmod__int,axiom,
% 13.77/7.81 ! [A: nat,B: nat] :
% 13.77/7.81 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 13.77/7.81 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7353_int__mod__eq,axiom,
% 13.77/7.81 ! [B: int,N: int,A: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( ord_less_int @ B @ N )
% 13.77/7.81 => ( ( ( modulo_modulo_int @ A @ N )
% 13.77/7.81 = ( modulo_modulo_int @ B @ N ) )
% 13.77/7.81 => ( ( modulo_modulo_int @ A @ N )
% 13.77/7.81 = B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7354_int__mod__lem,axiom,
% 13.77/7.81 ! [N: int,B: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ N )
% 13.77/7.81 => ( ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.81 & ( ord_less_int @ B @ N ) )
% 13.77/7.81 = ( ( modulo_modulo_int @ B @ N )
% 13.77/7.81 = B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7355_neg__mod__sign,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_int @ L @ zero_zero_int )
% 13.77/7.81 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7356_Euclidean__Division_Opos__mod__sign,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7357_int__mod__ge,axiom,
% 13.77/7.81 ! [A: int,N: int] :
% 13.77/7.81 ( ( ord_less_int @ A @ N )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ N )
% 13.77/7.81 => ( ord_less_eq_int @ A @ ( modulo_modulo_int @ A @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7358_neg__mod__conj,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 13.77/7.81 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7359_pos__mod__conj,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 13.77/7.81 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7360_zmod__trivial__iff,axiom,
% 13.77/7.81 ! [I: int,K: int] :
% 13.77/7.81 ( ( ( modulo_modulo_int @ I @ K )
% 13.77/7.81 = I )
% 13.77/7.81 = ( ( K = zero_zero_int )
% 13.77/7.81 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 13.77/7.81 & ( ord_less_int @ I @ K ) )
% 13.77/7.81 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 13.77/7.81 & ( ord_less_int @ K @ I ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7361_int__mod__le_H,axiom,
% 13.77/7.81 ! [B: int,N: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ B @ N ) )
% 13.77/7.81 => ( ord_less_eq_int @ ( modulo_modulo_int @ B @ N ) @ ( minus_minus_int @ B @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7362_zmod__zminus2__eq__if,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 13.77/7.81 = zero_zero_int ) )
% 13.77/7.81 & ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 != zero_zero_int )
% 13.77/7.81 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 13.77/7.81 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7363_zmod__zminus1__eq__if,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 13.77/7.81 = zero_zero_int ) )
% 13.77/7.81 & ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 != zero_zero_int )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 13.77/7.81 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7364_nonneg__mod__div,axiom,
% 13.77/7.81 ! [A: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 13.77/7.81 & ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7365_zdiv__mono__strict,axiom,
% 13.77/7.81 ! [A4: int,B4: int,N: int] :
% 13.77/7.81 ( ( ord_less_int @ A4 @ B4 )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ N )
% 13.77/7.81 => ( ( ( modulo_modulo_int @ A4 @ N )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 => ( ( ( modulo_modulo_int @ B4 @ N )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 => ( ord_less_int @ ( divide_divide_int @ A4 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7366_int__mod__ge_H,axiom,
% 13.77/7.81 ! [B: int,N: int] :
% 13.77/7.81 ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ N )
% 13.77/7.81 => ( ord_less_eq_int @ ( plus_plus_int @ B @ N ) @ ( modulo_modulo_int @ B @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7367_mod__pos__neg__trivial,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 13.77/7.81 => ( ( modulo_modulo_int @ K @ L )
% 13.77/7.81 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7368_mod__pos__geq,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ( ord_less_eq_int @ L @ K )
% 13.77/7.81 => ( ( modulo_modulo_int @ K @ L )
% 13.77/7.81 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7369_mod__power__lem,axiom,
% 13.77/7.81 ! [A: int,M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_int @ one_one_int @ A )
% 13.77/7.81 => ( ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ M ) )
% 13.77/7.81 = zero_zero_int ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ M ) )
% 13.77/7.81 = ( power_power_int @ A @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7370_split__zmod,axiom,
% 13.77/7.81 ! [P2: int > $o,N: int,K: int] :
% 13.77/7.81 ( ( P2 @ ( modulo_modulo_int @ N @ K ) )
% 13.77/7.81 = ( ( ( K = zero_zero_int )
% 13.77/7.81 => ( P2 @ N ) )
% 13.77/7.81 & ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.81 => ! [I3: int,J3: int] :
% 13.77/7.81 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 13.77/7.81 & ( ord_less_int @ J3 @ K )
% 13.77/7.81 & ( N
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 13.77/7.81 => ( P2 @ J3 ) ) )
% 13.77/7.81 & ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.81 => ! [I3: int,J3: int] :
% 13.77/7.81 ( ( ( ord_less_int @ K @ J3 )
% 13.77/7.81 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 13.77/7.81 & ( N
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 13.77/7.81 => ( P2 @ J3 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7371_int__mod__neg__eq,axiom,
% 13.77/7.81 ! [A: int,B: int,Q3: int,R: int] :
% 13.77/7.81 ( ( A
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ B @ R )
% 13.77/7.81 => ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 = R ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7372_int__mod__pos__eq,axiom,
% 13.77/7.81 ! [A: int,B: int,Q3: int,R: int] :
% 13.77/7.81 ( ( A
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 13.77/7.81 => ( ( ord_less_int @ R @ B )
% 13.77/7.81 => ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 = R ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7373_minus__mod__int__eq,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 13.77/7.81 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7374_zmod__minus1,axiom,
% 13.77/7.81 ! [B: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 13.77/7.81 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7375_mod__add__if__z,axiom,
% 13.77/7.81 ! [X: int,Z: int,Y: int] :
% 13.77/7.81 ( ( ord_less_int @ X @ Z )
% 13.77/7.81 => ( ( ord_less_int @ Y @ Z )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 13.77/7.81 = ( plus_plus_int @ X @ Y ) ) )
% 13.77/7.81 & ( ~ ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( plus_plus_int @ X @ Y ) @ Z )
% 13.77/7.81 = ( minus_minus_int @ ( plus_plus_int @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7376_mod__sub__if__z,axiom,
% 13.77/7.81 ! [X: int,Z: int,Y: int] :
% 13.77/7.81 ( ( ord_less_int @ X @ Z )
% 13.77/7.81 => ( ( ord_less_int @ Y @ Z )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( ( ord_less_eq_int @ Y @ X )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( minus_minus_int @ X @ Y ) @ Z )
% 13.77/7.81 = ( minus_minus_int @ X @ Y ) ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_int @ Y @ X )
% 13.77/7.81 => ( ( modulo_modulo_int @ ( minus_minus_int @ X @ Y ) @ Z )
% 13.77/7.81 = ( plus_plus_int @ ( minus_minus_int @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7377_zmod__zmult2__eq,axiom,
% 13.77/7.81 ! [C2: int,A: int,B: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 13.77/7.81 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7378_zdiv__zminus1__eq__if,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( B != zero_zero_int )
% 13.77/7.81 => ( ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 13.77/7.81 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 13.77/7.81 & ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 != zero_zero_int )
% 13.77/7.81 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 13.77/7.81 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7379_zdiv__zminus2__eq__if,axiom,
% 13.77/7.81 ! [B: int,A: int] :
% 13.77/7.81 ( ( B != zero_zero_int )
% 13.77/7.81 => ( ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 13.77/7.81 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 13.77/7.81 & ( ( ( modulo_modulo_int @ A @ B )
% 13.77/7.81 != zero_zero_int )
% 13.77/7.81 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 13.77/7.81 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7380_verit__le__mono__div__int,axiom,
% 13.77/7.81 ! [A4: int,B4: int,N: int] :
% 13.77/7.81 ( ( ord_less_int @ A4 @ B4 )
% 13.77/7.81 => ( ( ord_less_int @ zero_zero_int @ N )
% 13.77/7.81 => ( ord_less_eq_int
% 13.77/7.81 @ ( plus_plus_int @ ( divide_divide_int @ A4 @ N )
% 13.77/7.81 @ ( if_int
% 13.77/7.81 @ ( ( modulo_modulo_int @ B4 @ N )
% 13.77/7.81 = zero_zero_int )
% 13.77/7.81 @ one_one_int
% 13.77/7.81 @ zero_zero_int ) )
% 13.77/7.81 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7381_split__neg__lemma,axiom,
% 13.77/7.81 ! [K: int,P2: int > int > $o,N: int] :
% 13.77/7.81 ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.81 => ( ( P2 @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 13.77/7.81 = ( ! [I3: int,J3: int] :
% 13.77/7.81 ( ( ( ord_less_int @ K @ J3 )
% 13.77/7.81 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 13.77/7.81 & ( N
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 13.77/7.81 => ( P2 @ I3 @ J3 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7382_split__pos__lemma,axiom,
% 13.77/7.81 ! [K: int,P2: int > int > $o,N: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( P2 @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 13.77/7.81 = ( ! [I3: int,J3: int] :
% 13.77/7.81 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 13.77/7.81 & ( ord_less_int @ J3 @ K )
% 13.77/7.81 & ( N
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 13.77/7.81 => ( P2 @ I3 @ J3 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7383_vebt__assn__raw_Oelims,axiom,
% 13.77/7.81 ! [X: vEBT_VEBT,Xa2: vEBT_VEBTi,Y: assn] :
% 13.77/7.81 ( ( ( vEBT_vebt_assn_raw @ X @ Xa2 )
% 13.77/7.81 = Y )
% 13.77/7.81 => ( ! [A3: $o,B3: $o] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.81 => ! [Ai: $o,Bi: $o] :
% 13.77/7.81 ( ( Xa2
% 13.77/7.81 = ( vEBT_Leafi @ Ai @ Bi ) )
% 13.77/7.81 => ( Y
% 13.77/7.81 != ( pure_assn
% 13.77/7.81 @ ( ( Ai = A3 )
% 13.77/7.81 & ( Bi = B3 ) ) ) ) ) )
% 13.77/7.81 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) )
% 13.77/7.81 => ! [Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 13.77/7.81 ( ( Xa2
% 13.77/7.81 = ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) )
% 13.77/7.81 => ( Y
% 13.77/7.81 != ( times_times_assn
% 13.77/7.81 @ ( times_times_assn
% 13.77/7.81 @ ( pure_assn
% 13.77/7.81 @ ( ( Mmoi2 = Mmo2 )
% 13.77/7.81 & ( Degi2 = Deg2 ) ) )
% 13.77/7.81 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi2 ) )
% 13.77/7.81 @ ( ex_ass463751140784270563_VEBTi
% 13.77/7.81 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array2 @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list2 @ Tree_is2 ) ) ) ) ) ) )
% 13.77/7.81 => ( ( ? [V: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 13.77/7.81 ( X
% 13.77/7.81 = ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) )
% 13.77/7.81 => ( ? [Vd3: $o,Ve3: $o] :
% 13.77/7.81 ( Xa2
% 13.77/7.81 = ( vEBT_Leafi @ Vd3 @ Ve3 ) )
% 13.77/7.81 => ( Y != bot_bot_assn ) ) )
% 13.77/7.81 => ~ ( ? [Vd3: $o,Ve3: $o] :
% 13.77/7.81 ( X
% 13.77/7.81 = ( vEBT_Leaf @ Vd3 @ Ve3 ) )
% 13.77/7.81 => ( ? [V: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 13.77/7.81 ( Xa2
% 13.77/7.81 = ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) )
% 13.77/7.81 => ( Y != bot_bot_assn ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7384_exp__ge__one__minus__x__over__n__power__n,axiom,
% 13.77/7.81 ! [X: real,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( 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 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7385_exp__ge__one__plus__x__over__n__power__n,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7386_VEBTi_Oinject_I2_J,axiom,
% 13.77/7.81 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 13.77/7.81 ( ( ( vEBT_Leafi @ X21 @ X22 )
% 13.77/7.81 = ( vEBT_Leafi @ Y21 @ Y22 ) )
% 13.77/7.81 = ( ( X21 = Y21 )
% 13.77/7.81 & ( X22 = Y22 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7387_exp__less__mono,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ X @ Y )
% 13.77/7.81 => ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7388_exp__less__cancel__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 13.77/7.81 = ( ord_less_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7389_exp__le__cancel__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7390_one__less__exp__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 13.77/7.81 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7391_exp__less__one__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 13.77/7.81 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7392_one__le__exp__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7393_exp__le__one__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7394_exp__less__cancel,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 13.77/7.81 => ( ord_less_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7395_VEBTi_Odistinct_I1_J,axiom,
% 13.77/7.81 ! [X11: option4927543243414619207at_nat,X12: nat,X13: array_VEBT_VEBTi,X14: vEBT_VEBTi,X21: $o,X22: $o] :
% 13.77/7.81 ( ( vEBT_Nodei @ X11 @ X12 @ X13 @ X14 )
% 13.77/7.81 != ( vEBT_Leafi @ X21 @ X22 ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7396_VEBTi_Oexhaust,axiom,
% 13.77/7.81 ! [Y: vEBT_VEBTi] :
% 13.77/7.81 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: array_VEBT_VEBTi,X142: vEBT_VEBTi] :
% 13.77/7.81 ( Y
% 13.77/7.81 != ( vEBT_Nodei @ X112 @ X122 @ X132 @ X142 ) )
% 13.77/7.81 => ~ ! [X212: $o,X222: $o] :
% 13.77/7.81 ( Y
% 13.77/7.81 != ( vEBT_Leafi @ X212 @ X222 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7397_not__exp__less__zero,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7398_exp__gt__zero,axiom,
% 13.77/7.81 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7399_exp__total,axiom,
% 13.77/7.81 ! [Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ? [X3: real] :
% 13.77/7.81 ( ( exp_real @ X3 )
% 13.77/7.81 = Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7400_exp__ge__zero,axiom,
% 13.77/7.81 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7401_not__exp__le__zero,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7402_VEBTi_Osize_I4_J,axiom,
% 13.77/7.81 ! [X21: $o,X22: $o] :
% 13.77/7.81 ( ( size_size_VEBT_VEBTi @ ( vEBT_Leafi @ X21 @ X22 ) )
% 13.77/7.81 = zero_zero_nat ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7403_VEBTi_Osize__gen_I2_J,axiom,
% 13.77/7.81 ! [X21: $o,X22: $o] :
% 13.77/7.81 ( ( vEBT_size_VEBTi @ ( vEBT_Leafi @ X21 @ X22 ) )
% 13.77/7.81 = zero_zero_nat ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7404_exp__gt__one,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7405_exp__ge__add__one__self,axiom,
% 13.77/7.81 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7406_vebt__assn__raw_Ocases,axiom,
% 13.77/7.81 ! [X: produc3625547720036274456_VEBTi] :
% 13.77/7.81 ( ! [A3: $o,B3: $o,Ai: $o,Bi: $o] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A3 @ B3 ) @ ( vEBT_Leafi @ Ai @ Bi ) ) )
% 13.77/7.81 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) @ ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) ) )
% 13.77/7.81 => ( ! [V: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT,Vd3: $o,Ve3: $o] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd3 @ Ve3 ) ) )
% 13.77/7.81 => ~ ! [Vd3: $o,Ve3: $o,V: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd3 @ Ve3 ) @ ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7407_VEBT__internal_OminNulli_Ocases,axiom,
% 13.77/7.81 ! [X: vEBT_VEBTi] :
% 13.77/7.81 ( ( X
% 13.77/7.81 != ( vEBT_Leafi @ $false @ $false ) )
% 13.77/7.81 => ( ! [Uv: $o] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( vEBT_Leafi @ $true @ Uv ) )
% 13.77/7.81 => ( ! [Uu: $o] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( vEBT_Leafi @ Uu @ $true ) )
% 13.77/7.81 => ( ! [Uw: nat,Ux: array_VEBT_VEBTi,Uy: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 13.77/7.81 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: array_VEBT_VEBTi,Vc2: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7408_vebt__assn__raw_Osimps_I1_J,axiom,
% 13.77/7.81 ! [A: $o,B: $o,Ai2: $o,Bi2: $o] :
% 13.77/7.81 ( ( vEBT_vebt_assn_raw @ ( vEBT_Leaf @ A @ B ) @ ( vEBT_Leafi @ Ai2 @ Bi2 ) )
% 13.77/7.81 = ( pure_assn
% 13.77/7.81 @ ( ( Ai2 = A )
% 13.77/7.81 & ( Bi2 = B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7409_vebt__assn__raw_Osimps_I3_J,axiom,
% 13.77/7.81 ! [V2: option4927543243414619207at_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,Vd2: $o,Ve2: $o] :
% 13.77/7.81 ( ( vEBT_vebt_assn_raw @ ( vEBT_Node @ V2 @ Va2 @ Vb @ Vc ) @ ( vEBT_Leafi @ Vd2 @ Ve2 ) )
% 13.77/7.81 = bot_bot_assn ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7410_exp__ge__add__one__self__aux,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7411_lemma__exp__total,axiom,
% 13.77/7.81 ! [Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ one_one_real @ Y )
% 13.77/7.81 => ? [X3: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 13.77/7.81 & ( ord_less_eq_real @ X3 @ ( minus_minus_real @ Y @ one_one_real ) )
% 13.77/7.81 & ( ( exp_real @ X3 )
% 13.77/7.81 = Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7412_vebt__minti_Ocases,axiom,
% 13.77/7.81 ! [X: vEBT_VEBTi] :
% 13.77/7.81 ( ! [A3: $o,B3: $o] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( vEBT_Leafi @ A3 @ B3 ) )
% 13.77/7.81 => ( ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.81 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 != ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7413_vebt__assn__def,axiom,
% 13.77/7.81 ( vEBT_Intf_vebt_assn
% 13.77/7.81 = ( ^ [N6: nat,S8: set_nat,Ti2: vEBT_VEBTi] :
% 13.77/7.81 ( ex_assn_VEBT_VEBT
% 13.77/7.81 @ ^ [T2: vEBT_VEBT] :
% 13.77/7.81 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T2 @ Ti2 )
% 13.77/7.81 @ ( pure_assn
% 13.77/7.81 @ ( ( S8
% 13.77/7.81 = ( vEBT_set_vebt @ T2 ) )
% 13.77/7.81 & ( vEBT_invar_vebt @ T2 @ N6 ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7414_vebt__assn__raw_Opelims,axiom,
% 13.77/7.81 ! [X: vEBT_VEBT,Xa2: vEBT_VEBTi,Y: assn] :
% 13.77/7.81 ( ( ( vEBT_vebt_assn_raw @ X @ Xa2 )
% 13.77/7.81 = Y )
% 13.77/7.81 => ( ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ X @ Xa2 ) )
% 13.77/7.81 => ( ! [A3: $o,B3: $o] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.81 => ! [Ai: $o,Bi: $o] :
% 13.77/7.81 ( ( Xa2
% 13.77/7.81 = ( vEBT_Leafi @ Ai @ Bi ) )
% 13.77/7.81 => ( ( Y
% 13.77/7.81 = ( pure_assn
% 13.77/7.81 @ ( ( Ai = A3 )
% 13.77/7.81 & ( Bi = B3 ) ) ) )
% 13.77/7.81 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ A3 @ B3 ) @ ( vEBT_Leafi @ Ai @ Bi ) ) ) ) ) )
% 13.77/7.81 => ( ! [Mmo2: option4927543243414619207at_nat,Deg2: nat,Tree_list2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) )
% 13.77/7.81 => ! [Mmoi2: option4927543243414619207at_nat,Degi2: nat,Tree_array2: array_VEBT_VEBTi,Summaryi2: vEBT_VEBTi] :
% 13.77/7.81 ( ( Xa2
% 13.77/7.81 = ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) )
% 13.77/7.81 => ( ( Y
% 13.77/7.81 = ( times_times_assn
% 13.77/7.81 @ ( times_times_assn
% 13.77/7.81 @ ( pure_assn
% 13.77/7.81 @ ( ( Mmoi2 = Mmo2 )
% 13.77/7.81 & ( Degi2 = Deg2 ) ) )
% 13.77/7.81 @ ( vEBT_vebt_assn_raw @ Summary2 @ Summaryi2 ) )
% 13.77/7.81 @ ( ex_ass463751140784270563_VEBTi
% 13.77/7.81 @ ^ [Tree_is2: list_VEBT_VEBTi] : ( times_times_assn @ ( snga_assn_VEBT_VEBTi @ Tree_array2 @ Tree_is2 ) @ ( vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ Tree_list2 @ Tree_is2 ) ) ) ) )
% 13.77/7.81 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ Mmo2 @ Deg2 @ Tree_list2 @ Summary2 ) @ ( vEBT_Nodei @ Mmoi2 @ Degi2 @ Tree_array2 @ Summaryi2 ) ) ) ) ) )
% 13.77/7.81 => ( ! [V: option4927543243414619207at_nat,Va: nat,Vb3: list_VEBT_VEBT,Vc3: vEBT_VEBT] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) )
% 13.77/7.81 => ! [Vd3: $o,Ve3: $o] :
% 13.77/7.81 ( ( Xa2
% 13.77/7.81 = ( vEBT_Leafi @ Vd3 @ Ve3 ) )
% 13.77/7.81 => ( ( Y = bot_bot_assn )
% 13.77/7.81 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Node @ V @ Va @ Vb3 @ Vc3 ) @ ( vEBT_Leafi @ Vd3 @ Ve3 ) ) ) ) ) )
% 13.77/7.81 => ~ ! [Vd3: $o,Ve3: $o] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Leaf @ Vd3 @ Ve3 ) )
% 13.77/7.81 => ! [V: option4927543243414619207at_nat,Va: nat,Vb3: array_VEBT_VEBTi,Vc3: vEBT_VEBTi] :
% 13.77/7.81 ( ( Xa2
% 13.77/7.81 = ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) )
% 13.77/7.81 => ( ( Y = bot_bot_assn )
% 13.77/7.81 => ~ ( accp_P7675410724331315407_VEBTi @ vEBT_v8524038756793281170aw_rel @ ( produc6084888613844515218_VEBTi @ ( vEBT_Leaf @ Vd3 @ Ve3 ) @ ( vEBT_Nodei @ V @ Va @ Vb3 @ Vc3 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7415_vebt__minti_Oelims,axiom,
% 13.77/7.81 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 13.77/7.81 ( ( ( vEBT_vebt_minti @ X )
% 13.77/7.81 = Y )
% 13.77/7.81 => ( ! [A3: $o,B3: $o] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Leafi @ A3 @ B3 ) )
% 13.77/7.81 => ~ ( ( A3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 13.77/7.81 & ( ~ A3
% 13.77/7.81 => ( ( B3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 13.77/7.81 & ( ~ B3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) )
% 13.77/7.81 => ( ( ? [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.81 => ( Y
% 13.77/7.81 != ( heap_T3487192422709364219on_nat @ none_nat ) ) )
% 13.77/7.81 => ~ ! [Mi2: nat] :
% 13.77/7.81 ( ? [Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.81 => ( Y
% 13.77/7.81 != ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi2 ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7416_vebt__maxti_Oelims,axiom,
% 13.77/7.81 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 13.77/7.81 ( ( ( vEBT_vebt_maxti @ X )
% 13.77/7.81 = Y )
% 13.77/7.81 => ( ! [A3: $o,B3: $o] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Leafi @ A3 @ B3 ) )
% 13.77/7.81 => ~ ( ( B3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 13.77/7.81 & ( ~ B3
% 13.77/7.81 => ( ( A3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 13.77/7.81 & ( ~ A3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) )
% 13.77/7.81 => ( ( ? [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.81 => ( Y
% 13.77/7.81 != ( heap_T3487192422709364219on_nat @ none_nat ) ) )
% 13.77/7.81 => ~ ! [Mi2: nat,Ma2: nat] :
% 13.77/7.81 ( ? [Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 13.77/7.81 ( X
% 13.77/7.81 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.81 => ( Y
% 13.77/7.81 != ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma2 ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7417_fact__ge__self,axiom,
% 13.77/7.81 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7418_fact__mono__nat,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7419_fact__less__mono__nat,axiom,
% 13.77/7.81 ! [M: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.81 => ( ( ord_less_nat @ M @ N )
% 13.77/7.81 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7420_fact__ge__Suc__0__nat,axiom,
% 13.77/7.81 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7421_fact__div__fact__le__pow,axiom,
% 13.77/7.81 ! [R: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ R @ N )
% 13.77/7.81 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7422_binomial__fact__lemma,axiom,
% 13.77/7.81 ! [K: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.81 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 13.77/7.81 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7423_prod__Suc__fact,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 13.77/7.81 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7424_prod__Suc__Suc__fact,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 13.77/7.81 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7425_vebt__minti_Osimps_I2_J,axiom,
% 13.77/7.81 ! [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 13.77/7.81 ( ( vEBT_vebt_minti @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7426_vebt__maxti_Osimps_I2_J,axiom,
% 13.77/7.81 ! [Uu2: nat,Uv2: array_VEBT_VEBTi,Uw2: vEBT_VEBTi] :
% 13.77/7.81 ( ( vEBT_vebt_maxti @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7427_binomial__altdef__nat,axiom,
% 13.77/7.81 ! [K: nat,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ K @ N )
% 13.77/7.81 => ( ( binomial @ N @ K )
% 13.77/7.81 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7428_vebt__minti_Osimps_I3_J,axiom,
% 13.77/7.81 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz: vEBT_VEBTi] :
% 13.77/7.81 ( ( vEBT_vebt_minti @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7429_vebt__maxti_Osimps_I3_J,axiom,
% 13.77/7.81 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: array_VEBT_VEBTi,Uz: vEBT_VEBTi] :
% 13.77/7.81 ( ( vEBT_vebt_maxti @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7430_fact__eq__fact__times,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.81 => ( ( semiri1408675320244567234ct_nat @ M )
% 13.77/7.81 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 13.77/7.81 @ ( groups708209901874060359at_nat
% 13.77/7.81 @ ^ [X4: nat] : X4
% 13.77/7.81 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7431_vebt__maxti_Osimps_I1_J,axiom,
% 13.77/7.81 ! [B: $o,A: $o] :
% 13.77/7.81 ( ( B
% 13.77/7.81 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A @ B ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 13.77/7.81 & ( ~ B
% 13.77/7.81 => ( ( A
% 13.77/7.81 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A @ B ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 13.77/7.81 & ( ~ A
% 13.77/7.81 => ( ( vEBT_vebt_maxti @ ( vEBT_Leafi @ A @ B ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7432_vebt__minti_Osimps_I1_J,axiom,
% 13.77/7.81 ! [A: $o,B: $o] :
% 13.77/7.81 ( ( A
% 13.77/7.81 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A @ B ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 13.77/7.81 & ( ~ A
% 13.77/7.81 => ( ( B
% 13.77/7.81 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A @ B ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 13.77/7.81 & ( ~ B
% 13.77/7.81 => ( ( vEBT_vebt_minti @ ( vEBT_Leafi @ A @ B ) )
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7433_fact__div__fact,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.81 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 13.77/7.81 = ( groups708209901874060359at_nat
% 13.77/7.81 @ ^ [X4: nat] : X4
% 13.77/7.81 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7434_vebt__maxti_Opelims,axiom,
% 13.77/7.81 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 13.77/7.81 ( ( ( vEBT_vebt_maxti @ X )
% 13.77/7.81 = Y )
% 13.77/7.81 => ( ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ X )
% 13.77/7.81 => ( ! [A3: $o,B3: $o] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Leafi @ A3 @ B3 ) )
% 13.77/7.81 => ( ( ( B3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 13.77/7.81 & ( ~ B3
% 13.77/7.81 => ( ( A3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 13.77/7.81 & ( ~ A3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) )
% 13.77/7.81 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Leafi @ A3 @ B3 ) ) ) )
% 13.77/7.81 => ( ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.81 => ( ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) )
% 13.77/7.81 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 13.77/7.81 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.81 => ( ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Ma2 ) ) )
% 13.77/7.81 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_maxti_rel @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7435_vebt__minti_Opelims,axiom,
% 13.77/7.81 ! [X: vEBT_VEBTi,Y: heap_T2636463487746394924on_nat] :
% 13.77/7.81 ( ( ( vEBT_vebt_minti @ X )
% 13.77/7.81 = Y )
% 13.77/7.81 => ( ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ X )
% 13.77/7.81 => ( ! [A3: $o,B3: $o] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Leafi @ A3 @ B3 ) )
% 13.77/7.81 => ( ( ( A3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ zero_zero_nat ) ) ) )
% 13.77/7.81 & ( ~ A3
% 13.77/7.81 => ( ( B3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ one_one_nat ) ) ) )
% 13.77/7.81 & ( ~ B3
% 13.77/7.81 => ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) ) ) ) ) )
% 13.77/7.81 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Leafi @ A3 @ B3 ) ) ) )
% 13.77/7.81 => ( ! [Uu: nat,Uv: array_VEBT_VEBTi,Uw: vEBT_VEBTi] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.81 => ( ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ none_nat ) )
% 13.77/7.81 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Nodei @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 13.77/7.81 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: array_VEBT_VEBTi,Uz2: vEBT_VEBTi] :
% 13.77/7.81 ( ( X
% 13.77/7.81 = ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 13.77/7.81 => ( ( Y
% 13.77/7.81 = ( heap_T3487192422709364219on_nat @ ( some_nat @ Mi2 ) ) )
% 13.77/7.81 => ~ ( accp_VEBT_VEBTi @ vEBT_vebt_minti_rel @ ( vEBT_Nodei @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7436_Maclaurin__lemma,axiom,
% 13.77/7.81 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ H2 )
% 13.77/7.81 => ? [B8: real] :
% 13.77/7.81 ( ( F @ H2 )
% 13.77/7.81 = ( plus_plus_real
% 13.77/7.81 @ ( groups6591440286371151544t_real
% 13.77/7.81 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 13.77/7.81 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.81 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7437_fact__diff__Suc,axiom,
% 13.77/7.81 ! [N: nat,M: nat] :
% 13.77/7.81 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 13.77/7.81 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 13.77/7.81 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7438_sumr__cos__zero__one,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( groups6591440286371151544t_real
% 13.77/7.81 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ zero_zero_real @ M5 ) )
% 13.77/7.81 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 13.77/7.81 = one_one_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7439_Maclaurin__exp__lt,axiom,
% 13.77/7.81 ! [X: real,N: nat] :
% 13.77/7.81 ( ( X != zero_zero_real )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ? [T6: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 13.77/7.81 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.81 & ( ( exp_real @ X )
% 13.77/7.81 = ( plus_plus_real
% 13.77/7.81 @ ( groups6591440286371151544t_real
% 13.77/7.81 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 13.77/7.81 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.81 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7440_Maclaurin__exp__le,axiom,
% 13.77/7.81 ! [X: real,N: nat] :
% 13.77/7.81 ? [T6: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.81 & ( ( exp_real @ X )
% 13.77/7.81 = ( plus_plus_real
% 13.77/7.81 @ ( groups6591440286371151544t_real
% 13.77/7.81 @ ^ [M5: nat] : ( divide_divide_real @ ( power_power_real @ X @ M5 ) @ ( semiri2265585572941072030t_real @ M5 ) )
% 13.77/7.81 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.81 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7441_Least__eq__0,axiom,
% 13.77/7.81 ! [P2: nat > $o] :
% 13.77/7.81 ( ( P2 @ zero_zero_nat )
% 13.77/7.81 => ( ( ord_Least_nat @ P2 )
% 13.77/7.81 = zero_zero_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7442_cos__coeff__0,axiom,
% 13.77/7.81 ( ( cos_coeff @ zero_zero_nat )
% 13.77/7.81 = one_one_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7443_artanh__minus__real,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.81 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 13.77/7.81 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7444_Least__Suc2,axiom,
% 13.77/7.81 ! [P2: nat > $o,N: nat,Q2: nat > $o,M: nat] :
% 13.77/7.81 ( ( P2 @ N )
% 13.77/7.81 => ( ( Q2 @ M )
% 13.77/7.81 => ( ~ ( P2 @ zero_zero_nat )
% 13.77/7.81 => ( ! [K2: nat] :
% 13.77/7.81 ( ( P2 @ ( suc @ K2 ) )
% 13.77/7.81 = ( Q2 @ K2 ) )
% 13.77/7.81 => ( ( ord_Least_nat @ P2 )
% 13.77/7.81 = ( suc @ ( ord_Least_nat @ Q2 ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7445_Least__Suc,axiom,
% 13.77/7.81 ! [P2: nat > $o,N: nat] :
% 13.77/7.81 ( ( P2 @ N )
% 13.77/7.81 => ( ~ ( P2 @ zero_zero_nat )
% 13.77/7.81 => ( ( ord_Least_nat @ P2 )
% 13.77/7.81 = ( suc
% 13.77/7.81 @ ( ord_Least_nat
% 13.77/7.81 @ ^ [M5: nat] : ( P2 @ ( suc @ M5 ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7446_abs__real__def,axiom,
% 13.77/7.81 ( abs_abs_real
% 13.77/7.81 = ( ^ [A7: real] : ( if_real @ ( ord_less_real @ A7 @ zero_zero_real ) @ ( uminus_uminus_real @ A7 ) @ A7 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7447_sin__bound__lemma,axiom,
% 13.77/7.81 ! [X: real,Y: real,U: real,V2: real] :
% 13.77/7.81 ( ( X = Y )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V2 )
% 13.77/7.81 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V2 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7448_lemma__interval,axiom,
% 13.77/7.81 ! [A: real,X: real,B: real] :
% 13.77/7.81 ( ( ord_less_real @ A @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ B )
% 13.77/7.81 => ? [D2: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.81 & ! [Y5: real] :
% 13.77/7.81 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D2 )
% 13.77/7.81 => ( ( ord_less_eq_real @ A @ Y5 )
% 13.77/7.81 & ( ord_less_eq_real @ Y5 @ B ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7449_lemma__interval__lt,axiom,
% 13.77/7.81 ! [A: real,X: real,B: real] :
% 13.77/7.81 ( ( ord_less_real @ A @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ B )
% 13.77/7.81 => ? [D2: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.81 & ! [Y5: real] :
% 13.77/7.81 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D2 )
% 13.77/7.81 => ( ( ord_less_real @ A @ Y5 )
% 13.77/7.81 & ( ord_less_real @ Y5 @ B ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7450_set__vebt__succ_H,axiom,
% 13.77/7.81 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.81 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.81 => ( ( ? [X5: nat] :
% 13.77/7.81 ( ( member_nat @ X5 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.81 & ( ord_less_nat @ X @ X5 ) )
% 13.77/7.81 => ( ( vEBT_vebt_succ @ T @ X )
% 13.77/7.81 = ( some_nat
% 13.77/7.81 @ ( ord_Least_nat
% 13.77/7.81 @ ^ [Y4: nat] :
% 13.77/7.81 ( ( member_nat @ Y4 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.81 & ( ord_less_nat @ X @ Y4 ) ) ) ) ) )
% 13.77/7.81 & ( ~ ? [X3: nat] :
% 13.77/7.81 ( ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.81 & ( ord_less_nat @ X @ X3 ) )
% 13.77/7.81 => ( ( vEBT_vebt_succ @ T @ X )
% 13.77/7.81 = none_nat ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7451_arctan__add,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.81 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 13.77/7.81 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7452_cos__coeff__Suc,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( cos_coeff @ ( suc @ N ) )
% 13.77/7.81 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7453_zabs__less__one__iff,axiom,
% 13.77/7.81 ! [Z: int] :
% 13.77/7.81 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 13.77/7.81 = ( Z = zero_zero_int ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7454_zero__less__arctan__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 13.77/7.81 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7455_arctan__less__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7456_zero__le__arctan__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7457_arctan__le__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7458_sin__coeff__0,axiom,
% 13.77/7.81 ( ( sin_coeff @ zero_zero_nat )
% 13.77/7.81 = zero_zero_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7459_set__vebt__pred_H,axiom,
% 13.77/7.81 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.81 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.81 => ( ( ? [X5: nat] :
% 13.77/7.81 ( ( member_nat @ X5 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.81 & ( ord_less_nat @ X5 @ X ) )
% 13.77/7.81 => ( ( vEBT_vebt_pred @ T @ X )
% 13.77/7.81 = ( some_nat
% 13.77/7.81 @ ( order_Greatest_nat
% 13.77/7.81 @ ^ [Y4: nat] :
% 13.77/7.81 ( ( member_nat @ Y4 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.81 & ( ord_less_nat @ Y4 @ X ) ) ) ) ) )
% 13.77/7.81 & ( ~ ? [X3: nat] :
% 13.77/7.81 ( ( member_nat @ X3 @ ( vEBT_set_vebt @ T ) )
% 13.77/7.81 & ( ord_less_nat @ X3 @ X ) )
% 13.77/7.81 => ( ( vEBT_vebt_pred @ T @ X )
% 13.77/7.81 = none_nat ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7460_arctan__less__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 13.77/7.81 = ( ord_less_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7461_arctan__monotone,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ X @ Y )
% 13.77/7.81 => ( ord_less_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7462_arctan__monotone_H,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.81 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7463_arctan__le__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7464_finite__int__iff__bounded__le,axiom,
% 13.77/7.81 ( finite_finite_int
% 13.77/7.81 = ( ^ [S6: set_int] :
% 13.77/7.81 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7465_finite__int__iff__bounded,axiom,
% 13.77/7.81 ( finite_finite_int
% 13.77/7.81 = ( ^ [S6: set_int] :
% 13.77/7.81 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7466_infinite__int__iff__unbounded__le,axiom,
% 13.77/7.81 ! [S3: set_int] :
% 13.77/7.81 ( ( ~ ( finite_finite_int @ S3 ) )
% 13.77/7.81 = ( ! [M5: int] :
% 13.77/7.81 ? [N6: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ M5 @ ( abs_abs_int @ N6 ) )
% 13.77/7.81 & ( member_int @ N6 @ S3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7467_infinite__int__iff__unbounded,axiom,
% 13.77/7.81 ! [S3: set_int] :
% 13.77/7.81 ( ( ~ ( finite_finite_int @ S3 ) )
% 13.77/7.81 = ( ! [M5: int] :
% 13.77/7.81 ? [N6: int] :
% 13.77/7.81 ( ( ord_less_int @ M5 @ ( abs_abs_int @ N6 ) )
% 13.77/7.81 & ( member_int @ N6 @ S3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7468_zabs__def,axiom,
% 13.77/7.81 ( abs_abs_int
% 13.77/7.81 = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7469_abs__mod__less,axiom,
% 13.77/7.81 ! [L: int,K: int] :
% 13.77/7.81 ( ( L != zero_zero_int )
% 13.77/7.81 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7470_nat__intermed__int__val,axiom,
% 13.77/7.81 ! [M: nat,N: nat,F: nat > int,K: int] :
% 13.77/7.81 ( ! [I2: nat] :
% 13.77/7.81 ( ( ( ord_less_eq_nat @ M @ I2 )
% 13.77/7.81 & ( ord_less_nat @ I2 @ N ) )
% 13.77/7.81 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 13.77/7.81 => ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.81 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 13.77/7.81 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 13.77/7.81 => ? [I2: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ M @ I2 )
% 13.77/7.81 & ( ord_less_eq_nat @ I2 @ N )
% 13.77/7.81 & ( ( F @ I2 )
% 13.77/7.81 = K ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7471_incr__lemma,axiom,
% 13.77/7.81 ! [D: int,Z: int,X: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D )
% 13.77/7.81 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7472_decr__lemma,axiom,
% 13.77/7.81 ! [D: int,X: int,Z: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ D )
% 13.77/7.81 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7473_nat__ivt__aux,axiom,
% 13.77/7.81 ! [N: nat,F: nat > int,K: int] :
% 13.77/7.81 ( ! [I2: nat] :
% 13.77/7.81 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.81 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 13.77/7.81 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 13.77/7.81 => ? [I2: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ I2 @ N )
% 13.77/7.81 & ( ( F @ I2 )
% 13.77/7.81 = K ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7474_sin__coeff__Suc,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( sin_coeff @ ( suc @ N ) )
% 13.77/7.81 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7475_nat0__intermed__int__val,axiom,
% 13.77/7.81 ! [N: nat,F: nat > int,K: int] :
% 13.77/7.81 ( ! [I2: nat] :
% 13.77/7.81 ( ( ord_less_nat @ I2 @ N )
% 13.77/7.81 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 13.77/7.81 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 13.77/7.81 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 13.77/7.81 => ? [I2: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ I2 @ N )
% 13.77/7.81 & ( ( F @ I2 )
% 13.77/7.81 = K ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7476_VEBT_Osize_I3_J,axiom,
% 13.77/7.81 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 13.77/7.81 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 13.77/7.81 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7477_VEBT_Osize__gen_I1_J,axiom,
% 13.77/7.81 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 13.77/7.81 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 13.77/7.81 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7478_ln__inj__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ( ln_ln_real @ X )
% 13.77/7.81 = ( ln_ln_real @ Y ) )
% 13.77/7.81 = ( X = Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7479_ln__less__cancel__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 13.77/7.81 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7480_ln__le__cancel__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7481_ln__eq__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ( ln_ln_real @ X )
% 13.77/7.81 = zero_zero_real )
% 13.77/7.81 = ( X = one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7482_ln__gt__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 13.77/7.81 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7483_ln__less__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7484_exp__ln,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 13.77/7.81 = X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7485_exp__ln__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 13.77/7.81 = X )
% 13.77/7.81 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7486_ln__ge__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7487_ln__le__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7488_ln__less__self,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7489_GreatestI__ex__nat,axiom,
% 13.77/7.81 ! [P2: nat > $o,B: nat] :
% 13.77/7.81 ( ? [X_12: nat] : ( P2 @ X_12 )
% 13.77/7.81 => ( ! [Y3: nat] :
% 13.77/7.81 ( ( P2 @ Y3 )
% 13.77/7.81 => ( ord_less_eq_nat @ Y3 @ B ) )
% 13.77/7.81 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7490_Greatest__le__nat,axiom,
% 13.77/7.81 ! [P2: nat > $o,K: nat,B: nat] :
% 13.77/7.81 ( ( P2 @ K )
% 13.77/7.81 => ( ! [Y3: nat] :
% 13.77/7.81 ( ( P2 @ Y3 )
% 13.77/7.81 => ( ord_less_eq_nat @ Y3 @ B ) )
% 13.77/7.81 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7491_GreatestI__nat,axiom,
% 13.77/7.81 ! [P2: nat > $o,K: nat,B: nat] :
% 13.77/7.81 ( ( P2 @ K )
% 13.77/7.81 => ( ! [Y3: nat] :
% 13.77/7.81 ( ( P2 @ Y3 )
% 13.77/7.81 => ( ord_less_eq_nat @ Y3 @ B ) )
% 13.77/7.81 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7492_ln__bound,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7493_ln__gt__zero,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7494_ln__less__zero,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.81 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7495_ln__gt__zero__imp__gt__one,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7496_ln__ge__zero,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7497_ln__ge__zero__imp__ge__one,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7498_ln__add__one__self__le__self,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7499_ln__mult,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 13.77/7.81 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7500_ln__eq__minus__one,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ( ln_ln_real @ X )
% 13.77/7.81 = ( minus_minus_real @ X @ one_one_real ) )
% 13.77/7.81 => ( X = one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7501_ln__div,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 13.77/7.81 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7502_ln__ge__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7503_ln__x__over__x__mono,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.81 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7504_ln__le__minus__one,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7505_ln__diff__le,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7506_ln__add__one__self__le__self2,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.81 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7507_ln__realpow,axiom,
% 13.77/7.81 ! [X: real,N: nat] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 13.77/7.81 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7508_ln__one__minus__pos__upper__bound,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.81 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7509_upto_Opinduct,axiom,
% 13.77/7.81 ! [A0: int,A12: int,P2: int > int > $o] :
% 13.77/7.81 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 13.77/7.81 => ( ! [I2: int,J2: int] :
% 13.77/7.81 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 13.77/7.81 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 13.77/7.81 => ( P2 @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 13.77/7.81 => ( P2 @ I2 @ J2 ) ) )
% 13.77/7.81 => ( P2 @ A0 @ A12 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7510_card__length__sum__list__rec,axiom,
% 13.77/7.81 ! [M: nat,N8: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 13.77/7.81 => ( ( finite_card_list_nat
% 13.77/7.81 @ ( collect_list_nat
% 13.77/7.81 @ ^ [L4: list_nat] :
% 13.77/7.81 ( ( ( size_size_list_nat @ L4 )
% 13.77/7.81 = M )
% 13.77/7.81 & ( ( groups4561878855575611511st_nat @ L4 )
% 13.77/7.81 = N8 ) ) ) )
% 13.77/7.81 = ( plus_plus_nat
% 13.77/7.81 @ ( finite_card_list_nat
% 13.77/7.81 @ ( collect_list_nat
% 13.77/7.81 @ ^ [L4: list_nat] :
% 13.77/7.81 ( ( ( size_size_list_nat @ L4 )
% 13.77/7.81 = ( minus_minus_nat @ M @ one_one_nat ) )
% 13.77/7.81 & ( ( groups4561878855575611511st_nat @ L4 )
% 13.77/7.81 = N8 ) ) ) )
% 13.77/7.81 @ ( finite_card_list_nat
% 13.77/7.81 @ ( collect_list_nat
% 13.77/7.81 @ ^ [L4: list_nat] :
% 13.77/7.81 ( ( ( size_size_list_nat @ L4 )
% 13.77/7.81 = M )
% 13.77/7.81 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L4 ) @ one_one_nat )
% 13.77/7.81 = N8 ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7511_eucl__rel__int__iff,axiom,
% 13.77/7.81 ! [K: int,L: int,Q3: int,R: int] :
% 13.77/7.81 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.81 = ( ( K
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R ) )
% 13.77/7.81 & ( ( ord_less_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 13.77/7.81 & ( ord_less_int @ R @ L ) ) )
% 13.77/7.81 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 13.77/7.81 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 13.77/7.81 => ( ( ord_less_int @ L @ R )
% 13.77/7.81 & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 13.77/7.81 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 13.77/7.81 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7512_bezw__0,axiom,
% 13.77/7.81 ! [X: nat] :
% 13.77/7.81 ( ( bezw @ X @ zero_zero_nat )
% 13.77/7.81 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7513_unique__quotient,axiom,
% 13.77/7.81 ! [A: int,B: int,Q3: int,R: int,Q7: int,R6: int] :
% 13.77/7.81 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.81 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q7 @ R6 ) )
% 13.77/7.81 => ( Q3 = Q7 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7514_unique__remainder,axiom,
% 13.77/7.81 ! [A: int,B: int,Q3: int,R: int,Q7: int,R6: int] :
% 13.77/7.81 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.81 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q7 @ R6 ) )
% 13.77/7.81 => ( R = R6 ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7515_eucl__rel__int__by0,axiom,
% 13.77/7.81 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7516_mod__int__unique,axiom,
% 13.77/7.81 ! [K: int,L: int,Q3: int,R: int] :
% 13.77/7.81 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.81 => ( ( modulo_modulo_int @ K @ L )
% 13.77/7.81 = R ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7517_div__int__unique,axiom,
% 13.77/7.81 ! [K: int,L: int,Q3: int,R: int] :
% 13.77/7.81 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.81 => ( ( divide_divide_int @ K @ L )
% 13.77/7.81 = Q3 ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7518_eucl__rel__int__dividesI,axiom,
% 13.77/7.81 ! [L: int,K: int,Q3: int] :
% 13.77/7.81 ( ( L != zero_zero_int )
% 13.77/7.81 => ( ( K
% 13.77/7.81 = ( times_times_int @ Q3 @ L ) )
% 13.77/7.81 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7519_eucl__rel__int,axiom,
% 13.77/7.81 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7520_zminus1__lemma,axiom,
% 13.77/7.81 ! [A: int,B: int,Q3: int,R: int] :
% 13.77/7.81 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.81 => ( ( B != zero_zero_int )
% 13.77/7.81 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7521_finite__enumerate,axiom,
% 13.77/7.81 ! [S3: set_nat] :
% 13.77/7.81 ( ( finite_finite_nat @ S3 )
% 13.77/7.81 => ? [R4: nat > nat] :
% 13.77/7.81 ( ( strict1292158309912662752at_nat @ R4 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 13.77/7.81 & ! [N9: nat] :
% 13.77/7.81 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S3 ) )
% 13.77/7.81 => ( member_nat @ ( R4 @ N9 ) @ S3 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7522_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 13.77/7.81 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 13.77/7.81 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 13.77/7.81 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7523_Suc__funpow,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( compow_nat_nat @ N @ suc )
% 13.77/7.81 = ( plus_plus_nat @ N ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7524_eucl__rel__int_Osimps,axiom,
% 13.77/7.81 ( eucl_rel_int
% 13.77/7.81 = ( ^ [A13: int,A24: int,A32: product_prod_int_int] :
% 13.77/7.81 ( ? [K3: int] :
% 13.77/7.81 ( ( A13 = K3 )
% 13.77/7.81 & ( A24 = zero_zero_int )
% 13.77/7.81 & ( A32
% 13.77/7.81 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 13.77/7.81 | ? [L4: int,K3: int,Q8: int] :
% 13.77/7.81 ( ( A13 = K3 )
% 13.77/7.81 & ( A24 = L4 )
% 13.77/7.81 & ( A32
% 13.77/7.81 = ( product_Pair_int_int @ Q8 @ zero_zero_int ) )
% 13.77/7.81 & ( L4 != zero_zero_int )
% 13.77/7.81 & ( K3
% 13.77/7.81 = ( times_times_int @ Q8 @ L4 ) ) )
% 13.77/7.81 | ? [R5: int,L4: int,K3: int,Q8: int] :
% 13.77/7.81 ( ( A13 = K3 )
% 13.77/7.81 & ( A24 = L4 )
% 13.77/7.81 & ( A32
% 13.77/7.81 = ( product_Pair_int_int @ Q8 @ R5 ) )
% 13.77/7.81 & ( ( sgn_sgn_int @ R5 )
% 13.77/7.81 = ( sgn_sgn_int @ L4 ) )
% 13.77/7.81 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L4 ) )
% 13.77/7.81 & ( K3
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ Q8 @ L4 ) @ R5 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7525_eucl__rel__int_Ocases,axiom,
% 13.77/7.81 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 13.77/7.81 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 13.77/7.81 => ( ( ( A23 = zero_zero_int )
% 13.77/7.81 => ( A33
% 13.77/7.81 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 13.77/7.81 => ( ! [Q5: int] :
% 13.77/7.81 ( ( A33
% 13.77/7.81 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 13.77/7.81 => ( ( A23 != zero_zero_int )
% 13.77/7.81 => ( A12
% 13.77/7.81 != ( times_times_int @ Q5 @ A23 ) ) ) )
% 13.77/7.81 => ~ ! [R4: int,Q5: int] :
% 13.77/7.81 ( ( A33
% 13.77/7.81 = ( product_Pair_int_int @ Q5 @ R4 ) )
% 13.77/7.81 => ( ( ( sgn_sgn_int @ R4 )
% 13.77/7.81 = ( sgn_sgn_int @ A23 ) )
% 13.77/7.81 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ A23 ) )
% 13.77/7.81 => ( A12
% 13.77/7.81 != ( plus_plus_int @ ( times_times_int @ Q5 @ A23 ) @ R4 ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7526_div__eq__sgn__abs,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( ( sgn_sgn_int @ K )
% 13.77/7.81 = ( sgn_sgn_int @ L ) )
% 13.77/7.81 => ( ( divide_divide_int @ K @ L )
% 13.77/7.81 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7527_zsgn__def,axiom,
% 13.77/7.81 ( sgn_sgn_int
% 13.77/7.81 = ( ^ [I3: int] : ( if_int @ ( I3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7528_div__sgn__abs__cancel,axiom,
% 13.77/7.81 ! [V2: int,K: int,L: int] :
% 13.77/7.81 ( ( V2 != zero_zero_int )
% 13.77/7.81 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ L ) ) )
% 13.77/7.81 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7529_eucl__rel__int__remainderI,axiom,
% 13.77/7.81 ! [R: int,L: int,K: int,Q3: int] :
% 13.77/7.81 ( ( ( sgn_sgn_int @ R )
% 13.77/7.81 = ( sgn_sgn_int @ L ) )
% 13.77/7.81 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L ) )
% 13.77/7.81 => ( ( K
% 13.77/7.81 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R ) )
% 13.77/7.81 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7530_sinh__real__less__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 13.77/7.81 = ( ord_less_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7531_sinh__real__le__iff,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7532_sinh__real__pos__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 13.77/7.81 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7533_sinh__real__neg__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7534_sgn__le__0__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7535_zero__le__sgn__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7536_sinh__real__nonpos__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7537_sinh__real__nonneg__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7538_sgn__real__def,axiom,
% 13.77/7.81 ( sgn_sgn_real
% 13.77/7.81 = ( ^ [A7: real] : ( if_real @ ( A7 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A7 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7539_sgn__power__injE,axiom,
% 13.77/7.81 ! [A: real,N: nat,X: real,B: real] :
% 13.77/7.81 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 13.77/7.81 = X )
% 13.77/7.81 => ( ( X
% 13.77/7.81 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( A = B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7540_divmod__nat__def,axiom,
% 13.77/7.81 ( divmod_nat
% 13.77/7.81 = ( ^ [M5: nat,N6: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M5 @ N6 ) @ ( modulo_modulo_nat @ M5 @ N6 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7541_ln__root,axiom,
% 13.77/7.81 ! [N: nat,B: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.81 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 13.77/7.81 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7542_real__root__Suc__0,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 13.77/7.81 = X ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7543_real__root__eq__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ( root @ N @ X )
% 13.77/7.81 = ( root @ N @ Y ) )
% 13.77/7.81 = ( X = Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7544_root__0,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( root @ zero_zero_nat @ X )
% 13.77/7.81 = zero_zero_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7545_real__root__eq__0__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ( root @ N @ X )
% 13.77/7.81 = zero_zero_real )
% 13.77/7.81 = ( X = zero_zero_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7546_real__root__less__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 13.77/7.81 = ( ord_less_real @ X @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7547_real__root__le__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7548_real__root__eq__1__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ( root @ N @ X )
% 13.77/7.81 = one_one_real )
% 13.77/7.81 = ( X = one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7549_real__root__one,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( root @ N @ one_one_real )
% 13.77/7.81 = one_one_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7550_real__root__lt__0__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7551_real__root__gt__0__iff,axiom,
% 13.77/7.81 ! [N: nat,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 13.77/7.81 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7552_real__root__le__0__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7553_real__root__ge__0__iff,axiom,
% 13.77/7.81 ! [N: nat,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7554_real__root__lt__1__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 13.77/7.81 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7555_real__root__gt__1__iff,axiom,
% 13.77/7.81 ! [N: nat,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 13.77/7.81 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7556_real__root__le__1__iff,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7557_real__root__ge__1__iff,axiom,
% 13.77/7.81 ! [N: nat,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7558_real__root__pow__pos2,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 13.77/7.81 = X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7559_sgn__root,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 13.77/7.81 = ( sgn_sgn_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7560_real__root__pos__pos__le,axiom,
% 13.77/7.81 ! [X: real,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7561_real__root__less__mono,axiom,
% 13.77/7.81 ! [N: nat,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ X @ Y )
% 13.77/7.81 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7562_real__root__le__mono,axiom,
% 13.77/7.81 ! [N: nat,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.81 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7563_real__root__power,axiom,
% 13.77/7.81 ! [N: nat,X: real,K: nat] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 13.77/7.81 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7564_real__root__abs,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 13.77/7.81 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7565_real__root__gt__zero,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7566_real__root__strict__decreasing,axiom,
% 13.77/7.81 ! [N: nat,N8: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_nat @ N @ N8 )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ord_less_real @ ( root @ N8 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7567_root__abs__power,axiom,
% 13.77/7.81 ! [N: nat,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 13.77/7.81 = ( abs_abs_real @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7568_real__root__pos__pos,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7569_real__root__strict__increasing,axiom,
% 13.77/7.81 ! [N: nat,N8: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_nat @ N @ N8 )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.81 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N8 @ X ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7570_real__root__decreasing,axiom,
% 13.77/7.81 ! [N: nat,N8: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.81 => ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ ( root @ N8 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7571_real__root__pow__pos,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 13.77/7.81 = X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7572_real__root__pos__unique,axiom,
% 13.77/7.81 ! [N: nat,Y: real,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ( power_power_real @ Y @ N )
% 13.77/7.81 = X )
% 13.77/7.81 => ( ( root @ N @ X )
% 13.77/7.81 = Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7573_real__root__power__cancel,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 13.77/7.81 = X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7574_sgn__power__root,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 13.77/7.81 = X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7575_root__sgn__power,axiom,
% 13.77/7.81 ! [N: nat,Y: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 13.77/7.81 = Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7576_real__root__increasing,axiom,
% 13.77/7.81 ! [N: nat,N8: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_eq_nat @ N @ N8 )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.81 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N8 @ X ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7577_split__root,axiom,
% 13.77/7.81 ! [P2: real > $o,N: nat,X: real] :
% 13.77/7.81 ( ( P2 @ ( root @ N @ X ) )
% 13.77/7.81 = ( ( ( N = zero_zero_nat )
% 13.77/7.81 => ( P2 @ zero_zero_real ) )
% 13.77/7.81 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ! [Y4: real] :
% 13.77/7.81 ( ( ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 13.77/7.81 = X )
% 13.77/7.81 => ( P2 @ Y4 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7578_root__powr__inverse,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( root @ N @ X )
% 13.77/7.81 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7579_log__base__root,axiom,
% 13.77/7.81 ! [N: nat,B: real,X: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.81 => ( ( log @ ( root @ N @ B ) @ X )
% 13.77/7.81 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7580_log__root,axiom,
% 13.77/7.81 ! [N: nat,A: real,B: real] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( log @ B @ ( root @ N @ A ) )
% 13.77/7.81 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7581_powr__gt__zero,axiom,
% 13.77/7.81 ! [X: real,A: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 13.77/7.81 = ( X != zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7582_powr__nonneg__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 13.77/7.81 = ( A = zero_zero_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7583_powr__less__cancel__iff,axiom,
% 13.77/7.81 ! [X: real,A: real,B: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 13.77/7.81 = ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7584_zero__less__log__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 13.77/7.81 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7585_log__less__zero__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7586_one__less__log__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 13.77/7.81 = ( ord_less_real @ A @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7587_log__less__one__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 13.77/7.81 = ( ord_less_real @ X @ A ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7588_log__less__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 13.77/7.81 = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7589_log__eq__one,axiom,
% 13.77/7.81 ! [A: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( log @ A @ A )
% 13.77/7.81 = one_one_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7590_powr__eq__one__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ( powr_real @ A @ X )
% 13.77/7.81 = one_one_real )
% 13.77/7.81 = ( X = zero_zero_real ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7591_powr__one__gt__zero__iff,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ( powr_real @ X @ one_one_real )
% 13.77/7.81 = X )
% 13.77/7.81 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7592_powr__one,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( powr_real @ X @ one_one_real )
% 13.77/7.81 = X ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7593_powr__le__cancel__iff,axiom,
% 13.77/7.81 ! [X: real,A: real,B: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 13.77/7.81 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7594_zero__le__log__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7595_log__le__zero__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7596_one__le__log__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7597_log__le__one__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 13.77/7.81 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7598_log__le__cancel__iff,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ A )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7599_log__powr__cancel,axiom,
% 13.77/7.81 ! [A: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 13.77/7.81 = Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7600_powr__log__cancel,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 13.77/7.81 = X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7601_log__pow__cancel,axiom,
% 13.77/7.81 ! [A: real,B: nat] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 13.77/7.81 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7602_less__log__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 13.77/7.81 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7603_log__less__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 13.77/7.81 = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7604_less__powr__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 13.77/7.81 = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7605_powr__less__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 13.77/7.81 = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7606_le__log__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 13.77/7.81 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7607_log__le__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 13.77/7.81 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7608_le__powr__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 13.77/7.81 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7609_powr__le__iff,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 13.77/7.81 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7610_powr__less__mono2__neg,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ A @ zero_zero_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ Y )
% 13.77/7.81 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7611_powr__non__neg,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7612_powr__mono2,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.81 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7613_powr__ge__pzero,axiom,
% 13.77/7.81 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7614_powr__less__cancel,axiom,
% 13.77/7.81 ! [X: real,A: real,B: real] :
% 13.77/7.81 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ord_less_real @ A @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7615_powr__less__mono,axiom,
% 13.77/7.81 ! [A: real,B: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ A @ B )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7616_powr__mono,axiom,
% 13.77/7.81 ! [A: real,B: real,X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.81 => ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.81 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7617_add__log__eq__powr,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.81 => ( ( B != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 13.77/7.81 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7618_log__add__eq__powr,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.81 => ( ( B != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 13.77/7.81 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7619_minus__log__eq__powr,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.81 => ( ( B != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 13.77/7.81 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7620_log__minus__eq__powr,axiom,
% 13.77/7.81 ! [B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.81 => ( ( B != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 13.77/7.81 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7621_powr__less__mono2,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ Y )
% 13.77/7.81 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7622_powr__mono2_H,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.81 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7623_gr__one__powr,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7624_powr__inj,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( ( powr_real @ A @ X )
% 13.77/7.81 = ( powr_real @ A @ Y ) )
% 13.77/7.81 = ( X = Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7625_ge__one__powr__ge__zero,axiom,
% 13.77/7.81 ! [X: real,A: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7626_powr__mono__both,axiom,
% 13.77/7.81 ! [A: real,B: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( ord_less_eq_real @ A @ B )
% 13.77/7.81 => ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.81 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7627_powr__le1,axiom,
% 13.77/7.81 ! [A: real,X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.81 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7628_powr__divide,axiom,
% 13.77/7.81 ! [X: real,Y: real,A: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 13.77/7.81 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7629_powr__mult,axiom,
% 13.77/7.81 ! [X: real,Y: real,A: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 13.77/7.81 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7630_log__base__change,axiom,
% 13.77/7.81 ! [A: real,B: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( log @ B @ X )
% 13.77/7.81 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7631_powr__realpow,axiom,
% 13.77/7.81 ! [X: real,N: nat] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.81 = ( power_power_real @ X @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7632_log__of__power__eq,axiom,
% 13.77/7.81 ! [M: nat,B: real,N: nat] :
% 13.77/7.81 ( ( ( semiri5074537144036343181t_real @ M )
% 13.77/7.81 = ( power_power_real @ B @ N ) )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( semiri5074537144036343181t_real @ N )
% 13.77/7.81 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7633_less__log__of__power,axiom,
% 13.77/7.81 ! [B: real,N: nat,M: real] :
% 13.77/7.81 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7634_powr__neg__one,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 13.77/7.81 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7635_powr__mult__base,axiom,
% 13.77/7.81 ! [X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 13.77/7.81 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7636_log__mult,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 13.77/7.81 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7637_le__log__of__power,axiom,
% 13.77/7.81 ! [B: real,N: nat,M: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7638_log__base__pow,axiom,
% 13.77/7.81 ! [A: real,N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 13.77/7.81 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7639_log__nat__power,axiom,
% 13.77/7.81 ! [X: real,B: real,N: nat] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 13.77/7.81 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7640_log__divide,axiom,
% 13.77/7.81 ! [A: real,X: real,Y: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 13.77/7.81 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7641_log__of__power__less,axiom,
% 13.77/7.81 ! [M: nat,B: real,N: nat] :
% 13.77/7.81 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.81 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7642_ln__powr__bound,axiom,
% 13.77/7.81 ! [X: real,A: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7643_ln__powr__bound2,axiom,
% 13.77/7.81 ! [X: real,A: real] :
% 13.77/7.81 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7644_log__eq__div__ln__mult__log,axiom,
% 13.77/7.81 ! [A: real,B: real,X: real] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.81 => ( ( A != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ B )
% 13.77/7.81 => ( ( B != one_one_real )
% 13.77/7.81 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( log @ A @ X )
% 13.77/7.81 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7645_log__of__power__le,axiom,
% 13.77/7.81 ! [M: nat,B: real,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.81 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7646_ceiling__log__eq__powr__iff,axiom,
% 13.77/7.81 ! [X: real,B: real,K: nat] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 13.77/7.81 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 13.77/7.81 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 13.77/7.81 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7647_real__of__int__div4,axiom,
% 13.77/7.81 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7648_int__le__real__less,axiom,
% 13.77/7.81 ( ord_less_eq_int
% 13.77/7.81 = ( ^ [N6: int,M5: int] : ( ord_less_real @ ( ring_1_of_int_real @ N6 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M5 ) @ one_one_real ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7649_int__less__real__le,axiom,
% 13.77/7.81 ( ord_less_int
% 13.77/7.81 = ( ^ [N6: int,M5: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N6 ) @ one_one_real ) @ ( ring_1_of_int_real @ M5 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7650_real__of__int__div2,axiom,
% 13.77/7.81 ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7651_real__of__int__div3,axiom,
% 13.77/7.81 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7652_powr__int,axiom,
% 13.77/7.81 ! [X: real,I: int] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 13.77/7.81 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 13.77/7.81 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 13.77/7.81 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 13.77/7.81 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7653_floor__log__eq__powr__iff,axiom,
% 13.77/7.81 ! [X: real,B: real,K: int] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ord_less_real @ one_one_real @ B )
% 13.77/7.81 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 13.77/7.81 = K )
% 13.77/7.81 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 13.77/7.81 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7654_nat__1,axiom,
% 13.77/7.81 ( ( nat2 @ one_one_int )
% 13.77/7.81 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7655_nat__0__iff,axiom,
% 13.77/7.81 ! [I: int] :
% 13.77/7.81 ( ( ( nat2 @ I )
% 13.77/7.81 = zero_zero_nat )
% 13.77/7.81 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7656_nat__le__0,axiom,
% 13.77/7.81 ! [Z: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 13.77/7.81 => ( ( nat2 @ Z )
% 13.77/7.81 = zero_zero_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7657_zless__nat__conj,axiom,
% 13.77/7.81 ! [W2: int,Z: int] :
% 13.77/7.81 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 13.77/7.81 = ( ( ord_less_int @ zero_zero_int @ Z )
% 13.77/7.81 & ( ord_less_int @ W2 @ Z ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7658_nat__zminus__int,axiom,
% 13.77/7.81 ! [N: nat] :
% 13.77/7.81 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 13.77/7.81 = zero_zero_nat ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7659_int__nat__eq,axiom,
% 13.77/7.81 ! [Z: int] :
% 13.77/7.81 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 13.77/7.81 = Z ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 13.77/7.81 = zero_zero_int ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7660_zero__less__nat__eq,axiom,
% 13.77/7.81 ! [Z: int] :
% 13.77/7.81 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 13.77/7.81 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7661_nat__ceiling__le__eq,axiom,
% 13.77/7.81 ! [X: real,A: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 13.77/7.81 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7662_one__less__nat__eq,axiom,
% 13.77/7.81 ! [Z: int] :
% 13.77/7.81 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 13.77/7.81 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7663_nat__floor__neg,axiom,
% 13.77/7.81 ! [X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.81 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 13.77/7.81 = zero_zero_nat ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7664_floor__eq3,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 13.77/7.81 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 13.77/7.81 = N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7665_le__nat__floor,axiom,
% 13.77/7.81 ! [X: nat,A: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 13.77/7.81 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7666_floor__eq4,axiom,
% 13.77/7.81 ! [N: nat,X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 13.77/7.81 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 13.77/7.81 = N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7667_nat__zero__as__int,axiom,
% 13.77/7.81 ( zero_zero_nat
% 13.77/7.81 = ( nat2 @ zero_zero_int ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7668_nat__mono,axiom,
% 13.77/7.81 ! [X: int,Y: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ X @ Y )
% 13.77/7.81 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7669_eq__nat__nat__iff,axiom,
% 13.77/7.81 ! [Z: int,Z7: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 13.77/7.81 => ( ( ( nat2 @ Z )
% 13.77/7.81 = ( nat2 @ Z7 ) )
% 13.77/7.81 = ( Z = Z7 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7670_all__nat,axiom,
% 13.77/7.81 ( ( ^ [P4: nat > $o] :
% 13.77/7.81 ! [X7: nat] : ( P4 @ X7 ) )
% 13.77/7.81 = ( ^ [P5: nat > $o] :
% 13.77/7.81 ! [X4: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 13.77/7.81 => ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7671_ex__nat,axiom,
% 13.77/7.81 ( ( ^ [P4: nat > $o] :
% 13.77/7.81 ? [X7: nat] : ( P4 @ X7 ) )
% 13.77/7.81 = ( ^ [P5: nat > $o] :
% 13.77/7.81 ? [X4: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 13.77/7.81 & ( P5 @ ( nat2 @ X4 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7672_real__of__int__floor__add__one__gt,axiom,
% 13.77/7.81 ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7673_floor__eq,axiom,
% 13.77/7.81 ! [N: int,X: real] :
% 13.77/7.81 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 13.77/7.81 => ( ( archim6058952711729229775r_real @ X )
% 13.77/7.81 = N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7674_real__of__int__floor__add__one__ge,axiom,
% 13.77/7.81 ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7675_real__of__int__floor__gt__diff__one,axiom,
% 13.77/7.81 ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7676_real__of__int__floor__ge__diff__one,axiom,
% 13.77/7.81 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7677_nat__mono__iff,axiom,
% 13.77/7.81 ! [Z: int,W2: int] :
% 13.77/7.81 ( ( ord_less_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 13.77/7.81 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7678_zless__nat__eq__int__zless,axiom,
% 13.77/7.81 ! [M: nat,Z: int] :
% 13.77/7.81 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 13.77/7.81 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7679_nat__le__iff,axiom,
% 13.77/7.81 ! [X: int,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 13.77/7.81 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7680_nat__0__le,axiom,
% 13.77/7.81 ! [Z: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 13.77/7.81 = Z ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7681_int__eq__iff,axiom,
% 13.77/7.81 ! [M: nat,Z: int] :
% 13.77/7.81 ( ( ( semiri1314217659103216013at_int @ M )
% 13.77/7.81 = Z )
% 13.77/7.81 = ( ( M
% 13.77/7.81 = ( nat2 @ Z ) )
% 13.77/7.81 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7682_real__nat__ceiling__ge,axiom,
% 13.77/7.81 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7683_floor__eq2,axiom,
% 13.77/7.81 ! [N: int,X: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 13.77/7.81 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 13.77/7.81 => ( ( archim6058952711729229775r_real @ X )
% 13.77/7.81 = N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7684_floor__divide__real__eq__div,axiom,
% 13.77/7.81 ! [B: int,A: real] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.81 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 13.77/7.81 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7685_nat__less__eq__zless,axiom,
% 13.77/7.81 ! [W2: int,Z: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 13.77/7.81 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 13.77/7.81 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7686_nat__eq__iff2,axiom,
% 13.77/7.81 ! [M: nat,W2: int] :
% 13.77/7.81 ( ( M
% 13.77/7.81 = ( nat2 @ W2 ) )
% 13.77/7.81 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 13.77/7.81 => ( W2
% 13.77/7.81 = ( semiri1314217659103216013at_int @ M ) ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 13.77/7.81 => ( M = zero_zero_nat ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7687_nat__eq__iff,axiom,
% 13.77/7.81 ! [W2: int,M: nat] :
% 13.77/7.81 ( ( ( nat2 @ W2 )
% 13.77/7.81 = M )
% 13.77/7.81 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 13.77/7.81 => ( W2
% 13.77/7.81 = ( semiri1314217659103216013at_int @ M ) ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 13.77/7.81 => ( M = zero_zero_nat ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7688_split__nat,axiom,
% 13.77/7.81 ! [P2: nat > $o,I: int] :
% 13.77/7.81 ( ( P2 @ ( nat2 @ I ) )
% 13.77/7.81 = ( ! [N6: nat] :
% 13.77/7.81 ( ( I
% 13.77/7.81 = ( semiri1314217659103216013at_int @ N6 ) )
% 13.77/7.81 => ( P2 @ N6 ) )
% 13.77/7.81 & ( ( ord_less_int @ I @ zero_zero_int )
% 13.77/7.81 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7689_nat__le__eq__zle,axiom,
% 13.77/7.81 ! [W2: int,Z: int] :
% 13.77/7.81 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 13.77/7.81 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 13.77/7.81 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 13.77/7.81 = ( ord_less_eq_int @ W2 @ Z ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7690_nat__add__distrib,axiom,
% 13.77/7.81 ! [Z: int,Z7: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 13.77/7.81 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 13.77/7.81 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7691_le__nat__iff,axiom,
% 13.77/7.81 ! [K: int,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.81 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 13.77/7.81 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7692_Suc__as__int,axiom,
% 13.77/7.81 ( suc
% 13.77/7.81 = ( ^ [A7: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A7 ) @ one_one_int ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7693_nat__mult__distrib,axiom,
% 13.77/7.81 ! [Z: int,Z7: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 13.77/7.81 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7694_nat__diff__distrib_H,axiom,
% 13.77/7.81 ! [X: int,Y: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.81 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 13.77/7.81 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7695_nat__diff__distrib,axiom,
% 13.77/7.81 ! [Z7: int,Z: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 13.77/7.81 => ( ( ord_less_eq_int @ Z7 @ Z )
% 13.77/7.81 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 13.77/7.81 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7696_nat__div__distrib,axiom,
% 13.77/7.81 ! [X: int,Y: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.81 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 13.77/7.81 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7697_nat__div__distrib_H,axiom,
% 13.77/7.81 ! [Y: int,X: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.81 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 13.77/7.81 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7698_nat__abs__triangle__ineq,axiom,
% 13.77/7.81 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7699_nat__power__eq,axiom,
% 13.77/7.81 ! [Z: int,N: nat] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 13.77/7.81 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7700_nat__mod__distrib,axiom,
% 13.77/7.81 ! [X: int,Y: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.81 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.81 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 13.77/7.81 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7701_div__abs__eq__div__nat,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 13.77/7.81 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7702_mod__abs__eq__div__nat,axiom,
% 13.77/7.81 ! [K: int,L: int] :
% 13.77/7.81 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 13.77/7.81 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7703_Suc__nat__eq__nat__zadd1,axiom,
% 13.77/7.81 ! [Z: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.81 => ( ( suc @ ( nat2 @ Z ) )
% 13.77/7.81 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7704_nat__less__iff,axiom,
% 13.77/7.81 ! [W2: int,M: nat] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 13.77/7.81 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 13.77/7.81 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7705_nat__mult__distrib__neg,axiom,
% 13.77/7.81 ! [Z: int,Z7: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 13.77/7.81 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 13.77/7.81 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7706_nat__abs__int__diff,axiom,
% 13.77/7.81 ! [A: nat,B: nat] :
% 13.77/7.81 ( ( ( ord_less_eq_nat @ A @ B )
% 13.77/7.81 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 13.77/7.81 = ( minus_minus_nat @ B @ A ) ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_nat @ A @ B )
% 13.77/7.81 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 13.77/7.81 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7707_image__atLeastZeroLessThan__int,axiom,
% 13.77/7.81 ! [U: int] :
% 13.77/7.81 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 13.77/7.81 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 13.77/7.81 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7708_diff__nat__eq__if,axiom,
% 13.77/7.81 ! [Z7: int,Z: int] :
% 13.77/7.81 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 13.77/7.81 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 13.77/7.81 = ( nat2 @ Z ) ) )
% 13.77/7.81 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 13.77/7.81 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 13.77/7.81 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7709_powr__real__of__int,axiom,
% 13.77/7.81 ! [X: real,N: int] :
% 13.77/7.81 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.81 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 13.77/7.81 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 13.77/7.81 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 13.77/7.81 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 13.77/7.81 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 13.77/7.81 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7710_floor__real__def,axiom,
% 13.77/7.81 ( archim6058952711729229775r_real
% 13.77/7.81 = ( ^ [X4: real] :
% 13.77/7.81 ( the_int
% 13.77/7.81 @ ^ [Z2: int] :
% 13.77/7.81 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X4 )
% 13.77/7.81 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7711_inverse__powr,axiom,
% 13.77/7.81 ! [Y: real,A: real] :
% 13.77/7.81 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.81 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 13.77/7.81 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 13.77/7.81
% 13.77/7.81 thf(fact_7712_forall__pos__mono__1,axiom,
% 13.77/7.81 ! [P2: real > $o,E2: real] :
% 13.77/7.81 ( ! [D2: real,E: real] :
% 13.77/7.81 ( ( ord_less_real @ D2 @ E )
% 13.77/7.81 => ( ( P2 @ D2 )
% 13.77/7.81 => ( P2 @ E ) ) )
% 13.77/7.81 => ( ! [N2: nat] : ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 13.77/7.82 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 13.77/7.82 => ( P2 @ E2 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7713_forall__pos__mono,axiom,
% 13.77/7.82 ! [P2: real > $o,E2: real] :
% 13.77/7.82 ( ! [D2: real,E: real] :
% 13.77/7.82 ( ( ord_less_real @ D2 @ E )
% 13.77/7.82 => ( ( P2 @ D2 )
% 13.77/7.82 => ( P2 @ E ) ) )
% 13.77/7.82 => ( ! [N2: nat] :
% 13.77/7.82 ( ( N2 != zero_zero_nat )
% 13.77/7.82 => ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) )
% 13.77/7.82 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 13.77/7.82 => ( P2 @ E2 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7714_real__arch__inverse,axiom,
% 13.77/7.82 ! [E2: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ E2 )
% 13.77/7.82 = ( ? [N6: nat] :
% 13.77/7.82 ( ( N6 != zero_zero_nat )
% 13.77/7.82 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N6 ) ) )
% 13.77/7.82 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N6 ) ) @ E2 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7715_ln__inverse,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 13.77/7.82 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7716_log__inverse,axiom,
% 13.77/7.82 ! [A: real,X: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ A )
% 13.77/7.82 => ( ( A != one_one_real )
% 13.77/7.82 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 13.77/7.82 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7717_Sup__nat__empty,axiom,
% 13.77/7.82 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 13.77/7.82 = zero_zero_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7718_Inf__nat__def1,axiom,
% 13.77/7.82 ! [K4: set_nat] :
% 13.77/7.82 ( ( K4 != bot_bot_set_nat )
% 13.77/7.82 => ( member_nat @ ( complete_Inf_Inf_nat @ K4 ) @ K4 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7719_Sup__nat__def,axiom,
% 13.77/7.82 ( complete_Sup_Sup_nat
% 13.77/7.82 = ( ^ [X8: set_nat] : ( if_nat @ ( X8 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X8 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7720_ln__neg__is__const,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.82 => ( ( ln_ln_real @ X )
% 13.77/7.82 = ( the_real
% 13.77/7.82 @ ^ [X4: real] : $false ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7721_floor__rat__def,axiom,
% 13.77/7.82 ( archim3151403230148437115or_rat
% 13.77/7.82 = ( ^ [X4: rat] :
% 13.77/7.82 ( the_int
% 13.77/7.82 @ ^ [Z2: int] :
% 13.77/7.82 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 )
% 13.77/7.82 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7722_less__eq__rat__def,axiom,
% 13.77/7.82 ( ord_less_eq_rat
% 13.77/7.82 = ( ^ [X4: rat,Y4: rat] :
% 13.77/7.82 ( ( ord_less_rat @ X4 @ Y4 )
% 13.77/7.82 | ( X4 = Y4 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7723_sgn__rat__def,axiom,
% 13.77/7.82 ( sgn_sgn_rat
% 13.77/7.82 = ( ^ [A7: rat] : ( if_rat @ ( A7 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A7 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7724_abs__rat__def,axiom,
% 13.77/7.82 ( abs_abs_rat
% 13.77/7.82 = ( ^ [A7: rat] : ( if_rat @ ( ord_less_rat @ A7 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A7 ) @ A7 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7725_obtain__pos__sum,axiom,
% 13.77/7.82 ! [R: rat] :
% 13.77/7.82 ( ( ord_less_rat @ zero_zero_rat @ R )
% 13.77/7.82 => ~ ! [S4: rat] :
% 13.77/7.82 ( ( ord_less_rat @ zero_zero_rat @ S4 )
% 13.77/7.82 => ! [T6: rat] :
% 13.77/7.82 ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 13.77/7.82 => ( R
% 13.77/7.82 != ( plus_plus_rat @ S4 @ T6 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7726_Maclaurin__sin__bound,axiom,
% 13.77/7.82 ! [X: real,N: nat] :
% 13.77/7.82 ( ord_less_eq_real
% 13.77/7.82 @ ( abs_abs_real
% 13.77/7.82 @ ( minus_minus_real @ ( sin_real @ X )
% 13.77/7.82 @ ( groups6591440286371151544t_real
% 13.77/7.82 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.82 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 13.77/7.82 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7727_normalize__negative,axiom,
% 13.77/7.82 ! [Q3: int,P3: int] :
% 13.77/7.82 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 13.77/7.82 => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q3 ) )
% 13.77/7.82 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P3 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7728_Cauchy__iff2,axiom,
% 13.77/7.82 ( topolo4055970368930404560y_real
% 13.77/7.82 = ( ^ [X8: nat > real] :
% 13.77/7.82 ! [J3: nat] :
% 13.77/7.82 ? [M9: nat] :
% 13.77/7.82 ! [M5: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ M9 @ M5 )
% 13.77/7.82 => ! [N6: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ M9 @ N6 )
% 13.77/7.82 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N6 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7729_sin__x__le__x,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7730_sin__le__one,axiom,
% 13.77/7.82 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7731_abs__sin__x__le__abs__x,axiom,
% 13.77/7.82 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7732_sin__x__ge__neg__x,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7733_sin__ge__minus__one,axiom,
% 13.77/7.82 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7734_abs__sin__le__one,axiom,
% 13.77/7.82 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7735_normalize__denom__pos,axiom,
% 13.77/7.82 ! [R: product_prod_int_int,P3: int,Q3: int] :
% 13.77/7.82 ( ( ( normalize @ R )
% 13.77/7.82 = ( product_Pair_int_int @ P3 @ Q3 ) )
% 13.77/7.82 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7736_mod__or__dist,axiom,
% 13.77/7.82 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ H2 )
% 13.77/7.82 = ( ( rep_assn @ P2 @ H2 )
% 13.77/7.82 | ( rep_assn @ Q2 @ H2 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7737_merge__pure__or,axiom,
% 13.77/7.82 ! [A: $o,B: $o] :
% 13.77/7.82 ( ( sup_sup_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 13.77/7.82 = ( pure_assn
% 13.77/7.82 @ ( A
% 13.77/7.82 | B ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7738_mod__h__bot__iff_I7_J,axiom,
% 13.77/7.82 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 13.77/7.82 ( ( rep_assn @ ( sup_sup_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.77/7.82 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.77/7.82 | ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7739_sup__nat__def,axiom,
% 13.77/7.82 sup_sup_nat = ord_max_nat ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7740_ent__disjE,axiom,
% 13.77/7.82 ! [A4: assn,C3: assn,B4: assn] :
% 13.77/7.82 ( ( entails @ A4 @ C3 )
% 13.77/7.82 => ( ( entails @ B4 @ C3 )
% 13.77/7.82 => ( entails @ ( sup_sup_assn @ A4 @ B4 ) @ C3 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7741_ent__disjI1,axiom,
% 13.77/7.82 ! [P2: assn,Q2: assn,R2: assn] :
% 13.77/7.82 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R2 )
% 13.77/7.82 => ( entails @ P2 @ R2 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7742_ent__disjI2,axiom,
% 13.77/7.82 ! [P2: assn,Q2: assn,R2: assn] :
% 13.77/7.82 ( ( entails @ ( sup_sup_assn @ P2 @ Q2 ) @ R2 )
% 13.77/7.82 => ( entails @ Q2 @ R2 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7743_ent__disjI1_H,axiom,
% 13.77/7.82 ! [A4: assn,B4: assn,C3: assn] :
% 13.77/7.82 ( ( entails @ A4 @ B4 )
% 13.77/7.82 => ( entails @ A4 @ ( sup_sup_assn @ B4 @ C3 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7744_ent__disjI2_H,axiom,
% 13.77/7.82 ! [A4: assn,C3: assn,B4: assn] :
% 13.77/7.82 ( ( entails @ A4 @ C3 )
% 13.77/7.82 => ( entails @ A4 @ ( sup_sup_assn @ B4 @ C3 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7745_ent__disjI1__direct,axiom,
% 13.77/7.82 ! [A4: assn,B4: assn] : ( entails @ A4 @ ( sup_sup_assn @ A4 @ B4 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7746_ent__disjI2__direct,axiom,
% 13.77/7.82 ! [B4: assn,A4: assn] : ( entails @ B4 @ ( sup_sup_assn @ A4 @ B4 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7747_star__or__dist1,axiom,
% 13.77/7.82 ! [A4: assn,B4: assn,C3: assn] :
% 13.77/7.82 ( ( times_times_assn @ ( sup_sup_assn @ A4 @ B4 ) @ C3 )
% 13.77/7.82 = ( sup_sup_assn @ ( times_times_assn @ A4 @ C3 ) @ ( times_times_assn @ B4 @ C3 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7748_star__or__dist2,axiom,
% 13.77/7.82 ! [C3: assn,A4: assn,B4: assn] :
% 13.77/7.82 ( ( times_times_assn @ C3 @ ( sup_sup_assn @ A4 @ B4 ) )
% 13.77/7.82 = ( sup_sup_assn @ ( times_times_assn @ C3 @ A4 ) @ ( times_times_assn @ C3 @ B4 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7749_infinite__UNIV__nat,axiom,
% 13.77/7.82 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7750_nat__not__finite,axiom,
% 13.77/7.82 ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7751_mod__star__conv,axiom,
% 13.77/7.82 ! [A4: assn,B4: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ( rep_assn @ ( times_times_assn @ A4 @ B4 ) @ H2 )
% 13.77/7.82 = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As2: set_nat] :
% 13.77/7.82 ( ( H2
% 13.77/7.82 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As2 ) ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( rep_assn @ A4 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 13.77/7.82 & ( rep_assn @ B4 @ ( produc7507926704131184380et_nat @ Hr @ As2 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7752_star__assnI,axiom,
% 13.77/7.82 ! [P2: assn,H2: heap_e7401611519738050253t_unit,As3: set_nat,Q2: assn,As4: set_nat] :
% 13.77/7.82 ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 13.77/7.82 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As4 ) )
% 13.77/7.82 => ( ( ( inf_inf_set_nat @ As3 @ As4 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 => ( rep_assn @ ( times_times_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ ( sup_sup_set_nat @ As3 @ As4 ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7753_atLeastLessThan__add__Un,axiom,
% 13.77/7.82 ! [I: nat,J: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.82 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 13.77/7.82 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7754_range__enumerate,axiom,
% 13.77/7.82 ! [S3: set_nat] :
% 13.77/7.82 ( ~ ( finite_finite_nat @ S3 )
% 13.77/7.82 => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S3 ) @ top_top_set_nat )
% 13.77/7.82 = S3 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7755_UNIV__nat__eq,axiom,
% 13.77/7.82 ( top_top_set_nat
% 13.77/7.82 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7756_range__mod,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.82 => ( ( image_nat_nat
% 13.77/7.82 @ ^ [M5: nat] : ( modulo_modulo_nat @ M5 @ N )
% 13.77/7.82 @ top_top_set_nat )
% 13.77/7.82 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7757_card__nat,axiom,
% 13.77/7.82 ( ( finite_card_nat @ top_top_set_nat )
% 13.77/7.82 = zero_zero_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7758_card__num0,axiom,
% 13.77/7.82 ( ( finite6454714172617411596l_num0 @ top_to3689904424835650196l_num0 )
% 13.77/7.82 = zero_zero_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7759_card__UNIV__unit,axiom,
% 13.77/7.82 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 13.77/7.82 = one_one_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7760_merge__true__star,axiom,
% 13.77/7.82 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 13.77/7.82 = top_top_assn ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7761_merge__pure__and,axiom,
% 13.77/7.82 ! [A: $o,B: $o] :
% 13.77/7.82 ( ( inf_inf_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 13.77/7.82 = ( pure_assn
% 13.77/7.82 @ ( A
% 13.77/7.82 & B ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7762_assn__basic__inequalities_I1_J,axiom,
% 13.77/7.82 top_top_assn != one_one_assn ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7763_assn__basic__inequalities_I5_J,axiom,
% 13.77/7.82 top_top_assn != bot_bot_assn ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7764_mod__h__bot__iff_I6_J,axiom,
% 13.77/7.82 ! [P2: assn,Q2: assn,H2: heap_e7401611519738050253t_unit] :
% 13.77/7.82 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.77/7.82 = ( ( rep_assn @ P2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) )
% 13.77/7.82 & ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7765_card__literal,axiom,
% 13.77/7.82 ( ( finite_card_literal @ top_top_set_literal )
% 13.77/7.82 = zero_zero_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7766_ent__conjE2,axiom,
% 13.77/7.82 ! [B4: assn,C3: assn,A4: assn] :
% 13.77/7.82 ( ( entails @ B4 @ C3 )
% 13.77/7.82 => ( entails @ ( inf_inf_assn @ A4 @ B4 ) @ C3 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7767_ent__conjE1,axiom,
% 13.77/7.82 ! [A4: assn,C3: assn,B4: assn] :
% 13.77/7.82 ( ( entails @ A4 @ C3 )
% 13.77/7.82 => ( entails @ ( inf_inf_assn @ A4 @ B4 ) @ C3 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7768_ent__conjI,axiom,
% 13.77/7.82 ! [A4: assn,B4: assn,C3: assn] :
% 13.77/7.82 ( ( entails @ A4 @ B4 )
% 13.77/7.82 => ( ( entails @ A4 @ C3 )
% 13.77/7.82 => ( entails @ A4 @ ( inf_inf_assn @ B4 @ C3 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7769_mod__and__dist,axiom,
% 13.77/7.82 ! [P2: assn,Q2: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ( rep_assn @ ( inf_inf_assn @ P2 @ Q2 ) @ H2 )
% 13.77/7.82 = ( ( rep_assn @ P2 @ H2 )
% 13.77/7.82 & ( rep_assn @ Q2 @ H2 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7770_ent__true,axiom,
% 13.77/7.82 ! [P2: assn] : ( entails @ P2 @ top_top_assn ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7771_mod__star__trueE,axiom,
% 13.77/7.82 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 )
% 13.77/7.82 => ~ ! [H5: produc3658429121746597890et_nat] :
% 13.77/7.82 ~ ( rep_assn @ P2 @ H5 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7772_mod__star__trueI,axiom,
% 13.77/7.82 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ( rep_assn @ P2 @ H2 )
% 13.77/7.82 => ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7773_mod__h__bot__iff_I2_J,axiom,
% 13.77/7.82 ! [H2: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H2 @ bot_bot_set_nat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7774_root__def,axiom,
% 13.77/7.82 ( root
% 13.77/7.82 = ( ^ [N6: nat,X4: real] :
% 13.77/7.82 ( if_real @ ( N6 = zero_zero_nat ) @ zero_zero_real
% 13.77/7.82 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 13.77/7.82 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N6 ) )
% 13.77/7.82 @ X4 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7775_less__eq__assn__def,axiom,
% 13.77/7.82 ( ord_less_eq_assn
% 13.77/7.82 = ( ^ [A7: assn,B7: assn] :
% 13.77/7.82 ( A7
% 13.77/7.82 = ( inf_inf_assn @ A7 @ B7 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7776_minus__assn__def,axiom,
% 13.77/7.82 ( minus_minus_assn
% 13.77/7.82 = ( ^ [A7: assn,B7: assn] : ( inf_inf_assn @ A7 @ ( uminus_uminus_assn @ B7 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7777_times__assn__raw_Oelims_I3_J,axiom,
% 13.77/7.82 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ~ ( times_assn_raw @ X @ Xa2 @ Xb )
% 13.77/7.82 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.77/7.82 ( ( Xb
% 13.77/7.82 = ( produc7507926704131184380et_nat @ H @ As ) )
% 13.77/7.82 => ? [As12: set_nat,As22: set_nat] :
% 13.77/7.82 ( ( As
% 13.77/7.82 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 13.77/7.82 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7778_less__assn__def,axiom,
% 13.77/7.82 ( ord_less_assn
% 13.77/7.82 = ( ^ [A7: assn,B7: assn] :
% 13.77/7.82 ( ( ord_less_eq_assn @ A7 @ B7 )
% 13.77/7.82 & ( A7 != B7 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7779_binomial__def,axiom,
% 13.77/7.82 ( binomial
% 13.77/7.82 = ( ^ [N6: nat,K3: nat] :
% 13.77/7.82 ( finite_card_set_nat
% 13.77/7.82 @ ( collect_set_nat
% 13.77/7.82 @ ^ [K5: set_nat] :
% 13.77/7.82 ( ( member_set_nat @ K5 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N6 ) ) )
% 13.77/7.82 & ( ( finite_card_nat @ K5 )
% 13.77/7.82 = K3 ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7780_times__assn__raw_Osimps,axiom,
% 13.77/7.82 ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H2: heap_e7401611519738050253t_unit,As3: set_nat] :
% 13.77/7.82 ( ( times_assn_raw @ P2 @ Q2 @ ( produc7507926704131184380et_nat @ H2 @ As3 ) )
% 13.77/7.82 = ( ? [As1: set_nat,As2: set_nat] :
% 13.77/7.82 ( ( As3
% 13.77/7.82 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As1 ) )
% 13.77/7.82 & ( Q2 @ ( produc7507926704131184380et_nat @ H2 @ As2 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7781_times__assn__raw_Oelims_I1_J,axiom,
% 13.77/7.82 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 13.77/7.82 ( ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 13.77/7.82 = Y )
% 13.77/7.82 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.77/7.82 ( ( Xb
% 13.77/7.82 = ( produc7507926704131184380et_nat @ H @ As ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( ~ ? [As1: set_nat,As2: set_nat] :
% 13.77/7.82 ( ( As
% 13.77/7.82 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 13.77/7.82 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7782_times__assn__raw_Oelims_I2_J,axiom,
% 13.77/7.82 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 13.77/7.82 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.77/7.82 ( ( Xb
% 13.77/7.82 = ( produc7507926704131184380et_nat @ H @ As ) )
% 13.77/7.82 => ~ ? [As13: set_nat,As23: set_nat] :
% 13.77/7.82 ( ( As
% 13.77/7.82 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 13.77/7.82 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7783_times__assn__raw_Opelims_I1_J,axiom,
% 13.77/7.82 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 13.77/7.82 ( ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ Xb ) ) )
% 13.77/7.82 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.77/7.82 ( ( Xb
% 13.77/7.82 = ( produc7507926704131184380et_nat @ H @ As ) )
% 13.77/7.82 => ( ( Y
% 13.77/7.82 = ( ? [As1: set_nat,As2: set_nat] :
% 13.77/7.82 ( ( As
% 13.77/7.82 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 13.77/7.82 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) )
% 13.77/7.82 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7784_times__assn__raw_Opelims_I2_J,axiom,
% 13.77/7.82 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ( times_assn_raw @ X @ Xa2 @ Xb )
% 13.77/7.82 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ Xb ) ) )
% 13.77/7.82 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.77/7.82 ( ( Xb
% 13.77/7.82 = ( produc7507926704131184380et_nat @ H @ As ) )
% 13.77/7.82 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 13.77/7.82 => ~ ? [As13: set_nat,As23: set_nat] :
% 13.77/7.82 ( ( As
% 13.77/7.82 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 13.77/7.82 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7785_times__assn__raw_Opelims_I3_J,axiom,
% 13.77/7.82 ! [X: produc3658429121746597890et_nat > $o,Xa2: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 13.77/7.82 ( ~ ( times_assn_raw @ X @ Xa2 @ Xb )
% 13.77/7.82 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ Xb ) ) )
% 13.77/7.82 => ~ ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 13.77/7.82 ( ( Xb
% 13.77/7.82 = ( produc7507926704131184380et_nat @ H @ As ) )
% 13.77/7.82 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa2 @ ( produc7507926704131184380et_nat @ H @ As ) ) ) )
% 13.77/7.82 => ? [As12: set_nat,As22: set_nat] :
% 13.77/7.82 ( ( As
% 13.77/7.82 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 13.77/7.82 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 13.77/7.82 = bot_bot_set_nat )
% 13.77/7.82 & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 13.77/7.82 & ( Xa2 @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7786_sorted__list__of__set__lessThan__Suc,axiom,
% 13.77/7.82 ! [K: nat] :
% 13.77/7.82 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 13.77/7.82 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7787_sorted__list__of__set__atMost__Suc,axiom,
% 13.77/7.82 ! [K: nat] :
% 13.77/7.82 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 13.77/7.82 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7788_upto_Opelims,axiom,
% 13.77/7.82 ! [X: int,Xa2: int,Y: list_int] :
% 13.77/7.82 ( ( ( upto @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 13.77/7.82 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 13.77/7.82 => ( Y = nil_int ) ) )
% 13.77/7.82 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7789_upto__empty,axiom,
% 13.77/7.82 ! [J: int,I: int] :
% 13.77/7.82 ( ( ord_less_int @ J @ I )
% 13.77/7.82 => ( ( upto @ I @ J )
% 13.77/7.82 = nil_int ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7790_upto__Nil2,axiom,
% 13.77/7.82 ! [I: int,J: int] :
% 13.77/7.82 ( ( nil_int
% 13.77/7.82 = ( upto @ I @ J ) )
% 13.77/7.82 = ( ord_less_int @ J @ I ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7791_upto__Nil,axiom,
% 13.77/7.82 ! [I: int,J: int] :
% 13.77/7.82 ( ( ( upto @ I @ J )
% 13.77/7.82 = nil_int )
% 13.77/7.82 = ( ord_less_int @ J @ I ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7792_nth__upto,axiom,
% 13.77/7.82 ! [I: int,K: nat,J: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 13.77/7.82 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 13.77/7.82 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7793_sorted__wrt__upto,axiom,
% 13.77/7.82 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7794_sorted__upto,axiom,
% 13.77/7.82 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7795_upto__split2,axiom,
% 13.77/7.82 ! [I: int,J: int,K: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ I @ J )
% 13.77/7.82 => ( ( ord_less_eq_int @ J @ K )
% 13.77/7.82 => ( ( upto @ I @ K )
% 13.77/7.82 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7796_upto__split1,axiom,
% 13.77/7.82 ! [I: int,J: int,K: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ I @ J )
% 13.77/7.82 => ( ( ord_less_eq_int @ J @ K )
% 13.77/7.82 => ( ( upto @ I @ K )
% 13.77/7.82 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7797_upto_Osimps,axiom,
% 13.77/7.82 ( upto
% 13.77/7.82 = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7798_upto_Oelims,axiom,
% 13.77/7.82 ! [X: int,Xa2: int,Y: list_int] :
% 13.77/7.82 ( ( ( upto @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 13.77/7.82 => ( Y = nil_int ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7799_upto__rec1,axiom,
% 13.77/7.82 ! [I: int,J: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ I @ J )
% 13.77/7.82 => ( ( upto @ I @ J )
% 13.77/7.82 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7800_upto__rec2,axiom,
% 13.77/7.82 ! [I: int,J: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ I @ J )
% 13.77/7.82 => ( ( upto @ I @ J )
% 13.77/7.82 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7801_upto__split3,axiom,
% 13.77/7.82 ! [I: int,J: int,K: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ I @ J )
% 13.77/7.82 => ( ( ord_less_eq_int @ J @ K )
% 13.77/7.82 => ( ( upto @ I @ K )
% 13.77/7.82 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7802_upto_Opsimps,axiom,
% 13.77/7.82 ! [I: int,J: int] :
% 13.77/7.82 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 13.77/7.82 => ( ( ( ord_less_eq_int @ I @ J )
% 13.77/7.82 => ( ( upto @ I @ J )
% 13.77/7.82 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_int @ I @ J )
% 13.77/7.82 => ( ( upto @ I @ J )
% 13.77/7.82 = nil_int ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7803_upto__rec__numeral_I2_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 = nil_int ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7804_upto__rec__numeral_I3_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 = nil_int ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7805_upto__rec__numeral_I4_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.82 = nil_int ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7806_nat__neg__numeral,axiom,
% 13.77/7.82 ! [K: num] :
% 13.77/7.82 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 13.77/7.82 = zero_zero_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7807_upto__rec__numeral_I1_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.82 = nil_int ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7808_numeral__less__real__of__nat__iff,axiom,
% 13.77/7.82 ! [W2: num,N: nat] :
% 13.77/7.82 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.82 = ( ord_less_nat @ ( numeral_numeral_nat @ W2 ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7809_real__of__nat__less__numeral__iff,axiom,
% 13.77/7.82 ! [N: nat,W2: num] :
% 13.77/7.82 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W2 ) )
% 13.77/7.82 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W2 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7810_numeral__le__real__of__nat__iff,axiom,
% 13.77/7.82 ! [N: num,M: nat] :
% 13.77/7.82 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 13.77/7.82 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7811_Suc__times__numeral__mod__eq,axiom,
% 13.77/7.82 ! [K: num,N: nat] :
% 13.77/7.82 ( ( ( numeral_numeral_nat @ K )
% 13.77/7.82 != one_one_nat )
% 13.77/7.82 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 13.77/7.82 = one_one_nat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7812_powr__numeral,axiom,
% 13.77/7.82 ! [X: real,N: num] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 13.77/7.82 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7813_nat__less__numeral__power__cancel__iff,axiom,
% 13.77/7.82 ! [A: int,X: num,N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 13.77/7.82 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7814_numeral__power__less__nat__cancel__iff,axiom,
% 13.77/7.82 ! [X: num,N: nat,A: int] :
% 13.77/7.82 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 13.77/7.82 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7815_numeral__power__le__nat__cancel__iff,axiom,
% 13.77/7.82 ! [X: num,N: nat,A: int] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 13.77/7.82 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7816_nat__le__numeral__power__cancel__iff,axiom,
% 13.77/7.82 ! [A: int,X: num,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 13.77/7.82 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7817_powr__neg__numeral,axiom,
% 13.77/7.82 ! [X: real,N: num] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 13.77/7.82 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7818_enat__ord__number_I1_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 13.77/7.82 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7819_enat__ord__number_I2_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 13.77/7.82 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7820_i0__less,axiom,
% 13.77/7.82 ! [N: extended_enat] :
% 13.77/7.82 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 13.77/7.82 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7821_enat__less__induct,axiom,
% 13.77/7.82 ! [P2: extended_enat > $o,N: extended_enat] :
% 13.77/7.82 ( ! [N2: extended_enat] :
% 13.77/7.82 ( ! [M2: extended_enat] :
% 13.77/7.82 ( ( ord_le72135733267957522d_enat @ M2 @ N2 )
% 13.77/7.82 => ( P2 @ M2 ) )
% 13.77/7.82 => ( P2 @ N2 ) )
% 13.77/7.82 => ( P2 @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7822_not__iless0,axiom,
% 13.77/7.82 ! [N: extended_enat] :
% 13.77/7.82 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7823_enat__0__less__mult__iff,axiom,
% 13.77/7.82 ! [M: extended_enat,N: extended_enat] :
% 13.77/7.82 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 13.77/7.82 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 13.77/7.82 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7824_add__diff__assoc__enat,axiom,
% 13.77/7.82 ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 13.77/7.82 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 13.77/7.82 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 13.77/7.82 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7825_ile0__eq,axiom,
% 13.77/7.82 ! [N: extended_enat] :
% 13.77/7.82 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 13.77/7.82 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7826_i0__lb,axiom,
% 13.77/7.82 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7827_insert_H__correct,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( vEBT_set_vebt @ ( vEBT_VEBT_insert @ T @ X ) )
% 13.77/7.82 = ( 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 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7828_setceilmax,axiom,
% 13.77/7.82 ! [S: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ S @ M )
% 13.77/7.82 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 13.77/7.82 => ( vEBT_invar_vebt @ X3 @ N ) )
% 13.77/7.82 => ( ( M
% 13.77/7.82 = ( suc @ N ) )
% 13.77/7.82 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Listy ) )
% 13.77/7.82 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X3 ) )
% 13.77/7.82 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 13.77/7.82 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S ) )
% 13.77/7.82 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 13.77/7.82 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 13.77/7.82 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7829_pow__sum,axiom,
% 13.77/7.82 ! [A: nat,B: nat] :
% 13.77/7.82 ( ( 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 ) )
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7830_mulcomm,axiom,
% 13.77/7.82 ! [I: nat,Va2: nat] :
% 13.77/7.82 ( ( times_times_nat @ I @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 = ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ I ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7831_two__realpow__ge__two,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_eq_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7832_member__bound,axiom,
% 13.77/7.82 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 13.77/7.82 ( ( vEBT_vebt_member @ Tree @ X )
% 13.77/7.82 => ( ( vEBT_invar_vebt @ Tree @ N )
% 13.77/7.82 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7833_valid__pres__insert,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ T @ X ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7834_misiz,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ( some_nat @ M )
% 13.77/7.82 = ( vEBT_vebt_mint @ T ) )
% 13.77/7.82 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7835_insert__simp__mima,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( X = Mi )
% 13.77/7.82 | ( X = Ma ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7836_two__powr__height__bound__deg,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7837_helpyd,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ( vEBT_vebt_succ @ T @ X )
% 13.77/7.82 = ( some_nat @ Y ) )
% 13.77/7.82 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7838_helpypredd,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ( vEBT_vebt_pred @ T @ X )
% 13.77/7.82 = ( some_nat @ Y ) )
% 13.77/7.82 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7839_valid__insert__both__member__options__add,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7840_valid__insert__both__member__options__pres,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 13.77/7.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7841_post__member__pre__member,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 13.77/7.82 => ( ( vEBT_vebt_member @ T @ Y )
% 13.77/7.82 | ( X = Y ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7842_log__ceil__idem,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.82 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 13.77/7.82 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7843_count__buildup,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7844_delt__out__of__range,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 | ( ord_less_nat @ Ma @ X ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7845_del__single__cont,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( X = Mi )
% 13.77/7.82 & ( X = Ma ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7846_semiring__norm_I78_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 13.77/7.82 = ( ord_less_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7847_semiring__norm_I71_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 13.77/7.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7848_set__n__deg__not__0,axiom,
% 13.77/7.82 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 13.77/7.82 ( ! [X3: vEBT_VEBT] :
% 13.77/7.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.82 => ( vEBT_invar_vebt @ X3 @ N ) )
% 13.77/7.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.82 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7849_semiring__norm_I75_J,axiom,
% 13.77/7.82 ! [M: num] :
% 13.77/7.82 ~ ( ord_less_num @ M @ one ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7850_semiring__norm_I68_J,axiom,
% 13.77/7.82 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7851_tdeletemimi_H,axiom,
% 13.77/7.82 ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X ) @ one_one_nat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7852_count__buildup_H,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( semiri5074537144036343181t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7853_heigt__uplog__rel,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 13.77/7.82 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7854_mi__ma__2__deg,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 13.77/7.82 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 13.77/7.82 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7855_succ__min,axiom,
% 13.77/7.82 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( some_nat @ Mi ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7856_pred__max,axiom,
% 13.77/7.82 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_nat @ Ma @ X )
% 13.77/7.82 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( some_nat @ Ma ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7857_cnt__bound_H,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7858_delete__bound__size__univ_H,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V1232361888498592333_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7859_bit__concat__def,axiom,
% 13.77/7.82 ( vEBT_VEBT_bit_concat
% 13.77/7.82 = ( ^ [H4: nat,L4: nat,D5: nat] : ( plus_plus_nat @ ( times_times_nat @ H4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D5 ) ) @ L4 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7860_TBOUND__vebt__memberi,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_TBOUND_o @ ( vEBT_V854960066525838166emberi @ T @ Ti @ X ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7861_height__double__log__univ__size,axiom,
% 13.77/7.82 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 13.77/7.82 ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 13.77/7.82 => ( ( vEBT_invar_vebt @ T @ Deg )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7862_inrange,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( 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 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7863_Suc__numeral,axiom,
% 13.77/7.82 ! [N: num] :
% 13.77/7.82 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7864_insert__correct,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.82 = ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7865_set__vebt__insert,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) )
% 13.77/7.82 = ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7866_insert__corr,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( sup_sup_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 13.77/7.82 = ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7867_zdiv__numeral__Bit0,axiom,
% 13.77/7.82 ! [V2: num,W2: num] :
% 13.77/7.82 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 13.77/7.82 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7868_semiring__norm_I76_J,axiom,
% 13.77/7.82 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7869_semiring__norm_I69_J,axiom,
% 13.77/7.82 ! [M: num] :
% 13.77/7.82 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7870_mintlistlength,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_nat @ Mi @ Ma )
% 13.77/7.82 & ? [M3: nat] :
% 13.77/7.82 ( ( ( some_nat @ M3 )
% 13.77/7.82 = ( vEBT_vebt_mint @ Summary ) )
% 13.77/7.82 & ( ord_less_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7871_add__2__eq__Suc_H,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 = ( suc @ ( suc @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7872_add__2__eq__Suc,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.82 = ( suc @ ( suc @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7873_Suc__1,axiom,
% 13.77/7.82 ( ( suc @ one_one_nat )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7874_div2__Suc__Suc,axiom,
% 13.77/7.82 ! [M: nat] :
% 13.77/7.82 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7875_mod2__Suc__Suc,axiom,
% 13.77/7.82 ! [M: nat] :
% 13.77/7.82 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7876_zmod__numeral__Bit0,axiom,
% 13.77/7.82 ! [V2: num,W2: num] :
% 13.77/7.82 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 13.77/7.82 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7877_not__mod2__eq__Suc__0__eq__0,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 != ( suc @ zero_zero_nat ) )
% 13.77/7.82 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 = zero_zero_nat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7878_add__self__mod__2,axiom,
% 13.77/7.82 ! [M: nat] :
% 13.77/7.82 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 = zero_zero_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7879_half__nonnegative__int__iff,axiom,
% 13.77/7.82 ! [K: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7880_half__negative__int__iff,axiom,
% 13.77/7.82 ! [K: int] :
% 13.77/7.82 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 13.77/7.82 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7881_mod2__gr__0,axiom,
% 13.77/7.82 ! [M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 = one_one_nat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7882_self__le__ge2__pow,axiom,
% 13.77/7.82 ! [K: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 13.77/7.82 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7883_power2__nat__le__eq__le,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7884_power2__nat__le__imp__le,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7885_numeral__2__eq__2,axiom,
% 13.77/7.82 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 13.77/7.82 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7886_double__not__eq__Suc__double,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 13.77/7.82 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7887_Suc__double__not__eq__double,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.82 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7888_pos2,axiom,
% 13.77/7.82 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7889_pos__mod__bound2,axiom,
% 13.77/7.82 ! [A: int] : ( ord_less_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7890_n__less__equal__power__2,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7891_le__num__One__iff,axiom,
% 13.77/7.82 ! [X: num] :
% 13.77/7.82 ( ( ord_less_eq_num @ X @ one )
% 13.77/7.82 = ( X = one ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7892_num_Osize_I4_J,axiom,
% 13.77/7.82 ( ( size_size_num @ one )
% 13.77/7.82 = zero_zero_nat ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7893_less__2__cases__iff,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 = ( ( N = zero_zero_nat )
% 13.77/7.82 | ( N
% 13.77/7.82 = ( suc @ zero_zero_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7894_less__2__cases,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 => ( ( N = zero_zero_nat )
% 13.77/7.82 | ( N
% 13.77/7.82 = ( suc @ zero_zero_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7895_nat__induct2,axiom,
% 13.77/7.82 ! [P2: nat > $o,N: nat] :
% 13.77/7.82 ( ( P2 @ zero_zero_nat )
% 13.77/7.82 => ( ( P2 @ one_one_nat )
% 13.77/7.82 => ( ! [N2: nat] :
% 13.77/7.82 ( ( P2 @ N2 )
% 13.77/7.82 => ( P2 @ ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 => ( P2 @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7896_diff__le__diff__pow,axiom,
% 13.77/7.82 ! [K: nat,M: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 13.77/7.82 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7897_nat__2,axiom,
% 13.77/7.82 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 13.77/7.82 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7898_realpow__square__minus__le,axiom,
% 13.77/7.82 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7899_binomial__antimono,axiom,
% 13.77/7.82 ! [K: nat,K6: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ K @ K6 )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 13.77/7.82 => ( ( ord_less_eq_nat @ K6 @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7900_binomial__maximum,axiom,
% 13.77/7.82 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7901_pos__mod__sign2,axiom,
% 13.77/7.82 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7902_not__exp__less__eq__0__int,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7903_binomial__mono,axiom,
% 13.77/7.82 ! [K: nat,K6: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ K @ K6 )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7904_binomial__maximum_H,axiom,
% 13.77/7.82 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7905_two__realpow__ge__one,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7906_binomial__le__pow2,axiom,
% 13.77/7.82 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7907_sin__gt__zero__02,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.82 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7908_mod__exp__less__eq__exp,axiom,
% 13.77/7.82 ! [A: int,N: nat] : ( ord_less_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7909_ln__2__less__1,axiom,
% 13.77/7.82 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7910_Suc__n__div__2__gt__zero,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.82 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7911_div__2__gt__zero,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.82 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7912_nat__bit__induct,axiom,
% 13.77/7.82 ! [P2: nat > $o,N: nat] :
% 13.77/7.82 ( ( P2 @ zero_zero_nat )
% 13.77/7.82 => ( ! [N2: nat] :
% 13.77/7.82 ( ( P2 @ N2 )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 13.77/7.82 => ( P2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 13.77/7.82 => ( ! [N2: nat] :
% 13.77/7.82 ( ( P2 @ N2 )
% 13.77/7.82 => ( P2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 13.77/7.82 => ( P2 @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7913_two__pow__div__gt__le,axiom,
% 13.77/7.82 ! [V2: nat,N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ V2 @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) )
% 13.77/7.82 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7914_nat__add__offset__less,axiom,
% 13.77/7.82 ! [Y: nat,N: nat,X: nat,M: nat,Sz: nat] :
% 13.77/7.82 ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.82 => ( ( Sz
% 13.77/7.82 = ( plus_plus_nat @ M @ N ) )
% 13.77/7.82 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ Y ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Sz ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7915_nat__power__less__diff,axiom,
% 13.77/7.82 ! [N: nat,Q3: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Q3 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.82 => ( ord_less_nat @ Q3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7916_power__minus__is__div,axiom,
% 13.77/7.82 ! [B: nat,A: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ B @ A )
% 13.77/7.82 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 13.77/7.82 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7917_nat__le__power__trans,axiom,
% 13.77/7.82 ! [N: nat,M: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ K @ M )
% 13.77/7.82 => ( ord_less_eq_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7918_binomial__less__binomial__Suc,axiom,
% 13.77/7.82 ! [K: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7919_binomial__strict__mono,axiom,
% 13.77/7.82 ! [K: nat,K6: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ K @ K6 )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 13.77/7.82 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7920_binomial__strict__antimono,axiom,
% 13.77/7.82 ! [K: nat,K6: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ K @ K6 )
% 13.77/7.82 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ K6 @ N )
% 13.77/7.82 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7921_square__fact__le__2__fact,axiom,
% 13.77/7.82 ! [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 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7922_exp__half__le2,axiom,
% 13.77/7.82 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7923_exp__plus__inverse__exp,axiom,
% 13.77/7.82 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7924_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J,axiom,
% 13.77/7.82 ! [V2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7925_triangle__def,axiom,
% 13.77/7.82 ( nat_triangle
% 13.77/7.82 = ( ^ [N6: nat] : ( divide_divide_nat @ ( times_times_nat @ N6 @ ( suc @ N6 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7926_ex__power__ivl1,axiom,
% 13.77/7.82 ! [B: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 13.77/7.82 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 13.77/7.82 => ? [N2: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 13.77/7.82 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7927_ex__power__ivl2,axiom,
% 13.77/7.82 ! [B: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 13.77/7.82 => ? [N2: nat] :
% 13.77/7.82 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 13.77/7.82 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7928_less__two__pow__divD,axiom,
% 13.77/7.82 ! [X: nat,N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ X @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.82 & ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7929_less__two__pow__divI,axiom,
% 13.77/7.82 ! [X: nat,N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.82 => ( ord_less_nat @ X @ ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7930_nat__less__power__trans,axiom,
% 13.77/7.82 ! [N: nat,M: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ K ) ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ K @ M )
% 13.77/7.82 => ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7931_num_Osize_I5_J,axiom,
% 13.77/7.82 ! [X2: num] :
% 13.77/7.82 ( ( size_size_num @ ( bit0 @ X2 ) )
% 13.77/7.82 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7932_L2__set__mult__ineq__lemma,axiom,
% 13.77/7.82 ! [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 ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7933_plus__inverse__ge__2,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7934_numeral__1__eq__Suc__0,axiom,
% 13.77/7.82 ( ( numeral_numeral_nat @ one )
% 13.77/7.82 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7935_Suc__nat__number__of__add,axiom,
% 13.77/7.82 ! [V2: num,N: nat] :
% 13.77/7.82 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ N ) )
% 13.77/7.82 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ one ) ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7936_VEBT__internal_Oinsert_H_Osimps_I2_J,axiom,
% 13.77/7.82 ! [Deg: nat,X: nat,Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 13.77/7.82 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 13.77/7.82 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7937_nat__div__eq__Suc__0__iff,axiom,
% 13.77/7.82 ! [N: nat,M: nat] :
% 13.77/7.82 ( ( ( divide_divide_nat @ N @ M )
% 13.77/7.82 = ( suc @ zero_zero_nat ) )
% 13.77/7.82 = ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.82 & ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7938_power__2__mult__step__le,axiom,
% 13.77/7.82 ! [N3: nat,N: nat,K6: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ N3 @ N )
% 13.77/7.82 => ( ( ord_less_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ K6 ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) )
% 13.77/7.82 => ( ord_less_eq_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( plus_plus_nat @ K6 @ one_one_nat ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7939_less__log2__of__power,axiom,
% 13.77/7.82 ! [N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 13.77/7.82 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7940_pos__zmod__mult__2,axiom,
% 13.77/7.82 ! [A: int,B: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.82 => ( ( 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 ) )
% 13.77/7.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7941_le__log2__of__power,axiom,
% 13.77/7.82 ! [N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7942_pos__zdiv__mult__2,axiom,
% 13.77/7.82 ! [A: int,B: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.82 => ( ( 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 ) )
% 13.77/7.82 = ( divide_divide_int @ B @ A ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7943_neg__zdiv__mult__2,axiom,
% 13.77/7.82 ! [A: int,B: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.82 => ( ( 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 ) )
% 13.77/7.82 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7944_exp__bound,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.82 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7945_sb__dec__lem_H,axiom,
% 13.77/7.82 ! [K: nat,A: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) @ A )
% 13.77/7.82 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7946_real__le__x__sinh,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7947_real__le__abs__sinh,axiom,
% 13.77/7.82 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7948_mask__eq__sum__exp__nat,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.82 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 @ ( collect_nat
% 13.77/7.82 @ ^ [Q8: nat] : ( ord_less_nat @ Q8 @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7949_gauss__sum__nat,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( groups3542108847815614940at_nat
% 13.77/7.82 @ ^ [X4: nat] : X4
% 13.77/7.82 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 13.77/7.82 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7950_sum__power2,axiom,
% 13.77/7.82 ! [K: nat] :
% 13.77/7.82 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 13.77/7.82 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7951_VEBT__internal_Oinsert_H_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 13.77/7.82 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) )
% 13.77/7.82 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ~ ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7952_log2__of__power__less,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.82 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7953_sb__inc__lem,axiom,
% 13.77/7.82 ! [A: int,K: nat] :
% 13.77/7.82 ( ( ord_less_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ zero_zero_int )
% 13.77/7.82 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7954_sb__inc__lem_H,axiom,
% 13.77/7.82 ! [A: int,K: nat] :
% 13.77/7.82 ( ( ord_less_int @ A @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) )
% 13.77/7.82 => ( ord_less_eq_int @ ( plus_plus_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ K ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7955_neg__zmod__mult__2,axiom,
% 13.77/7.82 ! [A: int,B: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.82 => ( ( 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 ) )
% 13.77/7.82 = ( 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 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7956_sb__dec__lem,axiom,
% 13.77/7.82 ! [K: nat,A: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) )
% 13.77/7.82 => ( ord_less_eq_int @ ( modulo_modulo_int @ ( plus_plus_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) @ A ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7957_ln__one__plus__pos__lower__bound,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.82 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7958_real__exp__bound__lemma,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7959_pos__eucl__rel__int__mult__2,axiom,
% 13.77/7.82 ! [B: int,A: int,Q3: int,R: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.82 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.82 => ( 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 @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7960_arith__series__nat,axiom,
% 13.77/7.82 ! [A: nat,D: nat,N: nat] :
% 13.77/7.82 ( ( groups3542108847815614940at_nat
% 13.77/7.82 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 13.77/7.82 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 13.77/7.82 = ( 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 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7961_sinh__ln__real,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 13.77/7.82 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7962_pred__bound__size__univ_H,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7963_succ__bound__size__univ_H,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c2 @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7964_Sum__Icc__int,axiom,
% 13.77/7.82 ! [M: int,N: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ M @ N )
% 13.77/7.82 => ( ( groups4538972089207619220nt_int
% 13.77/7.82 @ ^ [X4: int] : X4
% 13.77/7.82 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 13.77/7.82 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7965_log2__of__power__le,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.82 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7966_exp__lower__Taylor__quadratic,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7967_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.82 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7968_floor__log2__div2,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.82 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 13.77/7.82 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7969_invar__vebt_Ointros_I2_J,axiom,
% 13.77/7.82 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 13.77/7.82 ( ! [X3: vEBT_VEBT] :
% 13.77/7.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.82 => ( vEBT_invar_vebt @ X3 @ N ) )
% 13.77/7.82 => ( ( vEBT_invar_vebt @ Summary @ M )
% 13.77/7.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.82 => ( ( M = N )
% 13.77/7.82 => ( ( Deg
% 13.77/7.82 = ( plus_plus_nat @ N @ M ) )
% 13.77/7.82 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 13.77/7.82 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.82 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 13.77/7.82 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7970_neg__eucl__rel__int__mult__2,axiom,
% 13.77/7.82 ! [B: int,A: int,Q3: int,R: int] :
% 13.77/7.82 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 13.77/7.82 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.82 => ( 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 @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7971_binomial__code,axiom,
% 13.77/7.82 ( binomial
% 13.77/7.82 = ( ^ [N6: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N6 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N6 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N6 @ ( minus_minus_nat @ N6 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N6 @ K3 ) @ one_one_nat ) @ N6 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7972_floor__log__nat__eq__if,axiom,
% 13.77/7.82 ! [B: nat,N: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 13.77/7.82 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 13.77/7.82 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 13.77/7.82 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7973_invar__vebt_Ointros_I3_J,axiom,
% 13.77/7.82 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 13.77/7.82 ( ! [X3: vEBT_VEBT] :
% 13.77/7.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.82 => ( vEBT_invar_vebt @ X3 @ N ) )
% 13.77/7.82 => ( ( vEBT_invar_vebt @ Summary @ M )
% 13.77/7.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.82 => ( ( M
% 13.77/7.82 = ( suc @ N ) )
% 13.77/7.82 => ( ( Deg
% 13.77/7.82 = ( plus_plus_nat @ N @ M ) )
% 13.77/7.82 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 13.77/7.82 => ( ! [X3: vEBT_VEBT] :
% 13.77/7.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.82 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 13.77/7.82 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7974_arctan__double,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.82 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 13.77/7.82 = ( 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 ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7975_central__binomial__lower__bound,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.82 => ( 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 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7976_floor__log__nat__eq__powr__iff,axiom,
% 13.77/7.82 ! [B: nat,K: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.82 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 13.77/7.82 = ( semiri1314217659103216013at_int @ N ) )
% 13.77/7.82 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 13.77/7.82 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7977_ln__one__minus__pos__lower__bound,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.82 => ( 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 ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7978_abs__ln__one__plus__x__minus__x__bound,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.82 => ( 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 ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7979_ceiling__log__nat__eq__if,axiom,
% 13.77/7.82 ! [B: nat,N: nat,K: nat] :
% 13.77/7.82 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 13.77/7.82 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 13.77/7.82 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 13.77/7.82 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7980_ceiling__log2__div2,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.82 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 13.77/7.82 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( 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 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7981_ceiling__log__nat__eq__powr__iff,axiom,
% 13.77/7.82 ! [B: nat,K: nat,N: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.82 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 13.77/7.82 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 13.77/7.82 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 13.77/7.82 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7982_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.82 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.82 => ( 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 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7983_Tb__T__vebt__buildupi,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ ( vEBT_V441764108873111860ildupi @ N ) ) @ ( minus_minus_int @ ( vEBT_VEBT_Tb @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7984_Tb__T__vebt__buildupi_H,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_int @ ( vEBT_V9176841429113362141ildupi @ N ) @ ( minus_minus_int @ ( vEBT_VEBT_Tb @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7985_htt__vebt__memberi__invar__vebt,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X )
% 13.77/7.82 @ ^ [R5: $o] :
% 13.77/7.82 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.82 @ ( pure_assn
% 13.77/7.82 @ ( R5
% 13.77/7.82 = ( vEBT_vebt_member @ T @ X ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7986_Tb__T__vebt__buildupi_H_H,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_nat @ ( vEBT_V441764108873111860ildupi @ N ) @ ( minus_minus_nat @ ( vEBT_VEBT_Tb2 @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7987_htt__vebt__predi,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_predi @ Ti @ X )
% 13.77/7.82 @ ^ [R5: option_nat] :
% 13.77/7.82 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.82 @ ( pure_assn
% 13.77/7.82 @ ( R5
% 13.77/7.82 = ( vEBT_vebt_pred @ T @ X ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7988_Tb__Tb_H,axiom,
% 13.77/7.82 ( vEBT_VEBT_Tb
% 13.77/7.82 = ( ^ [T2: nat] : ( semiri1314217659103216013at_int @ ( vEBT_VEBT_Tb2 @ T2 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7989_T__vebt__buildupi__univ,axiom,
% 13.77/7.82 ! [U: nat,N: nat] :
% 13.77/7.82 ( ( U
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_V441764108873111860ildupi @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7990_tdeletemimi,axiom,
% 13.77/7.82 ! [Deg: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Mi ) ) @ Deg @ TreeList @ Summary ) @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7991_semiring__norm_I73_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 13.77/7.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7992_semiring__norm_I80_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 13.77/7.82 = ( ord_less_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7993_minNull__delete__time__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7994_Tb_H__cnt,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_nat @ ( vEBT_VEBT_Tb2 @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_cnt2 @ ( vEBT_vebt_buildup @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7995_TBOUND__vebt__predi,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T8353473612707095248on_nat @ ( vEBT_VEBT_vebt_predi @ T @ Ti @ X ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7996_TBOUND__vebt__succi,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T8353473612707095248on_nat @ ( vEBT_VEBT_vebt_succi @ T @ Ti @ X ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7997_T__vebt__buildupi__cnt_H,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V441764108873111860ildupi @ N ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7998_TBOUND__buildupi,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.82 => ( time_T5737551269749752165_VEBTi @ ( vEBT_vebt_buildupi @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_7999_delete__bound__height,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8000_cnt__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_real @ ( vEBT_VEBT_cnt @ T ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8001_TBOUND__vebt__inserti,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V3964819847710782039nserti @ T @ Ti @ X ) @ ( if_nat @ ( vEBT_VEBT_minNull @ T ) @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8002_htt__vebt__buildupi__univ,axiom,
% 13.77/7.82 ! [U: nat,N: nat] :
% 13.77/7.82 ( ( U
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8003_htt__vebt__buildupi_H__univ,axiom,
% 13.77/7.82 ! [U: nat,N: nat] :
% 13.77/7.82 ( ( U
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( time_htt_VEBT_VEBTi @ one_one_assn @ ( vEBT_V739175172307565963ildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ U ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8004_delete__bound__size__univ,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8005_time__vebt__delete,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_d_e_l_e_t_e @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8006_time__vebt__pred,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8007_time__vebt__succ,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8008_htt__vebt__inserti,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8009_semiring__norm_I81_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 13.77/7.82 = ( ord_less_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8010_semiring__norm_I72_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 13.77/7.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8011_semiring__norm_I77_J,axiom,
% 13.77/7.82 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8012_semiring__norm_I70_J,axiom,
% 13.77/7.82 ! [M: num] :
% 13.77/7.82 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8013_TBOUND__vebt__deletei,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] : ( time_T5737551269749752165_VEBTi @ ( vEBT_V1365221501068881998eletei @ T @ Ti @ X ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ T @ X ) ) @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8014_htt__vebt__memberi,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.82 ( time_htt_o @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X )
% 13.77/7.82 @ ^ [R5: $o] :
% 13.77/7.82 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.82 @ ( pure_assn
% 13.77/7.82 @ ( R5
% 13.77/7.82 = ( vEBT_vebt_member @ T @ X ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_height @ T ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8015_zdiv__numeral__Bit1,axiom,
% 13.77/7.82 ! [V2: num,W2: num] :
% 13.77/7.82 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 13.77/7.82 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8016_semiring__norm_I79_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 13.77/7.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8017_semiring__norm_I74_J,axiom,
% 13.77/7.82 ! [M: num,N: num] :
% 13.77/7.82 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 13.77/7.82 = ( ord_less_num @ M @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8018_htt__vebt__inserti__invar__vebt,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_insert @ T @ X ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8019_htt__vebt__deletei,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( time_htt_VEBT_VEBTi @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_deletei @ Ti @ X ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ T @ X ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8020_htt__vebt__succi,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( time_htt_option_nat @ ( vEBT_vebt_assn_raw @ T @ Ti ) @ ( vEBT_vebt_succi @ Ti @ X )
% 13.77/7.82 @ ^ [R5: option_nat] :
% 13.77/7.82 ( times_times_assn @ ( vEBT_vebt_assn_raw @ T @ Ti )
% 13.77/7.82 @ ( pure_assn
% 13.77/7.82 @ ( R5
% 13.77/7.82 = ( vEBT_vebt_succ @ T @ X ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8021_Suc__div__eq__add3__div__numeral,axiom,
% 13.77/7.82 ! [M: nat,V2: num] :
% 13.77/7.82 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 13.77/7.82 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8022_div__Suc__eq__div__add3,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 13.77/7.82 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8023_Suc__mod__eq__add3__mod__numeral,axiom,
% 13.77/7.82 ! [M: nat,V2: num] :
% 13.77/7.82 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 13.77/7.82 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8024_mod__Suc__eq__mod__add3,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 13.77/7.82 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8025_zmod__numeral__Bit1,axiom,
% 13.77/7.82 ! [V2: num,W2: num] :
% 13.77/7.82 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 13.77/7.82 = ( 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 ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8026_VEBT__internal_OTb_H_Osimps_I1_J,axiom,
% 13.77/7.82 ( ( vEBT_VEBT_Tb2 @ zero_zero_nat )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8027_VEBT__internal_OTb_H_Osimps_I2_J,axiom,
% 13.77/7.82 ( ( vEBT_VEBT_Tb2 @ ( suc @ zero_zero_nat ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8028_eval__nat__numeral_I3_J,axiom,
% 13.77/7.82 ! [N: num] :
% 13.77/7.82 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 13.77/7.82 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8029_numeral__3__eq__3,axiom,
% 13.77/7.82 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.82 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8030_Suc3__eq__add__3,axiom,
% 13.77/7.82 ! [N: nat] :
% 13.77/7.82 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 13.77/7.82 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8031_maxt__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_a_x_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8032_VEBT__internal_OTb_Osimps_I1_J,axiom,
% 13.77/7.82 ( ( vEBT_VEBT_Tb @ zero_zero_nat )
% 13.77/7.82 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8033_mint__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT] : ( ord_less_eq_nat @ ( vEBT_T_m_i_n_t @ T ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8034_num_Osize_I6_J,axiom,
% 13.77/7.82 ! [X32: num] :
% 13.77/7.82 ( ( size_size_num @ ( bit1 @ X32 ) )
% 13.77/7.82 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8035_Suc__div__eq__add3__div,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 13.77/7.82 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8036_Suc__mod__eq__add3__mod,axiom,
% 13.77/7.82 ! [M: nat,N: nat] :
% 13.77/7.82 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 13.77/7.82 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8037_exp__le,axiom,
% 13.77/7.82 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8038_VEBT__internal_OTb_Osimps_I2_J,axiom,
% 13.77/7.82 ( ( vEBT_VEBT_Tb @ ( suc @ zero_zero_nat ) )
% 13.77/7.82 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8039_mod__exhaust__less__4,axiom,
% 13.77/7.82 ! [M: nat] :
% 13.77/7.82 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = zero_zero_nat )
% 13.77/7.82 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = one_one_nat )
% 13.77/7.82 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.82 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8040_insersimp,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,Y: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ Y ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8041_insertsimp,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,L: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( vEBT_VEBT_minNull @ T )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ L ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8042_small__powers__of__2,axiom,
% 13.77/7.82 ! [X: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ X )
% 13.77/7.82 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ X @ one_one_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8043_log__base__10__eq2,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.82 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8044_pred__bound__height,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_p_r_e_d @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8045_insert__bound__height,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8046_succ__bound__height,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_T_s_u_c_c @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8047_log__base__10__eq1,axiom,
% 13.77/7.82 ! [X: real] :
% 13.77/7.82 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.82 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.82 = ( 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 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8048_pred__bound__size__univ,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_p_r_e_d @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8049_succ__bound__size__univ,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_s_u_c_c @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8050_insert__bound__size__univ,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_i_n_s_e_r_t @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8051_VEBT__internal_Ovebt__buildupi__rule,axiom,
% 13.77/7.82 ! [N: nat] : ( time_htt_VEBT_VEBTi @ ( pure_assn @ ( ord_less_nat @ zero_zero_nat @ N ) ) @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_buildup @ N ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8052_vebt__buildupi__rule,axiom,
% 13.77/7.82 ! [N: nat] : ( time_htt_VEBT_VEBTi @ ( pure_assn @ ( ord_less_nat @ zero_zero_nat @ N ) ) @ ( vEBT_vebt_buildupi @ N ) @ ( vEBT_Intf_vebt_assn @ N @ bot_bot_set_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8053_vebt__memberi__rule,axiom,
% 13.77/7.82 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,X: nat] :
% 13.77/7.82 ( time_htt_o @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_memberi @ Ti @ X )
% 13.77/7.82 @ ^ [R5: $o] :
% 13.77/7.82 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 13.77/7.82 @ ( pure_assn
% 13.77/7.82 @ ( R5
% 13.77/7.82 = ( member_nat @ X @ S ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8054_vebt__predi__rule,axiom,
% 13.77/7.82 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,X: nat,Y: nat] :
% 13.77/7.82 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_predi @ Ti @ X )
% 13.77/7.82 @ ^ [R5: option_nat] :
% 13.77/7.82 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 13.77/7.82 @ ( pure_assn
% 13.77/7.82 @ ( ( R5
% 13.77/7.82 = ( some_nat @ Y ) )
% 13.77/7.82 = ( vEBT_is_pred_in_set @ S @ X @ Y ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8055_vebt__succi__rule,axiom,
% 13.77/7.82 ! [N: nat,S: set_nat,Ti: vEBT_VEBTi,X: nat,Y: nat] :
% 13.77/7.82 ( time_htt_option_nat @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_succi @ Ti @ X )
% 13.77/7.82 @ ^ [R5: option_nat] :
% 13.77/7.82 ( times_times_assn @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti )
% 13.77/7.82 @ ( pure_assn
% 13.77/7.82 @ ( ( R5
% 13.77/7.82 = ( some_nat @ Y ) )
% 13.77/7.82 = ( vEBT_is_succ_in_set @ S @ X @ Y ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8056_vebt__inserti__rule,axiom,
% 13.77/7.82 ! [X: nat,N: nat,S: set_nat,Ti: vEBT_VEBTi] :
% 13.77/7.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( time_htt_VEBT_VEBTi @ ( vEBT_Intf_vebt_assn @ N @ S @ Ti ) @ ( vEBT_vebt_inserti @ Ti @ X ) @ ( vEBT_Intf_vebt_assn @ N @ ( sup_sup_set_nat @ S @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( nat2 @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8057_space__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_VEBT_space @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8058_vebt__space__linear__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_VEBT_space @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8059_space__2__pow__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( minus_minus_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) @ one_one_real ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8060_space__space_H,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT] : ( ord_less_nat @ ( vEBT_VEBT_space @ T ) @ ( vEBT_VEBT_space2 @ T ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8061_space_H__bound,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT,N: nat,U: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.82 => ( ( U
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_VEBT_space2 @ T ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ U ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8062_space__cnt,axiom,
% 13.77/7.82 ! [T: vEBT_VEBT] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_space2 @ T ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_cnt @ T ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8063_VEBT__internal_Ospace_H_Osimps_I1_J,axiom,
% 13.77/7.82 ! [A: $o,B: $o] :
% 13.77/7.82 ( ( vEBT_VEBT_space2 @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8064_VEBT__internal_Ospace_Osimps_I1_J,axiom,
% 13.77/7.82 ! [A: $o,B: $o] :
% 13.77/7.82 ( ( vEBT_VEBT_space @ ( vEBT_Leaf @ A @ B ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8065_VEBT__internal_Ospace_H_Osimps_I2_J,axiom,
% 13.77/7.82 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( vEBT_VEBT_space2 @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 13.77/7.82 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList ) @ zero_zero_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8066_VEBT__internal_Ospace_H_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.82 ( ( ( vEBT_VEBT_space2 @ X )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8067_VEBT__internal_Ospace_Osimps_I2_J,axiom,
% 13.77/7.82 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( vEBT_VEBT_space @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) )
% 13.77/7.82 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList ) @ zero_zero_nat ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8068_VEBT__internal_Ospace_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.82 ( ( ( vEBT_VEBT_space @ X )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 13.77/7.82 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8069_t__build__cnt,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8070_t__buildup__cnt,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_V8346862874174094_d_u_p @ N ) ) @ ( times_times_real @ ( vEBT_VEBT_cnt @ ( vEBT_vebt_buildup @ N ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8071_vebt__buildup__bound,axiom,
% 13.77/7.82 ! [U: nat,N: nat] :
% 13.77/7.82 ( ( U
% 13.77/7.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ord_less_eq_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) @ U ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8072_buildup__build__time,axiom,
% 13.77/7.82 ! [N: nat] : ( ord_less_nat @ ( vEBT_V8346862874174094_d_u_p @ N ) @ ( vEBT_V8646137997579335489_i_l_d @ N ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8073_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I1_J,axiom,
% 13.77/7.82 ( ( vEBT_V8346862874174094_d_u_p @ zero_zero_nat )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8074_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I1_J,axiom,
% 13.77/7.82 ( ( vEBT_V8646137997579335489_i_l_d @ zero_zero_nat )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8075_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I2_J,axiom,
% 13.77/7.82 ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ zero_zero_nat ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8076_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I2_J,axiom,
% 13.77/7.82 ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ zero_zero_nat ) )
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8077_div__half__nat,axiom,
% 13.77/7.82 ! [Y: nat,X: nat] :
% 13.77/7.82 ( ( Y != zero_zero_nat )
% 13.77/7.82 => ( ( product_Pair_nat_nat @ ( divide_divide_nat @ X @ Y ) @ ( modulo_modulo_nat @ X @ Y ) )
% 13.77/7.82 = ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ Y @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) @ Y ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ ( minus_minus_nat @ X @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) @ Y ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8078_VEBT__internal_Ospace_Opelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.82 ( ( ( vEBT_VEBT_space @ X )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ X )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ( Y
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.82 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.82 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( ( Y
% 13.77/7.82 = ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_space @ Summary2 ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space @ TreeList2 ) @ zero_zero_nat ) ) )
% 13.77/7.82 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel2 @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8079_VEBT__internal_Ospace_H_Opelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Y: nat] :
% 13.77/7.82 ( ( ( vEBT_VEBT_space2 @ X )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ X )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ( Y
% 13.77/7.82 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.82 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.82 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( ( Y
% 13.77/7.82 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_VEBT_space2 @ Summary2 ) ) @ ( foldr_nat_nat @ plus_plus_nat @ ( map_VEBT_VEBT_nat @ vEBT_VEBT_space2 @ TreeList2 ) @ zero_zero_nat ) ) )
% 13.77/7.82 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_space_rel @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8080_VEBT__internal_Oinsert_H_Opelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 13.77/7.82 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ( Y
% 13.77/7.82 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 13.77/7.82 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.82 => ~ ! [Info2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 13.77/7.82 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.82 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8081_pred__list__to__short,axiom,
% 13.77/7.82 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_eq_nat @ X @ Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = none_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8082_high__def,axiom,
% 13.77/7.82 ( vEBT_VEBT_high
% 13.77/7.82 = ( ^ [X4: nat,N6: nat] : ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8083_high__bound__aux,axiom,
% 13.77/7.82 ! [Ma: nat,N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 13.77/7.82 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8084_high__inv,axiom,
% 13.77/7.82 ! [X: nat,N: nat,Y: nat] :
% 13.77/7.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 13.77/7.82 = Y ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8085_succ__list__to__short,axiom,
% 13.77/7.82 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_eq_nat @ Mi @ X )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = none_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8086_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 13.77/7.82 ! [L: code_integer,U: code_integer] :
% 13.77/7.82 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 13.77/7.82 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8087_plus__integer__code_I1_J,axiom,
% 13.77/7.82 ! [K: code_integer] :
% 13.77/7.82 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 13.77/7.82 = K ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8088_plus__integer__code_I2_J,axiom,
% 13.77/7.82 ! [L: code_integer] :
% 13.77/7.82 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 13.77/7.82 = L ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8089_image__add__integer__atLeastLessThan,axiom,
% 13.77/7.82 ! [L: code_integer,U: code_integer] :
% 13.77/7.82 ( ( image_4470545334726330049nteger
% 13.77/7.82 @ ^ [X4: code_integer] : ( plus_p5714425477246183910nteger @ X4 @ L )
% 13.77/7.82 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 13.77/7.82 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8090_uminus__integer__code_I1_J,axiom,
% 13.77/7.82 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 13.77/7.82 = zero_z3403309356797280102nteger ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8091_minus__integer__code_I1_J,axiom,
% 13.77/7.82 ! [K: code_integer] :
% 13.77/7.82 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 13.77/7.82 = K ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8092_minus__integer__code_I2_J,axiom,
% 13.77/7.82 ! [L: code_integer] :
% 13.77/7.82 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 13.77/7.82 = ( uminus1351360451143612070nteger @ L ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8093_finite__atLeastZeroLessThan__integer,axiom,
% 13.77/7.82 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8094_times__integer__code_I2_J,axiom,
% 13.77/7.82 ! [L: code_integer] :
% 13.77/7.82 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 13.77/7.82 = zero_z3403309356797280102nteger ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8095_times__integer__code_I1_J,axiom,
% 13.77/7.82 ! [K: code_integer] :
% 13.77/7.82 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 13.77/7.82 = zero_z3403309356797280102nteger ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8096_less__eq__integer__code_I1_J,axiom,
% 13.77/7.82 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8097_sgn__integer__code,axiom,
% 13.77/7.82 ( sgn_sgn_Code_integer
% 13.77/7.82 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8098_abs__integer__code,axiom,
% 13.77/7.82 ( abs_abs_Code_integer
% 13.77/7.82 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8099_less__integer__code_I1_J,axiom,
% 13.77/7.82 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8100_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 13.77/7.82 ! [X: nat,N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.82 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8101_nested__mint,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va2: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 13.77/7.82 => ( ( N
% 13.77/7.82 = ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.82 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 13.77/7.82 => ( ( Ma != Mi )
% 13.77/7.82 => ( 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 @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8102_insert__simp__norm,axiom,
% 13.77/7.82 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( ord_less_nat @ Mi @ X )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( X != Ma )
% 13.77/7.82 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8103_insert__simp__excp,axiom,
% 13.77/7.82 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( X != Ma )
% 13.77/7.82 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8104_bit__split__inv,axiom,
% 13.77/7.82 ! [X: nat,D: nat] :
% 13.77/7.82 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 13.77/7.82 = X ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8105_low__def,axiom,
% 13.77/7.82 ( vEBT_VEBT_low
% 13.77/7.82 = ( ^ [X4: nat,N6: nat] : ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8106_low__inv,axiom,
% 13.77/7.82 ! [X: nat,N: nat,Y: nat] :
% 13.77/7.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.82 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 13.77/7.82 = X ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8107_summaxma,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 13.77/7.82 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8108_both__member__options__ding,axiom,
% 13.77/7.82 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 13.77/7.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 13.77/7.82 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) )
% 13.77/7.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8109_finite__atLeastLessThan__integer,axiom,
% 13.77/7.82 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8110_both__member__options__from__complete__tree__to__child,axiom,
% 13.77/7.82 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 13.77/7.82 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) )
% 13.77/7.82 | ( X = Mi )
% 13.77/7.82 | ( X = Ma ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8111_finite__atLeastAtMost__integer,axiom,
% 13.77/7.82 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8112_member__inv,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 & ( ( X = Mi )
% 13.77/7.82 | ( X = Ma )
% 13.77/7.82 | ( ( ord_less_nat @ X @ Ma )
% 13.77/7.82 & ( ord_less_nat @ Mi @ X )
% 13.77/7.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8113_both__member__options__from__chilf__to__complete__tree,axiom,
% 13.77/7.82 ! [X: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 13.77/7.82 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) )
% 13.77/7.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8114_del__x__not__mi__newnode__not__nil,axiom,
% 13.77/7.82 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_nat @ Mi @ X )
% 13.77/7.82 & ( ord_less_eq_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( Newnode
% 13.77/7.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( Newlist
% 13.77/7.82 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8115_del__x__mi__lets__in__not__minNull,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 13.77/7.82 ( ( ( X = Mi )
% 13.77/7.82 & ( ord_less_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( Xn
% 13.77/7.82 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( Newnode
% 13.77/7.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 => ( ( Newlist
% 13.77/7.82 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 13.77/7.82 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8116_del__x__not__mi,axiom,
% 13.77/7.82 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_nat @ Mi @ X )
% 13.77/7.82 & ( ord_less_eq_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( Newnode
% 13.77/7.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 => ( ( Newlist
% 13.77/7.82 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( product_Pair_nat_nat @ Mi
% 13.77/7.82 @ ( if_nat @ ( X = Ma )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ Mi
% 13.77/7.82 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ Newlist
% 13.77/7.82 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 13.77/7.82 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8117_del__x__not__mi__new__node__nil,axiom,
% 13.77/7.82 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,Newnode: vEBT_VEBT,TreeList: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_nat @ Mi @ X )
% 13.77/7.82 & ( ord_less_eq_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( Newnode
% 13.77/7.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 => ( ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( Sn
% 13.77/7.82 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 => ( ( Newlist
% 13.77/7.82 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( product_Pair_nat_nat @ Mi
% 13.77/7.82 @ ( if_nat @ ( X = Ma )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_maxt @ Sn )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ Mi
% 13.77/7.82 @ ( 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 ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ Newlist
% 13.77/7.82 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8118_del__x__not__mia,axiom,
% 13.77/7.82 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_nat @ Mi @ X )
% 13.77/7.82 & ( ord_less_eq_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( product_Pair_nat_nat @ Mi
% 13.77/7.82 @ ( if_nat @ ( X = Ma )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ Mi
% 13.77/7.82 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8119_del__x__mia,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( X = Mi )
% 13.77/7.82 & ( ord_less_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ Summary ) )
% 13.77/7.82 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8120_del__x__mi__lets__in__minNull,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 13.77/7.82 ( ( ( X = Mi )
% 13.77/7.82 & ( ord_less_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( Xn
% 13.77/7.82 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( Newnode
% 13.77/7.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 => ( ( Newlist
% 13.77/7.82 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 13.77/7.82 => ( ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( Sn
% 13.77/7.82 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( product_Pair_nat_nat @ Xn
% 13.77/7.82 @ ( if_nat @ ( Xn = Ma )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_maxt @ Sn )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ Xn
% 13.77/7.82 @ ( 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 ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ Newlist
% 13.77/7.82 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8121_del__x__mi__lets__in,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 13.77/7.82 ( ( ( X = Mi )
% 13.77/7.82 & ( ord_less_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( Xn
% 13.77/7.82 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( Newnode
% 13.77/7.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 => ( ( Newlist
% 13.77/7.82 = ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ Newnode ) )
% 13.77/7.82 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( product_Pair_nat_nat @ Xn
% 13.77/7.82 @ ( if_nat @ ( Xn = Ma )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ Xn
% 13.77/7.82 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ Newlist
% 13.77/7.82 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 13.77/7.82 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8122_del__x__mi,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList: list_VEBT_VEBT,L: nat] :
% 13.77/7.82 ( ( ( X = Mi )
% 13.77/7.82 & ( ord_less_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = H2 )
% 13.77/7.82 => ( ( Xn
% 13.77/7.82 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 13.77/7.82 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.82 = L )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( product_Pair_nat_nat @ Xn
% 13.77/7.82 @ ( if_nat @ ( Xn = Ma )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ Xn
% 13.77/7.82 @ ( 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 @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) )
% 13.77/7.82 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 13.77/7.82 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( 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 @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ H2 ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8123_del__in__range,axiom,
% 13.77/7.82 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_eq_nat @ Mi @ X )
% 13.77/7.82 & ( ord_less_eq_nat @ X @ Ma ) )
% 13.77/7.82 => ( ( Mi != Ma )
% 13.77/7.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( X = Mi )
% 13.77/7.82 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma ) )
% 13.77/7.82 & ( ( X != Mi )
% 13.77/7.82 => ( X = Ma ) ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( X = Mi )
% 13.77/7.82 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma ) )
% 13.77/7.82 & ( ( X != Mi )
% 13.77/7.82 => ( X = Ma ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ Deg
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ Summary ) )
% 13.77/7.82 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8124_succ__less__length__list,axiom,
% 13.77/7.82 ! [Deg: nat,Mi: nat,X: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_eq_nat @ Mi @ X )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ none_nat
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8125_succ__greatereq__min,axiom,
% 13.77/7.82 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_eq_nat @ Mi @ X )
% 13.77/7.82 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ none_nat
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ none_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8126_pred__lesseq__max,axiom,
% 13.77/7.82 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_eq_nat @ X @ Ma )
% 13.77/7.82 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ none_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8127_pred__less__length__list,axiom,
% 13.77/7.82 ! [Deg: nat,X: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 13.77/7.82 => ( ( ord_less_eq_nat @ X @ Ma )
% 13.77/7.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 13.77/7.82 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8128_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 13.77/7.82 ! [X: nat,N: nat,M: nat] :
% 13.77/7.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.82 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.82 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8129_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I7_J,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 | ( ord_less_nat @ Ma @ X ) )
% 13.77/7.82 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = one_one_nat ) )
% 13.77/7.82 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 | ( ord_less_nat @ Ma @ X ) )
% 13.77/7.82 => ( ( ( ( X = Mi )
% 13.77/7.82 & ( X = Ma ) )
% 13.77/7.82 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = one_one_nat ) )
% 13.77/7.82 & ( ~ ( ( X = Mi )
% 13.77/7.82 & ( X = Ma ) )
% 13.77/7.82 => ( ( vEBT_V1232361888498592333_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_nat @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8130_vebt__succ_Osimps_I6_J,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( some_nat @ Mi ) ) )
% 13.77/7.82 & ( ~ ( ord_less_nat @ X @ Mi )
% 13.77/7.82 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ none_nat
% 13.77/7.82 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ none_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8131_vebt__pred_Osimps_I7_J,axiom,
% 13.77/7.82 ! [Ma: nat,X: nat,Mi: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ord_less_nat @ Ma @ X )
% 13.77/7.82 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( some_nat @ Ma ) ) )
% 13.77/7.82 & ( ~ ( ord_less_nat @ Ma @ X )
% 13.77/7.82 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 13.77/7.82 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ none_nat ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8132_vebt__delete_Osimps_I7_J,axiom,
% 13.77/7.82 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.82 ( ( ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 | ( ord_less_nat @ Ma @ X ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 13.77/7.82 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 | ( ord_less_nat @ Ma @ X ) )
% 13.77/7.82 => ( ( ( ( X = Mi )
% 13.77/7.82 & ( X = Ma ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) )
% 13.77/7.82 & ( ~ ( ( X = Mi )
% 13.77/7.82 & ( X = Ma ) )
% 13.77/7.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( X = Mi )
% 13.77/7.82 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma ) )
% 13.77/7.82 & ( ( X != Mi )
% 13.77/7.82 => ( X = Ma ) ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 13.77/7.82 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ ( suc @ ( suc @ Va2 ) )
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( X = Mi )
% 13.77/7.82 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma ) )
% 13.77/7.82 & ( ( X != Mi )
% 13.77/7.82 => ( X = Ma ) ) )
% 13.77/7.82 @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma ) ) )
% 13.77/7.82 @ ( suc @ ( suc @ Va2 ) )
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ Summary ) )
% 13.77/7.82 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8133_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 13.77/7.82 ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList @ S ) @ X )
% 13.77/7.82 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8134_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I7_J,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_T_p_r_e_d @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( plus_plus_nat @ one_one_nat
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ one_one_nat ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8135_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I6_J,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_T_s_u_c_c @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( plus_plus_nat @ one_one_nat
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ one_one_nat ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8136_vebt__delete_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 13.77/7.82 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 13.77/7.82 => ( ! [A3: $o] :
% 13.77/7.82 ( ? [B3: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ( Xa2
% 13.77/7.82 = ( suc @ zero_zero_nat ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ? [N2: nat] :
% 13.77/7.82 ( Xa2
% 13.77/7.82 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 13.77/7.82 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) ) )
% 13.77/7.82 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 13.77/7.82 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 13.77/7.82 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.82 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 13.77/7.82 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.82 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.82 => ( ( ( ( Xa2 = Mi2 )
% 13.77/7.82 & ( Xa2 = Ma2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 13.77/7.82 & ( ~ ( ( Xa2 = Mi2 )
% 13.77/7.82 & ( Xa2 = Ma2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.82 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.82 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.82 = Ma2 ) )
% 13.77/7.82 & ( ( Xa2 != Mi2 )
% 13.77/7.82 => ( Xa2 = Ma2 ) ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma2 ) ) )
% 13.77/7.82 @ ( suc @ ( suc @ Va ) )
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( vEBT_Node
% 13.77/7.82 @ ( some_P7363390416028606310at_nat
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.82 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.82 = Ma2 ) )
% 13.77/7.82 & ( ( Xa2 != Mi2 )
% 13.77/7.82 => ( Xa2 = Ma2 ) ) )
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ Ma2 ) ) )
% 13.77/7.82 @ ( suc @ ( suc @ Va ) )
% 13.77/7.82 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ Summary2 ) )
% 13.77/7.82 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8137_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.82 ( ( ( vEBT_V1232361888498592333_e_t_e @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => ( Y != one_one_nat ) ) )
% 13.77/7.82 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ( Xa2
% 13.77/7.82 = ( suc @ zero_zero_nat ) )
% 13.77/7.82 => ( Y != one_one_nat ) ) )
% 13.77/7.82 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ? [N2: nat] :
% 13.77/7.82 ( Xa2
% 13.77/7.82 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.82 => ( Y != one_one_nat ) ) )
% 13.77/7.82 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.82 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.82 => ( Y = one_one_nat ) )
% 13.77/7.82 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.82 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.82 => ( ( ( ( Xa2 = Mi2 )
% 13.77/7.82 & ( Xa2 = Ma2 ) )
% 13.77/7.82 => ( Y = one_one_nat ) )
% 13.77/7.82 & ( ~ ( ( Xa2 = Mi2 )
% 13.77/7.82 & ( Xa2 = Ma2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8138_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 13.77/7.82 ! [V2: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList @ Vd2 ) @ X )
% 13.77/7.82 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8139_vebt__succ_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 13.77/7.82 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ! [Uu: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ Uu @ B3 ) )
% 13.77/7.82 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => ~ ( ( B3
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.82 & ( ~ B3
% 13.77/7.82 => ( Y = none_nat ) ) ) ) )
% 13.77/7.82 => ( ( ? [Uv: $o,Uw: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ Uv @ Uw ) )
% 13.77/7.82 => ( ? [N2: nat] :
% 13.77/7.82 ( Xa2
% 13.77/7.82 = ( suc @ N2 ) )
% 13.77/7.82 => ( Y != none_nat ) ) )
% 13.77/7.82 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 13.77/7.82 => ( Y != none_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 13.77/7.82 => ( Y != none_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 13.77/7.82 => ( Y != none_nat ) )
% 13.77/7.82 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( some_nat @ Mi2 ) ) )
% 13.77/7.82 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ none_nat
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8140_vebt__pred_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 13.77/7.82 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( ? [Uu: $o,Uv: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.82 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => ( Y != none_nat ) ) )
% 13.77/7.82 => ( ! [A3: $o] :
% 13.77/7.82 ( ? [Uw: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ Uw ) )
% 13.77/7.82 => ( ( Xa2
% 13.77/7.82 = ( suc @ zero_zero_nat ) )
% 13.77/7.82 => ~ ( ( A3
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.82 & ( ~ A3
% 13.77/7.82 => ( Y = none_nat ) ) ) ) )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ? [Va: nat] :
% 13.77/7.82 ( Xa2
% 13.77/7.82 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.82 => ~ ( ( B3
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.82 & ( ~ B3
% 13.77/7.82 => ( ( A3
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.82 & ( ~ A3
% 13.77/7.82 => ( Y = none_nat ) ) ) ) ) ) )
% 13.77/7.82 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 13.77/7.82 => ( Y != none_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 13.77/7.82 => ( Y != none_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 13.77/7.82 => ( Y != none_nat ) )
% 13.77/7.82 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( some_nat @ Ma2 ) ) )
% 13.77/7.82 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( if_option_nat
% 13.77/7.82 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 13.77/7.82 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8141_vebt__member_Osimps_I5_J,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( ( X != Mi )
% 13.77/7.82 => ( ( X != Ma )
% 13.77/7.82 => ( ~ ( ord_less_nat @ X @ Mi )
% 13.77/7.82 & ( ~ ( ord_less_nat @ X @ Mi )
% 13.77/7.82 => ( ~ ( ord_less_nat @ Ma @ X )
% 13.77/7.82 & ( ~ ( ord_less_nat @ Ma @ X )
% 13.77/7.82 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8142_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,V2: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V2 ) @ TreeList @ Vc ) @ X )
% 13.77/7.82 = ( ( X = Mi )
% 13.77/7.82 | ( X = Ma )
% 13.77/7.82 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8143_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.82 ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( ? [Uu: $o,Uv: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.82 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => ( Y != one_one_nat ) ) )
% 13.77/7.82 => ( ( ? [A3: $o,Uw: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ Uw ) )
% 13.77/7.82 => ( ( Xa2
% 13.77/7.82 = ( suc @ zero_zero_nat ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( ? [Va: nat] :
% 13.77/7.82 ( Xa2
% 13.77/7.82 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ) )
% 13.77/7.82 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( plus_plus_nat @ one_one_nat
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8144_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Oelims,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.82 ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ( ? [Uu: $o,B3: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ Uu @ B3 ) )
% 13.77/7.82 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 13.77/7.82 => ( ( ? [Uv: $o,Uw: $o] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Leaf @ Uv @ Uw ) )
% 13.77/7.82 => ( ? [N2: nat] :
% 13.77/7.82 ( Xa2
% 13.77/7.82 = ( suc @ N2 ) )
% 13.77/7.82 => ( Y != one_one_nat ) ) )
% 13.77/7.82 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 13.77/7.82 => ( Y != one_one_nat ) )
% 13.77/7.82 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 != ( plus_plus_nat @ one_one_nat
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 13.77/7.82 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 != none_nat )
% 13.77/7.82 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8145_vebt__member__code_I3_J,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( ~ ( ( Deg = zero_zero_nat )
% 13.77/7.82 | ( Deg
% 13.77/7.82 = ( suc @ zero_zero_nat ) ) )
% 13.77/7.82 & ( ~ ( ( Deg = zero_zero_nat )
% 13.77/7.82 | ( Deg
% 13.77/7.82 = ( suc @ zero_zero_nat ) ) )
% 13.77/7.82 => ( ( X != Mi )
% 13.77/7.82 => ( ( X != Ma )
% 13.77/7.82 => ( ~ ( ord_less_nat @ X @ Mi )
% 13.77/7.82 & ( ~ ( ord_less_nat @ X @ Mi )
% 13.77/7.82 => ( ~ ( ord_less_nat @ Ma @ X )
% 13.77/7.82 & ( ~ ( ord_less_nat @ Ma @ X )
% 13.77/7.82 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8146_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I7_J,axiom,
% 13.77/7.82 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.82 ( ( vEBT_T_d_e_l_e_t_e @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.82 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ord_less_nat @ X @ Mi )
% 13.77/7.82 | ( ord_less_nat @ Ma @ X ) )
% 13.77/7.82 @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( X = Mi )
% 13.77/7.82 & ( X = Ma ) )
% 13.77/7.82 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 13.77/7.82 @ ( if_nat @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.82 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( X = Mi )
% 13.77/7.82 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma ) )
% 13.77/7.82 & ( ( X != Mi )
% 13.77/7.82 => ( X = Ma ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ one_one_nat
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.82 = none_nat )
% 13.77/7.82 @ one_one_nat
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.82 @ one_one_nat ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 13.77/7.82 @ ( if_nat
% 13.77/7.82 @ ( ( ( X = Mi )
% 13.77/7.82 => ( ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.82 = Ma ) )
% 13.77/7.82 & ( ( X != Mi )
% 13.77/7.82 => ( X = Ma ) ) )
% 13.77/7.82 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.82 @ one_one_nat ) ) ) ) )
% 13.77/7.82 @ one_one_nat ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8147_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.82 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 13.77/7.82 = Y )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => A3 )
% 13.77/7.82 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.82 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.82 => B3 )
% 13.77/7.82 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 13.77/7.82 => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 13.77/7.82 => Y )
% 13.77/7.82 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.82 ( ? [S4: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 13.77/7.82 => ( Y
% 13.77/7.82 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.82 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.82
% 13.77/7.82 thf(fact_8148_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 13.77/7.82 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.82 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 13.77/7.82 => ( ! [A3: $o,B3: $o] :
% 13.77/7.82 ( ( X
% 13.77/7.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.82 => ~ ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.82 => A3 )
% 13.77/7.82 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.82 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.82 => B3 )
% 13.77/7.82 & ( Xa2 = one_one_nat ) ) ) ) )
% 13.77/7.82 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.82 ( ? [S4: vEBT_VEBT] :
% 13.77/7.82 ( X
% 13.77/7.82 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 13.77/7.83 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8149_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 13.77/7.83 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 13.77/7.83 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [S4: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8150_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat] :
% 13.77/7.83 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 13.77/7.83 => ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Vc2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 13.77/7.83 => ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 )
% 13.77/7.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 13.77/7.83 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Vd: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 13.77/7.83 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8151_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ? [N2: nat] :
% 13.77/7.83 ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.83 @ one_one_nat
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( Xa2 = Mi2 )
% 13.77/7.83 & ( Xa2 = Ma2 ) )
% 13.77/7.83 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 13.77/7.83 @ ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.83 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.83 = Ma2 ) )
% 13.77/7.83 & ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 = none_nat )
% 13.77/7.83 @ one_one_nat
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.83 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.83 = Ma2 ) )
% 13.77/7.83 & ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8152_invar__vebt_Ointros_I4_J,axiom,
% 13.77/7.83 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 13.77/7.83 ( ! [X3: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X3 @ N ) )
% 13.77/7.83 => ( ( vEBT_invar_vebt @ Summary @ M )
% 13.77/7.83 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.83 => ( ( M = N )
% 13.77/7.83 => ( ( Deg
% 13.77/7.83 = ( plus_plus_nat @ N @ M ) )
% 13.77/7.83 => ( ! [I2: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.83 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X8 ) )
% 13.77/7.83 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 13.77/7.83 => ( ( ( Mi = Ma )
% 13.77/7.83 => ! [X3: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.83 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 13.77/7.83 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 13.77/7.83 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 13.77/7.83 => ( ( ( Mi != Ma )
% 13.77/7.83 => ! [I2: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.83 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 13.77/7.83 = I2 )
% 13.77/7.83 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 13.77/7.83 & ! [X3: nat] :
% 13.77/7.83 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 13.77/7.83 = I2 )
% 13.77/7.83 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 13.77/7.83 => ( ( ord_less_nat @ Mi @ X3 )
% 13.77/7.83 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8153_vebt__member_Oelims_I2_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ( vEBT_vebt_member @ X @ Xa2 )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ~ ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ~ ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( ( Xa2 != Ma2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8154_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 13.77/7.83 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 != ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat] :
% 13.77/7.83 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 13.77/7.83 => ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Vc2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 13.77/7.83 => ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 )
% 13.77/7.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 13.77/7.83 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Vd: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8155_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.83 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [Uu: $o,Uv: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => Y )
% 13.77/7.83 => ( ( ? [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 13.77/7.83 => Y )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat] :
% 13.77/7.83 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Vc2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 )
% 13.77/7.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 13.77/7.83 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Vd: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8156_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 13.77/7.83 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat
% 13.77/7.83 @ ( if_nat @ ( X = Mi ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( X = Ma ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ord_less_nat @ Mi @ X )
% 13.77/7.83 & ( ord_less_nat @ X @ Ma ) )
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 13.77/7.83 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8157_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I5_J,axiom,
% 13.77/7.83 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_T_i_n_s_e_r_t2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( if_nat
% 13.77/7.83 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.83 & ~ ( ( X = Mi )
% 13.77/7.83 | ( X = Ma ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8158_vebt__insert_Osimps_I5_J,axiom,
% 13.77/7.83 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( if_VEBT_VEBT
% 13.77/7.83 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.83 & ~ ( ( X = Mi )
% 13.77/7.83 | ( X = Ma ) ) )
% 13.77/7.83 @ ( 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 @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( 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 @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 13.77/7.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8159_invar__vebt_Ointros_I5_J,axiom,
% 13.77/7.83 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 13.77/7.83 ( ! [X3: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X3 @ N ) )
% 13.77/7.83 => ( ( vEBT_invar_vebt @ Summary @ M )
% 13.77/7.83 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.83 => ( ( M
% 13.77/7.83 = ( suc @ N ) )
% 13.77/7.83 => ( ( Deg
% 13.77/7.83 = ( plus_plus_nat @ N @ M ) )
% 13.77/7.83 => ( ! [I2: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.83 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X8 ) )
% 13.77/7.83 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 13.77/7.83 => ( ( ( Mi = Ma )
% 13.77/7.83 => ! [X3: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.83 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 13.77/7.83 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 13.77/7.83 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 13.77/7.83 => ( ( ( Mi != Ma )
% 13.77/7.83 => ! [I2: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 13.77/7.83 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 13.77/7.83 = I2 )
% 13.77/7.83 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 13.77/7.83 & ! [X3: nat] :
% 13.77/7.83 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 13.77/7.83 = I2 )
% 13.77/7.83 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 13.77/7.83 => ( ( ord_less_nat @ Mi @ X3 )
% 13.77/7.83 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8160_vebt__member_Oelims_I3_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 13.77/7.83 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( ( Xa2 != Ma2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8161_vebt__member_Oelims_I1_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.83 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 13.77/7.83 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => Y )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => Y )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => Y )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( ~ ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( ( Xa2 != Ma2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8162_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( plus_plus_nat @ one_one_nat
% 13.77/7.83 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 13.77/7.83 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ zero_zero_nat )
% 13.77/7.83 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8163_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I5_J,axiom,
% 13.77/7.83 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_T_i_n_s_e_r_t @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.83 & ~ ( ( X = Mi )
% 13.77/7.83 | ( X = Ma ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8164_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( if_nat
% 13.77/7.83 @ ( ( 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 @ TreeList2 ) )
% 13.77/7.83 & ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8165_invar__vebt_Osimps,axiom,
% 13.77/7.83 ( vEBT_invar_vebt
% 13.77/7.83 = ( ^ [A13: vEBT_VEBT,A24: nat] :
% 13.77/7.83 ( ( ? [A7: $o,B7: $o] :
% 13.77/7.83 ( A13
% 13.77/7.83 = ( vEBT_Leaf @ A7 @ B7 ) )
% 13.77/7.83 & ( A24
% 13.77/7.83 = ( suc @ zero_zero_nat ) ) )
% 13.77/7.83 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT] :
% 13.77/7.83 ( ( A13
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary3 ) )
% 13.77/7.83 & ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 13.77/7.83 & ( vEBT_invar_vebt @ Summary3 @ N6 )
% 13.77/7.83 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 13.77/7.83 & ( A24
% 13.77/7.83 = ( plus_plus_nat @ N6 @ N6 ) )
% 13.77/7.83 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 13.77/7.83 & ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.83 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT] :
% 13.77/7.83 ( ( A13
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary3 ) )
% 13.77/7.83 & ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 13.77/7.83 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N6 ) )
% 13.77/7.83 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 13.77/7.83 & ( A24
% 13.77/7.83 = ( plus_plus_nat @ N6 @ ( suc @ N6 ) ) )
% 13.77/7.83 & ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X8 )
% 13.77/7.83 & ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.83 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 13.77/7.83 ( ( A13
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary3 ) )
% 13.77/7.83 & ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 13.77/7.83 & ( vEBT_invar_vebt @ Summary3 @ N6 )
% 13.77/7.83 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 13.77/7.83 & ( A24
% 13.77/7.83 = ( plus_plus_nat @ N6 @ N6 ) )
% 13.77/7.83 & ! [I3: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 13.77/7.83 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ X8 ) )
% 13.77/7.83 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 13.77/7.83 & ( ( Mi3 = Ma3 )
% 13.77/7.83 => ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.83 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.83 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 13.77/7.83 & ( ( Mi3 != Ma3 )
% 13.77/7.83 => ! [I3: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) )
% 13.77/7.83 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N6 )
% 13.77/7.83 = I3 )
% 13.77/7.83 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N6 ) ) )
% 13.77/7.83 & ! [X4: nat] :
% 13.77/7.83 ( ( ( ( vEBT_VEBT_high @ X4 @ N6 )
% 13.77/7.83 = I3 )
% 13.77/7.83 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N6 ) ) )
% 13.77/7.83 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.83 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) )
% 13.77/7.83 | ? [TreeList4: list_VEBT_VEBT,N6: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 13.77/7.83 ( ( A13
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary3 ) )
% 13.77/7.83 & ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X4 @ N6 ) )
% 13.77/7.83 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N6 ) )
% 13.77/7.83 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 13.77/7.83 & ( A24
% 13.77/7.83 = ( plus_plus_nat @ N6 @ ( suc @ N6 ) ) )
% 13.77/7.83 & ! [I3: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 13.77/7.83 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ X8 ) )
% 13.77/7.83 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 13.77/7.83 & ( ( Mi3 = Ma3 )
% 13.77/7.83 => ! [X4: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 13.77/7.83 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.83 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.83 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 13.77/7.83 & ( ( Mi3 != Ma3 )
% 13.77/7.83 => ! [I3: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) )
% 13.77/7.83 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N6 )
% 13.77/7.83 = I3 )
% 13.77/7.83 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ Ma3 @ N6 ) ) )
% 13.77/7.83 & ! [X4: nat] :
% 13.77/7.83 ( ( ( ( vEBT_VEBT_high @ X4 @ N6 )
% 13.77/7.83 = I3 )
% 13.77/7.83 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N6 ) ) )
% 13.77/7.83 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.83 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8166_invar__vebt_Ocases,axiom,
% 13.77/7.83 ! [A12: vEBT_VEBT,A23: nat] :
% 13.77/7.83 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( A12
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( A23
% 13.77/7.83 != ( suc @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 13.77/7.83 ( ( A12
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( A23 = Deg2 )
% 13.77/7.83 => ( ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 13.77/7.83 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 13.77/7.83 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( M3 = N2 )
% 13.77/7.83 => ( ( Deg2
% 13.77/7.83 = ( plus_plus_nat @ N2 @ M3 ) )
% 13.77/7.83 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 13.77/7.83 => ~ ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 13.77/7.83 ( ( A12
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( A23 = Deg2 )
% 13.77/7.83 => ( ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 13.77/7.83 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 13.77/7.83 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( M3
% 13.77/7.83 = ( suc @ N2 ) )
% 13.77/7.83 => ( ( Deg2
% 13.77/7.83 = ( plus_plus_nat @ N2 @ M3 ) )
% 13.77/7.83 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 13.77/7.83 => ~ ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 13.77/7.83 ( ( A12
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( A23 = Deg2 )
% 13.77/7.83 => ( ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 13.77/7.83 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 13.77/7.83 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( M3 = N2 )
% 13.77/7.83 => ( ( Deg2
% 13.77/7.83 = ( plus_plus_nat @ N2 @ M3 ) )
% 13.77/7.83 => ( ! [I4: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 13.77/7.83 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 13.77/7.83 => ( ( ( Mi2 = Ma2 )
% 13.77/7.83 => ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 13.77/7.83 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 13.77/7.83 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.83 => ~ ( ( Mi2 != Ma2 )
% 13.77/7.83 => ! [I4: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 13.77/7.83 = I4 )
% 13.77/7.83 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 13.77/7.83 & ! [X5: nat] :
% 13.77/7.83 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 13.77/7.83 = I4 )
% 13.77/7.83 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 13.77/7.83 => ( ( ord_less_nat @ Mi2 @ X5 )
% 13.77/7.83 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 13.77/7.83 ( ( A12
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( A23 = Deg2 )
% 13.77/7.83 => ( ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 13.77/7.83 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 13.77/7.83 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.83 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( M3
% 13.77/7.83 = ( suc @ N2 ) )
% 13.77/7.83 => ( ( Deg2
% 13.77/7.83 = ( plus_plus_nat @ N2 @ M3 ) )
% 13.77/7.83 => ( ! [I4: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X8 ) )
% 13.77/7.83 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 13.77/7.83 => ( ( ( Mi2 = Ma2 )
% 13.77/7.83 => ! [X5: vEBT_VEBT] :
% 13.77/7.83 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.83 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 13.77/7.83 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 13.77/7.83 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.83 => ~ ( ( Mi2 != Ma2 )
% 13.77/7.83 => ! [I4: nat] :
% 13.77/7.83 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 13.77/7.83 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N2 )
% 13.77/7.83 = I4 )
% 13.77/7.83 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N2 ) ) )
% 13.77/7.83 & ! [X5: nat] :
% 13.77/7.83 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 13.77/7.83 = I4 )
% 13.77/7.83 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 13.77/7.83 => ( ( ord_less_nat @ Mi2 @ X5 )
% 13.77/7.83 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8167_vebt__insert_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 13.77/7.83 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ~ ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 13.77/7.83 & ( ( Xa2 != one_one_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) ) )
% 13.77/7.83 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( if_VEBT_VEBT
% 13.77/7.83 @ ( ( 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 @ TreeList2 ) )
% 13.77/7.83 & ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 ) )
% 13.77/7.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8168_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I7_J,axiom,
% 13.77/7.83 ! [Ma: nat,X: nat,Mi: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.83 ( ( ( ord_less_nat @ Ma @ X )
% 13.77/7.83 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma @ X )
% 13.77/7.83 => ( ( vEBT_T_p_r_e_d2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8169_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I6_J,axiom,
% 13.77/7.83 ! [X: nat,Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 13.77/7.83 ( ( ( ord_less_nat @ X @ Mi )
% 13.77/7.83 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ X @ Mi )
% 13.77/7.83 => ( ( vEBT_T_s_u_c_c2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8170_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 13.77/7.83 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( 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 @ TreeList2 ) )
% 13.77/7.83 & ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8171_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [Uu: $o,Uv: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [A3: $o,Uw: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ Uw ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ? [Va: nat] :
% 13.77/7.83 ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( Y = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8172_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [Uu: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [Uv: $o,Uw: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uv @ Uw ) )
% 13.77/7.83 => ( ? [N2: nat] :
% 13.77/7.83 ( Xa2
% 13.77/7.83 = ( suc @ N2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) ) )
% 13.77/7.83 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 13.77/7.83 => ( Y != one_one_nat ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( Y = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8173_in__children__def,axiom,
% 13.77/7.83 ( vEBT_V5917875025757280293ildren
% 13.77/7.83 = ( ^ [N6: nat,TreeList4: list_VEBT_VEBT,X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ ( vEBT_VEBT_high @ X4 @ N6 ) ) @ ( vEBT_VEBT_low @ X4 @ N6 ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8174_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_d_e_l_e_t_e @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ! [N2: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.83 @ one_one_nat
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( Xa2 = Mi2 )
% 13.77/7.83 & ( Xa2 = Ma2 ) )
% 13.77/7.83 @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_m_i_n_t @ Summary2 ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) ) @ one_one_nat ) ) @ one_one_nat )
% 13.77/7.83 @ ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_d_e_l_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_i_n_N_u_l_l @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_d_e_l_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.83 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.83 = Ma2 ) )
% 13.77/7.83 & ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 = none_nat )
% 13.77/7.83 @ one_one_nat
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.83 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.83 = Ma2 ) )
% 13.77/7.83 & ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8441311223069195367_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8175_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_s_u_c_c @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [Uv: $o,Uw: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uv @ Uw ) )
% 13.77/7.83 => ! [N2: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ N2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 13.77/7.83 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) )
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_s_u_c_c @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 = none_nat )
% 13.77/7.83 @ one_one_nat
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8176_vebt__succ_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 13.77/7.83 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( ( B3
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.83 & ( ~ B3
% 13.77/7.83 => ( Y = none_nat ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [Uv: $o,Uw: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uv @ Uw ) )
% 13.77/7.83 => ! [N2: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ N2 ) )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 13.77/7.83 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( some_nat @ Mi2 ) ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( if_option_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( if_option_nat
% 13.77/7.83 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 = none_nat )
% 13.77/7.83 @ none_nat
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 @ none_nat ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8177_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_p_r_e_d @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,Uw: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ Uw ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ one_one_nat ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ! [Va: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ B3 @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_T_m_i_n_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_p_r_e_d @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 = none_nat )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 13.77/7.83 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( vEBT_T_m_a_x_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 @ one_one_nat ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel2 @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8178_vebt__pred_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 13.77/7.83 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,Uw: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ Uw ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( ( A3
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.83 & ( ~ A3
% 13.77/7.83 => ( Y = none_nat ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ! [Va: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( ( ( B3
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( some_nat @ one_one_nat ) ) )
% 13.77/7.83 & ( ~ B3
% 13.77/7.83 => ( ( A3
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( some_nat @ zero_zero_nat ) ) )
% 13.77/7.83 & ( ~ A3
% 13.77/7.83 => ( Y = none_nat ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 13.77/7.83 => ( ( Y = none_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( some_nat @ Ma2 ) ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( if_option_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( if_option_nat
% 13.77/7.83 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 = none_nat )
% 13.77/7.83 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 @ none_nat ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8179_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_V1232361888498592333_e_t_e @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ! [N2: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.83 => ( Y = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.83 => ( ( ( ( Xa2 = Mi2 )
% 13.77/7.83 & ( Xa2 = Ma2 ) )
% 13.77/7.83 => ( Y = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 & ( Xa2 = Ma2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( if_nat @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ ( vEBT_V1232361888498592333_e_t_e @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_V1232361888498592333_e_t_e @ 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) ) @ one_one_nat ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V6368547301243506412_e_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8180_vebt__delete_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 13.77/7.83 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Leaf @ $false @ B3 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ $false ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ! [N2: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N2 ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 13.77/7.83 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 13.77/7.83 => ( ( ( ( Xa2 = Mi2 )
% 13.77/7.83 & ( Xa2 = Ma2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 13.77/7.83 & ( ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 & ( Xa2 = Ma2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( vEBT_Node
% 13.77/7.83 @ ( some_P7363390416028606310at_nat
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.83 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.83 = Ma2 ) )
% 13.77/7.83 & ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 = none_nat )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 @ Ma2 ) ) )
% 13.77/7.83 @ ( suc @ ( suc @ Va ) )
% 13.77/7.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ ( vEBT_Node
% 13.77/7.83 @ ( some_P7363390416028606310at_nat
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( Xa2 = Mi2 )
% 13.77/7.83 => ( ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 13.77/7.83 = Ma2 ) )
% 13.77/7.83 & ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ Ma2 ) ) )
% 13.77/7.83 @ ( suc @ ( suc @ Va ) )
% 13.77/7.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 @ Summary2 ) )
% 13.77/7.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8181_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_s_u_c_c2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ B3 ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B3 ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [Uv: $o,Uw: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uv @ Uw ) )
% 13.77/7.83 => ! [N2: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ N2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N2 ) ) ) ) ) )
% 13.77/7.83 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( Y = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_s_u_c_c2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_s_u_c_c2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_s_u_c_c_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8182_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_i_n_s_e_r_t @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( 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 @ TreeList2 ) )
% 13.77/7.83 & ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ ( vEBT_T_m_i_n_N_u_l_l @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( if_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T9217963907923527482_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8183_vebt__insert_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 13.77/7.83 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 13.77/7.83 & ( ( Xa2 != one_one_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( if_VEBT_VEBT
% 13.77/7.83 @ ( ( 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 @ TreeList2 ) )
% 13.77/7.83 & ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 @ TreeList2 @ ( 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 ) )
% 13.77/7.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8184_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_p_r_e_d2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,Uw: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ Uw ) )
% 13.77/7.83 => ( ( Xa2
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ! [Va: nat] :
% 13.77/7.83 ( ( Xa2
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 13.77/7.83 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( Y = one_one_nat ) )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.83 != none_nat )
% 13.77/7.83 & ( 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 @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_p_r_e_d2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_p_r_e_d2 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T_p_r_e_d_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8185_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_i_n_s_e_r_t2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S4 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S4 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( if_nat
% 13.77/7.83 @ ( ( 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 @ TreeList2 ) )
% 13.77/7.83 & ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 @ ( plus_plus_nat @ ( vEBT_T_i_n_s_e_r_t2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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_nat @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_T_i_n_s_e_r_t2 @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ one_one_nat ) )
% 13.77/7.83 @ one_one_nat ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5076183648494686801_t_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8186_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => ( ( Y = one_one_nat )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat
% 13.77/7.83 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 13.77/7.83 @ ( if_nat
% 13.77/7.83 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 13.77/7.83 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 13.77/7.83 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) @ zero_zero_nat )
% 13.77/7.83 @ zero_zero_nat ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8187_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ? [A3: $o,B3: $o] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 13.77/7.83 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 13.77/7.83 ( ? [Summary2: vEBT_VEBT] :
% 13.77/7.83 ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8188_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 13.77/7.83 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X )
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8189_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 13.77/7.83 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X )
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8190_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 13.77/7.83 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X )
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8191_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 13.77/7.83 ! [A: $o,B: $o,X: nat] :
% 13.77/7.83 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X )
% 13.77/7.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8192_member__bound__height,axiom,
% 13.77/7.83 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 13.77/7.83 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.83 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8193_member__bound__size__univ,axiom,
% 13.77/7.83 ! [T: vEBT_VEBT,N: nat,U: real,X: nat] :
% 13.77/7.83 ( ( vEBT_invar_vebt @ T @ N )
% 13.77/7.83 => ( ( U
% 13.77/7.83 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.83 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_T_m_e_m_b_e_r @ T @ X ) ) @ ( plus_plus_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8194_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 13.77/7.83 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8195_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_T_m_e_m_b_e_r @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8196_vebt__member_Opelims_I1_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.83 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => ( ~ Y
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => ( ~ Y
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => ( ~ Y
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( ( Xa2 != Ma2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8197_vebt__member_Opelims_I3_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 13.77/7.83 => ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) )
% 13.77/7.83 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 13.77/7.83 => ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( ( Xa2 != Ma2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8198_vebt__member_Opelims_I2_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ( vEBT_vebt_member @ X @ Xa2 )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 13.77/7.83 => ~ ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 13.77/7.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 13.77/7.83 => ~ ( ( Xa2 != Mi2 )
% 13.77/7.83 => ( ( Xa2 != Ma2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 13.77/7.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8199_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 13.77/7.83 => ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 13.77/7.83 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) )
% 13.77/7.83 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ Xa2 ) )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8200_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 13.77/7.83 => ~ ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 13.77/7.83 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ Xa2 ) )
% 13.77/7.83 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8201_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.83 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [A3: $o,B3: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.83 => A3 )
% 13.77/7.83 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.83 => ( ( ( Xa2 = one_one_nat )
% 13.77/7.83 => B3 )
% 13.77/7.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 13.77/7.83 => ( ~ Y
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S4: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S4 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8202_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.83 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => ( ~ Y
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 13.77/7.83 => ( ~ Y
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 )
% 13.77/7.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 13.77/7.83 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8203_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) )
% 13.77/7.83 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 13.77/7.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 13.77/7.83 => ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 13.77/7.83 => ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 )
% 13.77/7.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 13.77/7.83 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ Xa2 ) )
% 13.77/7.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8204_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 13.77/7.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.83 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 13.77/7.83 => ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 ) ) ) )
% 13.77/7.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 13.77/7.83 => ~ ( ( Xa2 = Mi2 )
% 13.77/7.83 | ( Xa2 = Ma2 )
% 13.77/7.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 13.77/7.83 => ~ ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) )
% 13.77/7.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ Xa2 ) )
% 13.77/7.83 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 13.77/7.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( 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 ) ) ) ) ) )
% 13.77/7.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8205_Maclaurin__sin__expansion3,axiom,
% 13.77/7.83 ! [N: nat,X: real] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.83 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ? [T6: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ T6 )
% 13.77/7.83 & ( ord_less_real @ T6 @ X )
% 13.77/7.83 & ( ( sin_real @ X )
% 13.77/7.83 = ( plus_plus_real
% 13.77/7.83 @ ( groups6591440286371151544t_real
% 13.77/7.83 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.83 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.83 @ ( 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 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8206_Maclaurin__sin__expansion4,axiom,
% 13.77/7.83 ! [X: real,N: nat] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ? [T6: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ T6 )
% 13.77/7.83 & ( ord_less_eq_real @ T6 @ X )
% 13.77/7.83 & ( ( sin_real @ X )
% 13.77/7.83 = ( plus_plus_real
% 13.77/7.83 @ ( groups6591440286371151544t_real
% 13.77/7.83 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.83 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.83 @ ( 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 ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8207_Maclaurin__sin__expansion2,axiom,
% 13.77/7.83 ! [X: real,N: nat] :
% 13.77/7.83 ? [T6: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.83 & ( ( sin_real @ X )
% 13.77/7.83 = ( plus_plus_real
% 13.77/7.83 @ ( groups6591440286371151544t_real
% 13.77/7.83 @ ^ [M5: nat] : ( times_times_real @ ( sin_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.83 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.83 @ ( 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 ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8208_sin__cos__npi,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( 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 ) ) ) )
% 13.77/7.83 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8209_pi__gt__zero,axiom,
% 13.77/7.83 ord_less_real @ zero_zero_real @ pi ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8210_pi__not__less__zero,axiom,
% 13.77/7.83 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8211_pi__ge__zero,axiom,
% 13.77/7.83 ord_less_eq_real @ zero_zero_real @ pi ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8212_sin__gt__zero,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ pi )
% 13.77/7.83 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8213_sin__ge__zero,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ pi )
% 13.77/7.83 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8214_pi__less__4,axiom,
% 13.77/7.83 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8215_pi__ge__two,axiom,
% 13.77/7.83 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8216_sin__eq__0__pi,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ pi )
% 13.77/7.83 => ( ( ( sin_real @ X )
% 13.77/7.83 = zero_zero_real )
% 13.77/7.83 => ( X = zero_zero_real ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8217_sin__zero__pi__iff,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 13.77/7.83 => ( ( ( sin_real @ X )
% 13.77/7.83 = zero_zero_real )
% 13.77/7.83 = ( X = zero_zero_real ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8218_pi__half__less__two,axiom,
% 13.77/7.83 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8219_pi__half__le__two,axiom,
% 13.77/7.83 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8220_pi__half__gt__zero,axiom,
% 13.77/7.83 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8221_pi__half__ge__zero,axiom,
% 13.77/7.83 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8222_m2pi__less__pi,axiom,
% 13.77/7.83 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8223_arctan__ubound,axiom,
% 13.77/7.83 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8224_sin__pi__divide__n__ge__0,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( N != zero_zero_nat )
% 13.77/7.83 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8225_minus__pi__half__less__zero,axiom,
% 13.77/7.83 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8226_sin__gt__zero2,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8227_sin__lt__zero,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ pi @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 13.77/7.83 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8228_sin__inj__pi,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ( sin_real @ X )
% 13.77/7.83 = ( sin_real @ Y ) )
% 13.77/7.83 => ( X = Y ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8229_sin__mono__le__eq,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 13.77/7.83 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8230_sin__monotone__2pi__le,axiom,
% 13.77/7.83 ! [Y: real,X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8231_arctan__bounded,axiom,
% 13.77/7.83 ! [Y: real] :
% 13.77/7.83 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 13.77/7.83 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8232_arctan__lbound,axiom,
% 13.77/7.83 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8233_sin__le__zero,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ pi @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 13.77/7.83 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8234_sin__less__zero,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.83 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8235_sin__mono__less__eq,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 13.77/7.83 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8236_sin__monotone__2pi,axiom,
% 13.77/7.83 ! [Y: real,X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.83 => ( ( ord_less_real @ Y @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8237_sin__total,axiom,
% 13.77/7.83 ! [Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.83 => ? [X3: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 13.77/7.83 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 & ( ( sin_real @ X3 )
% 13.77/7.83 = Y )
% 13.77/7.83 & ! [Y5: real] :
% 13.77/7.83 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 13.77/7.83 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 & ( ( sin_real @ Y5 )
% 13.77/7.83 = Y ) )
% 13.77/7.83 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8238_sin__pi__divide__n__gt__0,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8239_Maclaurin__cos__expansion2,axiom,
% 13.77/7.83 ! [X: real,N: nat] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.83 => ? [T6: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ T6 )
% 13.77/7.83 & ( ord_less_real @ T6 @ X )
% 13.77/7.83 & ( ( cos_real @ X )
% 13.77/7.83 = ( plus_plus_real
% 13.77/7.83 @ ( groups6591440286371151544t_real
% 13.77/7.83 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.83 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.83 @ ( 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 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8240_Maclaurin__minus__cos__expansion,axiom,
% 13.77/7.83 ! [N: nat,X: real] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.83 => ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.83 => ? [T6: real] :
% 13.77/7.83 ( ( ord_less_real @ X @ T6 )
% 13.77/7.83 & ( ord_less_real @ T6 @ zero_zero_real )
% 13.77/7.83 & ( ( cos_real @ X )
% 13.77/7.83 = ( plus_plus_real
% 13.77/7.83 @ ( groups6591440286371151544t_real
% 13.77/7.83 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.83 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.83 @ ( 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 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8241_monoseq__arctan__series,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.83 => ( topolo6980174941875973593q_real
% 13.77/7.83 @ ^ [N6: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8242_cos__pi__eq__zero,axiom,
% 13.77/7.83 ! [M: nat] :
% 13.77/7.83 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 = zero_zero_real ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8243_cos__le__one,axiom,
% 13.77/7.83 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8244_cos__monotone__0__pi__le,axiom,
% 13.77/7.83 ! [Y: real,X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ pi )
% 13.77/7.83 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8245_cos__mono__le__eq,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ pi )
% 13.77/7.83 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ pi )
% 13.77/7.83 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 13.77/7.83 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8246_cos__inj__pi,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ pi )
% 13.77/7.83 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ pi )
% 13.77/7.83 => ( ( ( cos_real @ X )
% 13.77/7.83 = ( cos_real @ Y ) )
% 13.77/7.83 => ( X = Y ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8247_cos__ge__minus__one,axiom,
% 13.77/7.83 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8248_abs__cos__le__one,axiom,
% 13.77/7.83 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8249_cos__mono__less__eq,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ pi )
% 13.77/7.83 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ pi )
% 13.77/7.83 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 13.77/7.83 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8250_cos__monotone__0__pi,axiom,
% 13.77/7.83 ! [Y: real,X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.83 => ( ( ord_less_real @ Y @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ pi )
% 13.77/7.83 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8251_cos__monotone__minus__pi__0_H,axiom,
% 13.77/7.83 ! [Y: real,X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.83 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8252_cos__two__less__zero,axiom,
% 13.77/7.83 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8253_cos__is__zero,axiom,
% 13.77/7.83 ? [X3: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 13.77/7.83 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.83 & ( ( cos_real @ X3 )
% 13.77/7.83 = zero_zero_real )
% 13.77/7.83 & ! [Y5: real] :
% 13.77/7.83 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 13.77/7.83 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.83 & ( ( cos_real @ Y5 )
% 13.77/7.83 = zero_zero_real ) )
% 13.77/7.83 => ( Y5 = X3 ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8254_cos__two__le__zero,axiom,
% 13.77/7.83 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8255_cos__monotone__minus__pi__0,axiom,
% 13.77/7.83 ! [Y: real,X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 13.77/7.83 => ( ( ord_less_real @ Y @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.83 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8256_cos__total,axiom,
% 13.77/7.83 ! [Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.83 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.83 => ? [X3: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 13.77/7.83 & ( ord_less_eq_real @ X3 @ pi )
% 13.77/7.83 & ( ( cos_real @ X3 )
% 13.77/7.83 = Y )
% 13.77/7.83 & ! [Y5: real] :
% 13.77/7.83 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 13.77/7.83 & ( ord_less_eq_real @ Y5 @ pi )
% 13.77/7.83 & ( ( cos_real @ Y5 )
% 13.77/7.83 = Y ) )
% 13.77/7.83 => ( Y5 = X3 ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8257_sincos__principal__value,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ? [Y3: real] :
% 13.77/7.83 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 13.77/7.83 & ( ord_less_eq_real @ Y3 @ pi )
% 13.77/7.83 & ( ( sin_real @ Y3 )
% 13.77/7.83 = ( sin_real @ X ) )
% 13.77/7.83 & ( ( cos_real @ Y3 )
% 13.77/7.83 = ( cos_real @ X ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8258_monoseq__realpow,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.83 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8259_sin__cos__le1,axiom,
% 13.77/7.83 ! [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 ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8260_cos__double__less__one,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.83 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8261_cos__gt__zero,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8262_cos__gt__zero__pi,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8263_cos__ge__zero,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8264_pi__half,axiom,
% 13.77/7.83 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.83 = ( the_real
% 13.77/7.83 @ ^ [X4: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 13.77/7.83 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.83 & ( ( cos_real @ X4 )
% 13.77/7.83 = zero_zero_real ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8265_pi__def,axiom,
% 13.77/7.83 ( pi
% 13.77/7.83 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 13.77/7.83 @ ( the_real
% 13.77/7.83 @ ^ [X4: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 13.77/7.83 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.83 & ( ( cos_real @ X4 )
% 13.77/7.83 = zero_zero_real ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8266_sincos__total__pi,axiom,
% 13.77/7.83 ! [Y: real,X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.83 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 = one_one_real )
% 13.77/7.83 => ? [T6: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.83 & ( ord_less_eq_real @ T6 @ pi )
% 13.77/7.83 & ( X
% 13.77/7.83 = ( cos_real @ T6 ) )
% 13.77/7.83 & ( Y
% 13.77/7.83 = ( sin_real @ T6 ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8267_sin__expansion__lemma,axiom,
% 13.77/7.83 ! [X: real,M: nat] :
% 13.77/7.83 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8268_cos__expansion__lemma,axiom,
% 13.77/7.83 ! [X: real,M: nat] :
% 13.77/7.83 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8269_sincos__total__pi__half,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.83 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 = one_one_real )
% 13.77/7.83 => ? [T6: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.83 & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.83 & ( X
% 13.77/7.83 = ( cos_real @ T6 ) )
% 13.77/7.83 & ( Y
% 13.77/7.83 = ( sin_real @ T6 ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8270_sincos__total__2pi__le,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 = one_one_real )
% 13.77/7.83 => ? [T6: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.83 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 13.77/7.83 & ( X
% 13.77/7.83 = ( cos_real @ T6 ) )
% 13.77/7.83 & ( Y
% 13.77/7.83 = ( sin_real @ T6 ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8271_sincos__total__2pi,axiom,
% 13.77/7.83 ! [X: real,Y: real] :
% 13.77/7.83 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.83 = one_one_real )
% 13.77/7.83 => ~ ! [T6: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.83 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 13.77/7.83 => ( ( X
% 13.77/7.83 = ( cos_real @ T6 ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8272_Maclaurin__cos__expansion,axiom,
% 13.77/7.83 ! [X: real,N: nat] :
% 13.77/7.83 ? [T6: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.83 & ( ( cos_real @ X )
% 13.77/7.83 = ( plus_plus_real
% 13.77/7.83 @ ( groups6591440286371151544t_real
% 13.77/7.83 @ ^ [M5: nat] : ( times_times_real @ ( cos_coeff @ M5 ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.83 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.83 @ ( 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 ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8273_lowi__hT,axiom,
% 13.77/7.83 ! [X: nat,N: nat] :
% 13.77/7.83 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X @ N )
% 13.77/7.83 @ ^ [R5: nat] :
% 13.77/7.83 ( pure_assn
% 13.77/7.83 @ ( R5
% 13.77/7.83 = ( vEBT_VEBT_low @ X @ N ) ) )
% 13.77/7.83 @ one_one_nat ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8274_highi__hT,axiom,
% 13.77/7.83 ! [X: nat,N: nat] :
% 13.77/7.83 ( time_htt_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X @ N )
% 13.77/7.83 @ ^ [R5: nat] :
% 13.77/7.83 ( pure_assn
% 13.77/7.83 @ ( R5
% 13.77/7.83 = ( vEBT_VEBT_high @ X @ N ) ) )
% 13.77/7.83 @ one_one_nat ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8275_TBOUND__highi,axiom,
% 13.77/7.83 ! [X: nat,N: nat] : ( time_TBOUND_nat @ ( vEBT_VEBT_highi @ X @ N ) @ one_one_nat ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8276_TBOUND__lowi,axiom,
% 13.77/7.83 ! [X: nat,N: nat] : ( time_TBOUND_nat @ ( vEBT_VEBT_lowi @ X @ N ) @ one_one_nat ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8277_highi__h,axiom,
% 13.77/7.83 ! [X: nat,N: nat] :
% 13.77/7.83 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_highi @ X @ N )
% 13.77/7.83 @ ^ [R5: nat] :
% 13.77/7.83 ( pure_assn
% 13.77/7.83 @ ( R5
% 13.77/7.83 = ( vEBT_VEBT_high @ X @ N ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8278_lowi__h,axiom,
% 13.77/7.83 ! [X: nat,N: nat] :
% 13.77/7.83 ( hoare_3067605981109127869le_nat @ one_one_assn @ ( vEBT_VEBT_lowi @ X @ N )
% 13.77/7.83 @ ^ [R5: nat] :
% 13.77/7.83 ( pure_assn
% 13.77/7.83 @ ( R5
% 13.77/7.83 = ( vEBT_VEBT_low @ X @ N ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8279_set__bit__nonnegative__int__iff,axiom,
% 13.77/7.83 ! [N: nat,K: int] :
% 13.77/7.83 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 13.77/7.83 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8280_set__bit__negative__int__iff,axiom,
% 13.77/7.83 ! [N: nat,K: int] :
% 13.77/7.83 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 13.77/7.83 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8281_set__bit__greater__eq,axiom,
% 13.77/7.83 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8282_set__encode__insert,axiom,
% 13.77/7.83 ! [A4: set_nat,N: nat] :
% 13.77/7.83 ( ( finite_finite_nat @ A4 )
% 13.77/7.83 => ( ~ ( member_nat @ N @ A4 )
% 13.77/7.83 => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 13.77/7.83 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8283_sin__coeff__def,axiom,
% 13.77/7.83 ( sin_coeff
% 13.77/7.83 = ( ^ [N6: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N6 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N6 ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8284_ln__series,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 13.77/7.83 => ( ( ln_ln_real @ X )
% 13.77/7.83 = ( suminf_real
% 13.77/7.83 @ ^ [N6: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N6 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N6 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N6 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8285_nat__dvd__1__iff__1,axiom,
% 13.77/7.83 ! [M: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 13.77/7.83 = ( M = one_one_nat ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8286_dvd__1__left,axiom,
% 13.77/7.83 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8287_dvd__1__iff__1,axiom,
% 13.77/7.83 ! [M: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 13.77/7.83 = ( M
% 13.77/7.83 = ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8288_nat__mult__dvd__cancel__disj,axiom,
% 13.77/7.83 ! [K: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.83 = ( ( K = zero_zero_nat )
% 13.77/7.83 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8289_set__encode__empty,axiom,
% 13.77/7.83 ( ( nat_set_encode @ bot_bot_set_nat )
% 13.77/7.83 = zero_zero_nat ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8290_Max__divisors__self__nat,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( N != zero_zero_nat )
% 13.77/7.83 => ( ( lattic8265883725875713057ax_nat
% 13.77/7.83 @ ( collect_nat
% 13.77/7.83 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ N ) ) )
% 13.77/7.83 = N ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8291_even__Suc,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 13.77/7.83 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8292_even__Suc__Suc__iff,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8293_odd__Suc__div__two,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.83 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8294_even__Suc__div__two,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.83 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8295_odd__Suc__minus__one,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 13.77/7.83 = N ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8296_even__diff__nat,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.83 = ( ( ord_less_nat @ M @ N )
% 13.77/7.83 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8297_dvd__diff__nat,axiom,
% 13.77/7.83 ! [K: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ K @ M )
% 13.77/7.83 => ( ( dvd_dvd_nat @ K @ N )
% 13.77/7.83 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8298_gcd__nat_Oextremum__uniqueI,axiom,
% 13.77/7.83 ! [A: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 13.77/7.83 => ( A = zero_zero_nat ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8299_gcd__nat_Onot__eq__extremum,axiom,
% 13.77/7.83 ! [A: nat] :
% 13.77/7.83 ( ( A != zero_zero_nat )
% 13.77/7.83 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 13.77/7.83 & ( A != zero_zero_nat ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8300_gcd__nat_Oextremum__unique,axiom,
% 13.77/7.83 ! [A: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 13.77/7.83 = ( A = zero_zero_nat ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8301_gcd__nat_Oextremum__strict,axiom,
% 13.77/7.83 ! [A: nat] :
% 13.77/7.83 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 13.77/7.83 & ( zero_zero_nat != A ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8302_gcd__nat_Oextremum,axiom,
% 13.77/7.83 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8303_dvd__antisym,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ M @ N )
% 13.77/7.83 => ( ( dvd_dvd_nat @ N @ M )
% 13.77/7.83 => ( M = N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8304_dvd__pos__nat,axiom,
% 13.77/7.83 ! [N: nat,M: nat] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.83 => ( ( dvd_dvd_nat @ M @ N )
% 13.77/7.83 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8305_nat__dvd__not__less,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.83 => ( ( ord_less_nat @ M @ N )
% 13.77/7.83 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8306_dvd__minus__self,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 13.77/7.83 = ( ( ord_less_nat @ N @ M )
% 13.77/7.83 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8307_dvd__diffD,axiom,
% 13.77/7.83 ! [K: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.83 => ( ( dvd_dvd_nat @ K @ N )
% 13.77/7.83 => ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.83 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8308_dvd__diffD1,axiom,
% 13.77/7.83 ! [K: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 13.77/7.83 => ( ( dvd_dvd_nat @ K @ M )
% 13.77/7.83 => ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.83 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8309_less__eq__dvd__minus,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.83 => ( ( dvd_dvd_nat @ M @ N )
% 13.77/7.83 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8310_set__encode__eq,axiom,
% 13.77/7.83 ! [A4: set_nat,B4: set_nat] :
% 13.77/7.83 ( ( finite_finite_nat @ A4 )
% 13.77/7.83 => ( ( finite_finite_nat @ B4 )
% 13.77/7.83 => ( ( ( nat_set_encode @ A4 )
% 13.77/7.83 = ( nat_set_encode @ B4 ) )
% 13.77/7.83 = ( A4 = B4 ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8311_even__set__encode__iff,axiom,
% 13.77/7.83 ! [A4: set_nat] :
% 13.77/7.83 ( ( finite_finite_nat @ A4 )
% 13.77/7.83 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 13.77/7.83 = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8312_dvd__imp__le,axiom,
% 13.77/7.83 ! [K: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ K @ N )
% 13.77/7.83 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.83 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8313_dvd__mult__cancel,axiom,
% 13.77/7.83 ! [K: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.83 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.83 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8314_nat__mult__dvd__cancel1,axiom,
% 13.77/7.83 ! [K: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ K )
% 13.77/7.83 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 13.77/7.83 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8315_bezout__add__strong__nat,axiom,
% 13.77/7.83 ! [A: nat,B: nat] :
% 13.77/7.83 ( ( A != zero_zero_nat )
% 13.77/7.83 => ? [D2: nat,X3: nat,Y3: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ D2 @ A )
% 13.77/7.83 & ( dvd_dvd_nat @ D2 @ B )
% 13.77/7.83 & ( ( times_times_nat @ A @ X3 )
% 13.77/7.83 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D2 ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8316_mod__greater__zero__iff__not__dvd,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 13.77/7.83 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8317_mod__eq__dvd__iff__nat,axiom,
% 13.77/7.83 ! [N: nat,M: nat,Q3: nat] :
% 13.77/7.83 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.83 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 13.77/7.83 = ( modulo_modulo_nat @ N @ Q3 ) )
% 13.77/7.83 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8318_dvd__fact,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 13.77/7.83 => ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.83 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8319_finite__divisors__nat,axiom,
% 13.77/7.83 ! [M: nat] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.83 => ( finite_finite_nat
% 13.77/7.83 @ ( collect_nat
% 13.77/7.83 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8320_gcd__nat_Oordering__top__axioms,axiom,
% 13.77/7.83 ( ordering_top_nat @ dvd_dvd_nat
% 13.77/7.83 @ ^ [M5: nat,N6: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ M5 @ N6 )
% 13.77/7.83 & ( M5 != N6 ) )
% 13.77/7.83 @ zero_zero_nat ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8321_set__encode__inf,axiom,
% 13.77/7.83 ! [A4: set_nat] :
% 13.77/7.83 ( ~ ( finite_finite_nat @ A4 )
% 13.77/7.83 => ( ( nat_set_encode @ A4 )
% 13.77/7.83 = zero_zero_nat ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8322_dvd__mult__cancel1,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.83 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 13.77/7.83 = ( N = one_one_nat ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8323_dvd__mult__cancel2,axiom,
% 13.77/7.83 ! [M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_nat @ zero_zero_nat @ M )
% 13.77/7.83 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 13.77/7.83 = ( N = one_one_nat ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8324_power__dvd__imp__le,axiom,
% 13.77/7.83 ! [I: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 13.77/7.83 => ( ( ord_less_nat @ one_one_nat @ I )
% 13.77/7.83 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8325_dvd__minus__add,axiom,
% 13.77/7.83 ! [Q3: nat,N: nat,R: nat,M: nat] :
% 13.77/7.83 ( ( ord_less_eq_nat @ Q3 @ N )
% 13.77/7.83 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R @ M ) )
% 13.77/7.83 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 13.77/7.83 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q3 ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8326_diff__mod__le,axiom,
% 13.77/7.83 ! [A: nat,D: nat,B: nat] :
% 13.77/7.83 ( ( ord_less_nat @ A @ D )
% 13.77/7.83 => ( ( dvd_dvd_nat @ B @ D )
% 13.77/7.83 => ( ord_less_eq_nat @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) @ ( minus_minus_nat @ D @ B ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8327_mod__nat__eqI,axiom,
% 13.77/7.83 ! [R: nat,N: nat,M: nat] :
% 13.77/7.83 ( ( ord_less_nat @ R @ N )
% 13.77/7.83 => ( ( ord_less_eq_nat @ R @ M )
% 13.77/7.83 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 13.77/7.83 => ( ( modulo_modulo_nat @ M @ N )
% 13.77/7.83 = R ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8328_odd__pos,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8329_dvd__power__iff__le,axiom,
% 13.77/7.83 ! [K: nat,M: nat,N: nat] :
% 13.77/7.83 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 13.77/7.83 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 13.77/7.83 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8330_central__binomial__odd,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8331_Gcd__eq__Max,axiom,
% 13.77/7.83 ! [M7: set_nat] :
% 13.77/7.83 ( ( finite_finite_nat @ M7 )
% 13.77/7.83 => ( ( M7 != bot_bot_set_nat )
% 13.77/7.83 => ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 13.77/7.83 => ( ( gcd_Gcd_nat @ M7 )
% 13.77/7.83 = ( lattic8265883725875713057ax_nat
% 13.77/7.83 @ ( comple7806235888213564991et_nat
% 13.77/7.83 @ ( image_nat_set_nat
% 13.77/7.83 @ ^ [M5: nat] :
% 13.77/7.83 ( collect_nat
% 13.77/7.83 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M5 ) )
% 13.77/7.83 @ M7 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8332_even__mod__4__div__2,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8333_odd__mod__4__div__2,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.83 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8334_Bernoulli__inequality__even,axiom,
% 13.77/7.83 ! [N: nat,X: real] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( 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 ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8335_VEBT__internal_OT__vebt__buildupi_Osimps_I3_J,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8336_vebt__buildup_Osimps_I3_J,axiom,
% 13.77/7.83 ! [Va2: nat] :
% 13.77/7.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8337_VEBT__internal_OT__vebt__buildupi_Oelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_V441764108873111860ildupi @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( suc @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( suc @ zero_zero_nat ) ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8338_VEBT__internal_OTb_H_Osimps_I3_J,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8339_VEBT__internal_OTb_H_Oelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_VEBT_Tb2 @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8340_cos__zero__lemma,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ( cos_real @ X )
% 13.77/7.83 = zero_zero_real )
% 13.77/7.83 => ? [N2: nat] :
% 13.77/7.83 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 & ( X
% 13.77/7.83 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8341_sin__zero__lemma,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.83 => ( ( ( sin_real @ X )
% 13.77/7.83 = zero_zero_real )
% 13.77/7.83 => ? [N2: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 & ( X
% 13.77/7.83 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8342_VEBT__internal_OTb_Osimps_I3_J,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_VEBT_Tb @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_VEBT_Tb @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8343_VEBT__internal_OT__vebt__buildupi_H_Osimps_I3_J,axiom,
% 13.77/7.83 ! [N: nat] :
% 13.77/7.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ N ) ) )
% 13.77/7.83 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8344_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Osimps_I3_J,axiom,
% 13.77/7.83 ! [Va2: nat] :
% 13.77/7.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 => ( ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8345_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Osimps_I3_J,axiom,
% 13.77/7.83 ! [Va2: nat] :
% 13.77/7.83 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 => ( ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( suc @ Va2 ) ) )
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8346_vebt__buildup_Oelims,axiom,
% 13.77/7.83 ! [X: nat,Y: vEBT_VEBT] :
% 13.77/7.83 ( ( ( vEBT_vebt_buildup @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( vEBT_Leaf @ $false @ $false ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( vEBT_Leaf @ $false @ $false ) ) )
% 13.77/7.83 => ~ ! [Va: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( 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 ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8347_VEBT__internal_OTb_Oelims,axiom,
% 13.77/7.83 ! [X: nat,Y: int] :
% 13.77/7.83 ( ( ( vEBT_VEBT_Tb @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_int @ ( bit1 @ one ) ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_int @ ( bit1 @ one ) ) ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8348_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Oelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit1 @ one ) ) ) )
% 13.77/7.83 => ~ ! [Va: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8349_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Oelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 != ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.83 => ~ ! [Va: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8350_VEBT__internal_OT__vebt__buildupi_H_Oelims,axiom,
% 13.77/7.83 ! [X: nat,Y: int] :
% 13.77/7.83 ( ( ( vEBT_V9176841429113362141ildupi @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( Y != one_one_int ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( Y != one_one_int ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8351_arctan__series,axiom,
% 13.77/7.83 ! [X: real] :
% 13.77/7.83 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.83 => ( ( arctan @ X )
% 13.77/7.83 = ( suminf_real
% 13.77/7.83 @ ^ [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 ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8352_VEBT__internal_OT__vebt__buildupi_H_Opelims,axiom,
% 13.77/7.83 ! [X: nat,Y: int] :
% 13.77/7.83 ( ( ( vEBT_V9176841429113362141ildupi @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_nat @ vEBT_V3352910403632780892pi_rel @ X )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( ( Y = one_one_int )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y = one_one_int )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) @ ( plus_plus_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( vEBT_V9176841429113362141ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V3352910403632780892pi_rel @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8353_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_Opelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_V8646137997579335489_i_l_d @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_nat @ vEBT_V5144397997797733112_d_rel @ X )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.83 => ~ ! [Va: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_V8646137997579335489_i_l_d @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V5144397997797733112_d_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8354_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Opelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_V8346862874174094_d_u_p @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_nat @ vEBT_V1247956027447740395_p_rel @ X )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.83 => ~ ! [Va: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ one_one_nat @ ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( vEBT_V8346862874174094_d_u_p @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( vEBT_V8346862874174094_d_u_p @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V1247956027447740395_p_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8355_zdvd__antisym__nonneg,axiom,
% 13.77/7.83 ! [M: int,N: int] :
% 13.77/7.83 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 13.77/7.83 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 13.77/7.83 => ( ( dvd_dvd_int @ M @ N )
% 13.77/7.83 => ( ( dvd_dvd_int @ N @ M )
% 13.77/7.83 => ( M = N ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8356_zdvd__not__zless,axiom,
% 13.77/7.83 ! [M: int,N: int] :
% 13.77/7.83 ( ( ord_less_int @ zero_zero_int @ M )
% 13.77/7.83 => ( ( ord_less_int @ M @ N )
% 13.77/7.83 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8357_abs__div,axiom,
% 13.77/7.83 ! [Y: int,X: int] :
% 13.77/7.83 ( ( dvd_dvd_int @ Y @ X )
% 13.77/7.83 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 13.77/7.83 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8358_zdvd__imp__le,axiom,
% 13.77/7.83 ! [Z: int,N: int] :
% 13.77/7.83 ( ( dvd_dvd_int @ Z @ N )
% 13.77/7.83 => ( ( ord_less_int @ zero_zero_int @ N )
% 13.77/7.83 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8359_dvd__imp__le__int,axiom,
% 13.77/7.83 ! [I: int,D: int] :
% 13.77/7.83 ( ( I != zero_zero_int )
% 13.77/7.83 => ( ( dvd_dvd_int @ D @ I )
% 13.77/7.83 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8360_mod__int__pos__iff,axiom,
% 13.77/7.83 ! [K: int,L: int] :
% 13.77/7.83 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 13.77/7.83 = ( ( dvd_dvd_int @ L @ K )
% 13.77/7.83 | ( ( L = zero_zero_int )
% 13.77/7.83 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 13.77/7.83 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8361_int__div__sub__1,axiom,
% 13.77/7.83 ! [M: int,N: int] :
% 13.77/7.83 ( ( ord_less_eq_int @ one_one_int @ M )
% 13.77/7.83 => ( ( ( dvd_dvd_int @ M @ N )
% 13.77/7.83 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 13.77/7.83 = ( minus_minus_int @ ( divide_divide_int @ N @ M ) @ one_one_int ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_int @ M @ N )
% 13.77/7.83 => ( ( divide_divide_int @ ( minus_minus_int @ N @ one_one_int ) @ M )
% 13.77/7.83 = ( divide_divide_int @ N @ M ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8362_div__dvd__sgn__abs,axiom,
% 13.77/7.83 ! [L: int,K: int] :
% 13.77/7.83 ( ( dvd_dvd_int @ L @ K )
% 13.77/7.83 => ( ( divide_divide_int @ K @ L )
% 13.77/7.83 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8363_nat__dvd__iff,axiom,
% 13.77/7.83 ! [Z: int,M: nat] :
% 13.77/7.83 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 13.77/7.83 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.83 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 13.77/7.83 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 13.77/7.83 => ( M = zero_zero_nat ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8364_even__nat__iff,axiom,
% 13.77/7.83 ! [K: int] :
% 13.77/7.83 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.83 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 13.77/7.83 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8365_eme1p,axiom,
% 13.77/7.83 ! [N: int,D: int] :
% 13.77/7.83 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D )
% 13.77/7.83 => ( ( ord_less_eq_int @ zero_zero_int @ D )
% 13.77/7.83 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ N ) @ D )
% 13.77/7.83 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ N @ D ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8366_emep1,axiom,
% 13.77/7.83 ! [N: int,D: int] :
% 13.77/7.83 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 13.77/7.83 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ D )
% 13.77/7.83 => ( ( ord_less_eq_int @ zero_zero_int @ D )
% 13.77/7.83 => ( ( modulo_modulo_int @ ( plus_plus_int @ N @ one_one_int ) @ D )
% 13.77/7.83 = ( plus_plus_int @ ( modulo_modulo_int @ N @ D ) @ one_one_int ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8367_vebt__buildup_Opelims,axiom,
% 13.77/7.83 ! [X: nat,Y: vEBT_VEBT] :
% 13.77/7.83 ( ( ( vEBT_vebt_buildup @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Leaf @ $false @ $false ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( vEBT_Leaf @ $false @ $false ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.83 => ~ ! [Va: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( 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 ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( 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 ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8368_VEBT__internal_OTb_Opelims,axiom,
% 13.77/7.83 ! [X: nat,Y: int] :
% 13.77/7.83 ( ( ( vEBT_VEBT_Tb @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_nat @ vEBT_VEBT_Tb_rel2 @ X )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_int @ ( bit1 @ one ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_int @ ( bit1 @ one ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_int @ ( vEBT_VEBT_Tb @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel2 @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8369_VEBT__internal_OTb_H_Opelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_VEBT_Tb2 @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_nat @ vEBT_VEBT_Tb_rel @ X )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ one ) ) ) @ ( vEBT_VEBT_Tb2 @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( times_times_nat @ ( vEBT_VEBT_Tb2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_VEBT_Tb_rel @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8370_VEBT__internal_OT__vebt__buildupi_Opelims,axiom,
% 13.77/7.83 ! [X: nat,Y: nat] :
% 13.77/7.83 ( ( ( vEBT_V441764108873111860ildupi @ X )
% 13.77/7.83 = Y )
% 13.77/7.83 => ( ( accp_nat @ vEBT_V2957053500504383685pi_rel @ X )
% 13.77/7.83 => ( ( ( X = zero_zero_nat )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ zero_zero_nat ) ) )
% 13.77/7.83 => ( ( ( X
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ( ( Y
% 13.77/7.83 = ( suc @ zero_zero_nat ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.83 => ~ ! [N2: nat] :
% 13.77/7.83 ( ( X
% 13.77/7.83 = ( suc @ ( suc @ N2 ) ) )
% 13.77/7.83 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 13.77/7.83 => ( Y
% 13.77/7.83 = ( suc @ ( suc @ ( suc @ ( plus_plus_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( vEBT_V441764108873111860ildupi @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.83 => ~ ( accp_nat @ vEBT_V2957053500504383685pi_rel @ ( suc @ ( suc @ N2 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.83
% 13.77/7.83 thf(fact_8371_vebt__delete__code_I2_J,axiom,
% 13.77/7.83 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.83 ( ( vEBT_vebt_delete @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.83 = ( case_o2442805151034396888at_nat @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary )
% 13.77/7.83 @ ^ [Mima: product_prod_nat_nat] :
% 13.77/7.83 ( if_VEBT_VEBT @ ( ord_less_eq_nat @ Deg @ one_one_nat ) @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary )
% 13.77/7.83 @ ( produc3169358591047799142T_VEBT
% 13.77/7.83 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.83 ( if_VEBT_VEBT
% 13.77/7.83 @ ( ( ord_less_nat @ X @ Mi3 )
% 13.77/7.83 | ( ord_less_nat @ Ma3 @ X ) )
% 13.77/7.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg @ TreeList @ Summary )
% 13.77/7.83 @ ( if_VEBT_VEBT
% 13.77/7.83 @ ( ( X = Mi3 )
% 13.77/7.83 & ( X = Ma3 ) )
% 13.77/7.83 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary )
% 13.77/7.83 @ ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.84 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 @ ( vEBT_Node
% 13.77/7.84 @ ( some_P7363390416028606310at_nat
% 13.77/7.84 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 13.77/7.84 @ ( if_nat
% 13.77/7.84 @ ( ( ( X = Mi3 )
% 13.77/7.84 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.84 = Ma3 ) )
% 13.77/7.84 & ( ( X != Mi3 )
% 13.77/7.84 => ( X = Ma3 ) ) )
% 13.77/7.84 @ ( if_nat
% 13.77/7.84 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 = none_nat )
% 13.77/7.84 @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 13.77/7.84 @ ( 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 = Mi3 ) @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( 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 = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.84 @ Ma3 ) ) )
% 13.77/7.84 @ Deg
% 13.77/7.84 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 @ ( vEBT_Node
% 13.77/7.84 @ ( some_P7363390416028606310at_nat
% 13.77/7.84 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi3 ) @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi3 )
% 13.77/7.84 @ ( if_nat
% 13.77/7.84 @ ( ( ( X = Mi3 )
% 13.77/7.84 => ( ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 13.77/7.84 = Ma3 ) )
% 13.77/7.84 & ( ( X != Mi3 )
% 13.77/7.84 => ( X = Ma3 ) ) )
% 13.77/7.84 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( 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 @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.84 @ Ma3 ) ) )
% 13.77/7.84 @ Deg
% 13.77/7.84 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi3 ) @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 @ Summary ) )
% 13.77/7.84 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg @ TreeList @ Summary ) ) ) )
% 13.77/7.84 @ Mima ) )
% 13.77/7.84 @ Info ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8372_divmod__int__def,axiom,
% 13.77/7.84 ( unique5052692396658037445od_int
% 13.77/7.84 = ( ^ [M5: num,N6: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8373_divmod_H__nat__def,axiom,
% 13.77/7.84 ( unique5055182867167087721od_nat
% 13.77/7.84 = ( ^ [M5: num,N6: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N6 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M5 ) @ ( numeral_numeral_nat @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8374_vebt__insert__code_I2_J,axiom,
% 13.77/7.84 ! [Deg: nat,Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.84 ( ( ( ord_less_eq_nat @ Deg @ one_one_nat )
% 13.77/7.84 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.84 = ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) )
% 13.77/7.84 & ( ~ ( ord_less_eq_nat @ Deg @ one_one_nat )
% 13.77/7.84 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.84 = ( case_o2442805151034396888at_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ Deg @ TreeList @ Summary )
% 13.77/7.84 @ ( produc3169358591047799142T_VEBT
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( if_VEBT_VEBT
% 13.77/7.84 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.84 & ~ ( ( X = Mi3 )
% 13.77/7.84 | ( X = Ma3 ) ) )
% 13.77/7.84 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ X @ Mi3 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ Ma3 ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi3 ) @ Mi3 @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 13.77/7.84 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg @ TreeList @ Summary ) ) )
% 13.77/7.84 @ Info ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8375_minus__one__div__numeral,axiom,
% 13.77/7.84 ! [N: num] :
% 13.77/7.84 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.84 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8376_one__div__minus__numeral,axiom,
% 13.77/7.84 ! [N: num] :
% 13.77/7.84 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.84 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8377_numeral__div__minus__numeral,axiom,
% 13.77/7.84 ! [M: num,N: num] :
% 13.77/7.84 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.84 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8378_minus__numeral__div__numeral,axiom,
% 13.77/7.84 ! [M: num,N: num] :
% 13.77/7.84 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.84 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8379_divmod__nat__if,axiom,
% 13.77/7.84 ( divmod_nat
% 13.77/7.84 = ( ^ [M5: nat,N6: nat] :
% 13.77/7.84 ( if_Pro6206227464963214023at_nat
% 13.77/7.84 @ ( ( N6 = zero_zero_nat )
% 13.77/7.84 | ( ord_less_nat @ M5 @ N6 ) )
% 13.77/7.84 @ ( product_Pair_nat_nat @ zero_zero_nat @ M5 )
% 13.77/7.84 @ ( produc2626176000494625587at_nat
% 13.77/7.84 @ ^ [Q8: nat] : ( product_Pair_nat_nat @ ( suc @ Q8 ) )
% 13.77/7.84 @ ( divmod_nat @ ( minus_minus_nat @ M5 @ N6 ) @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8380_divmod__step__integer__def,axiom,
% 13.77/7.84 ( unique4921790084139445826nteger
% 13.77/7.84 = ( ^ [L4: num] :
% 13.77/7.84 ( produc6916734918728496179nteger
% 13.77/7.84 @ ^ [Q8: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L4 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L4 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8381_divmod__step__nat__def,axiom,
% 13.77/7.84 ( unique5026877609467782581ep_nat
% 13.77/7.84 = ( ^ [L4: num] :
% 13.77/7.84 ( produc2626176000494625587at_nat
% 13.77/7.84 @ ^ [Q8: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L4 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L4 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8382_divmod__step__int__def,axiom,
% 13.77/7.84 ( unique5024387138958732305ep_int
% 13.77/7.84 = ( ^ [L4: num] :
% 13.77/7.84 ( produc4245557441103728435nt_int
% 13.77/7.84 @ ^ [Q8: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L4 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L4 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q8 ) @ R5 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8383_vebt__succ__code_I2_J,axiom,
% 13.77/7.84 ! [Deg: nat,Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 13.77/7.84 ( ( ( ord_less_eq_nat @ Deg @ one_one_nat )
% 13.77/7.84 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.84 = none_nat ) )
% 13.77/7.84 & ( ~ ( ord_less_eq_nat @ Deg @ one_one_nat )
% 13.77/7.84 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X )
% 13.77/7.84 = ( case_o1383228350324149268at_nat @ none_nat
% 13.77/7.84 @ ( produc2484365769952853102on_nat
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( if_option_nat @ ( ord_less_nat @ X @ Mi3 ) @ ( some_nat @ Mi3 )
% 13.77/7.84 @ ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 13.77/7.84 @ ( if_option_nat
% 13.77/7.84 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 != none_nat )
% 13.77/7.84 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 13.77/7.84 @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) )
% 13.77/7.84 @ ( if_option_nat
% 13.77/7.84 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 = none_nat )
% 13.77/7.84 @ none_nat
% 13.77/7.84 @ ( 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 @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 13.77/7.84 @ none_nat ) ) )
% 13.77/7.84 @ Info ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8384_integer__of__int__code,axiom,
% 13.77/7.84 ( code_integer_of_int
% 13.77/7.84 = ( ^ [K3: int] :
% 13.77/7.84 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 13.77/7.84 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 13.77/7.84 @ ( if_Code_integer
% 13.77/7.84 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8385_integer__of__int__eq__of__int,axiom,
% 13.77/7.84 code_integer_of_int = ring_18347121197199848620nteger ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8386_divmod__integer_H__def,axiom,
% 13.77/7.84 ( unique3479559517661332726nteger
% 13.77/7.84 = ( ^ [M5: num,N6: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N6 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M5 ) @ ( numera6620942414471956472nteger @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8387_one__integer__def,axiom,
% 13.77/7.84 ( one_one_Code_integer
% 13.77/7.84 = ( code_integer_of_int @ one_one_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8388_less__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( ord_less_int @ Xa2 @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8389_divide__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8390_modulo__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8391_integer__of__int__inject,axiom,
% 13.77/7.84 ! [X: int,Y: int] :
% 13.77/7.84 ( ( member_int @ X @ top_top_set_int )
% 13.77/7.84 => ( ( member_int @ Y @ top_top_set_int )
% 13.77/7.84 => ( ( ( code_integer_of_int @ X )
% 13.77/7.84 = ( code_integer_of_int @ Y ) )
% 13.77/7.84 = ( X = Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8392_integer__of__int__induct,axiom,
% 13.77/7.84 ! [P2: code_integer > $o,X: code_integer] :
% 13.77/7.84 ( ! [Y3: int] :
% 13.77/7.84 ( ( member_int @ Y3 @ top_top_set_int )
% 13.77/7.84 => ( P2 @ ( code_integer_of_int @ Y3 ) ) )
% 13.77/7.84 => ( P2 @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8393_integer__of__int__cases,axiom,
% 13.77/7.84 ! [X: code_integer] :
% 13.77/7.84 ~ ! [Y3: int] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( code_integer_of_int @ Y3 ) )
% 13.77/7.84 => ~ ( member_int @ Y3 @ top_top_set_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8394_zero__integer__def,axiom,
% 13.77/7.84 ( zero_z3403309356797280102nteger
% 13.77/7.84 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8395_Code__Numeral_Oset__bit__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: nat,X: int] :
% 13.77/7.84 ( ( bit_se2793503036327961859nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( bit_se7879613467334960850it_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8396_uminus__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [X: int] :
% 13.77/7.84 ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( uminus_uminus_int @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8397_less__eq__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8398_plus__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8399_minus__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8400_times__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8401_abs__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [X: int] :
% 13.77/7.84 ( ( abs_abs_Code_integer @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( abs_abs_int @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8402_sgn__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [X: int] :
% 13.77/7.84 ( ( sgn_sgn_Code_integer @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( sgn_sgn_int @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8403_signed__take__bit__Suc__bit0,axiom,
% 13.77/7.84 ! [N: nat,K: num] :
% 13.77/7.84 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 13.77/7.84 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8404_signed__take__bit__Suc__minus__bit0,axiom,
% 13.77/7.84 ! [N: nat,K: num] :
% 13.77/7.84 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 13.77/7.84 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8405_signed__take__bit__Suc__bit1,axiom,
% 13.77/7.84 ! [N: nat,K: num] :
% 13.77/7.84 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 13.77/7.84 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8406_signed__take__bit__Suc__minus__bit1,axiom,
% 13.77/7.84 ! [N: nat,K: num] :
% 13.77/7.84 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 13.77/7.84 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8407_signed__take__bit__int__less__exp,axiom,
% 13.77/7.84 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8408_signed__take__bit__int__greater__eq__self__iff,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 13.77/7.84 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8409_signed__take__bit__int__less__self__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 13.77/7.84 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8410_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 13.77/7.84 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8411_signed__take__bit__int__less__eq__self__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 13.77/7.84 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8412_signed__take__bit__int__greater__self__iff,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 13.77/7.84 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8413_signed__take__bit__int__less__eq,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 13.77/7.84 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8414_signed__take__bit__int__eq__self__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 13.77/7.84 = K )
% 13.77/7.84 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 13.77/7.84 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8415_signed__take__bit__int__eq__self,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 13.77/7.84 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 13.77/7.84 = K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8416_signed__take__bit__int__greater__eq,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 13.77/7.84 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8417_lowi__def,axiom,
% 13.77/7.84 ( vEBT_VEBT_lowi
% 13.77/7.84 = ( ^ [X4: nat,N6: nat] : ( heap_Time_return_nat @ ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8418_summable__arctan__series,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( summable_real
% 13.77/7.84 @ ^ [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 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8419_highi__def,axiom,
% 13.77/7.84 ( vEBT_VEBT_highi
% 13.77/7.84 = ( ^ [X4: nat,N6: nat] : ( heap_Time_return_nat @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8420_highsimp,axiom,
% 13.77/7.84 ! [X: nat,N: nat] :
% 13.77/7.84 ( ( heap_Time_return_nat @ ( vEBT_VEBT_high @ X @ N ) )
% 13.77/7.84 = ( vEBT_VEBT_highi @ X @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8421_lowsimp,axiom,
% 13.77/7.84 ! [X: nat,N: nat] :
% 13.77/7.84 ( ( heap_Time_return_nat @ ( vEBT_VEBT_low @ X @ N ) )
% 13.77/7.84 = ( vEBT_VEBT_lowi @ X @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8422_summable__rabs__comparison__test,axiom,
% 13.77/7.84 ! [F: nat > real,G: nat > real] :
% 13.77/7.84 ( ? [N10: nat] :
% 13.77/7.84 ! [N2: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N10 @ N2 )
% 13.77/7.84 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N2 ) ) @ ( G @ N2 ) ) )
% 13.77/7.84 => ( ( summable_real @ G )
% 13.77/7.84 => ( summable_real
% 13.77/7.84 @ ^ [N6: nat] : ( abs_abs_real @ ( F @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8423_summable__rabs,axiom,
% 13.77/7.84 ! [F: nat > real] :
% 13.77/7.84 ( ( summable_real
% 13.77/7.84 @ ^ [N6: nat] : ( abs_abs_real @ ( F @ N6 ) ) )
% 13.77/7.84 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [N6: nat] : ( abs_abs_real @ ( F @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8424_summable__power__series,axiom,
% 13.77/7.84 ! [F: nat > real,Z: real] :
% 13.77/7.84 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 13.77/7.84 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 13.77/7.84 => ( ( ord_less_real @ Z @ one_one_real )
% 13.77/7.84 => ( summable_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8425_suminf__eq__SUP__real,axiom,
% 13.77/7.84 ! [X6: nat > real] :
% 13.77/7.84 ( ( summable_real @ X6 )
% 13.77/7.84 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X6 @ I2 ) )
% 13.77/7.84 => ( ( suminf_real @ X6 )
% 13.77/7.84 = ( comple1385675409528146559p_real
% 13.77/7.84 @ ( image_nat_real
% 13.77/7.84 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X6 @ ( set_ord_lessThan_nat @ I3 ) )
% 13.77/7.84 @ top_top_set_nat ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8426_sum__pos__lt__pair,axiom,
% 13.77/7.84 ! [F: nat > real,K: nat] :
% 13.77/7.84 ( ( summable_real @ F )
% 13.77/7.84 => ( ! [D2: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D2 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D2 ) @ one_one_nat ) ) ) ) )
% 13.77/7.84 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8427_tanh__ln__real,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 13.77/7.84 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8428_unset__bit__nonnegative__int__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 13.77/7.84 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8429_flip__bit__nonnegative__int__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 13.77/7.84 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8430_unset__bit__negative__int__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 13.77/7.84 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8431_flip__bit__negative__int__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 13.77/7.84 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8432_tanh__real__less__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 13.77/7.84 = ( ord_less_real @ X @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8433_tanh__real__le__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8434_tanh__real__neg__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 13.77/7.84 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8435_tanh__real__pos__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 13.77/7.84 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8436_tanh__real__nonneg__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 13.77/7.84 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8437_tanh__real__nonpos__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 13.77/7.84 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8438_flip__bit__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: nat,X: int] :
% 13.77/7.84 ( ( bit_se1345352211410354436nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( bit_se2159334234014336723it_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8439_unset__bit__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: nat,X: int] :
% 13.77/7.84 ( ( bit_se8260200283734997820nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( bit_se4203085406695923979it_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8440_unset__bit__less__eq,axiom,
% 13.77/7.84 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8441_tanh__real__lt__1,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8442_tanh__real__gt__neg1,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8443_complex__unimodular__polar,axiom,
% 13.77/7.84 ! [Z: complex] :
% 13.77/7.84 ( ( ( real_V1022390504157884413omplex @ Z )
% 13.77/7.84 = one_one_real )
% 13.77/7.84 => ~ ! [T6: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.84 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 13.77/7.84 => ( Z
% 13.77/7.84 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8444_lemma__tan__total,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ Y )
% 13.77/7.84 => ? [X3: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X3 )
% 13.77/7.84 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ord_less_real @ Y @ ( tan_real @ X3 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8445_tan__gt__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8446_lemma__tan__total1,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ? [X3: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 13.77/7.84 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( tan_real @ X3 )
% 13.77/7.84 = Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8447_tan__mono__lt__eq,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.84 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 13.77/7.84 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8448_tan__monotone_H,axiom,
% 13.77/7.84 ! [Y: real,X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.84 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_real @ Y @ X )
% 13.77/7.84 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8449_tan__monotone,axiom,
% 13.77/7.84 ! [Y: real,X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.84 => ( ( ord_less_real @ Y @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8450_tan__total,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ? [X3: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 13.77/7.84 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( tan_real @ X3 )
% 13.77/7.84 = Y )
% 13.77/7.84 & ! [Y5: real] :
% 13.77/7.84 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 13.77/7.84 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( tan_real @ Y5 )
% 13.77/7.84 = Y ) )
% 13.77/7.84 => ( Y5 = X3 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8451_tan__total__pos,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ? [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 13.77/7.84 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( tan_real @ X3 )
% 13.77/7.84 = Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8452_tan__pos__pi2__le,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8453_tan__less__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.84 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8454_tan__mono__le__eq,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 13.77/7.84 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8455_tan__mono__le,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.84 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8456_tan__bound__pi2,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8457_arctan,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 13.77/7.84 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( tan_real @ ( arctan @ Y ) )
% 13.77/7.84 = Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8458_arctan__tan,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( arctan @ ( tan_real @ X ) )
% 13.77/7.84 = X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8459_arctan__unique,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ( tan_real @ X )
% 13.77/7.84 = Y )
% 13.77/7.84 => ( ( arctan @ Y )
% 13.77/7.84 = X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8460_tan__total__pi4,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ? [Z3: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 13.77/7.84 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( tan_real @ Z3 )
% 13.77/7.84 = X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8461_arctan__def,axiom,
% 13.77/7.84 ( arctan
% 13.77/7.84 = ( ^ [Y4: real] :
% 13.77/7.84 ( the_real
% 13.77/7.84 @ ^ [X4: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 13.77/7.84 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( tan_real @ X4 )
% 13.77/7.84 = Y4 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8462_arcsin__def,axiom,
% 13.77/7.84 ( arcsin
% 13.77/7.84 = ( ^ [Y4: real] :
% 13.77/7.84 ( the_real
% 13.77/7.84 @ ^ [X4: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 13.77/7.84 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( sin_real @ X4 )
% 13.77/7.84 = Y4 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8463_sin__tan,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( sin_real @ X )
% 13.77/7.84 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8464_real__sqrt__less__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 13.77/7.84 = ( ord_less_real @ X @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8465_real__sqrt__le__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ X @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8466_real__sqrt__gt__0__iff,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 13.77/7.84 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8467_real__sqrt__lt__0__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 13.77/7.84 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8468_real__sqrt__ge__0__iff,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8469_real__sqrt__le__0__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 13.77/7.84 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8470_real__sqrt__lt__1__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 13.77/7.84 = ( ord_less_real @ X @ one_one_real ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8471_real__sqrt__gt__1__iff,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 13.77/7.84 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8472_real__sqrt__ge__1__iff,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8473_real__sqrt__le__1__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 13.77/7.84 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8474_sin__arcsin,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( sin_real @ ( arcsin @ Y ) )
% 13.77/7.84 = Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8475_real__sqrt__pow2__iff,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.84 = X )
% 13.77/7.84 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8476_real__sqrt__pow2,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.84 = X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8477_real__sqrt__le__mono,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.84 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8478_real__sqrt__less__mono,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ X @ Y )
% 13.77/7.84 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8479_real__sqrt__ge__one,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.84 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8480_real__sqrt__eq__zero__cancel,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ( sqrt @ X )
% 13.77/7.84 = zero_zero_real )
% 13.77/7.84 => ( X = zero_zero_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8481_real__sqrt__ge__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8482_real__sqrt__gt__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8483_real__div__sqrt,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 13.77/7.84 = ( sqrt @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8484_sqrt__add__le__add__sqrt,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8485_le__real__sqrt__sumsq,axiom,
% 13.77/7.84 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8486_arcsin__le__arcsin,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8487_arcsin__minus,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.84 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 13.77/7.84 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8488_arcsin__le__mono,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8489_arcsin__eq__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.84 => ( ( ( arcsin @ X )
% 13.77/7.84 = ( arcsin @ Y ) )
% 13.77/7.84 = ( X = Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8490_sqrt2__less__2,axiom,
% 13.77/7.84 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8491_sqrt__divide__self__eq,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 13.77/7.84 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8492_cos__arcsin,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.84 => ( ( cos_real @ ( arcsin @ X ) )
% 13.77/7.84 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8493_real__less__rsqrt,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 13.77/7.84 => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8494_real__le__rsqrt,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 13.77/7.84 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8495_sqrt__le__D,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 13.77/7.84 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8496_arcsin__less__arcsin,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8497_arcsin__less__mono,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 13.77/7.84 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8498_real__le__lsqrt,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8499_real__sqrt__unique,axiom,
% 13.77/7.84 ! [Y: real,X: real] :
% 13.77/7.84 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.84 = X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ( sqrt @ X )
% 13.77/7.84 = Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8500_lemma__real__divide__sqrt__less,axiom,
% 13.77/7.84 ! [U: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ U )
% 13.77/7.84 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8501_real__sqrt__sum__squares__ge1,axiom,
% 13.77/7.84 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8502_real__sqrt__sum__squares__ge2,axiom,
% 13.77/7.84 ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8503_real__sqrt__sum__squares__triangle__ineq,axiom,
% 13.77/7.84 ! [A: real,C2: real,B: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8504_sqrt__ge__absD,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 13.77/7.84 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8505_cos__arcsin__nonzero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.84 => ( ( cos_real @ ( arcsin @ X ) )
% 13.77/7.84 != zero_zero_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8506_real__less__lsqrt,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8507_sqrt__sum__squares__le__sum,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8508_real__inv__sqrt__pow2,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 13.77/7.84 = ( inverse_inverse_real @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8509_real__sqrt__ge__abs1,axiom,
% 13.77/7.84 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8510_real__sqrt__ge__abs2,axiom,
% 13.77/7.84 ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8511_sqrt__sum__squares__le__sum__abs,axiom,
% 13.77/7.84 ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8512_ln__sqrt,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 13.77/7.84 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8513_real__sqrt__power__even,axiom,
% 13.77/7.84 ! [N: nat,X: real] :
% 13.77/7.84 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 13.77/7.84 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8514_arsinh__real__aux,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8515_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 13.77/7.84 ! [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 ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8516_arith__geo__mean__sqrt,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8517_powr__half__sqrt,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 = ( sqrt @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8518_cos__x__y__le__one,axiom,
% 13.77/7.84 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8519_real__sqrt__sum__squares__less,axiom,
% 13.77/7.84 ! [X: real,U: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8520_arcosh__real__def,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ one_one_real @ X )
% 13.77/7.84 => ( ( arcosh_real @ X )
% 13.77/7.84 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8521_arcsin__lt__bounded,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 13.77/7.84 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8522_arcsin__bounded,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 13.77/7.84 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8523_arcsin__ubound,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8524_arcsin__lbound,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8525_sqrt__sum__squares__half__less,axiom,
% 13.77/7.84 ! [X: real,U: real,Y: real] :
% 13.77/7.84 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8526_arcsin__sin,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( arcsin @ ( sin_real @ X ) )
% 13.77/7.84 = X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8527_sin__cos__sqrt,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 13.77/7.84 => ( ( sin_real @ X )
% 13.77/7.84 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8528_arcsin,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 13.77/7.84 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 & ( ( sin_real @ ( arcsin @ Y ) )
% 13.77/7.84 = Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8529_arcsin__pi,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 13.77/7.84 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 13.77/7.84 & ( ( sin_real @ ( arcsin @ Y ) )
% 13.77/7.84 = Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8530_arcsin__le__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 13.77/7.84 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8531_le__arcsin__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 13.77/7.84 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8532_cos__tan,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ( cos_real @ X )
% 13.77/7.84 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8533_sin__arccos__abs,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.84 => ( ( sin_real @ ( arccos @ Y ) )
% 13.77/7.84 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8534_sin__arccos,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.84 => ( ( sin_real @ ( arccos @ X ) )
% 13.77/7.84 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8535_cos__arccos,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( cos_real @ ( arccos @ Y ) )
% 13.77/7.84 = Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8536_arccos__le__arccos,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8537_arccos__eq__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 13.77/7.84 => ( ( ( arccos @ X )
% 13.77/7.84 = ( arccos @ Y ) )
% 13.77/7.84 = ( X = Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8538_arccos__le__mono,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8539_arccos__lbound,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8540_arccos__less__arccos,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8541_arccos__less__mono,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.84 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 13.77/7.84 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8542_arccos__ubound,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8543_arccos__cos,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ pi )
% 13.77/7.84 => ( ( arccos @ ( cos_real @ X ) )
% 13.77/7.84 = X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8544_cos__arccos__abs,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 13.77/7.84 => ( ( cos_real @ ( arccos @ Y ) )
% 13.77/7.84 = Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8545_arccos__cos__eq__abs,axiom,
% 13.77/7.84 ! [Theta: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 13.77/7.84 => ( ( arccos @ ( cos_real @ Theta ) )
% 13.77/7.84 = ( abs_abs_real @ Theta ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8546_arccos__lt__bounded,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 13.77/7.84 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8547_arccos__bounded,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 13.77/7.84 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8548_sin__arccos__nonzero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.84 => ( ( sin_real @ ( arccos @ X ) )
% 13.77/7.84 != zero_zero_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8549_arccos__cos2,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 13.77/7.84 => ( ( arccos @ ( cos_real @ X ) )
% 13.77/7.84 = ( uminus_uminus_real @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8550_arccos__minus,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.84 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 13.77/7.84 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8551_arccos__def,axiom,
% 13.77/7.84 ( arccos
% 13.77/7.84 = ( ^ [Y4: real] :
% 13.77/7.84 ( the_real
% 13.77/7.84 @ ^ [X4: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 13.77/7.84 & ( ord_less_eq_real @ X4 @ pi )
% 13.77/7.84 & ( ( cos_real @ X4 )
% 13.77/7.84 = Y4 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8552_arccos,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 13.77/7.84 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 13.77/7.84 & ( ( cos_real @ ( arccos @ Y ) )
% 13.77/7.84 = Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8553_arccos__minus__abs,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 13.77/7.84 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8554_arccos__le__pi2,axiom,
% 13.77/7.84 ! [Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 13.77/7.84 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8555_cot__less__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.84 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8556_power__half__series,axiom,
% 13.77/7.84 ( sums_real
% 13.77/7.84 @ ^ [N6: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N6 ) )
% 13.77/7.84 @ one_one_real ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8557_cot__gt__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 13.77/7.84 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8558_cosh__real__ge__1,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8559_cosh__real__nonneg,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8560_cosh__real__nonneg__le__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8561_cosh__real__nonpos__le__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 13.77/7.84 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8562_cosh__real__pos,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8563_sinh__less__cosh__real,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8564_sinh__le__cosh__real,axiom,
% 13.77/7.84 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8565_cosh__real__strict__mono,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ Y )
% 13.77/7.84 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8566_cosh__real__nonneg__less__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 13.77/7.84 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 13.77/7.84 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8567_cosh__real__nonpos__less__iff,axiom,
% 13.77/7.84 ! [X: real,Y: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 13.77/7.84 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 13.77/7.84 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 13.77/7.84 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8568_arcosh__cosh__real,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 13.77/7.84 = X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8569_cosh__ln__real,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 13.77/7.84 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8570_divmod__BitM__2__eq,axiom,
% 13.77/7.84 ! [M: num] :
% 13.77/7.84 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 13.77/7.84 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8571_eval__nat__numeral_I2_J,axiom,
% 13.77/7.84 ! [N: num] :
% 13.77/7.84 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 13.77/7.84 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8572_int__ge__less__than2__def,axiom,
% 13.77/7.84 ( int_ge_less_than2
% 13.77/7.84 = ( ^ [D5: int] :
% 13.77/7.84 ( collec213857154873943460nt_int
% 13.77/7.84 @ ( produc4947309494688390418_int_o
% 13.77/7.84 @ ^ [Z8: int,Z2: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ D5 @ Z2 )
% 13.77/7.84 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8573_int__ge__less__than__def,axiom,
% 13.77/7.84 ( int_ge_less_than
% 13.77/7.84 = ( ^ [D5: int] :
% 13.77/7.84 ( collec213857154873943460nt_int
% 13.77/7.84 @ ( produc4947309494688390418_int_o
% 13.77/7.84 @ ^ [Z8: int,Z2: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ D5 @ Z8 )
% 13.77/7.84 & ( ord_less_int @ Z8 @ Z2 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8574_set__decode__0,axiom,
% 13.77/7.84 ! [X: nat] :
% 13.77/7.84 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 13.77/7.84 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8575_Suc__0__mod__eq,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.84 = ( zero_n2687167440665602831ol_nat
% 13.77/7.84 @ ( N
% 13.77/7.84 != ( suc @ zero_zero_nat ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8576_set__decode__zero,axiom,
% 13.77/7.84 ( ( nat_set_decode @ zero_zero_nat )
% 13.77/7.84 = bot_bot_set_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8577_set__encode__inverse,axiom,
% 13.77/7.84 ! [A4: set_nat] :
% 13.77/7.84 ( ( finite_finite_nat @ A4 )
% 13.77/7.84 => ( ( nat_set_decode @ ( nat_set_encode @ A4 ) )
% 13.77/7.84 = A4 ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8578_Divides_Oadjust__div__eq,axiom,
% 13.77/7.84 ! [Q3: int,R: int] :
% 13.77/7.84 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R ) )
% 13.77/7.84 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8579_set__decode__Suc,axiom,
% 13.77/7.84 ! [N: nat,X: nat] :
% 13.77/7.84 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 13.77/7.84 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8580_finite__set__decode,axiom,
% 13.77/7.84 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8581_Divides_Oadjust__div__def,axiom,
% 13.77/7.84 ( adjust_div
% 13.77/7.84 = ( produc8211389475949308722nt_int
% 13.77/7.84 @ ^ [Q8: int,R5: int] : ( plus_plus_int @ Q8 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8582_subset__decode__imp__le,axiom,
% 13.77/7.84 ! [M: nat,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 13.77/7.84 => ( ord_less_eq_nat @ M @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8583_horner__sum__of__bool__2__less,axiom,
% 13.77/7.84 ! [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 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8584_div__noneq__sgn__abs,axiom,
% 13.77/7.84 ! [L: int,K: int] :
% 13.77/7.84 ( ( L != zero_zero_int )
% 13.77/7.84 => ( ( ( sgn_sgn_int @ K )
% 13.77/7.84 != ( sgn_sgn_int @ L ) )
% 13.77/7.84 => ( ( divide_divide_int @ K @ L )
% 13.77/7.84 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 13.77/7.84 @ ( zero_n2684676970156552555ol_int
% 13.77/7.84 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8585_divide__int__unfold,axiom,
% 13.77/7.84 ! [L: int,K: int,N: nat,M: nat] :
% 13.77/7.84 ( ( ( ( ( sgn_sgn_int @ L )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( ( sgn_sgn_int @ K )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( N = zero_zero_nat ) )
% 13.77/7.84 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 13.77/7.84 = zero_zero_int ) )
% 13.77/7.84 & ( ~ ( ( ( sgn_sgn_int @ L )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( ( sgn_sgn_int @ K )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( N = zero_zero_nat ) )
% 13.77/7.84 => ( ( ( ( sgn_sgn_int @ K )
% 13.77/7.84 = ( sgn_sgn_int @ L ) )
% 13.77/7.84 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 13.77/7.84 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 13.77/7.84 & ( ( ( sgn_sgn_int @ K )
% 13.77/7.84 != ( sgn_sgn_int @ L ) )
% 13.77/7.84 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 13.77/7.84 = ( uminus_uminus_int
% 13.77/7.84 @ ( semiri1314217659103216013at_int
% 13.77/7.84 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 13.77/7.84 @ ( zero_n2687167440665602831ol_nat
% 13.77/7.84 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8586_modulo__int__unfold,axiom,
% 13.77/7.84 ! [L: int,K: int,N: nat,M: nat] :
% 13.77/7.84 ( ( ( ( ( sgn_sgn_int @ L )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( ( sgn_sgn_int @ K )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( N = zero_zero_nat ) )
% 13.77/7.84 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 13.77/7.84 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 13.77/7.84 & ( ~ ( ( ( sgn_sgn_int @ L )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( ( sgn_sgn_int @ K )
% 13.77/7.84 = zero_zero_int )
% 13.77/7.84 | ( N = zero_zero_nat ) )
% 13.77/7.84 => ( ( ( ( sgn_sgn_int @ K )
% 13.77/7.84 = ( sgn_sgn_int @ L ) )
% 13.77/7.84 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 13.77/7.84 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 13.77/7.84 & ( ( ( sgn_sgn_int @ K )
% 13.77/7.84 != ( sgn_sgn_int @ L ) )
% 13.77/7.84 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 13.77/7.84 = ( times_times_int @ ( sgn_sgn_int @ L )
% 13.77/7.84 @ ( minus_minus_int
% 13.77/7.84 @ ( semiri1314217659103216013at_int
% 13.77/7.84 @ ( times_times_nat @ N
% 13.77/7.84 @ ( zero_n2687167440665602831ol_nat
% 13.77/7.84 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 13.77/7.84 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8587_False__map2__or,axiom,
% 13.77/7.84 ! [Xs: list_o,Ys: list_o] :
% 13.77/7.84 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ $false @ bot_bot_set_o ) )
% 13.77/7.84 => ( ( ( size_size_list_o @ Ys )
% 13.77/7.84 = ( size_size_list_o @ Xs ) )
% 13.77/7.84 => ( ( map_Pr7541730621154948341_o_o_o @ ( produc6197397395684419436_o_o_o @ (|) ) @ ( zip_o_o @ Xs @ Ys ) )
% 13.77/7.84 = Ys ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8588_False__map2__and,axiom,
% 13.77/7.84 ! [Xs: list_o,Ys: list_o] :
% 13.77/7.84 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ ( insert_o @ $false @ bot_bot_set_o ) )
% 13.77/7.84 => ( ( ( size_size_list_o @ Ys )
% 13.77/7.84 = ( size_size_list_o @ Xs ) )
% 13.77/7.84 => ( ( map_Pr7541730621154948341_o_o_o @ ( produc6197397395684419436_o_o_o @ (&) ) @ ( zip_o_o @ Xs @ Ys ) )
% 13.77/7.84 = Xs ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8589_take__bit__of__Suc__0,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8590_UNIV__bool,axiom,
% 13.77/7.84 ( top_top_set_o
% 13.77/7.84 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8591_take__bit__tightened__less__eq__int,axiom,
% 13.77/7.84 ! [M: nat,N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.84 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8592_take__bit__nat__less__eq__self,axiom,
% 13.77/7.84 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8593_take__bit__tightened__less__eq__nat,axiom,
% 13.77/7.84 ! [M: nat,N: nat,Q3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.84 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8594_nat__take__bit__eq,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.84 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 13.77/7.84 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8595_take__bit__nat__eq,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.84 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 13.77/7.84 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8596_not__take__bit__negative,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8597_take__bit__int__greater__self__iff,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 13.77/7.84 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8598_take__bit__nonnegative,axiom,
% 13.77/7.84 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8599_take__bit__int__less__eq__self__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 13.77/7.84 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8600_take__bit__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: nat,X: int] :
% 13.77/7.84 ( ( bit_se1745604003318907178nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( bit_se2923211474154528505it_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8601_take__bit__nat__eq__self,axiom,
% 13.77/7.84 ! [M: nat,N: nat] :
% 13.77/7.84 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 13.77/7.84 = M ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8602_take__bit__nat__less__exp,axiom,
% 13.77/7.84 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8603_take__bit__nat__eq__self__iff,axiom,
% 13.77/7.84 ! [N: nat,M: nat] :
% 13.77/7.84 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 13.77/7.84 = M )
% 13.77/7.84 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8604_take__bit__int__less__exp,axiom,
% 13.77/7.84 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8605_take__bit__nat__less__self__iff,axiom,
% 13.77/7.84 ! [N: nat,M: nat] :
% 13.77/7.84 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 13.77/7.84 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8606_take__bit__Suc__minus__bit0,axiom,
% 13.77/7.84 ! [N: nat,K: num] :
% 13.77/7.84 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 13.77/7.84 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8607_take__bit__int__less__self__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 13.77/7.84 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8608_take__bit__int__greater__eq__self__iff,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 13.77/7.84 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8609_take__bit__int__eq__self__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 13.77/7.84 = K )
% 13.77/7.84 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.84 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8610_take__bit__int__eq__self,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.84 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 13.77/7.84 = K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8611_take__bit__int__less__eq,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 13.77/7.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8612_take__bit__int__greater__eq,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.84 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8613_signed__take__bit__eq__take__bit__shift,axiom,
% 13.77/7.84 ( bit_ri631733984087533419it_int
% 13.77/7.84 = ( ^ [N6: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N6 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N6 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N6 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8614_take__bit__minus__small__eq,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( ord_less_int @ zero_zero_int @ K )
% 13.77/7.84 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 13.77/7.84 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8615_take__bit__Suc__minus__bit1,axiom,
% 13.77/7.84 ! [N: nat,K: num] :
% 13.77/7.84 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 13.77/7.84 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8616_take__upt,axiom,
% 13.77/7.84 ! [I: nat,M: nat,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 13.77/7.84 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 13.77/7.84 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8617_upt__0__eq__Nil__conv,axiom,
% 13.77/7.84 ! [J: nat] :
% 13.77/7.84 ( ( ( upt @ zero_zero_nat @ J )
% 13.77/7.84 = nil_nat )
% 13.77/7.84 = ( J = zero_zero_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8618_upt__conv__Nil,axiom,
% 13.77/7.84 ! [J: nat,I: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ J @ I )
% 13.77/7.84 => ( ( upt @ I @ J )
% 13.77/7.84 = nil_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8619_upt__merge,axiom,
% 13.77/7.84 ! [I: nat,J: nat,K: nat] :
% 13.77/7.84 ( ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.84 & ( ord_less_eq_nat @ J @ K ) )
% 13.77/7.84 => ( ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ K ) )
% 13.77/7.84 = ( upt @ I @ K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8620_last__upt,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I @ J )
% 13.77/7.84 => ( ( last_nat @ ( upt @ I @ J ) )
% 13.77/7.84 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8621_upt__eq__Nil__conv,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ( upt @ I @ J )
% 13.77/7.84 = nil_nat )
% 13.77/7.84 = ( ( J = zero_zero_nat )
% 13.77/7.84 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8622_nth__upt,axiom,
% 13.77/7.84 ! [I: nat,K: nat,J: nat] :
% 13.77/7.84 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 13.77/7.84 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 13.77/7.84 = ( plus_plus_nat @ I @ K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8623_sum__list__upt,axiom,
% 13.77/7.84 ! [M: nat,N: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.84 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 13.77/7.84 = ( groups3542108847815614940at_nat
% 13.77/7.84 @ ^ [X4: nat] : X4
% 13.77/7.84 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8624_upt__rec__numeral,axiom,
% 13.77/7.84 ! [M: num,N: num] :
% 13.77/7.84 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 13.77/7.84 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 13.77/7.84 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 13.77/7.84 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 13.77/7.84 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 13.77/7.84 = nil_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8625_upt__eq__append__conv,axiom,
% 13.77/7.84 ! [I: nat,J: nat,Xs: list_nat,Ys: list_nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.84 => ( ( ( upt @ I @ J )
% 13.77/7.84 = ( append_nat @ Xs @ Ys ) )
% 13.77/7.84 = ( ? [K3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ I @ K3 )
% 13.77/7.84 & ( ord_less_eq_nat @ K3 @ J )
% 13.77/7.84 & ( ( upt @ I @ K3 )
% 13.77/7.84 = Xs )
% 13.77/7.84 & ( ( upt @ K3 @ J )
% 13.77/7.84 = Ys ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8626_sorted__upt,axiom,
% 13.77/7.84 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8627_map__add__upt_H,axiom,
% 13.77/7.84 ! [Ofs: nat,A: nat,B: nat] :
% 13.77/7.84 ( ( map_nat_nat
% 13.77/7.84 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ Ofs )
% 13.77/7.84 @ ( upt @ A @ B ) )
% 13.77/7.84 = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8628_map__Suc__upt,axiom,
% 13.77/7.84 ! [M: nat,N: nat] :
% 13.77/7.84 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 13.77/7.84 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8629_map__add__upt,axiom,
% 13.77/7.84 ! [N: nat,M: nat] :
% 13.77/7.84 ( ( map_nat_nat
% 13.77/7.84 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 13.77/7.84 @ ( upt @ zero_zero_nat @ M ) )
% 13.77/7.84 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8630_sorted__wrt__upt,axiom,
% 13.77/7.84 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8631_upt__0,axiom,
% 13.77/7.84 ! [I: nat] :
% 13.77/7.84 ( ( upt @ I @ zero_zero_nat )
% 13.77/7.84 = nil_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8632_butlast__upt,axiom,
% 13.77/7.84 ! [M: nat,N: nat] :
% 13.77/7.84 ( ( butlast_nat @ ( upt @ M @ N ) )
% 13.77/7.84 = ( upt @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8633_upt__conv__Cons__Cons,axiom,
% 13.77/7.84 ! [M: nat,N: nat,Ns: list_nat,Q3: nat] :
% 13.77/7.84 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 13.77/7.84 = ( upt @ M @ Q3 ) )
% 13.77/7.84 = ( ( cons_nat @ N @ Ns )
% 13.77/7.84 = ( upt @ ( suc @ M ) @ Q3 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8634_upt__conv__Cons,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I @ J )
% 13.77/7.84 => ( ( upt @ I @ J )
% 13.77/7.84 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8635_upt__filter__extend,axiom,
% 13.77/7.84 ! [U: nat,U3: nat,P2: nat > $o] :
% 13.77/7.84 ( ( ord_less_eq_nat @ U @ U3 )
% 13.77/7.84 => ( ! [I2: nat] :
% 13.77/7.84 ( ( ( ord_less_eq_nat @ U @ I2 )
% 13.77/7.84 & ( ord_less_nat @ I2 @ U3 ) )
% 13.77/7.84 => ~ ( P2 @ I2 ) )
% 13.77/7.84 => ( ( filter_nat2 @ P2 @ ( upt @ zero_zero_nat @ U ) )
% 13.77/7.84 = ( filter_nat2 @ P2 @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8636_map__decr__upt,axiom,
% 13.77/7.84 ! [M: nat,N: nat] :
% 13.77/7.84 ( ( map_nat_nat
% 13.77/7.84 @ ^ [N6: nat] : ( minus_minus_nat @ N6 @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 13.77/7.84 = ( upt @ M @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8637_upt__append,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I @ J )
% 13.77/7.84 => ( ( append_nat @ ( upt @ zero_zero_nat @ I ) @ ( upt @ I @ J ) )
% 13.77/7.84 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8638_atLeastAtMost__upt,axiom,
% 13.77/7.84 ( set_or1269000886237332187st_nat
% 13.77/7.84 = ( ^ [N6: nat,M5: nat] : ( set_nat2 @ ( upt @ N6 @ ( suc @ M5 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8639_upt__add__eq__append,axiom,
% 13.77/7.84 ! [I: nat,J: nat,K: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.84 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 13.77/7.84 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8640_atLeast__upt,axiom,
% 13.77/7.84 ( set_ord_lessThan_nat
% 13.77/7.84 = ( ^ [N6: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N6 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8641_upt__eq__Cons__conv,axiom,
% 13.77/7.84 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 13.77/7.84 ( ( ( upt @ I @ J )
% 13.77/7.84 = ( cons_nat @ X @ Xs ) )
% 13.77/7.84 = ( ( ord_less_nat @ I @ J )
% 13.77/7.84 & ( I = X )
% 13.77/7.84 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 13.77/7.84 = Xs ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8642_atMost__upto,axiom,
% 13.77/7.84 ( set_ord_atMost_nat
% 13.77/7.84 = ( ^ [N6: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N6 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8643_upt__rec,axiom,
% 13.77/7.84 ( upt
% 13.77/7.84 = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8644_upt__eq__lel__conv,axiom,
% 13.77/7.84 ! [L: nat,H2: nat,Is1: list_nat,I: nat,Is2: list_nat] :
% 13.77/7.84 ( ( ( upt @ L @ H2 )
% 13.77/7.84 = ( append_nat @ Is1 @ ( cons_nat @ I @ Is2 ) ) )
% 13.77/7.84 = ( ( Is1
% 13.77/7.84 = ( upt @ L @ I ) )
% 13.77/7.84 & ( Is2
% 13.77/7.84 = ( upt @ ( suc @ I ) @ H2 ) )
% 13.77/7.84 & ( ord_less_eq_nat @ L @ I )
% 13.77/7.84 & ( ord_less_nat @ I @ H2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8645_upt__Suc__append,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.84 => ( ( upt @ I @ ( suc @ J ) )
% 13.77/7.84 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8646_upt__Suc,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ( ord_less_eq_nat @ I @ J )
% 13.77/7.84 => ( ( upt @ I @ ( suc @ J ) )
% 13.77/7.84 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 13.77/7.84 & ( ~ ( ord_less_eq_nat @ I @ J )
% 13.77/7.84 => ( ( upt @ I @ ( suc @ J ) )
% 13.77/7.84 = nil_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8647_signed__take__bit__eq__take__bit__minus,axiom,
% 13.77/7.84 ( bit_ri631733984087533419it_int
% 13.77/7.84 = ( ^ [N6: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N6 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N6 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N6 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8648_signed__take__bit__nonnegative__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 13.77/7.84 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8649_signed__take__bit__negative__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 13.77/7.84 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8650_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 13.77/7.84 ! [W2: num,N: nat] :
% 13.77/7.84 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( suc @ N ) )
% 13.77/7.84 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8651_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 13.77/7.84 ! [W2: num,N: nat] :
% 13.77/7.84 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( suc @ N ) )
% 13.77/7.84 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8652_bin__nth__minus__Bit0,axiom,
% 13.77/7.84 ! [N: nat,W2: num] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) @ N )
% 13.77/7.84 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8653_bin__nth__minus__Bit1,axiom,
% 13.77/7.84 ! [N: nat,W2: num] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) @ N )
% 13.77/7.84 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8654_map__bit__range__eq__if__take__bit__eq,axiom,
% 13.77/7.84 ! [N: nat,K: int,L: int] :
% 13.77/7.84 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 13.77/7.84 = ( bit_se2923211474154528505it_int @ N @ L ) )
% 13.77/7.84 => ( ( map_nat_o @ ( bit_se1146084159140164899it_int @ K ) @ ( upt @ zero_zero_nat @ N ) )
% 13.77/7.84 = ( map_nat_o @ ( bit_se1146084159140164899it_int @ L ) @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8655_bit__imp__take__bit__positive,axiom,
% 13.77/7.84 ! [N: nat,M: nat,K: int] :
% 13.77/7.84 ( ( ord_less_nat @ N @ M )
% 13.77/7.84 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 13.77/7.84 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8656_int__bit__bound,axiom,
% 13.77/7.84 ! [K: int] :
% 13.77/7.84 ~ ! [N2: nat] :
% 13.77/7.84 ( ! [M2: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N2 @ M2 )
% 13.77/7.84 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 13.77/7.84 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) )
% 13.77/7.84 => ~ ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 13.77/7.84 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 13.77/7.84 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8657_take__bit__Suc__from__most,axiom,
% 13.77/7.84 ! [N: nat,K: int] :
% 13.77/7.84 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 13.77/7.84 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8658_num_Osize__gen_I3_J,axiom,
% 13.77/7.84 ! [X32: num] :
% 13.77/7.84 ( ( size_num @ ( bit1 @ X32 ) )
% 13.77/7.84 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8659_bit__Suc__0__iff,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.84 = ( N = zero_zero_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8660_not__bit__Suc__0__Suc,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8661_bit__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [X: int] :
% 13.77/7.84 ( ( bit_se9216721137139052372nteger @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( bit_se1146084159140164899it_int @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8662_not__bit__Suc__0__numeral,axiom,
% 13.77/7.84 ! [N: num] :
% 13.77/7.84 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8663_bit__nat__iff,axiom,
% 13.77/7.84 ! [K: int,N: nat] :
% 13.77/7.84 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 13.77/7.84 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.84 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8664_num_Osize__gen_I1_J,axiom,
% 13.77/7.84 ( ( size_num @ one )
% 13.77/7.84 = zero_zero_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8665_num_Osize__gen_I2_J,axiom,
% 13.77/7.84 ! [X2: num] :
% 13.77/7.84 ( ( size_num @ ( bit0 @ X2 ) )
% 13.77/7.84 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8666_Code__Numeral_Opositive__def,axiom,
% 13.77/7.84 code_positive = numera6620942414471956472nteger ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8667_concat__bit__Suc,axiom,
% 13.77/7.84 ! [N: nat,K: int,L: int] :
% 13.77/7.84 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 13.77/7.84 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8668_concat__bit__0,axiom,
% 13.77/7.84 ! [K: int,L: int] :
% 13.77/7.84 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 13.77/7.84 = L ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8669_concat__bit__nonnegative__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int,L: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L ) )
% 13.77/7.84 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8670_concat__bit__negative__iff,axiom,
% 13.77/7.84 ! [N: nat,K: int,L: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 13.77/7.84 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8671_bit__concat__bit__iff,axiom,
% 13.77/7.84 ! [M: nat,K: int,L: int,N: nat] :
% 13.77/7.84 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 13.77/7.84 = ( ( ( ord_less_nat @ N @ M )
% 13.77/7.84 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 13.77/7.84 | ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.84 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8672_xor__Suc__0__eq,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 13.77/7.84 @ ( zero_n2687167440665602831ol_nat
% 13.77/7.84 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8673_xor__nat__numerals_I1_J,axiom,
% 13.77/7.84 ! [Y: num] :
% 13.77/7.84 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8674_xor__nat__numerals_I2_J,axiom,
% 13.77/7.84 ! [Y: num] :
% 13.77/7.84 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8675_xor__nat__numerals_I3_J,axiom,
% 13.77/7.84 ! [X: num] :
% 13.77/7.84 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8676_xor__nat__numerals_I4_J,axiom,
% 13.77/7.84 ! [X: num] :
% 13.77/7.84 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8677_xor__nat__unfold,axiom,
% 13.77/7.84 ( bit_se6528837805403552850or_nat
% 13.77/7.84 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N6 @ ( if_nat @ ( N6 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8678_Suc__0__xor__eq,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.84 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 13.77/7.84 @ ( zero_n2687167440665602831ol_nat
% 13.77/7.84 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8679_or__nat__unfold,axiom,
% 13.77/7.84 ( bit_se1412395901928357646or_nat
% 13.77/7.84 = ( ^ [M5: nat,N6: nat] : ( if_nat @ ( M5 = zero_zero_nat ) @ N6 @ ( if_nat @ ( N6 = zero_zero_nat ) @ M5 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8680_xor__nonnegative__int__iff,axiom,
% 13.77/7.84 ! [K: int,L: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 13.77/7.84 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.84 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8681_xor__negative__int__iff,axiom,
% 13.77/7.84 ! [K: int,L: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 13.77/7.84 = ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.84 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8682_or__nat__numerals_I2_J,axiom,
% 13.77/7.84 ! [Y: num] :
% 13.77/7.84 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8683_or__nat__numerals_I4_J,axiom,
% 13.77/7.84 ! [X: num] :
% 13.77/7.84 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8684_or__nat__numerals_I3_J,axiom,
% 13.77/7.84 ! [X: num] :
% 13.77/7.84 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8685_or__nat__numerals_I1_J,axiom,
% 13.77/7.84 ! [Y: num] :
% 13.77/7.84 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 13.77/7.84 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8686_xor__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( bit_se3222712562003087583nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( bit_se6526347334894502574or_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8687_XOR__lower,axiom,
% 13.77/7.84 ! [X: int,Y: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.84 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.84 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8688_XOR__upper,axiom,
% 13.77/7.84 ! [X: int,N: nat,Y: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.84 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8689_or__Suc__0__eq,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 13.77/7.84 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8690_Suc__0__or__eq,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.84 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8691_or__nonnegative__int__iff,axiom,
% 13.77/7.84 ! [K: int,L: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 13.77/7.84 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.84 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8692_or__negative__int__iff,axiom,
% 13.77/7.84 ! [K: int,L: int] :
% 13.77/7.84 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 13.77/7.84 = ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.84 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8693_OR__lower,axiom,
% 13.77/7.84 ! [X: int,Y: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.84 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.84 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8694_or__greater__eq,axiom,
% 13.77/7.84 ! [L: int,K: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 13.77/7.84 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8695_or__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [Xa2: int,X: int] :
% 13.77/7.84 ( ( bit_se1080825931792720795nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( code_integer_of_int @ ( bit_se1409905431419307370or_int @ Xa2 @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8696_OR__upper,axiom,
% 13.77/7.84 ! [X: int,N: nat,Y: int] :
% 13.77/7.84 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.84 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 13.77/7.84 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8697_DERIV__even__real__root,axiom,
% 13.77/7.84 ! [N: nat,X: real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.84 => ( 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 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8698_has__real__derivative__pos__inc__right,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real,S3: set_real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ L )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( member_real @ ( plus_plus_real @ X @ H6 ) @ S3 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H6 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8699_has__real__derivative__neg__dec__right,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real,S3: set_real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 13.77/7.84 => ( ( ord_less_real @ L @ zero_zero_real )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( member_real @ ( plus_plus_real @ X @ H6 ) @ S3 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8700_MVT2,axiom,
% 13.77/7.84 ! [A: real,B: real,F: real > real,F6: real > real] :
% 13.77/7.84 ( ( ord_less_real @ A @ B )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ A @ X3 )
% 13.77/7.84 => ( ( ord_less_eq_real @ X3 @ B )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ F @ ( F6 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 13.77/7.84 => ? [Z3: real] :
% 13.77/7.84 ( ( ord_less_real @ A @ Z3 )
% 13.77/7.84 & ( ord_less_real @ Z3 @ B )
% 13.77/7.84 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 13.77/7.84 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F6 @ Z3 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8701_DERIV__neg__dec__right,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ L @ zero_zero_real )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8702_DERIV__pos__inc__right,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ L )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H6 ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8703_DERIV__ln,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8704_DERIV__pos__imp__increasing,axiom,
% 13.77/7.84 ! [A: real,B: real,F: real > real] :
% 13.77/7.84 ( ( ord_less_real @ A @ B )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ A @ X3 )
% 13.77/7.84 => ( ( ord_less_eq_real @ X3 @ B )
% 13.77/7.84 => ? [Y5: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 13.77/7.84 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8705_DERIV__neg__imp__decreasing,axiom,
% 13.77/7.84 ! [A: real,B: real,F: real > real] :
% 13.77/7.84 ( ( ord_less_real @ A @ B )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ A @ X3 )
% 13.77/7.84 => ( ( ord_less_eq_real @ X3 @ B )
% 13.77/7.84 => ? [Y5: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 13.77/7.84 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8706_deriv__nonneg__imp__mono,axiom,
% 13.77/7.84 ! [A: real,B: real,G: real > real,G3: real > real] :
% 13.77/7.84 ( ! [X3: real] :
% 13.77/7.84 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ G @ ( G3 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( member_real @ X3 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 13.77/7.84 => ( ord_less_eq_real @ zero_zero_real @ ( G3 @ X3 ) ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ A @ B )
% 13.77/7.84 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8707_DERIV__nonpos__imp__nonincreasing,axiom,
% 13.77/7.84 ! [A: real,B: real,F: real > real] :
% 13.77/7.84 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ A @ X3 )
% 13.77/7.84 => ( ( ord_less_eq_real @ X3 @ B )
% 13.77/7.84 => ? [Y5: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 & ( ord_less_eq_real @ Y5 @ zero_zero_real ) ) ) )
% 13.77/7.84 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8708_DERIV__nonneg__imp__nondecreasing,axiom,
% 13.77/7.84 ! [A: real,B: real,F: real > real] :
% 13.77/7.84 ( ( ord_less_eq_real @ A @ B )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ A @ X3 )
% 13.77/7.84 => ( ( ord_less_eq_real @ X3 @ B )
% 13.77/7.84 => ? [Y5: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 & ( ord_less_eq_real @ zero_zero_real @ Y5 ) ) ) )
% 13.77/7.84 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8709_DERIV__neg__dec__left,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ L @ zero_zero_real )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H6 ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8710_DERIV__pos__inc__left,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ L )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8711_has__real__derivative__pos__inc__left,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real,S3: set_real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ L )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( member_real @ ( minus_minus_real @ X @ H6 ) @ S3 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H6 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8712_has__real__derivative__neg__dec__left,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real,S3: set_real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ S3 ) )
% 13.77/7.84 => ( ( ord_less_real @ L @ zero_zero_real )
% 13.77/7.84 => ? [D2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ D2 )
% 13.77/7.84 & ! [H6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H6 )
% 13.77/7.84 => ( ( member_real @ ( minus_minus_real @ X @ H6 ) @ S3 )
% 13.77/7.84 => ( ( ord_less_real @ H6 @ D2 )
% 13.77/7.84 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H6 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8713_DERIV__local__const,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real,D: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ D )
% 13.77/7.84 => ( ! [Y3: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 13.77/7.84 => ( ( F @ X )
% 13.77/7.84 = ( F @ Y3 ) ) )
% 13.77/7.84 => ( L = zero_zero_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8714_DERIV__local__max,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real,D: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ D )
% 13.77/7.84 => ( ! [Y3: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 13.77/7.84 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X ) ) )
% 13.77/7.84 => ( L = zero_zero_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8715_DERIV__local__min,axiom,
% 13.77/7.84 ! [F: real > real,L: real,X: real,D: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ D )
% 13.77/7.84 => ( ! [Y3: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y3 ) ) @ D )
% 13.77/7.84 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y3 ) ) )
% 13.77/7.84 => ( L = zero_zero_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8716_DERIV__ln__divide,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8717_DERIV__pow,axiom,
% 13.77/7.84 ! [N: nat,X: real,S: set_real] :
% 13.77/7.84 ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [X4: real] : ( power_power_real @ X4 @ N )
% 13.77/7.84 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8718_has__real__derivative__powr,axiom,
% 13.77/7.84 ! [Z: real,R: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ Z )
% 13.77/7.84 => ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [Z2: real] : ( powr_real @ Z2 @ R )
% 13.77/7.84 @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8719_DERIV__fun__powr,axiom,
% 13.77/7.84 ! [G: real > real,M: real,X: real,R: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [X4: real] : ( powr_real @ ( G @ X4 ) @ R )
% 13.77/7.84 @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8720_DERIV__log,axiom,
% 13.77/7.84 ! [X: real,B: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8721_DERIV__powr,axiom,
% 13.77/7.84 ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 13.77/7.84 => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [X4: real] : ( powr_real @ ( G @ X4 ) @ ( F @ X4 ) )
% 13.77/7.84 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8722_DERIV__real__sqrt,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8723_DERIV__real__sqrt__generic,axiom,
% 13.77/7.84 ! [X: real,D4: real] :
% 13.77/7.84 ( ( X != zero_zero_real )
% 13.77/7.84 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( D4
% 13.77/7.84 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.84 => ( D4
% 13.77/7.84 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8724_arcosh__real__has__field__derivative,axiom,
% 13.77/7.84 ! [X: real,A4: set_real] :
% 13.77/7.84 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A4 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8725_artanh__real__has__field__derivative,axiom,
% 13.77/7.84 ! [X: real,A4: set_real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A4 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8726_DERIV__real__root,axiom,
% 13.77/7.84 ! [N: nat,X: real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( 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 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8727_DERIV__arccos,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8728_DERIV__arcsin,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8729_Maclaurin__all__le,axiom,
% 13.77/7.84 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 13.77/7.84 ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.84 & ( ( F @ X )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8730_Maclaurin__all__le__objl,axiom,
% 13.77/7.84 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 13.77/7.84 ( ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 & ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.84 & ( ( F @ X )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8731_DERIV__odd__real__root,axiom,
% 13.77/7.84 ! [N: nat,X: real] :
% 13.77/7.84 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( ( X != zero_zero_real )
% 13.77/7.84 => ( 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 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8732_Maclaurin,axiom,
% 13.77/7.84 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H2 )
% 13.77/7.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ H2 ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ T6 )
% 13.77/7.84 & ( ord_less_real @ T6 @ H2 )
% 13.77/7.84 & ( ( F @ H2 )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8733_Maclaurin2,axiom,
% 13.77/7.84 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ H2 )
% 13.77/7.84 => ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ H2 ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ H2 )
% 13.77/7.84 & ( ( F @ H2 )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8734_Maclaurin__minus,axiom,
% 13.77/7.84 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 13.77/7.84 ( ( ord_less_real @ H2 @ zero_zero_real )
% 13.77/7.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ H2 @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_real @ H2 @ T6 )
% 13.77/7.84 & ( ord_less_real @ T6 @ zero_zero_real )
% 13.77/7.84 & ( ( F @ H2 )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ H2 @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8735_Maclaurin__all__lt,axiom,
% 13.77/7.84 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 13.77/7.84 ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( X != zero_zero_real )
% 13.77/7.84 => ( ! [M3: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 13.77/7.84 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.84 & ( ( F @ X )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8736_Maclaurin__bi__le,axiom,
% 13.77/7.84 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 13.77/7.84 ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 13.77/7.84 & ( ( F @ X )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ X @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8737_Taylor,axiom,
% 13.77/7.84 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C2: real,X: real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ A @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ B ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ A @ C2 )
% 13.77/7.84 => ( ( ord_less_eq_real @ C2 @ B )
% 13.77/7.84 => ( ( ord_less_eq_real @ A @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ B )
% 13.77/7.84 => ( ( X != C2 )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ( ord_less_real @ X @ C2 )
% 13.77/7.84 => ( ( ord_less_real @ X @ T6 )
% 13.77/7.84 & ( ord_less_real @ T6 @ C2 ) ) )
% 13.77/7.84 & ( ~ ( ord_less_real @ X @ C2 )
% 13.77/7.84 => ( ( ord_less_real @ C2 @ T6 )
% 13.77/7.84 & ( ord_less_real @ T6 @ X ) ) )
% 13.77/7.84 & ( ( F @ X )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C2 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8738_Taylor__up,axiom,
% 13.77/7.84 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C2: real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ A @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ B ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ( ( ord_less_eq_real @ A @ C2 )
% 13.77/7.84 => ( ( ord_less_real @ C2 @ B )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_real @ C2 @ T6 )
% 13.77/7.84 & ( ord_less_real @ T6 @ B )
% 13.77/7.84 & ( ( F @ B )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C2 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8739_Taylor__down,axiom,
% 13.77/7.84 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C2: real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( ( Diff @ zero_zero_nat )
% 13.77/7.84 = F )
% 13.77/7.84 => ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ A @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ B ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ( ( ord_less_real @ A @ C2 )
% 13.77/7.84 => ( ( ord_less_eq_real @ C2 @ B )
% 13.77/7.84 => ? [T6: real] :
% 13.77/7.84 ( ( ord_less_real @ A @ T6 )
% 13.77/7.84 & ( ord_less_real @ T6 @ C2 )
% 13.77/7.84 & ( ( F @ A )
% 13.77/7.84 = ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [M5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M5 @ C2 ) @ ( semiri2265585572941072030t_real @ M5 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ M5 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ N ) )
% 13.77/7.84 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8740_Maclaurin__lemma2,axiom,
% 13.77/7.84 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B4: real] :
% 13.77/7.84 ( ! [M3: nat,T6: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M3 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 13.77/7.84 & ( ord_less_eq_real @ T6 @ H2 ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 13.77/7.84 => ( ( N
% 13.77/7.84 = ( suc @ K ) )
% 13.77/7.84 => ! [M2: nat,T7: real] :
% 13.77/7.84 ( ( ( ord_less_nat @ M2 @ N )
% 13.77/7.84 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 13.77/7.84 & ( ord_less_eq_real @ T7 @ H2 ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [U2: real] :
% 13.77/7.84 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 13.77/7.84 @ ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [P7: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P7 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P7 ) ) @ ( power_power_real @ U2 @ P7 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 13.77/7.84 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 13.77/7.84 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 13.77/7.84 @ ( plus_plus_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [P7: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P7 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P7 ) ) @ ( power_power_real @ T7 @ P7 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 13.77/7.84 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8741_DERIV__arctan__series,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [X10: real] :
% 13.77/7.84 ( suminf_real
% 13.77/7.84 @ ^ [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 @ X10 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [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 ) ) ) ) ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8742_DERIV__real__root__generic,axiom,
% 13.77/7.84 ! [N: nat,X: real,D4: real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( X != zero_zero_real )
% 13.77/7.84 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ X )
% 13.77/7.84 => ( D4
% 13.77/7.84 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 13.77/7.84 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( ( ord_less_real @ X @ zero_zero_real )
% 13.77/7.84 => ( D4
% 13.77/7.84 = ( 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 ) ) ) ) ) ) ) ) )
% 13.77/7.84 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( D4
% 13.77/7.84 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8743_DERIV__power__series_H,axiom,
% 13.77/7.84 ! [R2: real,F: nat > real,X0: real] :
% 13.77/7.84 ( ! [X3: real] :
% 13.77/7.84 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 13.77/7.84 => ( summable_real
% 13.77/7.84 @ ^ [N6: nat] : ( times_times_real @ ( times_times_real @ ( F @ N6 ) @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) @ ( power_power_real @ X3 @ N6 ) ) ) )
% 13.77/7.84 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 13.77/7.84 => ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [X4: real] :
% 13.77/7.84 ( suminf_real
% 13.77/7.84 @ ^ [N6: nat] : ( times_times_real @ ( F @ N6 ) @ ( power_power_real @ X4 @ ( suc @ N6 ) ) ) )
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [N6: nat] : ( times_times_real @ ( times_times_real @ ( F @ N6 ) @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) @ ( power_power_real @ X0 @ N6 ) ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8744_DERIV__isconst3,axiom,
% 13.77/7.84 ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 13.77/7.84 ( ( ord_less_real @ A @ B )
% 13.77/7.84 => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 13.77/7.84 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 13.77/7.84 => ( ( F @ X )
% 13.77/7.84 = ( F @ Y ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8745_DERIV__series_H,axiom,
% 13.77/7.84 ! [F: real > nat > real,F6: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 13.77/7.84 ( ! [N2: nat] :
% 13.77/7.84 ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [X4: real] : ( F @ X4 @ N2 )
% 13.77/7.84 @ ( F6 @ X0 @ N2 )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 13.77/7.84 => ( ! [X3: real] :
% 13.77/7.84 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 13.77/7.84 => ( summable_real @ ( F @ X3 ) ) )
% 13.77/7.84 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 13.77/7.84 => ( ( summable_real @ ( F6 @ X0 ) )
% 13.77/7.84 => ( ( summable_real @ L5 )
% 13.77/7.84 => ( ! [N2: nat,X3: real,Y3: real] :
% 13.77/7.84 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 13.77/7.84 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 13.77/7.84 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X3 @ N2 ) @ ( F @ Y3 @ N2 ) ) ) @ ( times_times_real @ ( L5 @ N2 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 13.77/7.84 => ( has_fi5821293074295781190e_real
% 13.77/7.84 @ ^ [X4: real] : ( suminf_real @ ( F @ X4 ) )
% 13.77/7.84 @ ( suminf_real @ ( F6 @ X0 ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8746_int__of__integer__code,axiom,
% 13.77/7.84 ( code_int_of_integer
% 13.77/7.84 = ( ^ [K3: code_integer] :
% 13.77/7.84 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 13.77/7.84 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 13.77/7.84 @ ( produc1553301316500091796er_int
% 13.77/7.84 @ ^ [L4: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L4 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L4 ) ) @ one_one_int ) )
% 13.77/7.84 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8747_int__of__integer__max,axiom,
% 13.77/7.84 ! [K: code_integer,L: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( ord_max_Code_integer @ K @ L ) )
% 13.77/7.84 = ( ord_max_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8748_finite__greaterThanLessThan,axiom,
% 13.77/7.84 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8749_finite__greaterThanLessThan__integer,axiom,
% 13.77/7.84 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8750_int__of__integer__of__nat,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( code_int_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.84 = ( semiri1314217659103216013at_int @ N ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8751_integer__of__int__int__of__integer,axiom,
% 13.77/7.84 ! [K: code_integer] :
% 13.77/7.84 ( ( code_integer_of_int @ ( code_int_of_integer @ K ) )
% 13.77/7.84 = K ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8752_int__of__integer__integer__of__int,axiom,
% 13.77/7.84 ! [K: int] :
% 13.77/7.84 ( ( code_int_of_integer @ ( code_integer_of_int @ K ) )
% 13.77/7.84 = K ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8753_int__of__integer__inverse,axiom,
% 13.77/7.84 ! [X: code_integer] :
% 13.77/7.84 ( ( code_integer_of_int @ ( code_int_of_integer @ X ) )
% 13.77/7.84 = X ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8754_of__int__integer__of,axiom,
% 13.77/7.84 ! [K: code_integer] :
% 13.77/7.84 ( ( ring_18347121197199848620nteger @ ( code_int_of_integer @ K ) )
% 13.77/7.84 = K ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8755_int__of__integer__of__int,axiom,
% 13.77/7.84 ! [K: int] :
% 13.77/7.84 ( ( code_int_of_integer @ ( ring_18347121197199848620nteger @ K ) )
% 13.77/7.84 = K ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8756_zero__integer_Orep__eq,axiom,
% 13.77/7.84 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 13.77/7.84 = zero_zero_int ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8757_card__greaterThanLessThan,axiom,
% 13.77/7.84 ! [L: nat,U: nat] :
% 13.77/7.84 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 13.77/7.84 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8758_int__of__integer__numeral,axiom,
% 13.77/7.84 ! [K: num] :
% 13.77/7.84 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 13.77/7.84 = ( numeral_numeral_int @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8759_one__integer_Orep__eq,axiom,
% 13.77/7.84 ( ( code_int_of_integer @ one_one_Code_integer )
% 13.77/7.84 = one_one_int ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8760_uminus__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X ) )
% 13.77/7.84 = ( uminus_uminus_int @ ( code_int_of_integer @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8761_plus__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8762_minus__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8763_times__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8764_abs__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( abs_abs_Code_integer @ X ) )
% 13.77/7.84 = ( abs_abs_int @ ( code_int_of_integer @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8765_divide__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( divide_divide_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8766_modulo__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( modulo_modulo_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8767_sgn__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( sgn_sgn_Code_integer @ X ) )
% 13.77/7.84 = ( sgn_sgn_int @ ( code_int_of_integer @ X ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8768_atLeastSucLessThan__greaterThanLessThan,axiom,
% 13.77/7.84 ! [L: nat,U: nat] :
% 13.77/7.84 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 13.77/7.84 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8769_or__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( bit_se1080825931792720795nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( bit_se1409905431419307370or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8770_bit__integer_Orep__eq,axiom,
% 13.77/7.84 ( bit_se9216721137139052372nteger
% 13.77/7.84 = ( ^ [X4: code_integer] : ( bit_se1146084159140164899it_int @ ( code_int_of_integer @ X4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8771_int__of__integer__induct,axiom,
% 13.77/7.84 ! [Y: int,P2: int > $o] :
% 13.77/7.84 ( ( member_int @ Y @ top_top_set_int )
% 13.77/7.84 => ( ! [X3: code_integer] : ( P2 @ ( code_int_of_integer @ X3 ) )
% 13.77/7.84 => ( P2 @ Y ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8772_int__of__integer__cases,axiom,
% 13.77/7.84 ! [Y: int] :
% 13.77/7.84 ( ( member_int @ Y @ top_top_set_int )
% 13.77/7.84 => ~ ! [X3: code_integer] :
% 13.77/7.84 ( Y
% 13.77/7.84 != ( code_int_of_integer @ X3 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8773_int__of__integer,axiom,
% 13.77/7.84 ! [X: code_integer] : ( member_int @ ( code_int_of_integer @ X ) @ top_top_set_int ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8774_type__definition__integer,axiom,
% 13.77/7.84 type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8775_integer__of__int__inverse,axiom,
% 13.77/7.84 ! [Y: int] :
% 13.77/7.84 ( ( member_int @ Y @ top_top_set_int )
% 13.77/7.84 => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 13.77/7.84 = Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8776_int__of__integer__less__iff,axiom,
% 13.77/7.84 ! [X: code_integer,Y: code_integer] :
% 13.77/7.84 ( ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Y ) )
% 13.77/7.84 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8777_less__integer_Orep__eq,axiom,
% 13.77/7.84 ( ord_le6747313008572928689nteger
% 13.77/7.84 = ( ^ [X4: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8778_integer__less__iff,axiom,
% 13.77/7.84 ( ord_le6747313008572928689nteger
% 13.77/7.84 = ( ^ [K3: code_integer,L4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8779_int__of__integer__inject,axiom,
% 13.77/7.84 ! [X: code_integer,Y: code_integer] :
% 13.77/7.84 ( ( ( code_int_of_integer @ X )
% 13.77/7.84 = ( code_int_of_integer @ Y ) )
% 13.77/7.84 = ( X = Y ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8780_integer__eqI,axiom,
% 13.77/7.84 ! [K: code_integer,L: code_integer] :
% 13.77/7.84 ( ( ( code_int_of_integer @ K )
% 13.77/7.84 = ( code_int_of_integer @ L ) )
% 13.77/7.84 => ( K = L ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8781_integer__eq__iff,axiom,
% 13.77/7.84 ( ( ^ [Y6: code_integer,Z4: code_integer] : ( Y6 = Z4 ) )
% 13.77/7.84 = ( ^ [K3: code_integer,L4: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ K3 )
% 13.77/7.84 = ( code_int_of_integer @ L4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8782_less__eq__integer_Orep__eq,axiom,
% 13.77/7.84 ( ord_le3102999989581377725nteger
% 13.77/7.84 = ( ^ [X4: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8783_integer__less__eq__iff,axiom,
% 13.77/7.84 ( ord_le3102999989581377725nteger
% 13.77/7.84 = ( ^ [K3: code_integer,L4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8784_xor__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( bit_se3222712562003087583nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( bit_se6526347334894502574or_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8785_take__bit__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: nat,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( bit_se1745604003318907178nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( bit_se2923211474154528505it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8786_unset__bit__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: nat,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( bit_se8260200283734997820nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( bit_se4203085406695923979it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8787_LIM__fun__less__zero,axiom,
% 13.77/7.84 ! [F: real > real,L: real,C2: real] :
% 13.77/7.84 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ L @ zero_zero_real )
% 13.77/7.84 => ? [R4: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ R4 )
% 13.77/7.84 & ! [X5: real] :
% 13.77/7.84 ( ( ( X5 != C2 )
% 13.77/7.84 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X5 ) ) @ R4 ) )
% 13.77/7.84 => ( ord_less_real @ ( F @ X5 ) @ zero_zero_real ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8788_LIM__fun__not__zero,axiom,
% 13.77/7.84 ! [F: real > real,L: real,C2: real] :
% 13.77/7.84 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 13.77/7.84 => ( ( L != zero_zero_real )
% 13.77/7.84 => ? [R4: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ R4 )
% 13.77/7.84 & ! [X5: real] :
% 13.77/7.84 ( ( ( X5 != C2 )
% 13.77/7.84 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X5 ) ) @ R4 ) )
% 13.77/7.84 => ( ( F @ X5 )
% 13.77/7.84 != zero_zero_real ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8789_LIM__fun__gt__zero,axiom,
% 13.77/7.84 ! [F: real > real,L: real,C2: real] :
% 13.77/7.84 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ L )
% 13.77/7.84 => ? [R4: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ R4 )
% 13.77/7.84 & ! [X5: real] :
% 13.77/7.84 ( ( ( X5 != C2 )
% 13.77/7.84 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C2 @ X5 ) ) @ R4 ) )
% 13.77/7.84 => ( ord_less_real @ zero_zero_real @ ( F @ X5 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8790_Code__Numeral_Oset__bit__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: nat,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( bit_se2793503036327961859nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( bit_se7879613467334960850it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8791_flip__bit__integer_Orep__eq,axiom,
% 13.77/7.84 ! [X: nat,Xa2: code_integer] :
% 13.77/7.84 ( ( code_int_of_integer @ ( bit_se1345352211410354436nteger @ X @ Xa2 ) )
% 13.77/7.84 = ( bit_se2159334234014336723it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8792_greaterThanLessThan__upt,axiom,
% 13.77/7.84 ( set_or5834768355832116004an_nat
% 13.77/7.84 = ( ^ [N6: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N6 ) @ M5 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8793_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 13.77/7.84 ! [L: code_integer,U: code_integer] :
% 13.77/7.84 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 13.77/7.84 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8794_sorted__list__of__set__greaterThanLessThan,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 13.77/7.84 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 13.77/7.84 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8795_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 13.77/7.84 ! [N: nat,J: nat,I: nat] :
% 13.77/7.84 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 13.77/7.84 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 13.77/7.84 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8796_divmod__integer__def,axiom,
% 13.77/7.84 ( code_divmod_integer
% 13.77/7.84 = ( ^ [K3: code_integer,L4: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L4 ) @ ( modulo364778990260209775nteger @ K3 @ L4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8797_summable__Leibniz_I2_J,axiom,
% 13.77/7.84 ! [A: nat > real] :
% 13.77/7.84 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ( ( topolo6980174941875973593q_real @ A )
% 13.77/7.84 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 13.77/7.84 => ! [N9: nat] :
% 13.77/7.84 ( member_real
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 13.77/7.84 @ ( set_or1222579329274155063t_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8798_summable__Leibniz_I3_J,axiom,
% 13.77/7.84 ! [A: nat > real] :
% 13.77/7.84 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ( ( topolo6980174941875973593q_real @ A )
% 13.77/7.84 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 13.77/7.84 => ! [N9: nat] :
% 13.77/7.84 ( member_real
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 13.77/7.84 @ ( set_or1222579329274155063t_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) )
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8799_filterlim__Suc,axiom,
% 13.77/7.84 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8800_mult__nat__left__at__top,axiom,
% 13.77/7.84 ! [C2: nat] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.84 => ( filterlim_nat_nat @ ( times_times_nat @ C2 ) @ at_top_nat @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8801_mult__nat__right__at__top,axiom,
% 13.77/7.84 ! [C2: nat] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 13.77/7.84 => ( filterlim_nat_nat
% 13.77/7.84 @ ^ [X4: nat] : ( times_times_nat @ X4 @ C2 )
% 13.77/7.84 @ at_top_nat
% 13.77/7.84 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8802_monoseq__convergent,axiom,
% 13.77/7.84 ! [X6: nat > real,B4: real] :
% 13.77/7.84 ( ( topolo6980174941875973593q_real @ X6 )
% 13.77/7.84 => ( ! [I2: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X6 @ I2 ) ) @ B4 )
% 13.77/7.84 => ~ ! [L6: real] :
% 13.77/7.84 ~ ( filterlim_nat_real @ X6 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8803_nested__sequence__unique,axiom,
% 13.77/7.84 ! [F: nat > real,G: nat > real] :
% 13.77/7.84 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N2 ) ) @ ( G @ N2 ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 13.77/7.84 => ( ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( minus_minus_real @ ( F @ N6 ) @ ( G @ N6 ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 13.77/7.84 @ at_top_nat )
% 13.77/7.84 => ? [L2: real] :
% 13.77/7.84 ( ! [N9: nat] : ( ord_less_eq_real @ ( F @ N9 ) @ L2 )
% 13.77/7.84 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat )
% 13.77/7.84 & ! [N9: nat] : ( ord_less_eq_real @ L2 @ ( G @ N9 ) )
% 13.77/7.84 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8804_LIMSEQ__inverse__zero,axiom,
% 13.77/7.84 ! [X6: nat > real] :
% 13.77/7.84 ( ! [R4: real] :
% 13.77/7.84 ? [N10: nat] :
% 13.77/7.84 ! [N2: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N10 @ N2 )
% 13.77/7.84 => ( ord_less_real @ R4 @ ( X6 @ N2 ) ) )
% 13.77/7.84 => ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( inverse_inverse_real @ ( X6 @ N6 ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 13.77/7.84 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8805_LIMSEQ__inverse__real__of__nat,axiom,
% 13.77/7.84 ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 13.77/7.84 @ at_top_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8806_LIMSEQ__root__const,axiom,
% 13.77/7.84 ! [C2: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ C2 )
% 13.77/7.84 => ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( root @ N6 @ C2 )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ one_one_real )
% 13.77/7.84 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8807_LIMSEQ__inverse__real__of__nat__add,axiom,
% 13.77/7.84 ! [R: real] :
% 13.77/7.84 ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ R )
% 13.77/7.84 @ at_top_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8808_increasing__LIMSEQ,axiom,
% 13.77/7.84 ! [F: nat > real,L: real] :
% 13.77/7.84 ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( F @ N2 ) @ L )
% 13.77/7.84 => ( ! [E: real] :
% 13.77/7.84 ( ( ord_less_real @ zero_zero_real @ E )
% 13.77/7.84 => ? [N9: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N9 ) @ E ) ) )
% 13.77/7.84 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8809_LIMSEQ__realpow__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_real @ X @ one_one_real )
% 13.77/7.84 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8810_LIMSEQ__divide__realpow__zero,axiom,
% 13.77/7.84 ! [X: real,A: real] :
% 13.77/7.84 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.84 => ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N6 ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 13.77/7.84 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8811_LIMSEQ__abs__realpow__zero,axiom,
% 13.77/7.84 ! [C2: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ C2 ) @ one_one_real )
% 13.77/7.84 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C2 ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8812_LIMSEQ__abs__realpow__zero2,axiom,
% 13.77/7.84 ! [C2: real] :
% 13.77/7.84 ( ( ord_less_real @ ( abs_abs_real @ C2 ) @ one_one_real )
% 13.77/7.84 => ( filterlim_nat_real @ ( power_power_real @ C2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8813_LIMSEQ__inverse__realpow__zero,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_real @ one_one_real @ X )
% 13.77/7.84 => ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N6 ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 13.77/7.84 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8814_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 13.77/7.84 ! [R: real] :
% 13.77/7.84 ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ R )
% 13.77/7.84 @ at_top_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8815_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 13.77/7.84 ! [R: real] :
% 13.77/7.84 ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N6 ) ) ) ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ R )
% 13.77/7.84 @ at_top_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8816_summable,axiom,
% 13.77/7.84 ! [A: nat > real] :
% 13.77/7.84 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 13.77/7.84 => ( summable_real
% 13.77/7.84 @ ^ [N6: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N6 ) @ ( A @ N6 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8817_zeroseq__arctan__series,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 13.77/7.84 => ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 13.77/7.84 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8818_summable__Leibniz_H_I2_J,axiom,
% 13.77/7.84 ! [A: nat > real,N: nat] :
% 13.77/7.84 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 13.77/7.84 => ( ord_less_eq_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8819_summable__Leibniz_H_I3_J,axiom,
% 13.77/7.84 ! [A: nat > real] :
% 13.77/7.84 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 13.77/7.84 => ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] :
% 13.77/7.84 ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 13.77/7.84 @ at_top_nat ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8820_sums__alternating__upper__lower,axiom,
% 13.77/7.84 ! [A: nat > real] :
% 13.77/7.84 ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 13.77/7.84 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ? [L2: real] :
% 13.77/7.84 ( ! [N9: nat] :
% 13.77/7.84 ( ord_less_eq_real
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) ) )
% 13.77/7.84 @ L2 )
% 13.77/7.84 & ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] :
% 13.77/7.84 ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ L2 )
% 13.77/7.84 @ at_top_nat )
% 13.77/7.84 & ! [N9: nat] :
% 13.77/7.84 ( ord_less_eq_real @ L2
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N9 ) @ one_one_nat ) ) ) )
% 13.77/7.84 & ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] :
% 13.77/7.84 ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real @ L2 )
% 13.77/7.84 @ at_top_nat ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8821_summable__Leibniz_H_I4_J,axiom,
% 13.77/7.84 ! [A: nat > real,N: nat] :
% 13.77/7.84 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 13.77/7.84 => ( ord_less_eq_real
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 13.77/7.84 @ ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8822_summable__Leibniz_H_I5_J,axiom,
% 13.77/7.84 ! [A: nat > real] :
% 13.77/7.84 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N2 ) )
% 13.77/7.84 => ( ! [N2: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N2 ) ) @ ( A @ N2 ) )
% 13.77/7.84 => ( filterlim_nat_real
% 13.77/7.84 @ ^ [N6: nat] :
% 13.77/7.84 ( groups6591440286371151544t_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 13.77/7.84 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 13.77/7.84 @ ( topolo2815343760600316023s_real
% 13.77/7.84 @ ( suminf_real
% 13.77/7.84 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 13.77/7.84 @ at_top_nat ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8823_num__of__integer__code,axiom,
% 13.77/7.84 ( code_num_of_integer
% 13.77/7.84 = ( ^ [K3: code_integer] :
% 13.77/7.84 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 13.77/7.84 @ ( produc7336495610019696514er_num
% 13.77/7.84 @ ^ [L4: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L4 ) @ ( code_num_of_integer @ L4 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L4 ) @ ( code_num_of_integer @ L4 ) ) @ one ) )
% 13.77/7.84 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8824_nat__of__integer__code,axiom,
% 13.77/7.84 ( code_nat_of_integer
% 13.77/7.84 = ( ^ [K3: code_integer] :
% 13.77/7.84 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 13.77/7.84 @ ( produc1555791787009142072er_nat
% 13.77/7.84 @ ^ [L4: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L4 ) @ ( code_nat_of_integer @ L4 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L4 ) @ ( code_nat_of_integer @ L4 ) ) @ one_one_nat ) )
% 13.77/7.84 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8825_nat__of__integer__of__nat,axiom,
% 13.77/7.84 ! [N: nat] :
% 13.77/7.84 ( ( code_nat_of_integer @ ( semiri4939895301339042750nteger @ N ) )
% 13.77/7.84 = N ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8826_nat__of__integer__non__positive,axiom,
% 13.77/7.84 ! [K: code_integer] :
% 13.77/7.84 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 13.77/7.84 => ( ( code_nat_of_integer @ K )
% 13.77/7.84 = zero_zero_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8827_of__nat__of__integer,axiom,
% 13.77/7.84 ! [K: code_integer] :
% 13.77/7.84 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 13.77/7.84 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8828_nat__of__integer_Orep__eq,axiom,
% 13.77/7.84 ( code_nat_of_integer
% 13.77/7.84 = ( ^ [X4: code_integer] : ( nat2 @ ( code_int_of_integer @ X4 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8829_nat__of__integer_Oabs__eq,axiom,
% 13.77/7.84 ! [X: int] :
% 13.77/7.84 ( ( code_nat_of_integer @ ( code_integer_of_int @ X ) )
% 13.77/7.84 = ( nat2 @ X ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8830_nat__of__integer__code__post_I1_J,axiom,
% 13.77/7.84 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 13.77/7.84 = zero_zero_nat ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8831_nat__of__integer__less__iff,axiom,
% 13.77/7.84 ! [X: code_integer,Y: code_integer] :
% 13.77/7.84 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 13.77/7.84 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 13.77/7.84 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 13.77/7.84 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8832_image__atLeastZeroLessThan__integer,axiom,
% 13.77/7.84 ! [U: code_integer] :
% 13.77/7.84 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 13.77/7.84 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 13.77/7.84 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8833_filterlim__pow__at__bot__odd,axiom,
% 13.77/7.84 ! [N: nat,F: real > real,F2: filter_real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 13.77/7.84 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( filterlim_real_real
% 13.77/7.84 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N )
% 13.77/7.84 @ at_bot_real
% 13.77/7.84 @ F2 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8834_eventually__sequentially__Suc,axiom,
% 13.77/7.84 ! [P2: nat > $o] :
% 13.77/7.84 ( ( eventually_nat
% 13.77/7.84 @ ^ [I3: nat] : ( P2 @ ( suc @ I3 ) )
% 13.77/7.84 @ at_top_nat )
% 13.77/7.84 = ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8835_at__bot__le__at__infinity,axiom,
% 13.77/7.84 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8836_eventually__sequentiallyI,axiom,
% 13.77/7.84 ! [C2: nat,P2: nat > $o] :
% 13.77/7.84 ( ! [X3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ C2 @ X3 )
% 13.77/7.84 => ( P2 @ X3 ) )
% 13.77/7.84 => ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8837_eventually__sequentially,axiom,
% 13.77/7.84 ! [P2: nat > $o] :
% 13.77/7.84 ( ( eventually_nat @ P2 @ at_top_nat )
% 13.77/7.84 = ( ? [N7: nat] :
% 13.77/7.84 ! [N6: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N7 @ N6 )
% 13.77/7.84 => ( P2 @ N6 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8838_le__sequentially,axiom,
% 13.77/7.84 ! [F2: filter_nat] :
% 13.77/7.84 ( ( ord_le2510731241096832064er_nat @ F2 @ at_top_nat )
% 13.77/7.84 = ( ! [N7: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N7 ) @ F2 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8839_eventually__at__left__real,axiom,
% 13.77/7.84 ! [B: real,A: real] :
% 13.77/7.84 ( ( ord_less_real @ B @ A )
% 13.77/7.84 => ( eventually_real
% 13.77/7.84 @ ^ [X4: real] : ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ A ) )
% 13.77/7.84 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8840_DERIV__pos__imp__increasing__at__bot,axiom,
% 13.77/7.84 ! [B: real,F: real > real,Flim: real] :
% 13.77/7.84 ( ! [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ X3 @ B )
% 13.77/7.84 => ? [Y5: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 & ( ord_less_real @ zero_zero_real @ Y5 ) ) )
% 13.77/7.84 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 13.77/7.84 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8841_at__top__le__at__infinity,axiom,
% 13.77/7.84 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8842_Bseq__eq__bounded,axiom,
% 13.77/7.84 ! [F: nat > real,A: real,B: real] :
% 13.77/7.84 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 13.77/7.84 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8843_Bseq__realpow,axiom,
% 13.77/7.84 ! [X: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 13.77/7.84 => ( ( ord_less_eq_real @ X @ one_one_real )
% 13.77/7.84 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8844_DERIV__neg__imp__decreasing__at__top,axiom,
% 13.77/7.84 ! [B: real,F: real > real,Flim: real] :
% 13.77/7.84 ( ! [X3: real] :
% 13.77/7.84 ( ( ord_less_eq_real @ B @ X3 )
% 13.77/7.84 => ? [Y5: real] :
% 13.77/7.84 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 13.77/7.84 & ( ord_less_real @ Y5 @ zero_zero_real ) ) )
% 13.77/7.84 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 13.77/7.84 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8845_filterlim__pow__at__bot__even,axiom,
% 13.77/7.84 ! [N: nat,F: real > real,F2: filter_real] :
% 13.77/7.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.84 => ( ( filterlim_real_real @ F @ at_bot_real @ F2 )
% 13.77/7.84 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 13.77/7.84 => ( filterlim_real_real
% 13.77/7.84 @ ^ [X4: real] : ( power_power_real @ ( F @ X4 ) @ N )
% 13.77/7.84 @ at_top_real
% 13.77/7.84 @ F2 ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8846_finite__greaterThanAtMost,axiom,
% 13.77/7.84 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8847_atLeastSucAtMost__greaterThanAtMost,axiom,
% 13.77/7.84 ! [L: nat,U: nat] :
% 13.77/7.84 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 13.77/7.84 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8848_greaterThanAtMost__upt,axiom,
% 13.77/7.84 ( set_or6659071591806873216st_nat
% 13.77/7.84 = ( ^ [N6: nat,M5: nat] : ( set_nat2 @ ( upt @ ( suc @ N6 ) @ ( suc @ M5 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8849_sorted__list__of__set__greaterThanAtMost,axiom,
% 13.77/7.84 ! [I: nat,J: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 13.77/7.84 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 13.77/7.84 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8850_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 13.77/7.84 ! [N: nat,J: nat,I: nat] :
% 13.77/7.84 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 13.77/7.84 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 13.77/7.84 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8851_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 13.77/7.84 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.84 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 13.77/7.84 = Y )
% 13.77/7.84 => ( ( ? [Uu: $o,Uv: $o] :
% 13.77/7.84 ( X
% 13.77/7.84 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.84 => ( Y
% 13.77/7.84 = ( Xa2 != one_one_nat ) ) )
% 13.77/7.84 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.84 => ( Y
% 13.77/7.84 = ( ~ ( ( Deg2 = Xa2 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 & ( case_o184042715313410164at_nat
% 13.77/7.84 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 @ ( produc6081775807080527818_nat_o
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.84 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 & ! [I3: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 13.77/7.84 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 13.77/7.84 & ( ( Mi3 = Ma3 )
% 13.77/7.84 => ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 & ( ( Mi3 != Ma3 )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 13.77/7.84 & ! [X4: nat] :
% 13.77/7.84 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 13.77/7.84 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.84 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 13.77/7.84 @ Mima2 ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8852_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 13.77/7.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.84 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 13.77/7.84 => ( ( ? [Uu: $o,Uv: $o] :
% 13.77/7.84 ( X
% 13.77/7.84 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.84 => ( Xa2 != one_one_nat ) )
% 13.77/7.84 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.84 => ~ ( ( Deg2 = Xa2 )
% 13.77/7.84 & ! [X5: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 & ( case_o184042715313410164at_nat
% 13.77/7.84 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 @ ( produc6081775807080527818_nat_o
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.84 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 & ! [I3: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 13.77/7.84 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 13.77/7.84 & ( ( Mi3 = Ma3 )
% 13.77/7.84 => ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 & ( ( Mi3 != Ma3 )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 13.77/7.84 & ! [X4: nat] :
% 13.77/7.84 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 13.77/7.84 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.84 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 13.77/7.84 @ Mima2 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8853_finite__greaterThanAtMost__integer,axiom,
% 13.77/7.84 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8854_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 13.77/7.84 ! [L: code_integer,U: code_integer] :
% 13.77/7.84 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 13.77/7.84 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8855_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 13.77/7.84 ! [Mima3: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 13.77/7.84 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima3 @ Deg @ TreeList @ Summary ) @ Deg3 )
% 13.77/7.84 = ( ( Deg = Deg3 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.84 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 13.77/7.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 & ( case_o184042715313410164at_nat
% 13.77/7.84 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X8 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 @ ( produc6081775807080527818_nat_o
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.84 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 13.77/7.84 & ! [I3: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X8 ) )
% 13.77/7.84 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 13.77/7.84 & ( ( Mi3 = Ma3 )
% 13.77/7.84 => ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 & ( ( Mi3 != Ma3 )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 13.77/7.84 & ! [X4: nat] :
% 13.77/7.84 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 13.77/7.84 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.84 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 13.77/7.84 @ Mima3 ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8856_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 13.77/7.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.84 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 13.77/7.84 => ( ( ? [Uu: $o,Uv: $o] :
% 13.77/7.84 ( X
% 13.77/7.84 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.84 => ( Xa2 = one_one_nat ) )
% 13.77/7.84 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.84 => ( ( Deg2 = Xa2 )
% 13.77/7.84 & ! [X3: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 & ( case_o184042715313410164at_nat
% 13.77/7.84 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 @ ( produc6081775807080527818_nat_o
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.84 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 & ! [I3: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 13.77/7.84 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 13.77/7.84 & ( ( Mi3 = Ma3 )
% 13.77/7.84 => ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 & ( ( Mi3 != Ma3 )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 13.77/7.84 & ! [X4: nat] :
% 13.77/7.84 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 13.77/7.84 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.84 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 13.77/7.84 @ Mima2 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8857_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 13.77/7.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.84 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 13.77/7.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.84 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 13.77/7.84 => ( Xa2 = one_one_nat ) ) )
% 13.77/7.84 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 13.77/7.84 => ( ( Deg2 = Xa2 )
% 13.77/7.84 & ! [X3: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 & ( case_o184042715313410164at_nat
% 13.77/7.84 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 @ ( produc6081775807080527818_nat_o
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.84 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 & ! [I3: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 13.77/7.84 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 13.77/7.84 & ( ( Mi3 = Ma3 )
% 13.77/7.84 => ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 & ( ( Mi3 != Ma3 )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 13.77/7.84 & ! [X4: nat] :
% 13.77/7.84 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 13.77/7.84 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.84 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 13.77/7.84 @ Mima2 ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8858_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 13.77/7.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 13.77/7.84 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 13.77/7.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.84 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 13.77/7.84 => ( Xa2 != one_one_nat ) ) )
% 13.77/7.84 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 13.77/7.84 => ~ ( ( Deg2 = Xa2 )
% 13.77/7.84 & ! [X5: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 & ( case_o184042715313410164at_nat
% 13.77/7.84 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 @ ( produc6081775807080527818_nat_o
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.84 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 & ! [I3: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 13.77/7.84 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 13.77/7.84 & ( ( Mi3 = Ma3 )
% 13.77/7.84 => ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 & ( ( Mi3 != Ma3 )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 13.77/7.84 & ! [X4: nat] :
% 13.77/7.84 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 13.77/7.84 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.84 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 13.77/7.84 @ Mima2 ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8859_Sup__real__def,axiom,
% 13.77/7.84 ( comple1385675409528146559p_real
% 13.77/7.84 = ( ^ [X8: set_real] :
% 13.77/7.84 ( ord_Least_real
% 13.77/7.84 @ ^ [Z2: real] :
% 13.77/7.84 ! [X4: real] :
% 13.77/7.84 ( ( member_real @ X4 @ X8 )
% 13.77/7.84 => ( ord_less_eq_real @ X4 @ Z2 ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8860_Sup__int__def,axiom,
% 13.77/7.84 ( complete_Sup_Sup_int
% 13.77/7.84 = ( ^ [X8: set_int] :
% 13.77/7.84 ( the_int
% 13.77/7.84 @ ^ [X4: int] :
% 13.77/7.84 ( ( member_int @ X4 @ X8 )
% 13.77/7.84 & ! [Y4: int] :
% 13.77/7.84 ( ( member_int @ Y4 @ X8 )
% 13.77/7.84 => ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8861_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 13.77/7.84 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 13.77/7.84 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 13.77/7.84 = Y )
% 13.77/7.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 13.77/7.84 => ( ! [Uu: $o,Uv: $o] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Leaf @ Uu @ Uv ) )
% 13.77/7.84 => ( ( Y
% 13.77/7.84 = ( Xa2 = one_one_nat ) )
% 13.77/7.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 13.77/7.84 => ~ ! [Mima2: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 13.77/7.84 ( ( X
% 13.77/7.84 = ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) )
% 13.77/7.84 => ( ( Y
% 13.77/7.84 = ( ( Deg2 = Xa2 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 13.77/7.84 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 13.77/7.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 & ( case_o184042715313410164at_nat
% 13.77/7.84 @ ( ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X8 )
% 13.77/7.84 & ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 @ ( produc6081775807080527818_nat_o
% 13.77/7.84 @ ^ [Mi3: nat,Ma3: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 13.77/7.84 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 & ! [I3: nat] :
% 13.77/7.84 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 13.77/7.84 => ( ( ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X8 ) )
% 13.77/7.84 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 13.77/7.84 & ( ( Mi3 = Ma3 )
% 13.77/7.84 => ! [X4: vEBT_VEBT] :
% 13.77/7.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 13.77/7.84 => ~ ? [X8: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X8 ) ) )
% 13.77/7.84 & ( ( Mi3 != Ma3 )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 13.77/7.84 & ! [X4: nat] :
% 13.77/7.84 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 13.77/7.84 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 13.77/7.84 => ( ( ord_less_nat @ Mi3 @ X4 )
% 13.77/7.84 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 13.77/7.84 @ Mima2 ) ) )
% 13.77/7.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima2 @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8862_set__bits__int__def,axiom,
% 13.77/7.84 ( bit_bi6516823479961619367ts_int
% 13.77/7.84 = ( ^ [F5: nat > $o] :
% 13.77/7.84 ( if_int
% 13.77/7.84 @ ? [N6: nat] :
% 13.77/7.84 ! [M5: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N6 @ M5 )
% 13.77/7.84 => ( ( F5 @ M5 )
% 13.77/7.84 = ( F5 @ N6 ) ) )
% 13.77/7.84 @ ( bit_ri631733984087533419it_int
% 13.77/7.84 @ ( ord_Least_nat
% 13.77/7.84 @ ^ [N6: nat] :
% 13.77/7.84 ! [M5: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N6 @ M5 )
% 13.77/7.84 => ( ( F5 @ M5 )
% 13.77/7.84 = ( F5 @ N6 ) ) ) )
% 13.77/7.84 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 13.77/7.84 @ ( map_nat_o @ F5
% 13.77/7.84 @ ( upt @ zero_zero_nat
% 13.77/7.84 @ ( suc
% 13.77/7.84 @ ( ord_Least_nat
% 13.77/7.84 @ ^ [N6: nat] :
% 13.77/7.84 ! [M5: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N6 @ M5 )
% 13.77/7.84 => ( ( F5 @ M5 )
% 13.77/7.84 = ( F5 @ N6 ) ) ) ) ) ) ) ) )
% 13.77/7.84 @ zero_zero_int ) ) ) ).
% 13.77/7.84
% 13.77/7.84 thf(fact_8863_set__bits__int__unfold_H,axiom,
% 13.77/7.84 ( bit_bi6516823479961619367ts_int
% 13.77/7.84 = ( ^ [F5: nat > $o] :
% 13.77/7.84 ( if_int
% 13.77/7.84 @ ? [N6: nat] :
% 13.77/7.84 ! [N11: nat] :
% 13.77/7.84 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.84 => ~ ( F5 @ N11 ) )
% 13.77/7.84 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 13.77/7.84 @ ( map_nat_o @ F5
% 13.77/7.84 @ ( upt @ zero_zero_nat
% 13.77/7.84 @ ( ord_Least_nat
% 13.77/7.85 @ ^ [N6: nat] :
% 13.77/7.85 ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ~ ( F5 @ N11 ) ) ) ) ) )
% 13.77/7.85 @ ( if_int
% 13.77/7.85 @ ? [N6: nat] :
% 13.77/7.85 ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ( F5 @ N11 ) )
% 13.77/7.85 @ ( bit_ri631733984087533419it_int
% 13.77/7.85 @ ( ord_Least_nat
% 13.77/7.85 @ ^ [N6: nat] :
% 13.77/7.85 ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ( F5 @ N11 ) ) )
% 13.77/7.85 @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 13.77/7.85 @ ( append_o
% 13.77/7.85 @ ( map_nat_o @ F5
% 13.77/7.85 @ ( upt @ zero_zero_nat
% 13.77/7.85 @ ( ord_Least_nat
% 13.77/7.85 @ ^ [N6: nat] :
% 13.77/7.85 ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ( F5 @ N11 ) ) ) ) )
% 13.77/7.85 @ ( cons_o @ $true @ nil_o ) ) ) )
% 13.77/7.85 @ zero_zero_int ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8864_bin__last__set__bits,axiom,
% 13.77/7.85 ! [F: nat > $o] :
% 13.77/7.85 ( ( bit_wf_set_bits_int @ F )
% 13.77/7.85 => ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_bi6516823479961619367ts_int @ F ) ) )
% 13.77/7.85 = ( F @ zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8865_wf__set__bits__int__Suc,axiom,
% 13.77/7.85 ! [F: nat > $o] :
% 13.77/7.85 ( ( bit_wf_set_bits_int
% 13.77/7.85 @ ^ [N6: nat] : ( F @ ( suc @ N6 ) ) )
% 13.77/7.85 = ( bit_wf_set_bits_int @ F ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8866_wf__set__bits__int__simps,axiom,
% 13.77/7.85 ( bit_wf_set_bits_int
% 13.77/7.85 = ( ^ [F5: nat > $o] :
% 13.77/7.85 ? [N6: nat] :
% 13.77/7.85 ( ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ~ ( F5 @ N11 ) )
% 13.77/7.85 | ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ( F5 @ N11 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8867_zeros,axiom,
% 13.77/7.85 ! [N: nat,F: nat > $o] :
% 13.77/7.85 ( ! [N5: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N @ N5 )
% 13.77/7.85 => ~ ( F @ N5 ) )
% 13.77/7.85 => ( bit_wf_set_bits_int @ F ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8868_wf__set__bits__int_Osimps,axiom,
% 13.77/7.85 ( bit_wf_set_bits_int
% 13.77/7.85 = ( ^ [F5: nat > $o] :
% 13.77/7.85 ( ? [N6: nat] :
% 13.77/7.85 ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ~ ( F5 @ N11 ) )
% 13.77/7.85 | ? [N6: nat] :
% 13.77/7.85 ! [N11: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N6 @ N11 )
% 13.77/7.85 => ( F5 @ N11 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8869_wf__set__bits__int_Ocases,axiom,
% 13.77/7.85 ! [F: nat > $o] :
% 13.77/7.85 ( ( bit_wf_set_bits_int @ F )
% 13.77/7.85 => ( ! [N2: nat] :
% 13.77/7.85 ~ ! [N4: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N2 @ N4 )
% 13.77/7.85 => ~ ( F @ N4 ) )
% 13.77/7.85 => ~ ! [N2: nat] :
% 13.77/7.85 ~ ! [N4: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N2 @ N4 )
% 13.77/7.85 => ( F @ N4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8870_ones,axiom,
% 13.77/7.85 ! [N: nat,F: nat > $o] :
% 13.77/7.85 ( ! [N5: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N @ N5 )
% 13.77/7.85 => ( F @ N5 ) )
% 13.77/7.85 => ( bit_wf_set_bits_int @ F ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8871_int__set__bits__unfold__BIT,axiom,
% 13.77/7.85 ! [F: nat > $o] :
% 13.77/7.85 ( ( bit_wf_set_bits_int @ F )
% 13.77/7.85 => ( ( bit_bi6516823479961619367ts_int @ F )
% 13.77/7.85 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( F @ zero_zero_nat ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_bi6516823479961619367ts_int @ ( comp_nat_o_nat @ F @ suc ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8872_bin__rest__set__bits,axiom,
% 13.77/7.85 ! [F: nat > $o] :
% 13.77/7.85 ( ( bit_wf_set_bits_int @ F )
% 13.77/7.85 => ( ( divide_divide_int @ ( bit_bi6516823479961619367ts_int @ F ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 13.77/7.85 = ( bit_bi6516823479961619367ts_int @ ( comp_nat_o_nat @ F @ suc ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8873_less__eq__char__simp,axiom,
% 13.77/7.85 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o,C0: $o,C1: $o,C22: $o,C32: $o,C42: $o,C52: $o,C62: $o,C7: $o] :
% 13.77/7.85 ( ( ord_less_eq_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) @ ( char2 @ C0 @ C1 @ C22 @ C32 @ C42 @ C52 @ C62 @ C7 ) )
% 13.77/7.85 = ( ord_less_eq_nat
% 13.77/7.85 @ ( foldr_o_nat
% 13.77/7.85 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.85 @ ( cons_o @ B0 @ ( cons_o @ B1 @ ( cons_o @ B22 @ ( cons_o @ B32 @ ( cons_o @ B42 @ ( cons_o @ B52 @ ( cons_o @ B62 @ ( cons_o @ B72 @ nil_o ) ) ) ) ) ) ) )
% 13.77/7.85 @ zero_zero_nat )
% 13.77/7.85 @ ( foldr_o_nat
% 13.77/7.85 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.85 @ ( cons_o @ C0 @ ( cons_o @ C1 @ ( cons_o @ C22 @ ( cons_o @ C32 @ ( cons_o @ C42 @ ( cons_o @ C52 @ ( cons_o @ C62 @ ( cons_o @ C7 @ nil_o ) ) ) ) ) ) ) )
% 13.77/7.85 @ zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8874_less__char__simp,axiom,
% 13.77/7.85 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o,C0: $o,C1: $o,C22: $o,C32: $o,C42: $o,C52: $o,C62: $o,C7: $o] :
% 13.77/7.85 ( ( ord_less_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) @ ( char2 @ C0 @ C1 @ C22 @ C32 @ C42 @ C52 @ C62 @ C7 ) )
% 13.77/7.85 = ( ord_less_nat
% 13.77/7.85 @ ( foldr_o_nat
% 13.77/7.85 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.85 @ ( cons_o @ B0 @ ( cons_o @ B1 @ ( cons_o @ B22 @ ( cons_o @ B32 @ ( cons_o @ B42 @ ( cons_o @ B52 @ ( cons_o @ B62 @ ( cons_o @ B72 @ nil_o ) ) ) ) ) ) ) )
% 13.77/7.85 @ zero_zero_nat )
% 13.77/7.85 @ ( foldr_o_nat
% 13.77/7.85 @ ^ [B7: $o,K3: nat] : ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B7 ) @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 13.77/7.85 @ ( cons_o @ C0 @ ( cons_o @ C1 @ ( cons_o @ C22 @ ( cons_o @ C32 @ ( cons_o @ C42 @ ( cons_o @ C52 @ ( cons_o @ C62 @ ( cons_o @ C7 @ nil_o ) ) ) ) ) ) ) )
% 13.77/7.85 @ zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8875_card_Ocomp__fun__commute__on,axiom,
% 13.77/7.85 ( ( comp_nat_nat_nat @ suc @ suc )
% 13.77/7.85 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8876_infinite__int__iff__infinite__nat__abs,axiom,
% 13.77/7.85 ! [S3: set_int] :
% 13.77/7.85 ( ( ~ ( finite_finite_int @ S3 ) )
% 13.77/7.85 = ( ~ ( finite_finite_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ S3 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8877_Code__Numeral_Onegative__def,axiom,
% 13.77/7.85 ( code_negative
% 13.77/7.85 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8878_divmod__integer__eq__cases,axiom,
% 13.77/7.85 ( code_divmod_integer
% 13.77/7.85 = ( ^ [K3: code_integer,L4: code_integer] :
% 13.77/7.85 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 13.77/7.85 @ ( if_Pro6119634080678213985nteger @ ( L4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 13.77/7.85 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L4
% 13.77/7.85 @ ( if_Pro6119634080678213985nteger
% 13.77/7.85 @ ( ( sgn_sgn_Code_integer @ K3 )
% 13.77/7.85 = ( sgn_sgn_Code_integer @ L4 ) )
% 13.77/7.85 @ ( code_divmod_abs @ K3 @ L4 )
% 13.77/7.85 @ ( produc6916734918728496179nteger
% 13.77/7.85 @ ^ [R5: code_integer,S8: code_integer] : ( if_Pro6119634080678213985nteger @ ( S8 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L4 ) @ S8 ) ) )
% 13.77/7.85 @ ( code_divmod_abs @ K3 @ L4 ) ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8879_divmod__abs__code_I6_J,axiom,
% 13.77/7.85 ! [J: code_integer] :
% 13.77/7.85 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 13.77/7.85 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8880_divmod__abs__code_I5_J,axiom,
% 13.77/7.85 ! [J: code_integer] :
% 13.77/7.85 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 13.77/7.85 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8881_divmod__integer__code,axiom,
% 13.77/7.85 ( code_divmod_integer
% 13.77/7.85 = ( ^ [K3: code_integer,L4: code_integer] :
% 13.77/7.85 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 13.77/7.85 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L4 )
% 13.77/7.85 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L4 )
% 13.77/7.85 @ ( produc6916734918728496179nteger
% 13.77/7.85 @ ^ [R5: code_integer,S8: code_integer] : ( if_Pro6119634080678213985nteger @ ( S8 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L4 @ S8 ) ) )
% 13.77/7.85 @ ( code_divmod_abs @ K3 @ L4 ) ) )
% 13.77/7.85 @ ( if_Pro6119634080678213985nteger @ ( L4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 13.77/7.85 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 13.77/7.85 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L4 )
% 13.77/7.85 @ ( produc6916734918728496179nteger
% 13.77/7.85 @ ^ [R5: code_integer,S8: code_integer] : ( if_Pro6119634080678213985nteger @ ( S8 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L4 ) @ S8 ) ) )
% 13.77/7.85 @ ( code_divmod_abs @ K3 @ L4 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8882_divmod__abs__def,axiom,
% 13.77/7.85 ( code_divmod_abs
% 13.77/7.85 = ( ^ [K3: code_integer,L4: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L4 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L4 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8883_bit__cut__integer__code,axiom,
% 13.77/7.85 ( code_bit_cut_integer
% 13.77/7.85 = ( ^ [K3: code_integer] :
% 13.77/7.85 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 13.77/7.85 @ ( produc9125791028180074456eger_o
% 13.77/7.85 @ ^ [R5: code_integer,S8: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S8 ) ) @ ( S8 = one_one_Code_integer ) )
% 13.77/7.85 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8884_bit__cut__integer__def,axiom,
% 13.77/7.85 ( code_bit_cut_integer
% 13.77/7.85 = ( ^ [K3: code_integer] :
% 13.77/7.85 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 13.77/7.85 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8885_len__num0,axiom,
% 13.77/7.85 ( type_l4264026598287037464l_num0
% 13.77/7.85 = ( ^ [Uu4: itself_Numeral_num0] : zero_zero_nat ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8886_smod__int__compares_I3_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.85 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.85 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8887_smod__int__compares_I5_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.85 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.85 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A @ B ) @ ( uminus_uminus_int @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8888_smod__int__compares_I1_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.85 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.85 => ( ord_less_int @ ( signed6292675348222524329lo_int @ A @ B ) @ B ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8889_smod__int__compares_I2_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.85 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.85 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8890_smod__int__compares_I4_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.85 => ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.85 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8891_smod__int__compares_I6_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.85 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.85 => ( ord_less_eq_int @ zero_zero_int @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8892_smod__int__compares_I7_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.85 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.85 => ( ord_less_eq_int @ ( signed6292675348222524329lo_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8893_smod__int__compares_I8_J,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 13.77/7.85 => ( ( ord_less_int @ B @ zero_zero_int )
% 13.77/7.85 => ( ord_less_eq_int @ B @ ( signed6292675348222524329lo_int @ A @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8894_smod__mod__positive,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 13.77/7.85 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 13.77/7.85 => ( ( signed6292675348222524329lo_int @ A @ B )
% 13.77/7.85 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8895_min__Suc__Suc,axiom,
% 13.77/7.85 ! [M: nat,N: nat] :
% 13.77/7.85 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 13.77/7.85 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8896_min__0R,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( ord_min_nat @ N @ zero_zero_nat )
% 13.77/7.85 = zero_zero_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8897_min__0L,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( ord_min_nat @ zero_zero_nat @ N )
% 13.77/7.85 = zero_zero_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8898_min__Suc__gt_I2_J,axiom,
% 13.77/7.85 ! [A: nat,B: nat] :
% 13.77/7.85 ( ( ord_less_nat @ A @ B )
% 13.77/7.85 => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 13.77/7.85 = ( suc @ A ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8899_min__Suc__gt_I1_J,axiom,
% 13.77/7.85 ! [A: nat,B: nat] :
% 13.77/7.85 ( ( ord_less_nat @ A @ B )
% 13.77/7.85 => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 13.77/7.85 = ( suc @ A ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8900_nat__mult__min__left,axiom,
% 13.77/7.85 ! [M: nat,N: nat,Q3: nat] :
% 13.77/7.85 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 13.77/7.85 = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8901_nat__mult__min__right,axiom,
% 13.77/7.85 ! [M: nat,N: nat,Q3: nat] :
% 13.77/7.85 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 13.77/7.85 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8902_inf__nat__def,axiom,
% 13.77/7.85 inf_inf_nat = ord_min_nat ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8903_min__diff,axiom,
% 13.77/7.85 ! [M: nat,I: nat,N: nat] :
% 13.77/7.85 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 13.77/7.85 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8904_int__of__integer__min,axiom,
% 13.77/7.85 ! [K: code_integer,L: code_integer] :
% 13.77/7.85 ( ( code_int_of_integer @ ( ord_min_Code_integer @ K @ L ) )
% 13.77/7.85 = ( ord_min_int @ ( code_int_of_integer @ K ) @ ( code_int_of_integer @ L ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8905_drop__bit__nonnegative__int__iff,axiom,
% 13.77/7.85 ! [N: nat,K: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 13.77/7.85 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8906_drop__bit__negative__int__iff,axiom,
% 13.77/7.85 ! [N: nat,K: int] :
% 13.77/7.85 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 13.77/7.85 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8907_drop__bit__Suc__minus__bit0,axiom,
% 13.77/7.85 ! [N: nat,K: num] :
% 13.77/7.85 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 13.77/7.85 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8908_drop__bit__Suc__minus__bit1,axiom,
% 13.77/7.85 ! [N: nat,K: num] :
% 13.77/7.85 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 13.77/7.85 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8909_drop__bit__of__Suc__0,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 13.77/7.85 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8910_drop__bit__integer_Oabs__eq,axiom,
% 13.77/7.85 ! [Xa2: nat,X: int] :
% 13.77/7.85 ( ( bit_se3928097537394005634nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 13.77/7.85 = ( code_integer_of_int @ ( bit_se8568078237143864401it_int @ Xa2 @ X ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8911_drop__bit__integer_Orep__eq,axiom,
% 13.77/7.85 ! [X: nat,Xa2: code_integer] :
% 13.77/7.85 ( ( code_int_of_integer @ ( bit_se3928097537394005634nteger @ X @ Xa2 ) )
% 13.77/7.85 = ( bit_se8568078237143864401it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8912_mask__nat__positive__iff,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 13.77/7.85 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8913_push__bit__nonnegative__int__iff,axiom,
% 13.77/7.85 ! [N: nat,K: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 13.77/7.85 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8914_push__bit__negative__int__iff,axiom,
% 13.77/7.85 ! [N: nat,K: int] :
% 13.77/7.85 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 13.77/7.85 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8915_push__bit__of__Suc__0,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 13.77/7.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8916_bit__push__bit__iff__int,axiom,
% 13.77/7.85 ! [M: nat,K: int,N: nat] :
% 13.77/7.85 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 13.77/7.85 = ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.85 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8917_not__mask__negative__int,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8918_mask__nonnegative__int,axiom,
% 13.77/7.85 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8919_less__eq__mask,axiom,
% 13.77/7.85 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8920_mask__integer_Orep__eq,axiom,
% 13.77/7.85 ! [X: nat] :
% 13.77/7.85 ( ( code_int_of_integer @ ( bit_se2119862282449309892nteger @ X ) )
% 13.77/7.85 = ( bit_se2000444600071755411sk_int @ X ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8921_push__bit__integer_Orep__eq,axiom,
% 13.77/7.85 ! [X: nat,Xa2: code_integer] :
% 13.77/7.85 ( ( code_int_of_integer @ ( bit_se7788150548672797655nteger @ X @ Xa2 ) )
% 13.77/7.85 = ( bit_se545348938243370406it_int @ X @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8922_mask__integer_Oabs__eq,axiom,
% 13.77/7.85 ( bit_se2119862282449309892nteger
% 13.77/7.85 = ( ^ [X4: nat] : ( code_integer_of_int @ ( bit_se2000444600071755411sk_int @ X4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8923_push__bit__integer_Oabs__eq,axiom,
% 13.77/7.85 ! [Xa2: nat,X: int] :
% 13.77/7.85 ( ( bit_se7788150548672797655nteger @ Xa2 @ ( code_integer_of_int @ X ) )
% 13.77/7.85 = ( code_integer_of_int @ ( bit_se545348938243370406it_int @ Xa2 @ X ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8924_less__mask,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.85 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8925_bit__push__bit__iff__nat,axiom,
% 13.77/7.85 ! [M: nat,Q3: nat,N: nat] :
% 13.77/7.85 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 13.77/7.85 = ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.85 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8926_Suc__mask__eq__exp,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 13.77/7.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8927_mask__nat__less__exp,axiom,
% 13.77/7.85 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8928_and__nonnegative__int__iff,axiom,
% 13.77/7.85 ! [K: int,L: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 13.77/7.85 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 13.77/7.85 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8929_and__negative__int__iff,axiom,
% 13.77/7.85 ! [K: int,L: int] :
% 13.77/7.85 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 13.77/7.85 = ( ( ord_less_int @ K @ zero_zero_int )
% 13.77/7.85 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8930_AND__upper2_H_H,axiom,
% 13.77/7.85 ! [Y: int,Z: int,X: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( ( ord_less_int @ Y @ Z )
% 13.77/7.85 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8931_AND__upper1_H_H,axiom,
% 13.77/7.85 ! [Y: int,Z: int,Ya: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( ( ord_less_int @ Y @ Z )
% 13.77/7.85 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8932_and__less__eq,axiom,
% 13.77/7.85 ! [L: int,K: int] :
% 13.77/7.85 ( ( ord_less_int @ L @ zero_zero_int )
% 13.77/7.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8933_AND__upper2_H,axiom,
% 13.77/7.85 ! [Y: int,Z: int,X: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( ( ord_less_eq_int @ Y @ Z )
% 13.77/7.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8934_AND__upper1_H,axiom,
% 13.77/7.85 ! [Y: int,Z: int,Ya: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( ( ord_less_eq_int @ Y @ Z )
% 13.77/7.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8935_AND__upper2,axiom,
% 13.77/7.85 ! [Y: int,X: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8936_AND__upper1,axiom,
% 13.77/7.85 ! [X: int,Y: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.85 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8937_AND__lower,axiom,
% 13.77/7.85 ! [X: int,Y: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.85 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8938_drop__bit__int__code_I2_J,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ zero_zero_int )
% 13.77/7.85 = zero_zero_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8939_and__nat__numerals_I1_J,axiom,
% 13.77/7.85 ! [Y: num] :
% 13.77/7.85 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 13.77/7.85 = zero_zero_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8940_and__nat__numerals_I3_J,axiom,
% 13.77/7.85 ! [X: num] :
% 13.77/7.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.85 = zero_zero_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8941_and__nat__numerals_I4_J,axiom,
% 13.77/7.85 ! [X: num] :
% 13.77/7.85 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 13.77/7.85 = one_one_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8942_and__nat__numerals_I2_J,axiom,
% 13.77/7.85 ! [Y: num] :
% 13.77/7.85 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 13.77/7.85 = one_one_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8943_and__Suc__0__eq,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 13.77/7.85 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8944_Suc__0__and__eq,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.85 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8945_and__integer_Orep__eq,axiom,
% 13.77/7.85 ! [X: code_integer,Xa2: code_integer] :
% 13.77/7.85 ( ( code_int_of_integer @ ( bit_se3949692690581998587nteger @ X @ Xa2 ) )
% 13.77/7.85 = ( bit_se725231765392027082nd_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8946_and__integer_Oabs__eq,axiom,
% 13.77/7.85 ! [Xa2: int,X: int] :
% 13.77/7.85 ( ( bit_se3949692690581998587nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 13.77/7.85 = ( code_integer_of_int @ ( bit_se725231765392027082nd_int @ Xa2 @ X ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8947_and__nat__unfold,axiom,
% 13.77/7.85 ( bit_se727722235901077358nd_nat
% 13.77/7.85 = ( ^ [M5: nat,N6: nat] :
% 13.77/7.85 ( if_nat
% 13.77/7.85 @ ( ( M5 = zero_zero_nat )
% 13.77/7.85 | ( N6 = zero_zero_nat ) )
% 13.77/7.85 @ zero_zero_nat
% 13.77/7.85 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8948_drop__bit__int__code_I1_J,axiom,
% 13.77/7.85 ! [I: int] :
% 13.77/7.85 ( ( bit_se8568078237143864401it_int @ zero_zero_nat @ I )
% 13.77/7.85 = I ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8949_push__bit__int__code_I1_J,axiom,
% 13.77/7.85 ! [I: int] :
% 13.77/7.85 ( ( bit_se545348938243370406it_int @ zero_zero_nat @ I )
% 13.77/7.85 = I ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8950_not__negative__int__iff,axiom,
% 13.77/7.85 ! [K: int] :
% 13.77/7.85 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 13.77/7.85 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8951_not__nonnegative__int__iff,axiom,
% 13.77/7.85 ! [K: int] :
% 13.77/7.85 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 13.77/7.85 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8952_not__integer_Oabs__eq,axiom,
% 13.77/7.85 ! [X: int] :
% 13.77/7.85 ( ( bit_ri7632146776885996613nteger @ ( code_integer_of_int @ X ) )
% 13.77/7.85 = ( code_integer_of_int @ ( bit_ri7919022796975470100ot_int @ X ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8953_not__integer_Orep__eq,axiom,
% 13.77/7.85 ! [X: code_integer] :
% 13.77/7.85 ( ( code_int_of_integer @ ( bit_ri7632146776885996613nteger @ X ) )
% 13.77/7.85 = ( bit_ri7919022796975470100ot_int @ ( code_int_of_integer @ X ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8954_shiftl__Suc__0,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( bit_Sh3965577149348748681tl_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8955_shiftr__Suc__0,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( bit_Sh2154871086232339855tr_nat @ ( suc @ zero_zero_nat ) @ N )
% 13.77/7.85 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8956_not__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ bit_ri7919022796975470100ot_int
% 13.77/7.85 @ bit_ri7919022796975470100ot_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8957_xor__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se6526347334894502574or_int
% 13.77/7.85 @ bit_se6526347334894502574or_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8958_less__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re3403563459893282935_int_o
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5089333283451836215nt_o_o
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 13.77/7.85 @ ord_less_int
% 13.77/7.85 @ ord_less_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8959_less__eq__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re3403563459893282935_int_o
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5089333283451836215nt_o_o
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 13.77/7.85 @ ord_less_eq_int
% 13.77/7.85 @ ord_less_eq_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8960_minus__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ minus_minus_int
% 13.77/7.85 @ minus_minus_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8961_dup_Orsp,axiom,
% 13.77/7.85 ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
% 13.77/7.85 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8962_bit__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re3376528473927230327_nat_o
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat > $o,Z4: nat > $o] : ( Y6 = Z4 )
% 13.77/7.85 @ bit_se1146084159140164899it_int
% 13.77/7.85 @ bit_se1146084159140164899it_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8963_abs__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ abs_abs_int
% 13.77/7.85 @ abs_abs_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8964_sgn__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ sgn_sgn_int
% 13.77/7.85 @ sgn_sgn_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8965_natural__of__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re3715656647883201625at_nat
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ nat2
% 13.77/7.85 @ nat2 ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8966_divide__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ divide_divide_int
% 13.77/7.85 @ divide_divide_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8967_modulo__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ modulo_modulo_int
% 13.77/7.85 @ modulo_modulo_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8968_uminus__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ uminus_uminus_int
% 13.77/7.85 @ uminus_uminus_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8969_plus__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ plus_plus_int
% 13.77/7.85 @ plus_plus_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8970_times__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ times_times_int
% 13.77/7.85 @ times_times_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8971_or__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se1409905431419307370or_int
% 13.77/7.85 @ bit_se1409905431419307370or_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8972_and__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re711492959462206631nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se725231765392027082nd_int
% 13.77/7.85 @ bit_se725231765392027082nd_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8973_xor__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se6528837805403552850or_nat
% 13.77/7.85 @ bit_se6528837805403552850or_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8974_drop__bit__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4785983289428654063nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se8568078237143864401it_int
% 13.77/7.85 @ bit_se8568078237143864401it_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8975_drop__bit__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se8570568707652914677it_nat
% 13.77/7.85 @ bit_se8570568707652914677it_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8976_take__bit__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4785983289428654063nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se2923211474154528505it_int
% 13.77/7.85 @ bit_se2923211474154528505it_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8977_take__bit__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se2925701944663578781it_nat
% 13.77/7.85 @ bit_se2925701944663578781it_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8978_less__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re578469030762574527_nat_o
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4705727531993890431at_o_o
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 13.77/7.85 @ ord_less_nat
% 13.77/7.85 @ ord_less_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8979_less__eq__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re578469030762574527_nat_o
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4705727531993890431at_o_o
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 13.77/7.85 @ ord_less_eq_nat
% 13.77/7.85 @ ord_less_eq_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8980_inj__on__diff__nat,axiom,
% 13.77/7.85 ! [N8: set_nat,K: nat] :
% 13.77/7.85 ( ! [N2: nat] :
% 13.77/7.85 ( ( member_nat @ N2 @ N8 )
% 13.77/7.85 => ( ord_less_eq_nat @ K @ N2 ) )
% 13.77/7.85 => ( inj_on_nat_nat
% 13.77/7.85 @ ^ [N6: nat] : ( minus_minus_nat @ N6 @ K )
% 13.77/7.85 @ N8 ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8981_minus__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ minus_minus_nat
% 13.77/7.85 @ minus_minus_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8982_sub_Orsp,axiom,
% 13.77/7.85 ( bNF_re8402795839162346335um_int
% 13.77/7.85 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re1822329894187522285nt_int
% 13.77/7.85 @ ^ [Y6: num,Z4: num] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ ^ [M5: num,N6: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) )
% 13.77/7.85 @ ^ [M5: num,N6: num] : ( minus_minus_int @ ( numeral_numeral_int @ M5 ) @ ( numeral_numeral_int @ N6 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8983_bit__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re578469030762574527_nat_o
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat > $o,Z4: nat > $o] : ( Y6 = Z4 )
% 13.77/7.85 @ bit_se1148574629649215175it_nat
% 13.77/7.85 @ bit_se1148574629649215175it_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8984_unset__bit__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4785983289428654063nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se4203085406695923979it_int
% 13.77/7.85 @ bit_se4203085406695923979it_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8985_flip__bit__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4785983289428654063nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se2159334234014336723it_int
% 13.77/7.85 @ bit_se2159334234014336723it_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8986_inj__Suc,axiom,
% 13.77/7.85 ! [N8: set_nat] : ( inj_on_nat_nat @ suc @ N8 ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8987_Suc_Orsp,axiom,
% 13.77/7.85 ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ suc
% 13.77/7.85 @ suc ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8988_divide__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ divide_divide_nat
% 13.77/7.85 @ divide_divide_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8989_modulo__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ modulo_modulo_nat
% 13.77/7.85 @ modulo_modulo_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8990_Code__Numeral_Oset__bit__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4785983289428654063nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se7879613467334960850it_int
% 13.77/7.85 @ bit_se7879613467334960850it_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8991_plus__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ plus_plus_nat
% 13.77/7.85 @ plus_plus_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8992_times__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ times_times_nat
% 13.77/7.85 @ times_times_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8993_or__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se1412395901928357646or_nat
% 13.77/7.85 @ bit_se1412395901928357646or_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8994_integer__of__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re6650684261131312217nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ semiri1314217659103216013at_int
% 13.77/7.85 @ semiri1314217659103216013at_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8995_inj__on__set__encode,axiom,
% 13.77/7.85 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8996_mask__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re6650684261131312217nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ bit_se2000444600071755411sk_int
% 13.77/7.85 @ bit_se2000444600071755411sk_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8997_mask__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ bit_se2002935070580805687sk_nat
% 13.77/7.85 @ bit_se2002935070580805687sk_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8998_push__bit__integer_Orsp,axiom,
% 13.77/7.85 ( bNF_re4785983289428654063nt_int
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re4712519889275205905nt_int
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se545348938243370406it_int
% 13.77/7.85 @ bit_se545348938243370406it_int ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_8999_push__bit__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se547839408752420682it_nat
% 13.77/7.85 @ bit_se547839408752420682it_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9000_and__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se727722235901077358nd_nat
% 13.77/7.85 @ bit_se727722235901077358nd_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9001_summable__reindex,axiom,
% 13.77/7.85 ! [F: nat > real,G: nat > nat] :
% 13.77/7.85 ( ( summable_real @ F )
% 13.77/7.85 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 13.77/7.85 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 13.77/7.85 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9002_suminf__reindex__mono,axiom,
% 13.77/7.85 ! [F: nat > real,G: nat > nat] :
% 13.77/7.85 ( ( summable_real @ F )
% 13.77/7.85 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 13.77/7.85 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 13.77/7.85 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9003_suminf__reindex,axiom,
% 13.77/7.85 ! [F: nat > real,G: nat > nat] :
% 13.77/7.85 ( ( summable_real @ F )
% 13.77/7.85 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 13.77/7.85 => ( ! [X3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X3 ) )
% 13.77/7.85 => ( ! [X3: nat] :
% 13.77/7.85 ( ~ ( member_nat @ X3 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 13.77/7.85 => ( ( F @ X3 )
% 13.77/7.85 = zero_zero_real ) )
% 13.77/7.85 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 13.77/7.85 = ( suminf_real @ F ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9004_inj__sgn__power,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.85 => ( inj_on_real_real
% 13.77/7.85 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 13.77/7.85 @ top_top_set_real ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9005_unset__bit__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se4205575877204974255it_nat
% 13.77/7.85 @ bit_se4205575877204974255it_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9006_flip__bit__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se2161824704523386999it_nat
% 13.77/7.85 @ bit_se2161824704523386999it_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9007_set__bit__natural_Orsp,axiom,
% 13.77/7.85 ( bNF_re1345281282404953727at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5653821019739307937at_nat
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 13.77/7.85 @ bit_se7882103937844011126it_nat
% 13.77/7.85 @ bit_se7882103937844011126it_nat ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9008_integer__of__num_I3_J,axiom,
% 13.77/7.85 ! [N: num] :
% 13.77/7.85 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 13.77/7.85 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9009_integer__of__num__def,axiom,
% 13.77/7.85 code_integer_of_num = numera6620942414471956472nteger ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9010_integer__of__num__triv_I1_J,axiom,
% 13.77/7.85 ( ( code_integer_of_num @ one )
% 13.77/7.85 = one_one_Code_integer ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9011_integer__of__num_I2_J,axiom,
% 13.77/7.85 ! [N: num] :
% 13.77/7.85 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 13.77/7.85 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9012_integer__of__num__triv_I2_J,axiom,
% 13.77/7.85 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 13.77/7.85 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9013_hd__upt,axiom,
% 13.77/7.85 ! [I: nat,J: nat] :
% 13.77/7.85 ( ( ord_less_nat @ I @ J )
% 13.77/7.85 => ( ( hd_nat @ ( upt @ I @ J ) )
% 13.77/7.85 = I ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9014_Suc__0__div__numeral,axiom,
% 13.77/7.85 ! [K: num] :
% 13.77/7.85 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 13.77/7.85 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9015_fst__divmod__nat,axiom,
% 13.77/7.85 ! [M: nat,N: nat] :
% 13.77/7.85 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 13.77/7.85 = ( divide_divide_nat @ M @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9016_fst__divmod__integer,axiom,
% 13.77/7.85 ! [K: code_integer,L: code_integer] :
% 13.77/7.85 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 13.77/7.85 = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9017_fst__divmod__abs,axiom,
% 13.77/7.85 ! [K: code_integer,L: code_integer] :
% 13.77/7.85 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 13.77/7.85 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9018_bezw_Oelims,axiom,
% 13.77/7.85 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 13.77/7.85 ( ( ( bezw @ X @ Xa2 )
% 13.77/7.85 = Y )
% 13.77/7.85 => ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.85 => ( Y
% 13.77/7.85 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 13.77/7.85 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.85 => ( Y
% 13.77/7.85 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9019_bezw_Osimps,axiom,
% 13.77/7.85 ( bezw
% 13.77/7.85 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9020_bezw__non__0,axiom,
% 13.77/7.85 ! [Y: nat,X: nat] :
% 13.77/7.85 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 13.77/7.85 => ( ( bezw @ X @ Y )
% 13.77/7.85 = ( 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 ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9021_bezw_Opelims,axiom,
% 13.77/7.85 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 13.77/7.85 ( ( ( bezw @ X @ Xa2 )
% 13.77/7.85 = Y )
% 13.77/7.85 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 13.77/7.85 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.85 => ( Y
% 13.77/7.85 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 13.77/7.85 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.85 => ( Y
% 13.77/7.85 = ( 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 ) ) ) ) ) ) ) )
% 13.77/7.85 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9022_snd__divmod__nat,axiom,
% 13.77/7.85 ! [M: nat,N: nat] :
% 13.77/7.85 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 13.77/7.85 = ( modulo_modulo_nat @ M @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9023_snd__divmod__integer,axiom,
% 13.77/7.85 ! [K: code_integer,L: code_integer] :
% 13.77/7.85 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 13.77/7.85 = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9024_mod__pure,axiom,
% 13.77/7.85 ! [B: $o,H2: produc3658429121746597890et_nat] :
% 13.77/7.85 ( ( rep_assn @ ( pure_assn @ B ) @ H2 )
% 13.77/7.85 = ( ( ( produc8586169260539613262et_nat @ H2 )
% 13.77/7.85 = bot_bot_set_nat )
% 13.77/7.85 & B ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9025_snd__divmod__abs,axiom,
% 13.77/7.85 ! [K: code_integer,L: code_integer] :
% 13.77/7.85 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 13.77/7.85 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9026_Suc__0__mod__numeral,axiom,
% 13.77/7.85 ! [K: num] :
% 13.77/7.85 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 13.77/7.85 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9027_mod__emp,axiom,
% 13.77/7.85 ! [H2: produc3658429121746597890et_nat] :
% 13.77/7.85 ( ( rep_assn @ one_one_assn @ H2 )
% 13.77/7.85 = ( ( produc8586169260539613262et_nat @ H2 )
% 13.77/7.85 = bot_bot_set_nat ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9028_mod__star__trueE_H,axiom,
% 13.77/7.85 ! [P2: assn,H2: produc3658429121746597890et_nat] :
% 13.77/7.85 ( ( rep_assn @ ( times_times_assn @ P2 @ top_top_assn ) @ H2 )
% 13.77/7.85 => ~ ! [H5: produc3658429121746597890et_nat] :
% 13.77/7.85 ( ( ( produc1824681642469235216et_nat @ H5 )
% 13.77/7.85 = ( produc1824681642469235216et_nat @ H2 ) )
% 13.77/7.85 => ( ( ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ H5 ) @ ( produc8586169260539613262et_nat @ H2 ) )
% 13.77/7.85 => ~ ( rep_assn @ P2 @ H5 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9029_one__mod__minus__numeral,axiom,
% 13.77/7.85 ! [N: num] :
% 13.77/7.85 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.85 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9030_minus__one__mod__numeral,axiom,
% 13.77/7.85 ! [N: num] :
% 13.77/7.85 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.85 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9031_numeral__mod__minus__numeral,axiom,
% 13.77/7.85 ! [M: num,N: num] :
% 13.77/7.85 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 13.77/7.85 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9032_minus__numeral__mod__numeral,axiom,
% 13.77/7.85 ! [M: num,N: num] :
% 13.77/7.85 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 13.77/7.85 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9033_Divides_Oadjust__mod__def,axiom,
% 13.77/7.85 ( adjust_mod
% 13.77/7.85 = ( ^ [L4: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L4 @ R5 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9034_normalize__def,axiom,
% 13.77/7.85 ( normalize
% 13.77/7.85 = ( ^ [P7: product_prod_int_int] :
% 13.77/7.85 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P7 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P7 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P7 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) )
% 13.77/7.85 @ ( if_Pro3027730157355071871nt_int
% 13.77/7.85 @ ( ( product_snd_int_int @ P7 )
% 13.77/7.85 = zero_zero_int )
% 13.77/7.85 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 13.77/7.85 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P7 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P7 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9035_gcd__pos__int,axiom,
% 13.77/7.85 ! [M: int,N: int] :
% 13.77/7.85 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 13.77/7.85 = ( ( M != zero_zero_int )
% 13.77/7.85 | ( N != zero_zero_int ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9036_gcd__le1__int,axiom,
% 13.77/7.85 ! [A: int,B: int] :
% 13.77/7.85 ( ( ord_less_int @ zero_zero_int @ A )
% 13.77/7.85 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9037_gcd__le2__int,axiom,
% 13.77/7.85 ! [B: int,A: int] :
% 13.77/7.85 ( ( ord_less_int @ zero_zero_int @ B )
% 13.77/7.85 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9038_gcd__cases__int,axiom,
% 13.77/7.85 ! [X: int,Y: int,P2: int > $o] :
% 13.77/7.85 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.85 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( P2 @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 13.77/7.85 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 13.77/7.85 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 13.77/7.85 => ( P2 @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 13.77/7.85 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 13.77/7.85 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( P2 @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 13.77/7.85 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 13.77/7.85 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 13.77/7.85 => ( P2 @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 13.77/7.85 => ( P2 @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9039_gcd__ge__0__int,axiom,
% 13.77/7.85 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9040_gcd__unique__int,axiom,
% 13.77/7.85 ! [D: int,A: int,B: int] :
% 13.77/7.85 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 13.77/7.85 & ( dvd_dvd_int @ D @ A )
% 13.77/7.85 & ( dvd_dvd_int @ D @ B )
% 13.77/7.85 & ! [E3: int] :
% 13.77/7.85 ( ( ( dvd_dvd_int @ E3 @ A )
% 13.77/7.85 & ( dvd_dvd_int @ E3 @ B ) )
% 13.77/7.85 => ( dvd_dvd_int @ E3 @ D ) ) )
% 13.77/7.85 = ( D
% 13.77/7.85 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9041_gcd__non__0__int,axiom,
% 13.77/7.85 ! [Y: int,X: int] :
% 13.77/7.85 ( ( ord_less_int @ zero_zero_int @ Y )
% 13.77/7.85 => ( ( gcd_gcd_int @ X @ Y )
% 13.77/7.85 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9042_integer__set__bit__code,axiom,
% 13.77/7.85 ( bits_integer_set_bit
% 13.77/7.85 = ( ^ [X4: code_integer,N6: code_integer,B7: $o] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi1878487536576149250nteger @ X4 @ N6 @ B7 ) @ ( if_Code_integer @ B7 @ ( bit_se1080825931792720795nteger @ X4 @ ( bit_se7788150548672797655nteger @ ( code_nat_of_integer @ N6 ) @ one_one_Code_integer ) ) @ ( bit_se3949692690581998587nteger @ X4 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ ( code_nat_of_integer @ N6 ) @ one_one_Code_integer ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9043_gcd__nat_Oeq__neutr__iff,axiom,
% 13.77/7.85 ! [A: nat,B: nat] :
% 13.77/7.85 ( ( ( gcd_gcd_nat @ A @ B )
% 13.77/7.85 = zero_zero_nat )
% 13.77/7.85 = ( ( A = zero_zero_nat )
% 13.77/7.85 & ( B = zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9044_gcd__nat_Oleft__neutral,axiom,
% 13.77/7.85 ! [A: nat] :
% 13.77/7.85 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 13.77/7.85 = A ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9045_gcd__nat_Oneutr__eq__iff,axiom,
% 13.77/7.85 ! [A: nat,B: nat] :
% 13.77/7.85 ( ( zero_zero_nat
% 13.77/7.85 = ( gcd_gcd_nat @ A @ B ) )
% 13.77/7.85 = ( ( A = zero_zero_nat )
% 13.77/7.85 & ( B = zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9046_gcd__nat_Oright__neutral,axiom,
% 13.77/7.85 ! [A: nat] :
% 13.77/7.85 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 13.77/7.85 = A ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9047_gcd__0__nat,axiom,
% 13.77/7.85 ! [X: nat] :
% 13.77/7.85 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9048_gcd__0__left__nat,axiom,
% 13.77/7.85 ! [X: nat] :
% 13.77/7.85 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9049_gcd__Suc__0,axiom,
% 13.77/7.85 ! [M: nat] :
% 13.77/7.85 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 13.77/7.85 = ( suc @ zero_zero_nat ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9050_gcd__pos__nat,axiom,
% 13.77/7.85 ! [M: nat,N: nat] :
% 13.77/7.85 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 13.77/7.85 = ( ( M != zero_zero_nat )
% 13.77/7.85 | ( N != zero_zero_nat ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9051_Gcd__in,axiom,
% 13.77/7.85 ! [A4: set_nat] :
% 13.77/7.85 ( ! [A3: nat,B3: nat] :
% 13.77/7.85 ( ( member_nat @ A3 @ A4 )
% 13.77/7.85 => ( ( member_nat @ B3 @ A4 )
% 13.77/7.85 => ( member_nat @ ( gcd_gcd_nat @ A3 @ B3 ) @ A4 ) ) )
% 13.77/7.85 => ( ( A4 != bot_bot_set_nat )
% 13.77/7.85 => ( member_nat @ ( gcd_Gcd_nat @ A4 ) @ A4 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9052_bezout__gcd__nat_H,axiom,
% 13.77/7.85 ! [B: nat,A: nat] :
% 13.77/7.85 ? [X3: nat,Y3: nat] :
% 13.77/7.85 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 13.77/7.85 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 13.77/7.85 = ( gcd_gcd_nat @ A @ B ) ) )
% 13.77/7.85 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 13.77/7.85 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 13.77/7.85 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9053_gcd__le2__nat,axiom,
% 13.77/7.85 ! [B: nat,A: nat] :
% 13.77/7.85 ( ( B != zero_zero_nat )
% 13.77/7.85 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9054_gcd__le1__nat,axiom,
% 13.77/7.85 ! [A: nat,B: nat] :
% 13.77/7.85 ( ( A != zero_zero_nat )
% 13.77/7.85 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9055_gcd__diff1__nat,axiom,
% 13.77/7.85 ! [N: nat,M: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ N @ M )
% 13.77/7.85 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 13.77/7.85 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9056_gcd__diff2__nat,axiom,
% 13.77/7.85 ! [M: nat,N: nat] :
% 13.77/7.85 ( ( ord_less_eq_nat @ M @ N )
% 13.77/7.85 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 13.77/7.85 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9057_bezout__nat,axiom,
% 13.77/7.85 ! [A: nat,B: nat] :
% 13.77/7.85 ( ( A != zero_zero_nat )
% 13.77/7.85 => ? [X3: nat,Y3: nat] :
% 13.77/7.85 ( ( times_times_nat @ A @ X3 )
% 13.77/7.85 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9058_gcd__nat_Oelims,axiom,
% 13.77/7.85 ! [X: nat,Xa2: nat,Y: nat] :
% 13.77/7.85 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 13.77/7.85 = Y )
% 13.77/7.85 => ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.85 => ( Y = X ) )
% 13.77/7.85 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.85 => ( Y
% 13.77/7.85 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9059_gcd__nat_Osimps,axiom,
% 13.77/7.85 ( gcd_gcd_nat
% 13.77/7.85 = ( ^ [X4: nat,Y4: nat] : ( if_nat @ ( Y4 = zero_zero_nat ) @ X4 @ ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9060_gcd__non__0__nat,axiom,
% 13.77/7.85 ! [Y: nat,X: nat] :
% 13.77/7.85 ( ( Y != zero_zero_nat )
% 13.77/7.85 => ( ( gcd_gcd_nat @ X @ Y )
% 13.77/7.85 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9061_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 13.77/7.85 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 13.77/7.85 @ ^ [M5: nat,N6: nat] :
% 13.77/7.85 ( ( dvd_dvd_nat @ M5 @ N6 )
% 13.77/7.85 & ( M5 != N6 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9062_gcd__is__Max__divisors__nat,axiom,
% 13.77/7.85 ! [N: nat,M: nat] :
% 13.77/7.85 ( ( ord_less_nat @ zero_zero_nat @ N )
% 13.77/7.85 => ( ( gcd_gcd_nat @ M @ N )
% 13.77/7.85 = ( lattic8265883725875713057ax_nat
% 13.77/7.85 @ ( collect_nat
% 13.77/7.85 @ ^ [D5: nat] :
% 13.77/7.85 ( ( dvd_dvd_nat @ D5 @ M )
% 13.77/7.85 & ( dvd_dvd_nat @ D5 @ N ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9063_gcd__nat_Opelims,axiom,
% 13.77/7.85 ! [X: nat,Xa2: nat,Y: nat] :
% 13.77/7.85 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 13.77/7.85 = Y )
% 13.77/7.85 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 13.77/7.85 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 13.77/7.85 => ( Y = X ) )
% 13.77/7.85 & ( ( Xa2 != zero_zero_nat )
% 13.77/7.85 => ( Y
% 13.77/7.85 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 13.77/7.85 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9064_uint32__shiftl__def,axiom,
% 13.77/7.85 ( uint32_shiftl
% 13.77/7.85 = ( ^ [X4: uint32,N6: code_integer] :
% 13.77/7.85 ( if_uint32
% 13.77/7.85 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N6 ) )
% 13.77/7.85 @ ( undefi8952517107220742160uint32 @ bit_se5742574853984576102uint32 @ X4 @ N6 )
% 13.77/7.85 @ ( bit_se5742574853984576102uint32 @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9065_uint32__shiftr__def,axiom,
% 13.77/7.85 ( uint32_shiftr
% 13.77/7.85 = ( ^ [X4: uint32,N6: code_integer] :
% 13.77/7.85 ( if_uint32
% 13.77/7.85 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N6 ) )
% 13.77/7.85 @ ( undefi8952517107220742160uint32 @ bit_se3964402333458159761uint32 @ X4 @ N6 )
% 13.77/7.85 @ ( bit_se3964402333458159761uint32 @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9066_uint32__test__bit__def,axiom,
% 13.77/7.85 ( uint32_test_bit
% 13.77/7.85 = ( ^ [X4: uint32,N6: code_integer] :
% 13.77/7.85 ( ( ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 13.77/7.85 => ( undefi6981832269580975664eger_o @ bit_se5367290876889521763uint32 @ X4 @ N6 ) )
% 13.77/7.85 & ( ~ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 13.77/7.85 => ( bit_se5367290876889521763uint32 @ X4 @ ( code_nat_of_integer @ N6 ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9067_integer__set__bit__def,axiom,
% 13.77/7.85 ( bits_integer_set_bit
% 13.77/7.85 = ( ^ [X4: code_integer,N6: code_integer,B7: $o] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi1878487536576149250nteger @ X4 @ N6 @ B7 ) @ ( generi2397576812484419408nteger @ X4 @ ( code_nat_of_integer @ N6 ) @ B7 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9068_uint32__shiftr__code,axiom,
% 13.77/7.85 ! [N: code_integer,W2: uint32] :
% 13.77/7.85 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_shiftr @ W2 @ N ) )
% 13.77/7.85 = ( rep_uint32 @ ( undefi8952517107220742160uint32 @ bit_se3964402333458159761uint32 @ W2 @ N ) ) ) )
% 13.77/7.85 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_shiftr @ W2 @ N ) )
% 13.77/7.85 = ( bit_se5176125413884933531l_num1 @ ( code_nat_of_integer @ N ) @ ( rep_uint32 @ W2 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9069_uint32_Oless__iff__word__of,axiom,
% 13.77/7.85 ( ord_less_uint32
% 13.77/7.85 = ( ^ [P7: uint32,Q8: uint32] : ( ord_le750835935415966154l_num1 @ ( rep_uint32 @ P7 ) @ ( rep_uint32 @ Q8 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9070_less__uint32_Orep__eq,axiom,
% 13.77/7.85 ( ord_less_uint32
% 13.77/7.85 = ( ^ [X4: uint32,Xa4: uint32] : ( ord_le750835935415966154l_num1 @ ( rep_uint32 @ X4 ) @ ( rep_uint32 @ Xa4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9071_uint32_Oless__eq__iff__word__of,axiom,
% 13.77/7.85 ( ord_less_eq_uint32
% 13.77/7.85 = ( ^ [P7: uint32,Q8: uint32] : ( ord_le3335648743751981014l_num1 @ ( rep_uint32 @ P7 ) @ ( rep_uint32 @ Q8 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9072_less__eq__uint32_Orep__eq,axiom,
% 13.77/7.85 ( ord_less_eq_uint32
% 13.77/7.85 = ( ^ [X4: uint32,Xa4: uint32] : ( ord_le3335648743751981014l_num1 @ ( rep_uint32 @ X4 ) @ ( rep_uint32 @ Xa4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9073_uint32__test__bit__code,axiom,
% 13.77/7.85 ( uint32_test_bit
% 13.77/7.85 = ( ^ [W3: uint32,N6: code_integer] :
% 13.77/7.85 ( ( ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 13.77/7.85 => ( undefi6981832269580975664eger_o @ bit_se5367290876889521763uint32 @ W3 @ N6 ) )
% 13.77/7.85 & ( ~ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 13.77/7.85 => ( bit_se6859397288646540909l_num1 @ ( rep_uint32 @ W3 ) @ ( code_nat_of_integer @ N6 ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9074_uint32__shiftl__code,axiom,
% 13.77/7.85 ! [N: code_integer,W2: uint32] :
% 13.77/7.85 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_shiftl @ W2 @ N ) )
% 13.77/7.85 = ( rep_uint32 @ ( undefi8952517107220742160uint32 @ bit_se5742574853984576102uint32 @ W2 @ N ) ) ) )
% 13.77/7.85 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_shiftl @ W2 @ N ) )
% 13.77/7.85 = ( bit_se837345729053750000l_num1 @ ( code_nat_of_integer @ N ) @ ( rep_uint32 @ W2 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9075_integer__shiftl__def,axiom,
% 13.77/7.85 ( bits_integer_shiftl
% 13.77/7.85 = ( ^ [X4: code_integer,N6: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi8133104259855420269nteger @ X4 @ N6 ) @ ( bit_se7788150548672797655nteger @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9076_less__eq__uint32_Orsp,axiom,
% 13.77/7.85 ( bNF_re7364608769721783435num1_o
% 13.77/7.85 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5013357767504289739m1_o_o
% 13.77/7.85 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 13.77/7.85 @ ord_le3335648743751981014l_num1
% 13.77/7.85 @ ord_le3335648743751981014l_num1 ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9077_less__uint32_Orsp,axiom,
% 13.77/7.85 ( bNF_re7364608769721783435num1_o
% 13.77/7.85 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 13.77/7.85 @ ( bNF_re5013357767504289739m1_o_o
% 13.77/7.85 @ ^ [Y6: word_N3645301735248828278l_num1,Z4: word_N3645301735248828278l_num1] : ( Y6 = Z4 )
% 13.77/7.85 @ ^ [Y6: $o,Z4: $o] : ( Y6 = Z4 ) )
% 13.77/7.85 @ ord_le750835935415966154l_num1
% 13.77/7.85 @ ord_le750835935415966154l_num1 ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9078_uint32__set__bit__code,axiom,
% 13.77/7.85 ! [N: code_integer,W2: uint32,B: $o] :
% 13.77/7.85 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_set_bit @ W2 @ N @ B ) )
% 13.77/7.85 = ( rep_uint32 @ ( undefi8537048349889504752uint32 @ generi1993664874377053279uint32 @ W2 @ N @ B ) ) ) )
% 13.77/7.85 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_set_bit @ W2 @ N @ B ) )
% 13.77/7.85 = ( generi5268133209446125161l_num1 @ ( rep_uint32 @ W2 ) @ ( code_nat_of_integer @ N ) @ B ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9079_uint32__set__bit__def,axiom,
% 13.77/7.85 ( uint32_set_bit
% 13.77/7.85 = ( ^ [X4: uint32,N6: code_integer,B7: $o] :
% 13.77/7.85 ( if_uint32
% 13.77/7.85 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) @ N6 ) )
% 13.77/7.85 @ ( undefi8537048349889504752uint32 @ generi1993664874377053279uint32 @ X4 @ N6 @ B7 )
% 13.77/7.85 @ ( generi1993664874377053279uint32 @ X4 @ ( code_nat_of_integer @ N6 ) @ B7 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9080_integer__shiftr__def,axiom,
% 13.77/7.85 ( bits_integer_shiftr
% 13.77/7.85 = ( ^ [X4: code_integer,N6: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger ) @ ( undefi8133104259855420269nteger @ X4 @ N6 ) @ ( bit_se3928097537394005634nteger @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9081_uint32__divmod__code,axiom,
% 13.77/7.85 ( uint32_divmod
% 13.77/7.85 = ( ^ [X4: uint32,Y4: uint32] : ( if_Pro1135515155860407935uint32 @ ( ord_less_eq_uint32 @ ( numera9087168376688890119uint32 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ Y4 ) @ ( if_Pro1135515155860407935uint32 @ ( ord_less_uint32 @ X4 @ Y4 ) @ ( produc1400373151660368625uint32 @ zero_zero_uint32 @ X4 ) @ ( produc1400373151660368625uint32 @ one_one_uint32 @ ( minus_minus_uint32 @ X4 @ Y4 ) ) ) @ ( if_Pro1135515155860407935uint32 @ ( Y4 = zero_zero_uint32 ) @ ( produc1400373151660368625uint32 @ ( div0_uint32 @ X4 ) @ ( mod0_uint32 @ X4 ) ) @ ( if_Pro1135515155860407935uint32 @ ( ord_less_eq_uint32 @ Y4 @ ( minus_minus_uint32 @ X4 @ ( times_times_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ Y4 ) ) ) @ ( produc1400373151660368625uint32 @ ( plus_plus_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ one_one_uint32 ) @ ( minus_minus_uint32 @ ( minus_minus_uint32 @ X4 @ ( times_times_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ Y4 ) ) @ Y4 ) ) @ ( produc1400373151660368625uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ ( minus_minus_uint32 @ X4 @ ( times_times_uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ ( uint32_sdiv @ ( bit_se3964402333458159761uint32 @ one_one_nat @ X4 ) @ Y4 ) ) @ Y4 ) ) ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9082_uint32_Oset__bits__aux__code,axiom,
% 13.77/7.85 ( set_bits_aux_uint32
% 13.77/7.85 = ( ^ [F5: nat > $o,N6: nat,W3: uint32] : ( if_uint32 @ ( N6 = zero_zero_nat ) @ W3 @ ( set_bits_aux_uint32 @ F5 @ ( minus_minus_nat @ N6 @ one_one_nat ) @ ( bit_se2966626333419230250uint32 @ ( bit_se5742574853984576102uint32 @ one_one_nat @ W3 ) @ ( if_uint32 @ ( F5 @ ( minus_minus_nat @ N6 @ one_one_nat ) ) @ one_one_uint32 @ zero_zero_uint32 ) ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9083_shiftr__uint32__code,axiom,
% 13.77/7.85 ( bit_se3964402333458159761uint32
% 13.77/7.85 = ( ^ [N6: nat,X4: uint32] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_shiftr @ X4 @ ( code_integer_of_nat @ N6 ) ) @ zero_zero_uint32 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9084_nat__of__integer__integer__of__nat,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( code_nat_of_integer @ ( code_integer_of_nat @ N ) )
% 13.77/7.85 = N ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9085_integer__of__nat_Orep__eq,axiom,
% 13.77/7.85 ! [X: nat] :
% 13.77/7.85 ( ( code_int_of_integer @ ( code_integer_of_nat @ X ) )
% 13.77/7.85 = ( semiri1314217659103216013at_int @ X ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9086_int__of__integer__integer__of__nat,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ( ( code_int_of_integer @ ( code_integer_of_nat @ N ) )
% 13.77/7.85 = ( semiri1314217659103216013at_int @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9087_integer__of__nat__0,axiom,
% 13.77/7.85 ( ( code_integer_of_nat @ zero_zero_nat )
% 13.77/7.85 = zero_z3403309356797280102nteger ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9088_integer__of__nat__1,axiom,
% 13.77/7.85 ( ( code_integer_of_nat @ one_one_nat )
% 13.77/7.85 = one_one_Code_integer ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9089_integer__of__nat__less__0__conv,axiom,
% 13.77/7.85 ! [N: nat] :
% 13.77/7.85 ~ ( ord_le6747313008572928689nteger @ ( code_integer_of_nat @ N ) @ zero_z3403309356797280102nteger ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9090_integer__of__nat__eq__of__nat,axiom,
% 13.77/7.85 code_integer_of_nat = semiri4939895301339042750nteger ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9091_integer__of__nat_Oabs__eq,axiom,
% 13.77/7.85 ( code_integer_of_nat
% 13.77/7.85 = ( ^ [X4: nat] : ( code_integer_of_int @ ( semiri1314217659103216013at_int @ X4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9092_integer__of__nat__numeral,axiom,
% 13.77/7.85 ! [N: num] :
% 13.77/7.85 ( ( code_integer_of_nat @ ( numeral_numeral_nat @ N ) )
% 13.77/7.85 = ( numera6620942414471956472nteger @ N ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9093_test__bit__uint32__code,axiom,
% 13.77/7.85 ( bit_se5367290876889521763uint32
% 13.77/7.85 = ( ^ [X4: uint32,N6: nat] :
% 13.77/7.85 ( ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) )
% 13.77/7.85 & ( uint32_test_bit @ X4 @ ( code_integer_of_nat @ N6 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9094_set__bit__uint32__code,axiom,
% 13.77/7.85 ( generi1993664874377053279uint32
% 13.77/7.85 = ( ^ [X4: uint32,N6: nat,B7: $o] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_set_bit @ X4 @ ( code_integer_of_nat @ N6 ) @ B7 ) @ X4 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9095_shiftl__uint32__code,axiom,
% 13.77/7.85 ( bit_se5742574853984576102uint32
% 13.77/7.85 = ( ^ [N6: nat,X4: uint32] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_shiftl @ X4 @ ( code_integer_of_nat @ N6 ) ) @ zero_zero_uint32 ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9096_sshiftr__uint32__code,axiom,
% 13.77/7.85 ( signed489701013188660438uint32
% 13.77/7.85 = ( ^ [N6: nat,X4: uint32] : ( if_uint32 @ ( ord_less_nat @ N6 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) @ ( uint32_sshiftr @ X4 @ ( code_integer_of_nat @ N6 ) ) @ ( if_uint32 @ ( bit_se5367290876889521763uint32 @ X4 @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( uminus_uminus_uint32 @ one_one_uint32 ) @ zero_zero_uint32 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9097_uint32__sshiftr__def,axiom,
% 13.77/7.85 ( uint32_sshiftr
% 13.77/7.85 = ( ^ [X4: uint32,N6: code_integer] :
% 13.77/7.85 ( if_uint32
% 13.77/7.85 @ ( ( ord_le6747313008572928689nteger @ N6 @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N6 ) )
% 13.77/7.85 @ ( undefi7330133036835070352uint32 @ signed489701013188660438uint32 @ N6 @ X4 )
% 13.77/7.85 @ ( signed489701013188660438uint32 @ ( code_nat_of_integer @ N6 ) @ X4 ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(fact_9098_uint32__sshiftr__code,axiom,
% 13.77/7.85 ! [N: code_integer,W2: uint32] :
% 13.77/7.85 ( ( ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_sshiftr @ W2 @ N ) )
% 13.77/7.85 = ( rep_uint32 @ ( undefi7330133036835070352uint32 @ signed489701013188660438uint32 @ N @ W2 ) ) ) )
% 13.77/7.85 & ( ~ ( ( ord_le6747313008572928689nteger @ N @ zero_z3403309356797280102nteger )
% 13.77/7.85 | ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) @ N ) )
% 13.77/7.85 => ( ( rep_uint32 @ ( uint32_sshiftr @ W2 @ N ) )
% 13.77/7.85 = ( signed5000768011106662067l_num1 @ ( code_nat_of_integer @ N ) @ ( rep_uint32 @ W2 ) ) ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 13.77/7.85 ! [X: int,Y: int] :
% 13.77/7.85 ( ( if_int @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 13.77/7.85 ! [X: int,Y: int] :
% 13.77/7.85 ( ( if_int @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 13.77/7.85 ! [X: nat,Y: nat] :
% 13.77/7.85 ( ( if_nat @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 13.77/7.85 ! [X: nat,Y: nat] :
% 13.77/7.85 ( ( if_nat @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 13.77/7.85 ! [X: num,Y: num] :
% 13.77/7.85 ( ( if_num @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 13.77/7.85 ! [X: num,Y: num] :
% 13.77/7.85 ( ( if_num @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 13.77/7.85 ! [X: rat,Y: rat] :
% 13.77/7.85 ( ( if_rat @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 13.77/7.85 ! [X: rat,Y: rat] :
% 13.77/7.85 ( ( if_rat @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 13.77/7.85 ! [X: real,Y: real] :
% 13.77/7.85 ( ( if_real @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 13.77/7.85 ! [X: real,Y: real] :
% 13.77/7.85 ( ( if_real @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Uint32__Ouint32_T,axiom,
% 13.77/7.85 ! [X: uint32,Y: uint32] :
% 13.77/7.85 ( ( if_uint32 @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Uint32__Ouint32_T,axiom,
% 13.77/7.85 ! [X: uint32,Y: uint32] :
% 13.77/7.85 ( ( if_uint32 @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 13.77/7.85 ! [X: assn,Y: assn] :
% 13.77/7.85 ( ( if_assn @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 13.77/7.85 ! [X: assn,Y: assn] :
% 13.77/7.85 ( ( if_assn @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 13.77/7.85 ! [X: complex,Y: complex] :
% 13.77/7.85 ( ( if_complex @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 13.77/7.85 ! [X: complex,Y: complex] :
% 13.77/7.85 ( ( if_complex @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 13.77/7.85 ! [X: code_integer,Y: code_integer] :
% 13.77/7.85 ( ( if_Code_integer @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 13.77/7.85 ! [X: code_integer,Y: code_integer] :
% 13.77/7.85 ( ( if_Code_integer @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 13.77/7.85 ! [X: set_int,Y: set_int] :
% 13.77/7.85 ( ( if_set_int @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 13.77/7.85 ! [X: set_int,Y: set_int] :
% 13.77/7.85 ( ( if_set_int @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 13.77/7.85 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.85 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 13.77/7.85 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 13.77/7.85 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 13.77/7.85 ! [X: list_int,Y: list_int] :
% 13.77/7.85 ( ( if_list_int @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 13.77/7.85 ! [X: list_int,Y: list_int] :
% 13.77/7.85 ( ( if_list_int @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 13.77/7.85 ! [X: list_nat,Y: list_nat] :
% 13.77/7.85 ( ( if_list_nat @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 13.77/7.85 ! [X: list_nat,Y: list_nat] :
% 13.77/7.85 ( ( if_list_nat @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 13.77/7.85 ! [X: option_nat,Y: option_nat] :
% 13.77/7.85 ( ( if_option_nat @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 13.77/7.85 ! [X: option_nat,Y: option_nat] :
% 13.77/7.85 ( ( if_option_nat @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 13.77/7.85 ! [X: option_set_o,Y: option_set_o] :
% 13.77/7.85 ( ( if_option_set_o @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 13.77/7.85 ! [X: option_set_o,Y: option_set_o] :
% 13.77/7.85 ( ( if_option_set_o @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 13.77/7.85 ! [X: option_set_int,Y: option_set_int] :
% 13.77/7.85 ( ( if_option_set_int @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 13.77/7.85 ! [X: option_set_int,Y: option_set_int] :
% 13.77/7.85 ( ( if_option_set_int @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 13.77/7.85 ! [X: option_set_nat,Y: option_set_nat] :
% 13.77/7.85 ( ( if_option_set_nat @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 13.77/7.85 ! [X: option_set_nat,Y: option_set_nat] :
% 13.77/7.85 ( ( if_option_set_nat @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 13.77/7.85 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 13.77/7.85 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 13.77/7.85 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 13.77/7.85 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 13.77/7.85 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 13.77/7.85 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 13.77/7.85 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 13.77/7.85 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 13.77/7.85 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 13.77/7.85 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 13.77/7.85 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 13.77/7.85 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Uint32__Ouint32_Mt__Uint32__Ouint32_J_T,axiom,
% 13.77/7.85 ! [X: produc827990862158126777uint32,Y: produc827990862158126777uint32] :
% 13.77/7.85 ( ( if_Pro1135515155860407935uint32 @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Uint32__Ouint32_Mt__Uint32__Ouint32_J_T,axiom,
% 13.77/7.85 ! [X: produc827990862158126777uint32,Y: produc827990862158126777uint32] :
% 13.77/7.85 ( ( if_Pro1135515155860407935uint32 @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 13.77/7.85 ! [P2: $o] :
% 13.77/7.85 ( ( P2 = $true )
% 13.77/7.85 | ( P2 = $false ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 13.77/7.85 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 13.77/7.85 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 13.77/7.85 = Y ) ).
% 13.77/7.85
% 13.77/7.85 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 13.77/7.85 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 13.77/7.85 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 13.77/7.85 = X ) ).
% 13.77/7.85
% 13.77/7.85 thf(conj_0,hypothesis,
% 13.77/7.85 ( s
% 13.77/7.85 = ( vEBT_set_vebt @ t ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(conj_1,hypothesis,
% 13.77/7.85 vEBT_invar_vebt @ t @ n ).
% 13.77/7.85
% 13.77/7.85 thf(conj_2,hypothesis,
% 13.77/7.85 rep_assn @ ( vEBT_vebt_assn_raw @ ( vEBT_vebt_delete @ t @ x ) @ r ) @ ( produc7507926704131184380et_nat @ a @ b ) ).
% 13.77/7.85
% 13.77/7.85 thf(conj_3,hypothesis,
% 13.77/7.85 member_nat @ xa @ ( vEBT_set_vebt @ t ) ).
% 13.77/7.85
% 13.77/7.85 thf(conj_4,hypothesis,
% 13.77/7.85 ~ ( member_nat @ xa @ ( vEBT_set_vebt @ ( vEBT_vebt_delete @ t @ x ) ) ) ).
% 13.77/7.85
% 13.77/7.85 thf(conj_5,conjecture,
% 13.77/7.85 xa = x ).
% 13.77/7.85 ------------------------
% 14.51/8.67 % (8361)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_8220 for (2991ds/4Mi)
% 14.51/8.67 % (8362)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_8220 for (2991ds/27Mi)
% 14.51/8.67 % (8360)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/183Mi)
% 14.51/8.67 % (8363)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/2Mi)
% 14.51/8.67 % (8364)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_8220 for (2991ds/2Mi)
% 14.51/8.67 % (8365)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_8220 for (2991ds/275Mi)
% 14.51/8.67 % (8366)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/18Mi)
% 14.51/8.67 % (8363)Instruction limit reached!
% 14.51/8.67 % (8363)------------------------------
% 14.51/8.67 % (8363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/8.67 % (8363)Termination reason: Unknown
% 14.51/8.67 % (8363)Termination phase: shuffling
% 14.51/8.67
% 14.51/8.67 % (8363)Memory used [KB]: 14328
% 14.51/8.67 % (8363)Time elapsed: 0.004 s
% 14.51/8.67 % (8363)Instructions burned: 2 (million)
% 14.51/8.67 % (8363)------------------------------
% 14.51/8.67 % (8363)------------------------------
% 14.51/8.67 % (8364)Instruction limit reached!
% 14.51/8.67 % (8364)------------------------------
% 14.51/8.67 % (8364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/8.67 % (8364)Termination reason: Unknown
% 14.51/8.67 % (8364)Termination phase: shuffling
% 14.51/8.67
% 14.51/8.67 % (8364)Memory used [KB]: 14328
% 14.51/8.67 % (8364)Time elapsed: 0.003 s
% 14.51/8.67 % (8364)Instructions burned: 2 (million)
% 14.51/8.67 % (8364)------------------------------
% 14.51/8.67 % (8364)------------------------------
% 14.51/8.67 % (8361)Instruction limit reached!
% 14.51/8.67 % (8361)------------------------------
% 14.51/8.67 % (8361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/8.67 % (8361)Termination reason: Unknown
% 14.51/8.67 % (8361)Termination phase: shuffling
% 14.51/8.67
% 14.51/8.67 % (8361)Memory used [KB]: 14456
% 14.51/8.67 % (8361)Time elapsed: 0.006 s
% 14.51/8.67 % (8361)Instructions burned: 4 (million)
% 14.51/8.67 % (8361)------------------------------
% 14.51/8.67 % (8361)------------------------------
% 14.51/8.69 % (8366)Instruction limit reached!
% 14.51/8.69 % (8366)------------------------------
% 14.51/8.69 % (8366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/8.69 % (8366)Termination reason: Unknown
% 14.51/8.69 % (8366)Termination phase: shuffling
% 14.51/8.69
% 14.51/8.69 % (8366)Memory used [KB]: 15223
% 14.51/8.69 % (8366)Time elapsed: 0.020 s
% 14.51/8.69 % (8366)Instructions burned: 18 (million)
% 14.51/8.69 % (8366)------------------------------
% 14.51/8.69 % (8366)------------------------------
% 14.51/8.69 % (8368)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_8220 for (2991ds/37Mi)
% 14.51/8.69 % (8367)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/3Mi)
% 14.51/8.69 % (8369)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_8220 for (2991ds/15Mi)
% 14.51/8.69 % (8367)Instruction limit reached!
% 14.51/8.69 % (8367)------------------------------
% 14.51/8.69 % (8367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/8.69 % (8367)Termination reason: Unknown
% 14.51/8.69 % (8367)Termination phase: shuffling
% 14.51/8.69
% 14.51/8.69 % (8367)Memory used [KB]: 14456
% 14.51/8.69 % (8367)Time elapsed: 0.005 s
% 14.51/8.69 % (8367)Instructions burned: 3 (million)
% 14.51/8.69 % (8367)------------------------------
% 14.51/8.69 % (8367)------------------------------
% 14.51/8.69 % (8362)Instruction limit reached!
% 14.51/8.69 % (8362)------------------------------
% 14.51/8.69 % (8362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/8.69 % (8362)Termination reason: Unknown
% 14.51/8.69 % (8362)Termination phase: shuffling
% 14.51/8.69
% 14.51/8.69 % (8362)Memory used [KB]: 15351
% 14.51/8.69 % (8362)Time elapsed: 0.025 s
% 14.51/8.69 % (8362)Instructions burned: 27 (million)
% 14.51/8.69 % (8362)------------------------------
% 14.51/8.69 % (8362)------------------------------
% 14.73/8.71 % (8370)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_8220 for (2991ds/3Mi)
% 14.73/8.71 % (8369)Instruction limit reached!
% 14.73/8.71 % (8369)------------------------------
% 14.73/8.71 % (8369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.71 % (8369)Termination reason: Unknown
% 14.73/8.71 % (8369)Termination phase: shuffling
% 14.73/8.71
% 14.73/8.71 % (8369)Memory used [KB]: 15223
% 14.73/8.71 % (8369)Time elapsed: 0.018 s
% 14.73/8.71 % (8369)Instructions burned: 16 (million)
% 14.73/8.71 % (8369)------------------------------
% 14.73/8.71 % (8369)------------------------------
% 14.73/8.71 % (8370)Instruction limit reached!
% 14.73/8.71 % (8370)------------------------------
% 14.73/8.71 % (8370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.71 % (8370)Termination reason: Unknown
% 14.73/8.71 % (8370)Termination phase: shuffling
% 14.73/8.71
% 14.73/8.71 % (8370)Memory used [KB]: 14456
% 14.73/8.71 % (8370)Time elapsed: 0.005 s
% 14.73/8.71 % (8370)Instructions burned: 3 (million)
% 14.73/8.71 % (8370)------------------------------
% 14.73/8.71 % (8370)------------------------------
% 14.73/8.71 % (8371)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_8220 for (2991ds/1041Mi)
% 14.73/8.71 % (8372)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/7Mi)
% 14.73/8.72 % (8368)Instruction limit reached!
% 14.73/8.72 % (8368)------------------------------
% 14.73/8.72 % (8368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.72 % (8368)Termination reason: Unknown
% 14.73/8.72 % (8368)Termination phase: shuffling
% 14.73/8.72
% 14.73/8.72 % (8368)Memory used [KB]: 15607
% 14.73/8.72 % (8368)Time elapsed: 0.030 s
% 14.73/8.72 % (8368)Instructions burned: 38 (million)
% 14.73/8.72 % (8368)------------------------------
% 14.73/8.72 % (8368)------------------------------
% 14.73/8.72 % (8372)Instruction limit reached!
% 14.73/8.72 % (8372)------------------------------
% 14.73/8.72 % (8372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.72 % (8372)Termination reason: Unknown
% 14.73/8.72 % (8372)Termination phase: shuffling
% 14.73/8.72
% 14.73/8.72 % (8372)Memory used [KB]: 14711
% 14.73/8.72 % (8372)Time elapsed: 0.010 s
% 14.73/8.72 % (8372)Instructions burned: 7 (million)
% 14.73/8.72 % (8372)------------------------------
% 14.73/8.72 % (8372)------------------------------
% 14.73/8.73 % (8373)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/16Mi)
% 14.73/8.73 % (8374)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_8220 for (2991ds/3Mi)
% 14.73/8.73 % (8374)Instruction limit reached!
% 14.73/8.73 % (8374)------------------------------
% 14.73/8.73 % (8374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.73 % (8374)Termination reason: Unknown
% 14.73/8.73 % (8374)Termination phase: shuffling
% 14.73/8.73
% 14.73/8.73 % (8374)Memory used [KB]: 14456
% 14.73/8.73 % (8374)Time elapsed: 0.004 s
% 14.73/8.73 % (8374)Instructions burned: 3 (million)
% 14.73/8.73 % (8374)------------------------------
% 14.73/8.73 % (8374)------------------------------
% 14.73/8.74 % (8375)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_8220 for (2991ds/3Mi)
% 14.73/8.74 % (8376)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/7Mi)
% 14.73/8.74 % (8375)Instruction limit reached!
% 14.73/8.74 % (8375)------------------------------
% 14.73/8.74 % (8375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.74 % (8375)Termination reason: Unknown
% 14.73/8.74 % (8375)Termination phase: shuffling
% 14.73/8.74
% 14.73/8.74 % (8375)Memory used [KB]: 14456
% 14.73/8.74 % (8375)Time elapsed: 0.005 s
% 14.73/8.74 % (8375)Instructions burned: 3 (million)
% 14.73/8.74 % (8375)------------------------------
% 14.73/8.74 % (8375)------------------------------
% 14.73/8.74 % (8373)Instruction limit reached!
% 14.73/8.74 % (8373)------------------------------
% 14.73/8.74 % (8373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.74 % (8373)Termination reason: Unknown
% 14.73/8.74 % (8373)Termination phase: shuffling
% 14.73/8.74
% 14.73/8.74 % (8373)Memory used [KB]: 15223
% 14.73/8.74 % (8373)Time elapsed: 0.019 s
% 14.73/8.74 % (8373)Instructions burned: 16 (million)
% 14.73/8.74 % (8373)------------------------------
% 14.73/8.74 % (8373)------------------------------
% 14.73/8.74 % (8376)Instruction limit reached!
% 14.73/8.74 % (8376)------------------------------
% 14.73/8.74 % (8376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.74 % (8376)Termination reason: Unknown
% 14.73/8.74 % (8376)Termination phase: shuffling
% 14.73/8.74
% 14.73/8.74 % (8376)Memory used [KB]: 14711
% 14.73/8.74 % (8376)Time elapsed: 0.010 s
% 14.73/8.74 % (8376)Instructions burned: 7 (million)
% 14.73/8.74 % (8376)------------------------------
% 14.73/8.74 % (8376)------------------------------
% 14.73/8.75 % (8377)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/3Mi)
% 14.73/8.75 % (8377)Instruction limit reached!
% 14.73/8.75 % (8377)------------------------------
% 14.73/8.75 % (8377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.75 % (8377)Termination reason: Unknown
% 14.73/8.75 % (8377)Termination phase: shuffling
% 14.73/8.75
% 14.73/8.75 % (8377)Memory used [KB]: 14328
% 14.73/8.75 % (8377)Time elapsed: 0.005 s
% 14.73/8.75 % (8377)Instructions burned: 3 (million)
% 14.73/8.75 % (8377)------------------------------
% 14.73/8.75 % (8377)------------------------------
% 14.73/8.76 % (8378)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8220 for (2991ds/4Mi)
% 14.73/8.76 % (8378)Instruction limit reached!
% 14.73/8.76 % (8378)------------------------------
% 14.73/8.76 % (8378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.76 % (8378)Termination reason: Unknown
% 14.73/8.76 % (8378)Termination phase: shuffling
% 14.73/8.76
% 14.73/8.76 % (8378)Memory used [KB]: 14456
% 14.73/8.76 % (8378)Time elapsed: 0.006 s
% 14.73/8.76 % (8378)Instructions burned: 4 (million)
% 14.73/8.76 % (8378)------------------------------
% 14.73/8.76 % (8378)------------------------------
% 14.73/8.76 % (8380)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8220 for (2990ds/18Mi)
% 14.73/8.76 % (8381)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8220 for (2990ds/710Mi)
% 14.73/8.77 % (8382)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8220 for (2990ds/6Mi)
% 14.73/8.77 % (8360)Instruction limit reached!
% 14.73/8.77 % (8360)------------------------------
% 14.73/8.77 % (8360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.77 % (8360)Termination reason: Unknown
% 14.73/8.77 % (8360)Termination phase: shuffling
% 14.73/8.77
% 14.73/8.77 % (8360)Memory used [KB]: 17654
% 14.73/8.77 % (8360)Time elapsed: 0.106 s
% 14.73/8.77 % (8360)Instructions burned: 183 (million)
% 14.73/8.77 % (8360)------------------------------
% 14.73/8.77 % (8360)------------------------------
% 14.73/8.77 % (8382)Instruction limit reached!
% 14.73/8.77 % (8382)------------------------------
% 14.73/8.77 % (8382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.77 % (8382)Termination reason: Unknown
% 14.73/8.77 % (8382)Termination phase: shuffling
% 14.73/8.77
% 14.73/8.77 % (8382)Memory used [KB]: 14583
% 14.73/8.77 % (8382)Time elapsed: 0.009 s
% 14.73/8.77 % (8382)Instructions burned: 6 (million)
% 14.73/8.77 % (8382)------------------------------
% 14.73/8.77 % (8382)------------------------------
% 14.73/8.78 % (8380)Instruction limit reached!
% 14.73/8.78 % (8380)------------------------------
% 14.73/8.78 % (8380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.73/8.78 % (8383)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_8220 for (2990ds/902Mi)
% 14.73/8.78 % (8380)Termination reason: Unknown
% 14.73/8.78 % (8380)Termination phase: shuffling
% 14.73/8.78
% 14.73/8.78 % (8380)Memory used [KB]: 15223
% 14.73/8.78 % (8380)Time elapsed: 0.020 s
% 14.73/8.78 % (8380)Instructions burned: 18 (million)
% 14.73/8.78 % (8380)------------------------------
% 14.73/8.78 % (8380)------------------------------
% 14.73/8.79 % (8384)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_8220 for (2990ds/21Mi)
% 14.73/8.79 % (8385)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8220 for (2990ds/5Mi)
% 15.19/8.80 % (8385)Instruction limit reached!
% 15.19/8.80 % (8385)------------------------------
% 15.19/8.80 % (8385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/8.80 % (8385)Termination reason: Unknown
% 15.19/8.80 % (8385)Termination phase: shuffling
% 15.19/8.80
% 15.19/8.80 % (8385)Memory used [KB]: 14456
% 15.19/8.80 % (8385)Time elapsed: 0.007 s
% 15.19/8.80 % (8385)Instructions burned: 5 (million)
% 15.19/8.80 % (8385)------------------------------
% 15.19/8.80 % (8385)------------------------------
% 15.19/8.80 % (8386)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_8220 for (2990ds/6Mi)
% 15.19/8.81 % (8386)Instruction limit reached!
% 15.19/8.81 % (8386)------------------------------
% 15.19/8.81 % (8386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/8.81 % (8386)Termination reason: Unknown
% 15.19/8.81 % (8386)Termination phase: shuffling
% 15.19/8.81
% 15.19/8.81 % (8386)Memory used [KB]: 14583
% 15.19/8.81 % (8386)Time elapsed: 0.008 s
% 15.19/8.81 % (8386)Instructions burned: 6 (million)
% 15.19/8.81 % (8386)------------------------------
% 15.19/8.81 % (8386)------------------------------
% 15.19/8.81 % (8384)Instruction limit reached!
% 15.19/8.81 % (8384)------------------------------
% 15.19/8.81 % (8384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/8.81 % (8384)Termination reason: Unknown
% 15.19/8.81 % (8384)Termination phase: shuffling
% 15.19/8.81
% 15.19/8.81 % (8384)Memory used [KB]: 15223
% 15.19/8.81 % (8384)Time elapsed: 0.022 s
% 15.19/8.81 % (8384)Instructions burned: 21 (million)
% 15.19/8.81 % (8384)------------------------------
% 15.19/8.81 % (8384)------------------------------
% 15.19/8.82 % (8365)Instruction limit reached!
% 15.19/8.82 % (8365)------------------------------
% 15.19/8.82 % (8365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/8.82 % (8365)Termination reason: Unknown
% 15.19/8.82 % (8365)Termination phase: shuffling
% 15.19/8.82
% 15.19/8.82 % (8365)Memory used [KB]: 18549
% 15.19/8.82 % (8365)Time elapsed: 0.148 s
% 15.19/8.82 % (8365)Instructions burned: 276 (million)
% 15.19/8.82 % (8365)------------------------------
% 15.19/8.82 % (8365)------------------------------
% 15.19/8.82 % (8387)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8220 for (2990ds/377Mi)
% 15.19/8.82 % (8388)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_8220 for (2990ds/779Mi)
% 15.19/8.83 % (8389)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_8220 for (2990ds/19Mi)
% 15.19/8.83 % (8390)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8220 for (2990ds/879Mi)
% 15.19/8.85 % (8389)Instruction limit reached!
% 15.19/8.85 % (8389)------------------------------
% 15.19/8.85 % (8389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/8.85 % (8389)Termination reason: Unknown
% 15.19/8.85 % (8389)Termination phase: shuffling
% 15.19/8.85
% 15.19/8.85 % (8389)Memory used [KB]: 15223
% 15.19/8.85 % (8389)Time elapsed: 0.021 s
% 15.19/8.85 % (8389)Instructions burned: 19 (million)
% 15.19/8.85 % (8389)------------------------------
% 15.19/8.85 % (8389)------------------------------
% 15.19/8.87 % (8391)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8220 for (2990ds/17Mi)
% 15.19/8.89 % (8391)Instruction limit reached!
% 15.19/8.89 % (8391)------------------------------
% 15.19/8.89 % (8391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/8.89 % (8391)Termination reason: Unknown
% 15.19/8.89 % (8391)Termination phase: shuffling
% 15.19/8.89
% 15.19/8.89 % (8391)Memory used [KB]: 15223
% 15.19/8.89 % (8391)Time elapsed: 0.020 s
% 15.19/8.89 % (8391)Instructions burned: 17 (million)
% 15.19/8.89 % (8391)------------------------------
% 15.19/8.89 % (8391)------------------------------
% 15.51/8.91 % (8392)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_8220 for (2989ds/3Mi)
% 15.51/8.91 % (8392)Instruction limit reached!
% 15.51/8.91 % (8392)------------------------------
% 15.51/8.91 % (8392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.51/8.91 % (8392)Termination reason: Unknown
% 15.51/8.91 % (8392)Termination phase: shuffling
% 15.51/8.91
% 15.51/8.91 % (8392)Memory used [KB]: 14328
% 15.51/8.91 % (8392)Time elapsed: 0.005 s
% 15.51/8.91 % (8392)Instructions burned: 3 (million)
% 15.51/8.91 % (8392)------------------------------
% 15.51/8.91 % (8392)------------------------------
% 15.51/8.93 % (8393)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_8220 for (2989ds/30Mi)
% 15.51/8.95 % (8393)Instruction limit reached!
% 15.51/8.95 % (8393)------------------------------
% 15.51/8.95 % (8393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.51/8.95 % (8393)Termination reason: Unknown
% 15.51/8.95 % (8393)Termination phase: shuffling
% 15.51/8.95
% 15.51/8.95 % (8393)Memory used [KB]: 15479
% 15.51/8.95 % (8393)Time elapsed: 0.027 s
% 15.51/8.95 % (8393)Instructions burned: 31 (million)
% 15.51/8.95 % (8393)------------------------------
% 15.51/8.95 % (8393)------------------------------
% 15.51/8.97 % (8394)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_8220 for (2989ds/127Mi)
% 15.51/9.01 % (8387)Instruction limit reached!
% 15.51/9.01 % (8387)------------------------------
% 15.51/9.01 % (8387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.51/9.01 % (8387)Termination reason: Unknown
% 15.51/9.01 % (8387)Termination phase: shuffling
% 15.51/9.01
% 15.51/9.01 % (8387)Memory used [KB]: 19829
% 15.51/9.01 % (8387)Time elapsed: 0.200 s
% 15.51/9.01 % (8387)Instructions burned: 378 (million)
% 15.51/9.01 % (8387)------------------------------
% 15.51/9.01 % (8387)------------------------------
% 17.10/9.03 % (8395)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_8220 for (2988ds/100Mi)
% 17.10/9.05 % (8394)Instruction limit reached!
% 17.10/9.05 % (8394)------------------------------
% 17.10/9.05 % (8394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/9.05 % (8394)Termination reason: Unknown
% 17.10/9.05 % (8394)Termination phase: shuffling
% 17.10/9.05
% 17.10/9.05 % (8394)Memory used [KB]: 16758
% 17.10/9.05 % (8394)Time elapsed: 0.075 s
% 17.10/9.05 % (8394)Instructions burned: 127 (million)
% 17.10/9.05 % (8394)------------------------------
% 17.10/9.05 % (8394)------------------------------
% 17.10/9.07 % (8396)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_8220 for (2988ds/3Mi)
% 17.10/9.07 % (8396)Instruction limit reached!
% 17.10/9.07 % (8396)------------------------------
% 17.10/9.07 % (8396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/9.07 % (8396)Termination reason: Unknown
% 17.10/9.07 % (8396)Termination phase: shuffling
% 17.10/9.07
% 17.10/9.07 % (8396)Memory used [KB]: 14328
% 17.10/9.07 % (8396)Time elapsed: 0.005 s
% 17.10/9.07 % (8396)Instructions burned: 3 (million)
% 17.10/9.07 % (8396)------------------------------
% 17.10/9.07 % (8396)------------------------------
% 17.10/9.09 % (8397)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_8220 for (2987ds/20Mi)
% 17.10/9.09 % (8395)Instruction limit reached!
% 17.10/9.09 % (8395)------------------------------
% 17.10/9.09 % (8395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/9.09 % (8395)Termination reason: Unknown
% 17.10/9.09 % (8395)Termination phase: shuffling
% 17.10/9.09
% 17.10/9.09 % (8395)Memory used [KB]: 16630
% 17.10/9.09 % (8395)Time elapsed: 0.061 s
% 17.10/9.09 % (8395)Instructions burned: 101 (million)
% 17.10/9.09 % (8395)------------------------------
% 17.10/9.09 % (8395)------------------------------
% 17.10/9.11 % (8397)Instruction limit reached!
% 17.10/9.11 % (8397)------------------------------
% 17.10/9.11 % (8397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/9.11 % (8397)Termination reason: Unknown
% 17.10/9.11 % (8397)Termination phase: shuffling
% 17.10/9.11
% 17.10/9.11 % (8397)Memory used [KB]: 15223
% 17.10/9.11 % (8397)Time elapsed: 0.022 s
% 17.10/9.11 % (8397)Instructions burned: 20 (million)
% 17.10/9.11 % (8397)------------------------------
% 17.10/9.11 % (8397)------------------------------
% 17.10/9.11 % (8398)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_8220 for (2987ds/86Mi)
% 17.10/9.13 % (8399)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_8220 for (2987ds/107Mi)
% 17.79/9.13 % (8381)Instruction limit reached!
% 17.79/9.13 % (8381)------------------------------
% 17.79/9.13 % (8381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.79/9.13 % (8381)Termination reason: Unknown
% 17.79/9.13 % (8381)Termination phase: shuffling
% 17.79/9.13
% 17.79/9.13 % (8381)Memory used [KB]: 25969
% 17.79/9.13 % (8381)Time elapsed: 0.368 s
% 17.79/9.13 % (8381)Instructions burned: 712 (million)
% 17.79/9.13 % (8381)------------------------------
% 17.79/9.13 % (8381)------------------------------
% 17.79/9.15 % (8400)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_8220 for (2987ds/39Mi)
% 17.79/9.17 % (8398)Instruction limit reached!
% 17.79/9.17 % (8398)------------------------------
% 17.79/9.17 % (8398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.79/9.17 % (8398)Termination reason: Unknown
% 17.79/9.17 % (8398)Termination phase: shuffling
% 17.79/9.17
% 17.79/9.17 % (8398)Memory used [KB]: 16119
% 17.79/9.17 % (8398)Time elapsed: 0.054 s
% 17.79/9.17 % (8398)Instructions burned: 87 (million)
% 17.79/9.17 % (8398)------------------------------
% 17.79/9.17 % (8398)------------------------------
% 17.79/9.18 % (8400)Instruction limit reached!
% 17.79/9.18 % (8400)------------------------------
% 17.79/9.18 % (8400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.79/9.18 % (8400)Termination reason: Unknown
% 17.79/9.18 % (8400)Termination phase: shuffling
% 17.79/9.18
% 17.79/9.18 % (8400)Memory used [KB]: 15607
% 17.79/9.18 % (8400)Time elapsed: 0.031 s
% 17.79/9.18 % (8400)Instructions burned: 40 (million)
% 17.79/9.18 % (8400)------------------------------
% 17.79/9.18 % (8400)------------------------------
% 17.79/9.19 % (8401)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_8220 for (2986ds/448Mi)
% 17.79/9.19 % (8399)Instruction limit reached!
% 17.79/9.19 % (8399)------------------------------
% 17.79/9.19 % (8399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.79/9.19 % (8399)Termination reason: Unknown
% 17.79/9.19 % (8399)Termination phase: shuffling
% 17.79/9.19
% 17.79/9.19 % (8399)Memory used [KB]: 16630
% 17.79/9.19 % (8399)Time elapsed: 0.066 s
% 17.79/9.19 % (8399)Instructions burned: 108 (million)
% 17.79/9.19 % (8399)------------------------------
% 17.79/9.19 % (8399)------------------------------
% 18.29/9.20 % (8402)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_8220 for (2986ds/46Mi)
% 18.29/9.21 % (8388)Instruction limit reached!
% 18.29/9.21 % (8388)------------------------------
% 18.29/9.21 % (8388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.21 % (8388)Termination reason: Unknown
% 18.29/9.21 % (8388)Termination phase: shuffling
% 18.29/9.21
% 18.29/9.21 % (8388)Memory used [KB]: 27888
% 18.29/9.21 % (8388)Time elapsed: 0.386 s
% 18.29/9.21 % (8388)Instructions burned: 780 (million)
% 18.29/9.21 % (8388)------------------------------
% 18.29/9.21 % (8388)------------------------------
% 18.29/9.21 % (8403)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_8220 for (2986ds/98Mi)
% 18.29/9.22 % (8371)Instruction limit reached!
% 18.29/9.22 % (8371)------------------------------
% 18.29/9.22 % (8371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.22 % (8371)Termination reason: Unknown
% 18.29/9.22 % (8371)Termination phase: shuffling
% 18.29/9.22
% 18.29/9.22 % (8371)Memory used [KB]: 35436
% 18.29/9.22 % (8371)Time elapsed: 0.515 s
% 18.29/9.22 % (8371)Instructions burned: 1042 (million)
% 18.29/9.22 % (8371)------------------------------
% 18.29/9.22 % (8371)------------------------------
% 18.29/9.23 % (8404)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_8220 for (2986ds/507Mi)
% 18.29/9.23 % (8402)Instruction limit reached!
% 18.29/9.23 % (8402)------------------------------
% 18.29/9.23 % (8402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.23 % (8402)Termination reason: Unknown
% 18.29/9.23 % (8402)Termination phase: shuffling
% 18.29/9.23
% 18.29/9.23 % (8402)Memory used [KB]: 15735
% 18.29/9.23 % (8402)Time elapsed: 0.036 s
% 18.29/9.23 % (8402)Instructions burned: 47 (million)
% 18.29/9.23 % (8402)------------------------------
% 18.29/9.23 % (8402)------------------------------
% 18.29/9.24 % (8405)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_8220 for (2986ds/149Mi)
% 18.29/9.25 % (8383)Instruction limit reached!
% 18.29/9.25 % (8383)------------------------------
% 18.29/9.25 % (8383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.25 % (8383)Termination reason: Unknown
% 18.29/9.25 % (8383)Termination phase: shuffling
% 18.29/9.25
% 18.29/9.25 % (8383)Memory used [KB]: 28784
% 18.29/9.25 % (8383)Time elapsed: 0.470 s
% 18.29/9.25 % (8383)Instructions burned: 902 (million)
% 18.29/9.25 % (8383)------------------------------
% 18.29/9.25 % (8383)------------------------------
% 18.29/9.25 % (8406)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_8220 for (2986ds/39Mi)
% 18.29/9.27 % (8403)Instruction limit reached!
% 18.29/9.27 % (8403)------------------------------
% 18.29/9.27 % (8403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.27 % (8403)Termination reason: Unknown
% 18.29/9.27 % (8403)Termination phase: shuffling
% 18.29/9.27
% 18.29/9.27 % (8403)Memory used [KB]: 16502
% 18.29/9.27 % (8403)Time elapsed: 0.058 s
% 18.29/9.27 % (8403)Instructions burned: 98 (million)
% 18.29/9.27 % (8403)------------------------------
% 18.29/9.27 % (8403)------------------------------
% 18.29/9.27 % (8407)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_8220 for (2986ds/6Mi)
% 18.29/9.28 % (8407)Instruction limit reached!
% 18.29/9.28 % (8407)------------------------------
% 18.29/9.28 % (8407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.28 % (8407)Termination reason: Unknown
% 18.29/9.28 % (8407)Termination phase: shuffling
% 18.29/9.28
% 18.29/9.28 % (8407)Memory used [KB]: 14583
% 18.29/9.28 % (8407)Time elapsed: 0.009 s
% 18.29/9.28 % (8407)Instructions burned: 6 (million)
% 18.29/9.28 % (8407)------------------------------
% 18.29/9.28 % (8407)------------------------------
% 18.29/9.28 % (8406)Instruction limit reached!
% 18.29/9.28 % (8406)------------------------------
% 18.29/9.28 % (8406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.28 % (8406)Termination reason: Unknown
% 18.29/9.28 % (8406)Termination phase: shuffling
% 18.29/9.28
% 18.29/9.28 % (8406)Memory used [KB]: 15479
% 18.29/9.28 % (8406)Time elapsed: 0.031 s
% 18.29/9.28 % (8406)Instructions burned: 40 (million)
% 18.29/9.28 % (8406)------------------------------
% 18.29/9.28 % (8406)------------------------------
% 18.29/9.29 % (8408)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_8220 for (2985ds/1087Mi)
% 18.29/9.29 % (8390)Instruction limit reached!
% 18.29/9.29 % (8390)------------------------------
% 18.29/9.29 % (8390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.29/9.29 % (8390)Termination reason: Unknown
% 18.29/9.29 % (8390)Termination phase: shuffling
% 18.29/9.29
% 18.29/9.29 % (8390)Memory used [KB]: 28144
% 18.29/9.29 % (8390)Time elapsed: 0.455 s
% 18.29/9.29 % (8390)Instructions burned: 880 (million)
% 18.29/9.29 % (8390)------------------------------
% 18.29/9.29 % (8390)------------------------------
% 18.29/9.30 % (8409)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_8220 for (2985ds/47Mi)
% 18.73/9.30 % (8410)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_8220 for (2985ds/44Mi)
% 18.73/9.31 % (8411)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_8220 for (2985ds/432Mi)
% 18.73/9.33 % (8405)Instruction limit reached!
% 18.73/9.33 % (8405)------------------------------
% 18.73/9.33 % (8405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/9.33 % (8405)Termination reason: Unknown
% 18.73/9.33 % (8405)Termination phase: shuffling
% 18.73/9.33
% 18.73/9.33 % (8405)Memory used [KB]: 17014
% 18.73/9.33 % (8405)Time elapsed: 0.086 s
% 18.73/9.33 % (8405)Instructions burned: 150 (million)
% 18.73/9.33 % (8405)------------------------------
% 18.73/9.33 % (8405)------------------------------
% 18.73/9.33 % (8409)Instruction limit reached!
% 18.73/9.33 % (8409)------------------------------
% 18.73/9.33 % (8409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/9.33 % (8409)Termination reason: Unknown
% 18.73/9.33 % (8409)Termination phase: shuffling
% 18.73/9.33
% 18.73/9.33 % (8409)Memory used [KB]: 15735
% 18.73/9.33 % (8409)Time elapsed: 0.036 s
% 18.73/9.33 % (8409)Instructions burned: 48 (million)
% 18.73/9.33 % (8409)------------------------------
% 18.73/9.33 % (8409)------------------------------
% 18.73/9.33 % (8410)Instruction limit reached!
% 18.73/9.33 % (8410)------------------------------
% 18.73/9.33 % (8410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/9.33 % (8410)Termination reason: Unknown
% 18.73/9.33 % (8410)Termination phase: shuffling
% 18.73/9.33
% 18.73/9.33 % (8410)Memory used [KB]: 15607
% 18.73/9.33 % (8410)Time elapsed: 0.033 s
% 18.73/9.33 % (8410)Instructions burned: 45 (million)
% 18.73/9.33 % (8410)------------------------------
% 18.73/9.33 % (8410)------------------------------
% 18.73/9.35 % (8413)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_8220 for (2985ds/31Mi)
% 18.73/9.35 % (8412)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_8220 for (2985ds/62Mi)
% 18.73/9.35 % (8414)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_8220 for (2985ds/96Mi)
% 18.73/9.37 % (8413)Instruction limit reached!
% 18.73/9.37 % (8413)------------------------------
% 18.73/9.37 % (8413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/9.37 % (8413)Termination reason: Unknown
% 18.73/9.37 % (8413)Termination phase: shuffling
% 18.73/9.37
% 18.73/9.37 % (8413)Memory used [KB]: 15479
% 18.73/9.37 % (8413)Time elapsed: 0.027 s
% 18.73/9.37 % (8413)Instructions burned: 31 (million)
% 18.73/9.37 % (8413)------------------------------
% 18.73/9.37 % (8413)------------------------------
% 18.73/9.39 % (8412)Instruction limit reached!
% 18.73/9.39 % (8412)------------------------------
% 18.73/9.39 % (8412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.73/9.39 % (8412)Termination reason: Unknown
% 18.73/9.39 % (8412)Termination phase: shuffling
% 18.73/9.39
% 18.73/9.39 % (8412)Memory used [KB]: 15863
% 18.73/9.39 % (8412)Time elapsed: 0.041 s
% 18.73/9.39 % (8412)Instructions burned: 62 (million)
% 18.73/9.39 % (8412)------------------------------
% 18.73/9.39 % (8412)------------------------------
% 18.73/9.39 % (8415)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_8220 for (2984ds/453Mi)
% 19.04/9.41 % (8414)Instruction limit reached!
% 19.04/9.41 % (8414)------------------------------
% 19.04/9.41 % (8414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.41 % (8414)Termination reason: Unknown
% 19.04/9.41 % (8414)Termination phase: shuffling
% 19.04/9.41
% 19.04/9.41 % (8414)Memory used [KB]: 16375
% 19.04/9.41 % (8414)Time elapsed: 0.061 s
% 19.04/9.41 % (8414)Instructions burned: 97 (million)
% 19.04/9.41 % (8416)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_8220 for (2984ds/71Mi)
% 19.04/9.41 % (8414)------------------------------
% 19.04/9.41 % (8414)------------------------------
% 19.04/9.41 % (8401)Instruction limit reached!
% 19.04/9.41 % (8401)------------------------------
% 19.04/9.41 % (8401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.41 % (8401)Termination reason: Unknown
% 19.04/9.41 % (8401)Termination phase: shuffling
% 19.04/9.41
% 19.04/9.41 % (8401)Memory used [KB]: 23283
% 19.04/9.41 % (8401)Time elapsed: 0.227 s
% 19.04/9.41 % (8401)Instructions burned: 448 (million)
% 19.04/9.41 % (8401)------------------------------
% 19.04/9.41 % (8401)------------------------------
% 19.04/9.43 % (8417)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_8220 for (2984ds/83Mi)
% 19.04/9.43 % (8418)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_8220 for (2984ds/11Mi)
% 19.04/9.44 % (8418)Instruction limit reached!
% 19.04/9.44 % (8418)------------------------------
% 19.04/9.44 % (8418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.44 % (8418)Termination reason: Unknown
% 19.04/9.44 % (8418)Termination phase: shuffling
% 19.04/9.44
% 19.04/9.44 % (8418)Memory used [KB]: 14967
% 19.04/9.44 % (8418)Time elapsed: 0.013 s
% 19.04/9.44 % (8418)Instructions burned: 11 (million)
% 19.04/9.44 % (8418)------------------------------
% 19.04/9.44 % (8418)------------------------------
% 19.04/9.45 % (8416)Instruction limit reached!
% 19.04/9.45 % (8416)------------------------------
% 19.04/9.45 % (8416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.45 % (8416)Termination reason: Unknown
% 19.04/9.45 % (8416)Termination phase: shuffling
% 19.04/9.45
% 19.04/9.45 % (8416)Memory used [KB]: 16119
% 19.04/9.45 % (8416)Time elapsed: 0.048 s
% 19.04/9.45 % (8416)Instructions burned: 71 (million)
% 19.04/9.45 % (8416)------------------------------
% 19.04/9.45 % (8416)------------------------------
% 19.04/9.46 % (8419)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_8220 for (2983ds/41Mi)
% 19.04/9.47 % (8420)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8220 for (2983ds/6Mi)
% 19.04/9.48 % (8417)Instruction limit reached!
% 19.04/9.48 % (8417)------------------------------
% 19.04/9.48 % (8417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.48 % (8417)Termination reason: Unknown
% 19.04/9.48 % (8417)Termination phase: shuffling
% 19.04/9.48
% 19.04/9.48 % (8417)Memory used [KB]: 16119
% 19.04/9.48 % (8417)Time elapsed: 0.054 s
% 19.04/9.48 % (8417)Instructions burned: 83 (million)
% 19.04/9.48 % (8417)------------------------------
% 19.04/9.48 % (8417)------------------------------
% 19.04/9.48 % (8420)Instruction limit reached!
% 19.04/9.48 % (8420)------------------------------
% 19.04/9.48 % (8420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.48 % (8420)Termination reason: Unknown
% 19.04/9.48 % (8420)Termination phase: shuffling
% 19.04/9.48
% 19.04/9.48 % (8420)Memory used [KB]: 14583
% 19.04/9.48 % (8420)Time elapsed: 0.009 s
% 19.04/9.48 % (8420)Instructions burned: 6 (million)
% 19.04/9.48 % (8420)------------------------------
% 19.04/9.48 % (8420)------------------------------
% 19.04/9.49 % (8419)Instruction limit reached!
% 19.04/9.49 % (8419)------------------------------
% 19.04/9.49 % (8419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.49 % (8419)Termination reason: Unknown
% 19.04/9.49 % (8419)Termination phase: shuffling
% 19.04/9.49
% 19.04/9.49 % (8419)Memory used [KB]: 15607
% 19.04/9.49 % (8419)Time elapsed: 0.032 s
% 19.04/9.49 % (8419)Instructions burned: 42 (million)
% 19.04/9.49 % (8419)------------------------------
% 19.04/9.49 % (8419)------------------------------
% 19.04/9.49 % (8404)Instruction limit reached!
% 19.04/9.49 % (8404)------------------------------
% 19.04/9.49 % (8404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.04/9.49 % (8404)Termination reason: Unknown
% 19.04/9.49 % (8404)Termination phase: shuffling
% 19.04/9.49
% 19.04/9.49 % (8404)Memory used [KB]: 21620
% 19.04/9.49 % (8404)Time elapsed: 0.266 s
% 19.04/9.49 % (8404)Instructions burned: 508 (million)
% 19.04/9.49 % (8404)------------------------------
% 19.04/9.49 % (8404)------------------------------
% 19.60/9.50 % (8422)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_8220 for (2983ds/343Mi)
% 19.60/9.50 % (8421)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_8220 for (2983ds/150Mi)
% 19.60/9.51 % (8423)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_8220 for (2983ds/109Mi)
% 19.60/9.51 % (8424)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_8220 for (2983ds/253Mi)
% 19.60/9.53 % (8411)Instruction limit reached!
% 19.60/9.53 % (8411)------------------------------
% 19.60/9.53 % (8411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.60/9.53 % (8411)Termination reason: Unknown
% 19.60/9.53 % (8411)Termination phase: shuffling
% 19.60/9.53
% 19.60/9.53 % (8411)Memory used [KB]: 23155
% 19.60/9.53 % (8411)Time elapsed: 0.220 s
% 19.60/9.53 % (8411)Instructions burned: 433 (million)
% 19.60/9.53 % (8411)------------------------------
% 19.60/9.53 % (8411)------------------------------
% 19.60/9.55 % (8425)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_8220 for (2983ds/140Mi)
% 19.60/9.58 % (8423)Instruction limit reached!
% 19.60/9.58 % (8423)------------------------------
% 19.60/9.58 % (8423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.60/9.58 % (8423)Termination reason: Unknown
% 19.60/9.58 % (8423)Termination phase: shuffling
% 19.60/9.58
% 19.60/9.58 % (8423)Memory used [KB]: 16502
% 19.60/9.58 % (8423)Time elapsed: 0.067 s
% 19.60/9.58 % (8423)Instructions burned: 109 (million)
% 19.60/9.58 % (8423)------------------------------
% 19.60/9.58 % (8423)------------------------------
% 19.60/9.58 % (8421)Instruction limit reached!
% 19.60/9.58 % (8421)------------------------------
% 19.60/9.58 % (8421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.60/9.58 % (8421)Termination reason: Unknown
% 19.60/9.58 % (8421)Termination phase: shuffling
% 19.60/9.58
% 19.60/9.58 % (8421)Memory used [KB]: 16886
% 19.60/9.58 % (8421)Time elapsed: 0.085 s
% 19.60/9.58 % (8421)Instructions burned: 151 (million)
% 19.60/9.58 % (8421)------------------------------
% 19.60/9.58 % (8421)------------------------------
% 19.60/9.60 % (8426)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_8220 for (2982ds/614Mi)
% 20.33/9.60 % (8427)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_8220 for (2982ds/202Mi)
% 20.33/9.62 % (8415)Instruction limit reached!
% 20.33/9.62 % (8415)------------------------------
% 20.33/9.62 % (8415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.33/9.62 % (8415)Termination reason: Unknown
% 20.33/9.62 % (8415)Termination phase: shuffling
% 20.33/9.62
% 20.33/9.62 % (8415)Memory used [KB]: 23539
% 20.33/9.62 % (8415)Time elapsed: 0.229 s
% 20.33/9.62 % (8415)Instructions burned: 453 (million)
% 20.33/9.62 % (8415)------------------------------
% 20.33/9.62 % (8415)------------------------------
% 20.33/9.63 % (8425)Instruction limit reached!
% 20.33/9.63 % (8425)------------------------------
% 20.33/9.63 % (8425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.33/9.63 % (8425)Termination reason: Unknown
% 20.33/9.63 % (8425)Termination phase: shuffling
% 20.33/9.63
% 20.33/9.63 % (8425)Memory used [KB]: 16886
% 20.33/9.63 % (8425)Time elapsed: 0.082 s
% 20.33/9.63 % (8425)Instructions burned: 141 (million)
% 20.33/9.63 % (8425)------------------------------
% 20.33/9.63 % (8425)------------------------------
% 20.33/9.64 % (8428)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_8220 for (2982ds/339Mi)
% 20.33/9.65 % (8429)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_8220 for (2982ds/283Mi)
% 20.33/9.65 % (8424)Instruction limit reached!
% 20.33/9.65 % (8424)------------------------------
% 20.33/9.65 % (8424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.33/9.65 % (8424)Termination reason: Unknown
% 20.33/9.65 % (8424)Termination phase: shuffling
% 20.33/9.65
% 20.33/9.65 % (8424)Memory used [KB]: 18293
% 20.33/9.65 % (8424)Time elapsed: 0.137 s
% 20.33/9.65 % (8424)Instructions burned: 253 (million)
% 20.33/9.65 % (8424)------------------------------
% 20.33/9.65 % (8424)------------------------------
% 20.33/9.67 % (8430)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_8220 for (2981ds/134Mi)
% 20.33/9.68 % (8422)Instruction limit reached!
% 20.33/9.68 % (8422)------------------------------
% 20.33/9.68 % (8422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.33/9.68 % (8422)Termination reason: Unknown
% 20.33/9.68 % (8422)Termination phase: shuffling
% 20.33/9.68
% 20.33/9.68 % (8422)Memory used [KB]: 19701
% 20.33/9.68 % (8422)Time elapsed: 0.184 s
% 20.33/9.68 % (8422)Instructions burned: 344 (million)
% 20.33/9.68 % (8422)------------------------------
% 20.33/9.68 % (8422)------------------------------
% 21.03/9.70 % (8431)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_8220 for (2981ds/298Mi)
% 21.03/9.71 % (8427)Instruction limit reached!
% 21.03/9.71 % (8427)------------------------------
% 21.03/9.71 % (8427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.03/9.71 % (8427)Termination reason: Unknown
% 21.03/9.71 % (8427)Termination phase: shuffling
% 21.03/9.71
% 21.03/9.71 % (8427)Memory used [KB]: 17782
% 21.03/9.71 % (8427)Time elapsed: 0.113 s
% 21.03/9.71 % (8427)Instructions burned: 202 (million)
% 21.03/9.71 % (8427)------------------------------
% 21.03/9.71 % (8427)------------------------------
% 21.03/9.73 % (8432)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_8220 for (2981ds/192Mi)
% 21.03/9.75 % (8430)Instruction limit reached!
% 21.03/9.75 % (8430)------------------------------
% 21.03/9.75 % (8430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.03/9.75 % (8430)Termination reason: Unknown
% 21.03/9.75 % (8430)Termination phase: shuffling
% 21.03/9.75
% 21.03/9.75 % (8430)Memory used [KB]: 16886
% 21.03/9.75 % (8430)Time elapsed: 0.080 s
% 21.03/9.75 % (8430)Instructions burned: 134 (million)
% 21.03/9.75 % (8430)------------------------------
% 21.03/9.75 % (8430)------------------------------
% 21.03/9.77 % (8433)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_8220 for (2981ds/258Mi)
% 21.03/9.79 % (8429)Instruction limit reached!
% 21.03/9.79 % (8429)------------------------------
% 21.03/9.79 % (8429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.03/9.79 % (8429)Termination reason: Unknown
% 21.03/9.79 % (8429)Termination phase: shuffling
% 21.03/9.79
% 21.03/9.79 % (8429)Memory used [KB]: 21108
% 21.03/9.79 % (8429)Time elapsed: 0.148 s
% 21.03/9.79 % (8429)Instructions burned: 284 (million)
% 21.03/9.79 % (8429)------------------------------
% 21.03/9.79 % (8429)------------------------------
% 21.25/9.81 % (8434)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_8220 for (2980ds/90Mi)
% 21.25/9.82 % (8428)Instruction limit reached!
% 21.25/9.82 % (8428)------------------------------
% 21.25/9.82 % (8428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/9.82 % (8428)Termination reason: Unknown
% 21.25/9.82 % (8428)Termination phase: shuffling
% 21.25/9.82
% 21.25/9.82 % (8428)Memory used [KB]: 19189
% 21.25/9.82 % (8428)Time elapsed: 0.177 s
% 21.25/9.82 % (8428)Instructions burned: 339 (million)
% 21.25/9.82 % (8428)------------------------------
% 21.25/9.82 % (8428)------------------------------
% 21.25/9.84 % (8435)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_8220 for (2980ds/231Mi)
% 21.25/9.84 % (8432)Instruction limit reached!
% 21.25/9.84 % (8432)------------------------------
% 21.25/9.84 % (8432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/9.84 % (8432)Termination reason: Unknown
% 21.25/9.84 % (8432)Termination phase: shuffling
% 21.25/9.84
% 21.25/9.84 % (8432)Memory used [KB]: 17526
% 21.25/9.84 % (8432)Time elapsed: 0.107 s
% 21.25/9.84 % (8432)Instructions burned: 193 (million)
% 21.25/9.84 % (8432)------------------------------
% 21.25/9.84 % (8432)------------------------------
% 21.25/9.85 % (8408)Instruction limit reached!
% 21.25/9.85 % (8408)------------------------------
% 21.25/9.85 % (8408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/9.85 % (8408)Termination reason: Unknown
% 21.25/9.85 % (8408)Termination phase: shuffling
% 21.25/9.85
% 21.25/9.85 % (8408)Memory used [KB]: 30958
% 21.25/9.85 % (8408)Time elapsed: 0.563 s
% 21.25/9.85 % (8408)Instructions burned: 1087 (million)
% 21.25/9.85 % (8408)------------------------------
% 21.25/9.85 % (8408)------------------------------
% 21.25/9.85 % (8431)Instruction limit reached!
% 21.25/9.85 % (8431)------------------------------
% 21.25/9.85 % (8431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/9.85 % (8431)Termination reason: Unknown
% 21.25/9.85 % (8431)Termination phase: shuffling
% 21.25/9.85
% 21.25/9.85 % (8431)Memory used [KB]: 21364
% 21.25/9.85 % (8431)Time elapsed: 0.155 s
% 21.25/9.85 % (8431)Instructions burned: 300 (million)
% 21.25/9.85 % (8431)------------------------------
% 21.25/9.85 % (8431)------------------------------
% 21.25/9.86 % (8436)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_8220 for (2980ds/458Mi)
% 21.25/9.87 % (8434)Instruction limit reached!
% 21.25/9.87 % (8434)------------------------------
% 21.25/9.87 % (8434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/9.87 % (8434)Termination reason: Unknown
% 21.25/9.87 % (8434)Termination phase: shuffling
% 21.25/9.87
% 21.25/9.87 % (8434)Memory used [KB]: 16247
% 21.25/9.87 % (8434)Time elapsed: 0.057 s
% 21.25/9.87 % (8434)Instructions burned: 90 (million)
% 21.25/9.87 % (8434)------------------------------
% 21.25/9.87 % (8434)------------------------------
% 21.25/9.87 % (8437)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_8220 for (2980ds/31Mi)
% 21.25/9.87 % (8438)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_8220 for (2980ds/297Mi)
% 21.25/9.89 % (8439)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_8220 for (2979ds/987Mi)
% 21.25/9.90 % (8437)Instruction limit reached!
% 21.25/9.90 % (8437)------------------------------
% 21.25/9.90 % (8437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.25/9.90 % (8437)Termination reason: Unknown
% 21.25/9.90 % (8437)Termination phase: shuffling
% 21.25/9.90
% 21.25/9.90 % (8437)Memory used [KB]: 15479
% 21.25/9.90 % (8437)Time elapsed: 0.028 s
% 21.25/9.90 % (8437)Instructions burned: 31 (million)
% 21.25/9.90 % (8437)------------------------------
% 21.25/9.90 % (8437)------------------------------
% 22.58/9.91 % (8433)Instruction limit reached!
% 22.58/9.91 % (8433)------------------------------
% 22.58/9.91 % (8433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.58/9.91 % (8433)Termination reason: Unknown
% 22.58/9.91 % (8433)Termination phase: shuffling
% 22.58/9.91
% 22.58/9.91 % (8433)Memory used [KB]: 18549
% 22.58/9.91 % (8433)Time elapsed: 0.142 s
% 22.58/9.91 % (8433)Instructions burned: 259 (million)
% 22.58/9.91 % (8433)------------------------------
% 22.58/9.91 % (8433)------------------------------
% 22.58/9.91 % (8426)Instruction limit reached!
% 22.58/9.91 % (8426)------------------------------
% 22.58/9.91 % (8426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.58/9.91 % (8426)Termination reason: Unknown
% 22.58/9.91 % (8426)Termination phase: shuffling
% 22.58/9.91
% 22.58/9.91 % (8426)Memory used [KB]: 24946
% 22.58/9.91 % (8426)Time elapsed: 0.321 s
% 22.58/9.91 % (8426)Instructions burned: 614 (million)
% 22.58/9.91 % (8426)------------------------------
% 22.58/9.91 % (8426)------------------------------
% 22.58/9.92 % (8440)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_8220 for (2979ds/182Mi)
% 22.58/9.93 % (8441)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_8220 for (2979ds/182Mi)
% 22.58/9.94 % (8442)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_8220 for (2979ds/154Mi)
% 22.58/9.96 % (8435)Instruction limit reached!
% 22.58/9.96 % (8435)------------------------------
% 22.58/9.96 % (8435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.58/9.96 % (8435)Termination reason: Unknown
% 22.58/9.96 % (8435)Termination phase: shuffling
% 22.58/9.96
% 22.58/9.96 % (8435)Memory used [KB]: 20340
% 22.58/9.96 % (8435)Time elapsed: 0.123 s
% 22.58/9.96 % (8435)Instructions burned: 231 (million)
% 22.58/9.96 % (8435)------------------------------
% 22.58/9.96 % (8435)------------------------------
% 22.58/9.98 % (8443)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_8220 for (2978ds/79Mi)
% 22.58/10.02 % (8442)Instruction limit reached!
% 22.58/10.02 % (8442)------------------------------
% 22.58/10.02 % (8442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.58/10.02 % (8442)Termination reason: Unknown
% 22.58/10.02 % (8442)Termination phase: shuffling
% 22.58/10.02
% 22.58/10.02 % (8442)Memory used [KB]: 17270
% 22.58/10.02 % (8442)Time elapsed: 0.084 s
% 22.58/10.02 % (8442)Instructions burned: 154 (million)
% 22.58/10.02 % (8442)------------------------------
% 22.58/10.02 % (8442)------------------------------
% 22.58/10.02 % (8440)Instruction limit reached!
% 22.58/10.02 % (8440)------------------------------
% 22.58/10.02 % (8440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.58/10.02 % (8440)Termination reason: Unknown
% 22.58/10.02 % (8440)Termination phase: shuffling
% 22.58/10.02
% 22.58/10.02 % (8440)Memory used [KB]: 17654
% 22.58/10.02 % (8440)Time elapsed: 0.105 s
% 22.58/10.02 % (8440)Instructions burned: 183 (million)
% 22.58/10.02 % (8440)------------------------------
% 22.58/10.02 % (8440)------------------------------
% 22.58/10.03 % (8441)Instruction limit reached!
% 22.58/10.03 % (8441)------------------------------
% 22.58/10.03 % (8441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.58/10.03 % (8441)Termination reason: Unknown
% 22.58/10.03 % (8441)Termination phase: shuffling
% 22.58/10.03
% 22.58/10.03 % (8441)Memory used [KB]: 17270
% 22.58/10.03 % (8441)Time elapsed: 0.102 s
% 22.58/10.03 % (8441)Instructions burned: 183 (million)
% 22.58/10.03 % (8441)------------------------------
% 22.58/10.03 % (8441)------------------------------
% 24.12/10.03 % (8443)Instruction limit reached!
% 24.12/10.03 % (8443)------------------------------
% 24.12/10.03 % (8443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.12/10.03 % (8443)Termination reason: Unknown
% 24.12/10.03 % (8443)Termination phase: shuffling
% 24.12/10.03
% 24.12/10.03 % (8443)Memory used [KB]: 16119
% 24.12/10.03 % (8443)Time elapsed: 0.052 s
% 24.12/10.03 % (8443)Instructions burned: 79 (million)
% 24.12/10.03 % (8443)------------------------------
% 24.12/10.03 % (8443)------------------------------
% 24.12/10.03 % (8438)Instruction limit reached!
% 24.12/10.03 % (8438)------------------------------
% 24.12/10.03 % (8438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.12/10.03 % (8438)Termination reason: Unknown
% 24.12/10.03 % (8438)Termination phase: shuffling
% 24.12/10.03
% 24.12/10.03 % (8438)Memory used [KB]: 21364
% 24.12/10.03 % (8438)Time elapsed: 0.155 s
% 24.12/10.03 % (8438)Instructions burned: 298 (million)
% 24.12/10.03 % (8438)------------------------------
% 24.12/10.03 % (8438)------------------------------
% 24.12/10.04 % (8445)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_8220 for (2978ds/216Mi)
% 24.12/10.04 % (8446)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_8220 for (2978ds/114Mi)
% 24.12/10.05 % (8448)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_8220 for (2978ds/182Mi)
% 24.12/10.05 % (8447)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_8220 for (2978ds/922Mi)
% 24.12/10.05 % (8449)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_8220 for (2978ds/164Mi)
% 24.12/10.10 % (8436)Instruction limit reached!
% 24.12/10.10 % (8436)------------------------------
% 24.12/10.10 % (8436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.12/10.10 % (8436)Termination reason: Unknown
% 24.12/10.10 % (8436)Termination phase: shuffling
% 24.12/10.10
% 24.12/10.10 % (8436)Memory used [KB]: 21108
% 24.12/10.10 % (8436)Time elapsed: 0.244 s
% 24.12/10.10 % (8436)Instructions burned: 458 (million)
% 24.12/10.10 % (8436)------------------------------
% 24.12/10.10 % (8436)------------------------------
% 24.12/10.10 % (8446)Instruction limit reached!
% 24.12/10.10 % (8446)------------------------------
% 24.12/10.10 % (8446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.12/10.10 % (8446)Termination reason: Unknown
% 24.12/10.10 % (8446)Termination phase: shuffling
% 24.12/10.10
% 24.12/10.10 % (8446)Memory used [KB]: 16502
% 24.12/10.10 % (8446)Time elapsed: 0.068 s
% 24.12/10.10 % (8446)Instructions burned: 114 (million)
% 24.12/10.10 % (8446)------------------------------
% 24.12/10.10 % (8446)------------------------------
% 24.12/10.12 % (8450)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_8220 for (2977ds/50Mi)
% 24.12/10.12 % (8451)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_8220 for (2977ds/368Mi)
% 24.45/10.13 % (8449)Instruction limit reached!
% 24.45/10.13 % (8449)------------------------------
% 24.45/10.13 % (8449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.45/10.13 % (8449)Termination reason: Unknown
% 24.45/10.13 % (8449)Termination phase: shuffling
% 24.45/10.13
% 24.45/10.13 % (8449)Memory used [KB]: 17398
% 24.45/10.13 % (8449)Time elapsed: 0.088 s
% 24.45/10.13 % (8449)Instructions burned: 165 (million)
% 24.45/10.13 % (8449)------------------------------
% 24.45/10.13 % (8449)------------------------------
% 24.45/10.14 % (8448)Instruction limit reached!
% 24.45/10.14 % (8448)------------------------------
% 24.45/10.14 % (8448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.45/10.14 % (8448)Termination reason: Unknown
% 24.45/10.14 % (8448)Termination phase: shuffling
% 24.45/10.14
% 24.45/10.14 % (8448)Memory used [KB]: 17654
% 24.45/10.14 % (8448)Time elapsed: 0.098 s
% 24.45/10.14 % (8448)Instructions burned: 183 (million)
% 24.45/10.14 % (8448)------------------------------
% 24.45/10.14 % (8448)------------------------------
% 24.45/10.15 % (8445)Instruction limit reached!
% 24.45/10.15 % (8445)------------------------------
% 24.45/10.15 % (8445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.45/10.15 % (8445)Termination reason: Unknown
% 24.45/10.15 % (8445)Termination phase: shuffling
% 24.45/10.15
% 24.45/10.15 % (8445)Memory used [KB]: 18166
% 24.45/10.15 % (8445)Time elapsed: 0.115 s
% 24.45/10.15 % (8445)Instructions burned: 217 (million)
% 24.45/10.15 % (8445)------------------------------
% 24.45/10.15 % (8445)------------------------------
% 24.45/10.15 % (8452)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_8220 for (2977ds/1021Mi)
% 24.45/10.15 % (8450)Instruction limit reached!
% 24.45/10.15 % (8450)------------------------------
% 24.45/10.15 % (8450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.45/10.15 % (8450)Termination reason: Unknown
% 24.45/10.15 % (8450)Termination phase: shuffling
% 24.45/10.15
% 24.45/10.15 % (8450)Memory used [KB]: 15735
% 24.45/10.15 % (8450)Time elapsed: 0.036 s
% 24.45/10.15 % (8450)Instructions burned: 50 (million)
% 24.45/10.15 % (8450)------------------------------
% 24.45/10.15 % (8450)------------------------------
% 24.45/10.16 % (8453)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_8220 for (2977ds/267Mi)
% 24.45/10.17 % (8454)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_8220 for (2976ds/204Mi)
% 24.45/10.17 % (8455)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_8220 for (2976ds/26Mi)
% 24.45/10.20 % (8455)Instruction limit reached!
% 24.45/10.20 % (8455)------------------------------
% 24.45/10.20 % (8455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.91/10.20 % (8455)Termination reason: Unknown
% 24.91/10.20 % (8455)Termination phase: shuffling
% 24.91/10.20
% 24.91/10.20 % (8455)Memory used [KB]: 15351
% 24.91/10.20 % (8455)Time elapsed: 0.025 s
% 24.91/10.20 % (8455)Instructions burned: 27 (million)
% 24.91/10.20 % (8455)------------------------------
% 24.91/10.20 % (8455)------------------------------
% 24.91/10.22 % (8456)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_8220 for (2976ds/53Mi)
% 24.91/10.25 % (8456)Instruction limit reached!
% 24.91/10.25 % (8456)------------------------------
% 24.91/10.25 % (8456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.91/10.25 % (8456)Termination reason: Unknown
% 24.91/10.25 % (8456)Termination phase: shuffling
% 24.91/10.25
% 24.91/10.25 % (8456)Memory used [KB]: 15863
% 24.91/10.25 % (8456)Time elapsed: 0.037 s
% 24.91/10.25 % (8456)Instructions burned: 54 (million)
% 24.91/10.25 % (8456)------------------------------
% 24.91/10.25 % (8456)------------------------------
% 24.91/10.27 % (8457)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_8220 for (2975ds/4436Mi)
% 24.91/10.28 % (8454)Instruction limit reached!
% 24.91/10.28 % (8454)------------------------------
% 24.91/10.28 % (8454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.91/10.28 % (8454)Termination reason: Unknown
% 24.91/10.28 % (8454)Termination phase: shuffling
% 24.91/10.28
% 24.91/10.28 % (8454)Memory used [KB]: 17782
% 24.91/10.28 % (8454)Time elapsed: 0.114 s
% 24.91/10.28 % (8454)Instructions burned: 205 (million)
% 24.91/10.28 % (8454)------------------------------
% 24.91/10.28 % (8454)------------------------------
% 25.25/10.30 % (8453)Instruction limit reached!
% 25.25/10.30 % (8453)------------------------------
% 25.25/10.30 % (8453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.25/10.30 % (8453)Termination reason: Unknown
% 25.25/10.30 % (8453)Termination phase: shuffling
% 25.25/10.30
% 25.25/10.30 % (8453)Memory used [KB]: 20852
% 25.25/10.30 % (8453)Time elapsed: 0.139 s
% 25.25/10.30 % (8453)Instructions burned: 267 (million)
% 25.25/10.30 % (8453)------------------------------
% 25.25/10.30 % (8453)------------------------------
% 25.25/10.30 % (8458)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_8220 for (2975ds/1539Mi)
% 25.25/10.31 % (8451)Instruction limit reached!
% 25.25/10.31 % (8451)------------------------------
% 25.25/10.31 % (8451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.25/10.31 % (8451)Termination reason: Unknown
% 25.25/10.31 % (8451)Termination phase: shuffling
% 25.25/10.31
% 25.25/10.31 % (8451)Memory used [KB]: 19573
% 25.25/10.31 % (8451)Time elapsed: 0.191 s
% 25.25/10.31 % (8451)Instructions burned: 368 (million)
% 25.25/10.31 % (8451)------------------------------
% 25.25/10.31 % (8451)------------------------------
% 25.25/10.32 % (8459)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_8220 for (2975ds/408Mi)
% 25.25/10.33 % (8460)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_8220 for (2975ds/5205Mi)
% 25.25/10.38 % (8439)Instruction limit reached!
% 25.25/10.38 % (8439)------------------------------
% 25.25/10.38 % (8439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.25/10.38 % (8439)Termination reason: Unknown
% 25.25/10.38 % (8439)Termination phase: shuffling
% 25.25/10.38
% 25.25/10.38 % (8439)Memory used [KB]: 34796
% 25.25/10.38 % (8439)Time elapsed: 0.490 s
% 25.25/10.38 % (8439)Instructions burned: 988 (million)
% 25.25/10.38 % (8439)------------------------------
% 25.25/10.38 % (8439)------------------------------
% 25.71/10.40 % (8461)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_8220 for (2974ds/1913Mi)
% 25.71/10.52 % (8447)Instruction limit reached!
% 25.71/10.52 % (8447)------------------------------
% 25.71/10.52 % (8447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.71/10.52 % (8447)Termination reason: Unknown
% 25.71/10.52 % (8447)Termination phase: shuffling
% 25.71/10.52
% 25.71/10.52 % (8447)Memory used [KB]: 29040
% 25.71/10.52 % (8447)Time elapsed: 0.477 s
% 25.71/10.52 % (8447)Instructions burned: 922 (million)
% 25.71/10.52 % (8447)------------------------------
% 25.71/10.52 % (8447)------------------------------
% 25.71/10.53 % (8459)Instruction limit reached!
% 25.71/10.53 % (8459)------------------------------
% 25.71/10.53 % (8459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.71/10.53 % (8459)Termination reason: Unknown
% 25.71/10.53 % (8459)Termination phase: shuffling
% 25.71/10.53
% 25.71/10.53 % (8459)Memory used [KB]: 20340
% 25.71/10.53 % (8459)Time elapsed: 0.215 s
% 25.71/10.53 % (8459)Instructions burned: 409 (million)
% 25.71/10.53 % (8459)------------------------------
% 25.71/10.53 % (8459)------------------------------
% 25.71/10.54 % (8462)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_8220 for (2973ds/4350Mi)
% 25.71/10.56 % (8463)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_8220 for (2973ds/68Mi)
% 26.43/10.60 % (8463)Instruction limit reached!
% 26.43/10.60 % (8463)------------------------------
% 26.43/10.60 % (8463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.43/10.60 % (8463)Termination reason: Unknown
% 26.43/10.60 % (8463)Termination phase: shuffling
% 26.43/10.60
% 26.43/10.60 % (8463)Memory used [KB]: 15991
% 26.43/10.60 % (8463)Time elapsed: 0.046 s
% 26.43/10.60 % (8463)Instructions burned: 68 (million)
% 26.43/10.60 % (8463)------------------------------
% 26.43/10.60 % (8463)------------------------------
% 26.43/10.62 % (8464)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_8220 for (2972ds/358Mi)
% 26.43/10.68 % (8452)Instruction limit reached!
% 26.43/10.68 % (8452)------------------------------
% 26.43/10.68 % (8452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.43/10.68 % (8452)Termination reason: Unknown
% 26.43/10.68 % (8452)Termination phase: shuffling
% 26.43/10.68
% 26.43/10.68 % (8452)Memory used [KB]: 30191
% 26.43/10.68 % (8452)Time elapsed: 0.526 s
% 26.43/10.68 % (8452)Instructions burned: 1021 (million)
% 26.43/10.68 % (8452)------------------------------
% 26.43/10.68 % (8452)------------------------------
% 27.04/10.70 % (8465)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_8220 for (2971ds/31Mi)
% 27.04/10.73 % (8465)Instruction limit reached!
% 27.04/10.73 % (8465)------------------------------
% 27.04/10.73 % (8465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/10.73 % (8465)Termination reason: Unknown
% 27.04/10.73 % (8465)Termination phase: shuffling
% 27.04/10.73
% 27.04/10.73 % (8465)Memory used [KB]: 15479
% 27.04/10.73 % (8465)Time elapsed: 0.027 s
% 27.04/10.73 % (8465)Instructions burned: 32 (million)
% 27.04/10.73 % (8465)------------------------------
% 27.04/10.73 % (8465)------------------------------
% 27.04/10.75 % (8466)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_8220 for (2971ds/279Mi)
% 27.09/10.81 % (8464)Instruction limit reached!
% 27.09/10.81 % (8464)------------------------------
% 27.09/10.81 % (8464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.09/10.81 % (8464)Termination reason: Unknown
% 27.09/10.81 % (8464)Termination phase: shuffling
% 27.09/10.81
% 27.09/10.81 % (8464)Memory used [KB]: 19829
% 27.09/10.81 % (8464)Time elapsed: 0.191 s
% 27.09/10.81 % (8464)Instructions burned: 359 (million)
% 27.09/10.81 % (8464)------------------------------
% 27.09/10.81 % (8464)------------------------------
% 27.09/10.83 % (8467)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_8220 for (2970ds/258Mi)
% 27.09/10.89 % (8466)Instruction limit reached!
% 27.09/10.89 % (8466)------------------------------
% 27.09/10.89 % (8466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.09/10.89 % (8466)Termination reason: Unknown
% 27.09/10.89 % (8466)Termination phase: shuffling
% 27.09/10.89
% 27.09/10.89 % (8466)Memory used [KB]: 21108
% 27.09/10.89 % (8466)Time elapsed: 0.145 s
% 27.09/10.89 % (8466)Instructions burned: 280 (million)
% 27.09/10.89 % (8466)------------------------------
% 27.09/10.89 % (8466)------------------------------
% 27.46/10.91 % (8468)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_8220 for (2969ds/26Mi)
% 27.46/10.93 % (8468)Instruction limit reached!
% 27.46/10.93 % (8468)------------------------------
% 27.46/10.93 % (8468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.46/10.93 % (8468)Termination reason: Unknown
% 27.46/10.93 % (8468)Termination phase: shuffling
% 27.46/10.93
% 27.46/10.93 % (8468)Memory used [KB]: 15351
% 27.46/10.93 % (8468)Time elapsed: 0.025 s
% 27.46/10.93 % (8468)Instructions burned: 27 (million)
% 27.46/10.93 % (8468)------------------------------
% 27.46/10.93 % (8468)------------------------------
% 27.46/10.95 % (8469)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_8220 for (2969ds/995Mi)
% 27.46/10.97 % (8467)Instruction limit reached!
% 27.46/10.97 % (8467)------------------------------
% 27.46/10.97 % (8467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.46/10.97 % (8467)Termination reason: Unknown
% 27.46/10.97 % (8467)Termination phase: shuffling
% 27.46/10.97
% 27.46/10.97 % (8467)Memory used [KB]: 18549
% 27.46/10.97 % (8467)Time elapsed: 0.141 s
% 27.46/10.97 % (8467)Instructions burned: 259 (million)
% 27.46/10.97 % (8467)------------------------------
% 27.46/10.97 % (8467)------------------------------
% 27.46/10.99 % (8470)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_8220 for (2968ds/373Mi)
% 31.09/11.07 % (8458)Instruction limit reached!
% 31.09/11.07 % (8458)------------------------------
% 31.09/11.07 % (8458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.09/11.07 % (8458)Termination reason: Unknown
% 31.09/11.07 % (8458)Termination phase: Property scanning
% 31.09/11.07
% 31.09/11.07 % (8458)Memory used [KB]: 31470
% 31.09/11.07 % (8458)Time elapsed: 0.773 s
% 31.09/11.07 % (8458)Instructions burned: 1540 (million)
% 31.09/11.07 % (8458)------------------------------
% 31.09/11.07 % (8458)------------------------------
% 31.09/11.10 % (8471)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_8220 for (2967ds/253Mi)
% 31.77/11.18 % (8470)Instruction limit reached!
% 31.77/11.18 % (8470)------------------------------
% 31.77/11.18 % (8470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.77/11.18 % (8470)Termination reason: Unknown
% 31.77/11.18 % (8470)Termination phase: shuffling
% 31.77/11.18
% 31.77/11.18 % (8470)Memory used [KB]: 19829
% 31.77/11.18 % (8470)Time elapsed: 0.197 s
% 31.77/11.18 % (8470)Instructions burned: 374 (million)
% 31.77/11.18 % (8470)------------------------------
% 31.77/11.18 % (8470)------------------------------
% 32.18/11.20 % (8472)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_8220 for (2966ds/832Mi)
% 32.18/11.23 % (8471)Instruction limit reached!
% 32.18/11.23 % (8471)------------------------------
% 32.18/11.23 % (8471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.18/11.23 % (8471)Termination reason: Unknown
% 32.18/11.23 % (8471)Termination phase: shuffling
% 32.18/11.23
% 32.18/11.23 % (8471)Memory used [KB]: 20596
% 32.18/11.23 % (8471)Time elapsed: 0.133 s
% 32.18/11.23 % (8471)Instructions burned: 255 (million)
% 32.18/11.23 % (8471)------------------------------
% 32.18/11.23 % (8471)------------------------------
% 32.18/11.25 % (8473)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_8220 for (2966ds/668Mi)
% 32.83/11.35 % (8461)Instruction limit reached!
% 32.83/11.35 % (8461)------------------------------
% 32.83/11.35 % (8461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.83/11.35 % (8461)Termination reason: Unknown
% 32.83/11.35 % (8461)Termination phase: SInE selection
% 32.83/11.35
% 32.83/11.35 % (8461)Memory used [KB]: 31470
% 32.83/11.35 % (8461)Time elapsed: 0.950 s
% 32.83/11.35 % (8461)Instructions burned: 1914 (million)
% 32.83/11.35 % (8461)------------------------------
% 32.83/11.35 % (8461)------------------------------
% 32.83/11.37 % (8475)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_8220 for (2964ds/40Mi)
% 33.31/11.40 % (8475)Instruction limit reached!
% 33.31/11.40 % (8475)------------------------------
% 33.31/11.40 % (8475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.31/11.40 % (8475)Termination reason: Unknown
% 33.31/11.40 % (8475)Termination phase: shuffling
% 33.31/11.40
% 33.31/11.40 % (8475)Memory used [KB]: 15607
% 33.31/11.40 % (8475)Time elapsed: 0.031 s
% 33.31/11.40 % (8475)Instructions burned: 40 (million)
% 33.31/11.40 % (8475)------------------------------
% 33.31/11.40 % (8475)------------------------------
% 33.31/11.42 % (8476)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_8220 for (2964ds/294Mi)
% 33.31/11.44 % (8469)Instruction limit reached!
% 33.31/11.44 % (8469)------------------------------
% 33.31/11.44 % (8469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.31/11.44 % (8469)Termination reason: Unknown
% 33.31/11.44 % (8469)Termination phase: shuffling
% 33.31/11.44
% 33.31/11.44 % (8469)Memory used [KB]: 34924
% 33.31/11.44 % (8469)Time elapsed: 0.491 s
% 33.31/11.44 % (8469)Instructions burned: 995 (million)
% 33.31/11.44 % (8469)------------------------------
% 33.31/11.44 % (8469)------------------------------
% 33.31/11.46 % (8477)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_8220 for (2964ds/187Mi)
% 33.72/11.57 % (8477)Instruction limit reached!
% 33.72/11.57 % (8477)------------------------------
% 33.72/11.57 % (8477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.72/11.57 % (8477)Termination reason: Unknown
% 33.72/11.57 % (8477)Termination phase: shuffling
% 33.72/11.57
% 33.72/11.57 % (8477)Memory used [KB]: 17526
% 33.72/11.57 % (8477)Time elapsed: 0.105 s
% 33.72/11.57 % (8477)Instructions burned: 187 (million)
% 33.72/11.57 % (8477)------------------------------
% 33.72/11.57 % (8477)------------------------------
% 33.72/11.57 % (8476)Instruction limit reached!
% 33.72/11.57 % (8476)------------------------------
% 33.72/11.57 % (8476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.72/11.57 % (8476)Termination reason: Unknown
% 33.72/11.57 % (8476)Termination phase: shuffling
% 33.72/11.57
% 33.72/11.57 % (8476)Memory used [KB]: 21236
% 33.72/11.57 % (8476)Time elapsed: 0.153 s
% 33.72/11.57 % (8476)Instructions burned: 295 (million)
% 33.72/11.57 % (8476)------------------------------
% 33.72/11.57 % (8476)------------------------------
% 33.72/11.58 % (8473)Instruction limit reached!
% 33.72/11.58 % (8473)------------------------------
% 33.72/11.58 % (8473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.72/11.58 % (8473)Termination reason: Unknown
% 33.72/11.58 % (8473)Termination phase: shuffling
% 33.72/11.58
% 33.72/11.58 % (8473)Memory used [KB]: 26353
% 33.72/11.58 % (8473)Time elapsed: 0.331 s
% 33.72/11.58 % (8473)Instructions burned: 669 (million)
% 33.72/11.58 % (8473)------------------------------
% 33.72/11.58 % (8473)------------------------------
% 33.72/11.59 % (8478)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_8220 for (2962ds/371Mi)
% 33.72/11.59 % (8479)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_8220 for (2962ds/1827Mi)
% 33.72/11.60 % (8480)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_8220 for (2962ds/70Mi)
% 34.65/11.64 % (8472)Instruction limit reached!
% 34.65/11.64 % (8472)------------------------------
% 34.65/11.64 % (8472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.65/11.64 % (8472)Termination reason: Unknown
% 34.65/11.64 % (8472)Termination phase: shuffling
% 34.65/11.64
% 34.65/11.64 % (8472)Memory used [KB]: 27888
% 34.65/11.64 % (8472)Time elapsed: 0.437 s
% 34.65/11.64 % (8472)Instructions burned: 832 (million)
% 34.65/11.64 % (8472)------------------------------
% 34.65/11.64 % (8472)------------------------------
% 34.65/11.64 % (8480)Instruction limit reached!
% 34.65/11.64 % (8480)------------------------------
% 34.65/11.64 % (8480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.65/11.64 % (8480)Termination reason: Unknown
% 34.65/11.64 % (8480)Termination phase: shuffling
% 34.65/11.64
% 34.65/11.64 % (8480)Memory used [KB]: 15991
% 34.65/11.64 % (8480)Time elapsed: 0.046 s
% 34.65/11.64 % (8480)Instructions burned: 72 (million)
% 34.65/11.64 % (8480)------------------------------
% 34.65/11.64 % (8480)------------------------------
% 34.65/11.66 % (8481)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_8220 for (2962ds/316Mi)
% 34.65/11.66 % (8482)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_8220 for (2962ds/932Mi)
% 35.47/11.78 % (8478)Instruction limit reached!
% 35.47/11.78 % (8478)------------------------------
% 35.47/11.78 % (8478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.47/11.78 % (8478)Termination reason: Unknown
% 35.47/11.78 % (8478)Termination phase: shuffling
% 35.47/11.78
% 35.47/11.78 % (8478)Memory used [KB]: 19829
% 35.47/11.78 % (8478)Time elapsed: 0.197 s
% 35.47/11.78 % (8478)Instructions burned: 372 (million)
% 35.47/11.78 % (8478)------------------------------
% 35.47/11.78 % (8478)------------------------------
% 36.01/11.80 % (8483)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_8220 for (2960ds/4714Mi)
% 36.01/11.82 % (8481)Instruction limit reached!
% 36.01/11.82 % (8481)------------------------------
% 36.01/11.82 % (8481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.01/11.82 % (8481)Termination reason: Unknown
% 36.01/11.82 % (8481)Termination phase: shuffling
% 36.01/11.82
% 36.01/11.82 % (8481)Memory used [KB]: 21620
% 36.01/11.82 % (8481)Time elapsed: 0.163 s
% 36.01/11.82 % (8481)Instructions burned: 316 (million)
% 36.01/11.82 % (8481)------------------------------
% 36.01/11.82 % (8481)------------------------------
% 36.01/11.84 % (8484)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_8220 for (2960ds/8250Mi)
% 38.09/12.11 % (8482)Instruction limit reached!
% 38.09/12.11 % (8482)------------------------------
% 38.09/12.11 % (8482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.09/12.11 % (8482)Termination reason: Unknown
% 38.09/12.11 % (8482)Termination phase: shuffling
% 38.09/12.11
% 38.09/12.11 % (8482)Memory used [KB]: 34029
% 38.09/12.11 % (8482)Time elapsed: 0.457 s
% 38.09/12.11 % (8482)Instructions burned: 933 (million)
% 38.09/12.11 % (8482)------------------------------
% 38.09/12.11 % (8482)------------------------------
% 38.81/12.14 % (8485)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_8220 for (2957ds/770Mi)
% 41.02/12.52 % (8485)Instruction limit reached!
% 41.02/12.52 % (8485)------------------------------
% 41.02/12.52 % (8485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.02/12.52 % (8485)Termination reason: Unknown
% 41.02/12.52 % (8485)Termination phase: shuffling
% 41.02/12.52
% 41.02/12.52 % (8485)Memory used [KB]: 26737
% 41.02/12.52 % (8485)Time elapsed: 0.387 s
% 41.02/12.52 % (8485)Instructions burned: 770 (million)
% 41.02/12.52 % (8485)------------------------------
% 41.02/12.52 % (8485)------------------------------
% 41.02/12.52 % (8457)Instruction limit reached!
% 41.02/12.52 % (8457)------------------------------
% 41.02/12.52 % (8457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.02/12.52 % (8457)Termination reason: Unknown
% 41.02/12.52 % (8457)Termination phase: Saturation
% 41.02/12.52
% 41.02/12.52 % (8457)Memory used [KB]: 40169
% 41.02/12.52 % (8457)Time elapsed: 2.254 s
% 41.02/12.52 % (8457)Instructions burned: 4437 (million)
% 41.02/12.52 % (8457)------------------------------
% 41.02/12.52 % (8457)------------------------------
% 41.02/12.54 % (8487)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_8220 for (2953ds/794Mi)
% 41.02/12.54 % (8479)Instruction limit reached!
% 41.02/12.54 % (8479)------------------------------
% 41.02/12.54 % (8479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.02/12.54 % (8479)Termination reason: Unknown
% 41.02/12.54 % (8479)Termination phase: Preprocessing 1
% 41.02/12.54
% 41.02/12.54 % (8479)Memory used [KB]: 31470
% 41.02/12.54 % (8479)Time elapsed: 0.957 s
% 41.02/12.54 % (8479)Instructions burned: 1827 (million)
% 41.02/12.54 % (8479)------------------------------
% 41.02/12.54 % (8479)------------------------------
% 41.02/12.55 % (8488)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_8220 for (2953ds/464Mi)
% 41.02/12.57 % (8489)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_8220 for (2953ds/1376Mi)
% 42.32/12.70 % (8462)Instruction limit reached!
% 42.32/12.70 % (8462)------------------------------
% 42.32/12.70 % (8462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.32/12.70 % (8462)Termination reason: Unknown
% 42.32/12.70 % (8462)Termination phase: Saturation
% 42.32/12.70
% 42.32/12.70 % (8462)Memory used [KB]: 39402
% 42.32/12.70 % (8462)Time elapsed: 2.160 s
% 42.32/12.70 % (8462)Instructions burned: 4350 (million)
% 42.32/12.70 % (8462)------------------------------
% 42.32/12.70 % (8462)------------------------------
% 42.32/12.72 % (8490)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_8220 for (2951ds/906Mi)
% 42.32/12.77 % (8460)Instruction limit reached!
% 42.32/12.77 % (8460)------------------------------
% 42.32/12.77 % (8460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.32/12.77 % (8460)Termination reason: Unknown
% 42.32/12.77 % (8460)Termination phase: Property scanning
% 42.32/12.77
% 42.32/12.77 % (8460)Memory used [KB]: 62429
% 42.32/12.77 % (8460)Time elapsed: 2.441 s
% 42.32/12.77 % (8460)Instructions burned: 5206 (million)
% 42.32/12.77 % (8460)------------------------------
% 42.32/12.77 % (8460)------------------------------
% 42.32/12.78 % (8488)Instruction limit reached!
% 42.32/12.78 % (8488)------------------------------
% 42.32/12.78 % (8488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.32/12.78 % (8488)Termination reason: Unknown
% 42.32/12.78 % (8488)Termination phase: shuffling
% 42.32/12.78
% 42.32/12.78 % (8488)Memory used [KB]: 20980
% 42.32/12.78 % (8488)Time elapsed: 0.240 s
% 42.32/12.78 % (8488)Instructions burned: 464 (million)
% 42.32/12.78 % (8488)------------------------------
% 42.32/12.78 % (8488)------------------------------
% 42.32/12.80 % (8491)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_8220 for (2950ds/434Mi)
% 42.89/12.80 % (8492)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_8220 for (2950ds/865Mi)
% 43.09/12.95 % (8487)Instruction limit reached!
% 43.09/12.95 % (8487)------------------------------
% 43.09/12.95 % (8487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.09/12.95 % (8487)Termination reason: Unknown
% 43.09/12.95 % (8487)Termination phase: shuffling
% 43.09/12.95
% 43.09/12.95 % (8487)Memory used [KB]: 27376
% 43.09/12.95 % (8487)Time elapsed: 0.412 s
% 43.09/12.95 % (8487)Instructions burned: 795 (million)
% 43.09/12.95 % (8487)------------------------------
% 43.09/12.95 % (8487)------------------------------
% 43.09/12.98 % (8493)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_8220 for (2949ds/593Mi)
% 43.09/13.02 % (8491)Instruction limit reached!
% 43.09/13.02 % (8491)------------------------------
% 43.09/13.02 % (8491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.09/13.02 % (8491)Termination reason: Unknown
% 43.09/13.02 % (8491)Termination phase: shuffling
% 43.09/13.02
% 43.09/13.02 % (8491)Memory used [KB]: 20724
% 43.09/13.02 % (8491)Time elapsed: 0.228 s
% 43.09/13.02 % (8491)Instructions burned: 435 (million)
% 43.09/13.02 % (8491)------------------------------
% 43.09/13.02 % (8491)------------------------------
% 45.08/13.04 % (8494)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_8220 for (2948ds/443Mi)
% 45.72/13.19 % (8490)Instruction limit reached!
% 45.72/13.19 % (8490)------------------------------
% 45.72/13.19 % (8490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.72/13.19 % (8490)Termination reason: Unknown
% 45.72/13.19 % (8490)Termination phase: shuffling
% 45.72/13.19
% 45.72/13.19 % (8490)Memory used [KB]: 28784
% 45.72/13.19 % (8490)Time elapsed: 0.468 s
% 45.72/13.19 % (8490)Instructions burned: 906 (million)
% 45.72/13.19 % (8490)------------------------------
% 45.72/13.19 % (8490)------------------------------
% 46.13/13.21 % (8495)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_8220 for (2946ds/594Mi)
% 46.13/13.24 % (8492)Instruction limit reached!
% 46.13/13.24 % (8492)------------------------------
% 46.13/13.24 % (8492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.13/13.25 % (8492)Termination reason: Unknown
% 46.13/13.25 % (8492)Termination phase: shuffling
% 46.13/13.25
% 46.13/13.25 % (8492)Memory used [KB]: 33005
% 46.13/13.25 % (8492)Time elapsed: 0.443 s
% 46.13/13.25 % (8492)Instructions burned: 865 (million)
% 46.13/13.25 % (8492)------------------------------
% 46.13/13.25 % (8492)------------------------------
% 46.13/13.27 % (8496)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_8220 for (2946ds/327Mi)
% 46.13/13.28 % (8494)Instruction limit reached!
% 46.13/13.28 % (8494)------------------------------
% 46.13/13.28 % (8494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.13/13.28 % (8494)Termination reason: Unknown
% 46.13/13.28 % (8494)Termination phase: shuffling
% 46.13/13.28
% 46.13/13.28 % (8494)Memory used [KB]: 20724
% 46.13/13.28 % (8494)Time elapsed: 0.235 s
% 46.13/13.28 % (8494)Instructions burned: 444 (million)
% 46.13/13.28 % (8494)------------------------------
% 46.13/13.28 % (8494)------------------------------
% 46.13/13.29 % (8489)Instruction limit reached!
% 46.13/13.29 % (8489)------------------------------
% 46.13/13.29 % (8489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.13/13.29 % (8489)Termination reason: Unknown
% 46.13/13.29 % (8489)Termination phase: shuffling
% 46.13/13.29
% 46.13/13.29 % (8489)Memory used [KB]: 39914
% 46.13/13.29 % (8489)Time elapsed: 0.720 s
% 46.13/13.29 % (8489)Instructions burned: 1377 (million)
% 46.13/13.29 % (8489)------------------------------
% 46.13/13.29 % (8489)------------------------------
% 46.13/13.30 % (8497)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_8220 for (2945ds/5411Mi)
% 46.85/13.31 % (8493)Instruction limit reached!
% 46.85/13.31 % (8493)------------------------------
% 46.85/13.31 % (8493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.85/13.31 % (8493)Termination reason: Unknown
% 46.85/13.31 % (8493)Termination phase: shuffling
% 46.85/13.31
% 46.85/13.31 % (8493)Memory used [KB]: 25458
% 46.85/13.31 % (8493)Time elapsed: 0.330 s
% 46.85/13.31 % (8493)Instructions burned: 593 (million)
% 46.85/13.31 % (8493)------------------------------
% 46.85/13.31 % (8493)------------------------------
% 46.85/13.31 % (8498)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_8220 for (2945ds/1762Mi)
% 46.85/13.33 % (8499)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_8220 for (2945ds/96Mi)
% 46.85/13.38 % (8499)Instruction limit reached!
% 46.85/13.38 % (8499)------------------------------
% 46.85/13.38 % (8499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.85/13.38 % (8499)Termination reason: Unknown
% 46.85/13.38 % (8499)Termination phase: shuffling
% 46.85/13.38
% 46.85/13.38 % (8499)Memory used [KB]: 16502
% 46.85/13.38 % (8499)Time elapsed: 0.057 s
% 46.85/13.38 % (8499)Instructions burned: 96 (million)
% 46.85/13.38 % (8499)------------------------------
% 46.85/13.38 % (8499)------------------------------
% 47.14/13.40 % (8500)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_8220 for (2944ds/503Mi)
% 47.14/13.44 % (8496)Instruction limit reached!
% 47.14/13.44 % (8496)------------------------------
% 47.14/13.44 % (8496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.14/13.44 % (8496)Termination reason: Unknown
% 47.14/13.44 % (8496)Termination phase: shuffling
% 47.14/13.44
% 47.14/13.44 % (8496)Memory used [KB]: 19317
% 47.14/13.44 % (8496)Time elapsed: 0.179 s
% 47.14/13.44 % (8496)Instructions burned: 327 (million)
% 47.14/13.44 % (8496)------------------------------
% 47.14/13.44 % (8496)------------------------------
% 47.14/13.47 % (8501)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_8220 for (2943ds/90Mi)
% 47.54/13.52 % (8501)Instruction limit reached!
% 47.54/13.52 % (8501)------------------------------
% 47.54/13.52 % (8501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.54/13.52 % (8501)Termination reason: Unknown
% 47.54/13.52 % (8501)Termination phase: shuffling
% 47.54/13.52
% 47.54/13.52 % (8501)Memory used [KB]: 16247
% 47.54/13.52 % (8501)Time elapsed: 0.058 s
% 47.54/13.52 % (8501)Instructions burned: 92 (million)
% 47.54/13.52 % (8501)------------------------------
% 47.54/13.52 % (8501)------------------------------
% 47.54/13.52 % (8495)Instruction limit reached!
% 47.54/13.52 % (8495)------------------------------
% 47.54/13.52 % (8495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.54/13.52 % (8495)Termination reason: Unknown
% 47.54/13.52 % (8495)Termination phase: shuffling
% 47.54/13.52
% 47.54/13.52 % (8495)Memory used [KB]: 24946
% 47.54/13.52 % (8495)Time elapsed: 0.312 s
% 47.54/13.52 % (8495)Instructions burned: 594 (million)
% 47.54/13.52 % (8495)------------------------------
% 47.54/13.52 % (8495)------------------------------
% 47.54/13.54 % (8502)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_8220 for (2943ds/593Mi)
% 47.54/13.54 % (8503)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_8220 for (2943ds/1512Mi)
% 48.15/13.67 % (8500)Instruction limit reached!
% 48.15/13.67 % (8500)------------------------------
% 48.15/13.67 % (8500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.15/13.67 % (8500)Termination reason: Unknown
% 48.15/13.67 % (8500)Termination phase: shuffling
% 48.15/13.67
% 48.15/13.67 % (8500)Memory used [KB]: 21748
% 48.15/13.67 % (8500)Time elapsed: 0.264 s
% 48.15/13.67 % (8500)Instructions burned: 503 (million)
% 48.15/13.67 % (8500)------------------------------
% 48.15/13.67 % (8500)------------------------------
% 48.15/13.69 % (8504)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_8220 for (2941ds/569Mi)
% 48.83/13.85 % (8502)Instruction limit reached!
% 48.83/13.85 % (8502)------------------------------
% 48.83/13.85 % (8502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.83/13.85 % (8502)Termination reason: Unknown
% 48.83/13.85 % (8502)Termination phase: shuffling
% 48.83/13.85
% 48.83/13.85 % (8502)Memory used [KB]: 24690
% 48.83/13.85 % (8502)Time elapsed: 0.313 s
% 48.83/13.85 % (8502)Instructions burned: 593 (million)
% 48.83/13.85 % (8502)------------------------------
% 48.83/13.85 % (8502)------------------------------
% 48.83/13.87 % (8506)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_8220 for (2939ds/501Mi)
% 49.36/13.97 % (8504)Instruction limit reached!
% 49.36/13.97 % (8504)------------------------------
% 49.36/13.97 % (8504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.36/13.97 % (8504)Termination reason: Unknown
% 49.36/13.97 % (8504)Termination phase: shuffling
% 49.36/13.97
% 49.36/13.97 % (8504)Memory used [KB]: 25074
% 49.36/13.97 % (8504)Time elapsed: 0.286 s
% 49.36/13.97 % (8504)Instructions burned: 570 (million)
% 49.36/13.97 % (8504)------------------------------
% 49.36/13.97 % (8504)------------------------------
% 49.36/13.99 % (8507)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_8220 for (2938ds/562Mi)
% 52.05/14.05 % (8483)Instruction limit reached!
% 52.05/14.05 % (8483)------------------------------
% 52.05/14.05 % (8483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.05/14.05 % (8483)Termination reason: Unknown
% 52.05/14.05 % (8483)Termination phase: Function definition elimination
% 52.05/14.05
% 52.05/14.05 % (8483)Memory used [KB]: 61406
% 52.05/14.05 % (8483)Time elapsed: 2.248 s
% 52.05/14.05 % (8483)Instructions burned: 4715 (million)
% 52.05/14.05 % (8483)------------------------------
% 52.05/14.05 % (8483)------------------------------
% 52.05/14.07 % (8508)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_8220 for (2937ds/406Mi)
% 52.72/14.14 % (8506)Instruction limit reached!
% 52.72/14.14 % (8506)------------------------------
% 52.72/14.14 % (8506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.72/14.14 % (8506)Termination reason: Unknown
% 52.72/14.14 % (8506)Termination phase: shuffling
% 52.72/14.14
% 52.72/14.14 % (8506)Memory used [KB]: 21875
% 52.72/14.14 % (8506)Time elapsed: 0.266 s
% 52.72/14.14 % (8506)Instructions burned: 502 (million)
% 52.72/14.14 % (8506)------------------------------
% 52.72/14.14 % (8506)------------------------------
% 52.72/14.16 % (8509)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_8220 for (2937ds/582Mi)
% 52.72/14.17 % (8498)Instruction limit reached!
% 52.72/14.17 % (8498)------------------------------
% 52.72/14.17 % (8498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.72/14.17 % (8498)Termination reason: Unknown
% 52.72/14.17 % (8498)Termination phase: shuffling
% 52.72/14.17
% 52.72/14.17 % (8498)Memory used [KB]: 45031
% 52.72/14.17 % (8498)Time elapsed: 0.860 s
% 52.72/14.17 % (8498)Instructions burned: 1762 (million)
% 52.72/14.17 % (8498)------------------------------
% 52.72/14.17 % (8498)------------------------------
% 52.72/14.19 % (8510)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_8220 for (2936ds/456Mi)
% 53.09/14.27 % (8507)Instruction limit reached!
% 53.09/14.27 % (8507)------------------------------
% 53.09/14.27 % (8507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.09/14.27 % (8507)Termination reason: Unknown
% 53.09/14.27 % (8507)Termination phase: shuffling
% 53.09/14.27
% 53.09/14.27 % (8507)Memory used [KB]: 25074
% 53.09/14.27 % (8507)Time elapsed: 0.282 s
% 53.09/14.27 % (8507)Instructions burned: 563 (million)
% 53.09/14.27 % (8507)------------------------------
% 53.09/14.27 % (8507)------------------------------
% 53.09/14.28 % (8508)Instruction limit reached!
% 53.09/14.28 % (8508)------------------------------
% 53.09/14.28 % (8508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.09/14.28 % (8508)Termination reason: Unknown
% 53.09/14.28 % (8508)Termination phase: shuffling
% 53.09/14.28
% 53.09/14.28 % (8508)Memory used [KB]: 20468
% 53.09/14.28 % (8508)Time elapsed: 0.215 s
% 53.09/14.28 % (8508)Instructions burned: 406 (million)
% 53.09/14.28 % (8508)------------------------------
% 53.09/14.28 % (8508)------------------------------
% 53.09/14.29 % (8511)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_8220 for (2935ds/393Mi)
% 53.71/14.31 % (8512)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_8220 for (2935ds/1335Mi)
% 53.71/14.31 % (8503)Instruction limit reached!
% 53.71/14.31 % (8503)------------------------------
% 53.71/14.31 % (8503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.71/14.31 % (8503)Termination reason: Unknown
% 53.71/14.31 % (8503)Termination phase: Property scanning
% 53.71/14.31
% 53.71/14.31 % (8503)Memory used [KB]: 32622
% 53.71/14.31 % (8503)Time elapsed: 0.767 s
% 53.71/14.31 % (8503)Instructions burned: 1513 (million)
% 53.71/14.31 % (8503)------------------------------
% 53.71/14.31 % (8503)------------------------------
% 53.71/14.33 % (8513)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_8220 for (2935ds/3373Mi)
% 53.93/14.43 % (8510)Instruction limit reached!
% 53.93/14.43 % (8510)------------------------------
% 53.93/14.43 % (8510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.93/14.43 % (8510)Termination reason: Unknown
% 53.93/14.43 % (8510)Termination phase: shuffling
% 53.93/14.43
% 53.93/14.43 % (8510)Memory used [KB]: 20980
% 53.93/14.43 % (8510)Time elapsed: 0.240 s
% 53.93/14.43 % (8510)Instructions burned: 456 (million)
% 53.93/14.43 % (8510)------------------------------
% 53.93/14.43 % (8510)------------------------------
% 53.93/14.45 % (8514)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_8220 for (2934ds/474Mi)
% 53.93/14.46 % (8509)Instruction limit reached!
% 53.93/14.46 % (8509)------------------------------
% 53.93/14.46 % (8509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.93/14.46 % (8509)Termination reason: Unknown
% 53.93/14.46 % (8509)Termination phase: shuffling
% 53.93/14.46
% 53.93/14.46 % (8509)Memory used [KB]: 22643
% 53.93/14.46 % (8509)Time elapsed: 0.306 s
% 53.93/14.46 % (8509)Instructions burned: 583 (million)
% 53.93/14.46 % (8509)------------------------------
% 53.93/14.46 % (8509)------------------------------
% 53.93/14.48 % (8515)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_8220 for (2933ds/157Mi)
% 53.93/14.49 % (8497)First to succeed.
% 53.93/14.49 % (8511)Instruction limit reached!
% 53.93/14.49 % (8511)------------------------------
% 53.93/14.49 % (8511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.93/14.49 % (8511)Termination reason: Unknown
% 53.93/14.49 % (8511)Termination phase: shuffling
% 53.93/14.49
% 53.93/14.49 % (8511)Memory used [KB]: 22643
% 53.93/14.49 % (8511)Time elapsed: 0.201 s
% 53.93/14.49 % (8511)Instructions burned: 393 (million)
% 53.93/14.49 % (8511)------------------------------
% 53.93/14.49 % (8511)------------------------------
% 54.91/14.51 % (8497)Refutation found. Thanks to Tanya!
% 54.91/14.51 % SZS status Theorem for DTF2THF_8220
% 54.91/14.51 % SZS output start Proof for DTF2THF_8220
% 54.91/14.51 thf(type_def_5, type, real: $tType).
% 54.91/14.51 thf(type_def_6, type, int: $tType).
% 54.91/14.51 thf(type_def_8, type, rat: $tType).
% 54.91/14.51 thf(type_def_9, type, assn: $tType).
% 54.91/14.51 thf(type_def_10, type, produc3658429121746597890et_nat: $tType).
% 54.91/14.51 thf(type_def_11, type, list_VEBT_VEBTi: $tType).
% 54.91/14.51 thf(type_def_12, type, vEBT_VEBT: $tType).
% 54.91/14.51 thf(type_def_13, type, array_VEBT_VEBTi: $tType).
% 54.91/14.51 thf(type_def_14, type, produc2732055786443039994et_nat: $tType).
% 54.91/14.51 thf(type_def_15, type, nat: $tType).
% 54.91/14.51 thf(type_def_16, type, num: $tType).
% 54.91/14.51 thf(type_def_17, type, word_N3645301735248828278l_num1: $tType).
% 54.91/14.51 thf(type_def_18, type, code_integer: $tType).
% 54.91/14.51 thf(type_def_19, type, uint32: $tType).
% 54.91/14.51 thf(type_def_20, type, produc6271795597528267376eger_o: $tType).
% 54.91/14.51 thf(type_def_21, type, produc8923325533196201883nteger: $tType).
% 54.91/14.51 thf(type_def_22, type, set_nat: $tType).
% 54.91/14.51 thf(type_def_23, type, set_set_nat: $tType).
% 54.91/14.51 thf(type_def_24, type, set_int: $tType).
% 54.91/14.51 thf(type_def_25, type, set_real: $tType).
% 54.91/14.51 thf(type_def_26, type, complex: $tType).
% 54.91/14.51 thf(type_def_27, type, filter_real: $tType).
% 54.91/14.51 thf(type_def_28, type, product_prod_int_int: $tType).
% 54.91/14.51 thf(type_def_29, type, product_prod_nat_nat: $tType).
% 54.91/14.51 thf(type_def_30, type, filter_nat: $tType).
% 54.91/14.51 thf(type_def_31, type, set_o: $tType).
% 54.91/14.51 thf(type_def_32, type, set_set_o: $tType).
% 54.91/14.51 thf(type_def_33, type, set_Code_integer: $tType).
% 54.91/14.51 thf(type_def_34, type, set_set_Code_integer: $tType).
% 54.91/14.51 thf(type_def_35, type, set_complex: $tType).
% 54.91/14.51 thf(type_def_36, type, set_set_complex: $tType).
% 54.91/14.51 thf(type_def_37, type, set_set_int: $tType).
% 54.91/14.51 thf(type_def_38, type, set_set_set_nat: $tType).
% 54.91/14.51 thf(type_def_39, type, set_list_o: $tType).
% 54.91/14.51 thf(type_def_40, type, set_li6976499617229504675nteger: $tType).
% 54.91/14.51 thf(type_def_41, type, set_list_complex: $tType).
% 54.91/14.51 thf(type_def_42, type, set_list_int: $tType).
% 54.91/14.51 thf(type_def_43, type, set_list_list_nat: $tType).
% 54.91/14.51 thf(type_def_44, type, set_list_nat: $tType).
% 54.91/14.51 thf(type_def_45, type, set_list_real: $tType).
% 54.91/14.51 thf(type_def_46, type, set_list_set_nat: $tType).
% 54.91/14.51 thf(type_def_47, type, set_list_literal: $tType).
% 54.91/14.51 thf(type_def_48, type, set_list_VEBT_VEBT: $tType).
% 54.91/14.51 thf(type_def_49, type, set_num: $tType).
% 54.91/14.51 thf(type_def_50, type, set_Numeral_num0: $tType).
% 54.91/14.51 thf(type_def_51, type, set_Product_unit: $tType).
% 54.91/14.51 thf(type_def_52, type, set_rat: $tType).
% 54.91/14.51 thf(type_def_53, type, set_literal: $tType).
% 54.91/14.51 thf(type_def_54, type, set_VEBT_VEBT: $tType).
% 54.91/14.51 thf(type_def_55, type, set_set_real: $tType).
% 54.91/14.51 thf(type_def_56, type, set_set_VEBT_VEBT: $tType).
% 54.91/14.51 thf(type_def_57, type, list_nat: $tType).
% 54.91/14.51 thf(type_def_58, type, extended_enat: $tType).
% 54.91/14.51 thf(type_def_59, type, set_VEBT_VEBTi: $tType).
% 54.91/14.51 thf(type_def_60, type, literal: $tType).
% 54.91/14.51 thf(type_def_61, type, list_o: $tType).
% 54.91/14.51 thf(type_def_62, type, vEBT_VEBTi: $tType).
% 54.91/14.51 thf(type_def_63, type, heap_Time_Heap_nat: $tType).
% 54.91/14.51 thf(type_def_64, type, option_nat: $tType).
% 54.91/14.51 thf(type_def_65, type, heap_T2636463487746394924on_nat: $tType).
% 54.91/14.51 thf(type_def_66, type, heap_Time_Heap_o: $tType).
% 54.91/14.51 thf(type_def_67, type, heap_T8145700208782473153_VEBTi: $tType).
% 54.91/14.51 thf(type_def_68, type, list_int: $tType).
% 54.91/14.51 thf(type_def_69, type, option_set_o: $tType).
% 54.91/14.51 thf(type_def_70, type, option_set_int: $tType).
% 54.91/14.51 thf(type_def_71, type, option_set_nat: $tType).
% 54.91/14.51 thf(type_def_72, type, produc827990862158126777uint32: $tType).
% 54.91/14.51 thf(type_def_73, type, set_Pr958786334691620121nt_int: $tType).
% 54.91/14.51 thf(type_def_74, type, set_uint32: $tType).
% 54.91/14.51 thf(type_def_75, type, list_real: $tType).
% 54.91/14.51 thf(type_def_76, type, list_VEBT_VEBT: $tType).
% 54.91/14.51 thf(type_def_77, type, list_list_o: $tType).
% 54.91/14.51 thf(type_def_78, type, list_list_nat: $tType).
% 54.91/14.51 thf(type_def_79, type, list_list_real: $tType).
% 54.91/14.51 thf(type_def_80, type, list_list_VEBT_VEBT: $tType).
% 54.91/14.51 thf(type_def_81, type, list_Code_integer: $tType).
% 54.91/14.51 thf(type_def_82, type, list_complex: $tType).
% 54.91/14.51 thf(type_def_83, type, list_set_nat: $tType).
% 54.91/14.51 thf(type_def_84, type, list_num: $tType).
% 54.91/14.51 thf(type_def_85, type, list_rat: $tType).
% 54.91/14.51 thf(type_def_86, type, list_P7333126701944960589_nat_o: $tType).
% 54.91/14.51 thf(type_def_87, type, list_P3521021558325789923at_int: $tType).
% 54.91/14.51 thf(type_def_88, type, list_P6011104703257516679at_nat: $tType).
% 54.91/14.51 thf(type_def_89, type, list_P3644420460460130531t_real: $tType).
% 54.91/14.51 thf(type_def_90, type, list_P2320588648998582380_VEBTi: $tType).
% 54.91/14.51 thf(type_def_91, type, list_P5647936690300460905T_VEBT: $tType).
% 54.91/14.51 thf(type_def_92, type, list_assn: $tType).
% 54.91/14.51 thf(type_def_93, type, list_uint32: $tType).
% 54.91/14.51 thf(type_def_94, type, set_Product_prod_o_o: $tType).
% 54.91/14.51 thf(type_def_95, type, set_Pr6227168374412355847list_o: $tType).
% 54.91/14.51 thf(type_def_96, type, set_Pr765067013931698361st_int: $tType).
% 54.91/14.51 thf(type_def_97, type, set_Pr1261947904930325089at_nat: $tType).
% 54.91/14.51 thf(type_def_98, type, set_Pr3451248702717554689st_nat: $tType).
% 54.91/14.51 thf(type_def_99, type, set_Pr6218003697084177305l_real: $tType).
% 54.91/14.51 thf(type_def_100, type, set_Pr611352295856513593t_real: $tType).
% 54.91/14.51 thf(type_def_101, type, set_Pr1773385645901665561uint32: $tType).
% 54.91/14.51 thf(type_def_102, type, set_Pr2258164808687509945uint32: $tType).
% 54.91/14.51 thf(type_def_103, type, set_Pr6192946355708809607T_VEBT: $tType).
% 54.91/14.51 thf(type_def_104, type, set_Pr1916528119006554503T_VEBT: $tType).
% 54.91/14.51 thf(type_def_105, type, set_Pr2227491710730465451_VEBTi: $tType).
% 54.91/14.51 thf(type_def_106, type, set_Pr4797120415438012619_VEBTi: $tType).
% 54.91/14.51 thf(type_def_107, type, list_literal: $tType).
% 54.91/14.51 thf(type_def_108, type, product_prod_o_o: $tType).
% 54.91/14.51 thf(type_def_109, type, list_P4002435161011370285od_o_o: $tType).
% 54.91/14.51 thf(type_def_110, type, product_prod_o_int: $tType).
% 54.91/14.51 thf(type_def_111, type, list_P3795440434834930179_o_int: $tType).
% 54.91/14.51 thf(type_def_112, type, product_prod_o_nat: $tType).
% 54.91/14.51 thf(type_def_113, type, list_P6285523579766656935_o_nat: $tType).
% 54.91/14.51 thf(type_def_114, type, product_prod_int_o: $tType).
% 54.91/14.51 thf(type_def_115, type, list_P5087981734274514673_int_o: $tType).
% 54.91/14.51 thf(type_def_116, type, list_P5707943133018811711nt_int: $tType).
% 54.91/14.51 thf(type_def_117, type, product_prod_int_nat: $tType).
% 54.91/14.51 thf(type_def_118, type, list_P8198026277950538467nt_nat: $tType).
% 54.91/14.51 thf(type_def_119, type, product_prod_nat_o: $tType).
% 54.91/14.51 thf(type_def_120, type, product_prod_nat_int: $tType).
% 54.91/14.51 thf(type_def_121, type, list_P3069071885182933823uint32: $tType).
% 54.91/14.51 thf(type_def_122, type, list_P7985473006766602707_nat_o: $tType).
% 54.91/14.51 thf(type_def_123, type, set_Pr4532377907799695533_nat_o: $tType).
% 54.91/14.51 thf(type_def_124, type, list_list_int: $tType).
% 54.91/14.51 thf(type_def_125, type, list_P362550909693114634et_nat: $tType).
% 54.91/14.51 thf(type_def_126, type, set_Pr8536935166611901872et_nat: $tType).
% 54.91/14.51 thf(type_def_127, type, list_P2321686559999237006et_nat: $tType).
% 54.91/14.51 thf(type_def_128, type, set_Pr3286484037609594932et_nat: $tType).
% 54.91/14.51 thf(type_def_129, type, list_P9062070895058802706et_nat: $tType).
% 54.91/14.51 thf(type_def_130, type, set_Pr3948176798113811640et_nat: $tType).
% 54.91/14.51 thf(type_def_131, type, set_Pr903927857289325719_int_o: $tType).
% 54.91/14.51 thf(type_def_132, type, set_Pr3448869479623346877nt_nat: $tType).
% 54.91/14.51 thf(type_def_133, type, list_P6863124054624500543t_real: $tType).
% 54.91/14.51 thf(type_def_134, type, set_Pr3538720872664544793t_real: $tType).
% 54.91/14.51 thf(type_def_135, type, list_P7524865323317820941T_VEBT: $tType).
% 54.91/14.51 thf(type_def_136, type, set_Pr8044002425091019955T_VEBT: $tType).
% 54.91/14.51 thf(type_def_137, type, set_Pr7995236796853374141at_int: $tType).
% 54.91/14.51 thf(type_def_138, type, list_P4344331454722006975al_int: $tType).
% 54.91/14.51 thf(type_def_139, type, set_Pr1019928272762051225al_int: $tType).
% 54.91/14.51 thf(type_def_140, type, list_P8689742595348180415l_real: $tType).
% 54.91/14.51 thf(type_def_141, type, list_P877281246627933069T_VEBT: $tType).
% 54.91/14.51 thf(type_def_142, type, set_Pr6019664923565264691T_VEBT: $tType).
% 54.91/14.51 thf(type_def_143, type, list_P6254988961118846195et_nat: $tType).
% 54.91/14.51 thf(type_def_144, type, set_Pr5488025237498180813et_nat: $tType).
% 54.91/14.51 thf(type_def_145, type, list_P3126845725202233233VEBT_o: $tType).
% 54.91/14.51 thf(type_def_146, type, set_Pr3175402225741728619VEBT_o: $tType).
% 54.91/14.51 thf(type_def_147, type, list_P4547456442757143711BT_int: $tType).
% 54.91/14.51 thf(type_def_148, type, set_Pr5066593544530342725BT_int: $tType).
% 54.91/14.51 thf(type_def_149, type, list_P7037539587688870467BT_nat: $tType).
% 54.91/14.51 thf(type_def_150, type, set_Pr7556676689462069481BT_nat: $tType).
% 54.91/14.51 thf(type_def_151, type, list_P2623026923184700063T_real: $tType).
% 54.91/14.51 thf(type_def_152, type, set_Pr7765410600122031685T_real: $tType).
% 54.91/14.51 thf(type_def_153, type, list_P7413028617227757229T_VEBT: $tType).
% 54.91/14.51 thf(type_def_154, type, produc3925858234332021118et_nat: $tType).
% 54.91/14.51 thf(type_def_155, type, list_P785718909624839377_VEBTi: $tType).
% 54.91/14.51 thf(type_def_156, type, produc3777764054643897931_VEBTi: $tType).
% 54.91/14.51 thf(type_def_157, type, list_P5988454224134618948T_VEBT: $tType).
% 54.91/14.51 thf(type_def_158, type, produc2810682830582626868T_VEBT: $tType).
% 54.91/14.51 thf(type_def_159, type, list_P735349106241217576_VEBTi: $tType).
% 54.91/14.51 thf(type_def_160, type, produc3625547720036274456_VEBTi: $tType).
% 54.91/14.51 thf(type_def_161, type, produc8243902056947475879T_VEBT: $tType).
% 54.91/14.51 thf(type_def_162, type, produc679980390762269497t_real: $tType).
% 54.91/14.51 thf(type_def_163, type, list_P4447955379000644808_VEBTi: $tType).
% 54.91/14.51 thf(type_def_164, type, produc2062302194595185346_VEBTi: $tType).
% 54.91/14.51 thf(type_def_165, type, produc1531783533982839933T_VEBT: $tType).
% 54.91/14.51 thf(type_def_166, type, produc7716430852924023517t_real: $tType).
% 54.91/14.51 thf(type_def_167, type, produc214224863196444774_VEBTi: $tType).
% 54.91/14.51 thf(type_def_168, type, produc8025551001238799321T_VEBT: $tType).
% 54.91/14.51 thf(type_def_169, type, list_P8833571063612306856EBTi_o: $tType).
% 54.91/14.51 thf(type_def_170, type, produc5014006835512566296EBTi_o: $tType).
% 54.91/14.51 thf(type_def_171, type, list_P7392757774524453448Ti_int: $tType).
% 54.91/14.51 thf(type_def_172, type, produc8927069083091599426Ti_int: $tType).
% 54.91/14.51 thf(type_def_173, type, list_P8536626330812492744i_real: $tType).
% 54.91/14.51 thf(type_def_174, type, produc6680258955013199682i_real: $tType).
% 54.91/14.51 thf(type_def_175, type, list_P5232166724548748803o_real: $tType).
% 54.91/14.51 thf(type_def_176, type, list_P7495141550334521929T_VEBT: $tType).
% 54.91/14.51 thf(type_def_177, type, list_P3595434254542482545real_o: $tType).
% 54.91/14.51 thf(type_def_178, type, list_P6834414599653733731al_nat: $tType).
% 54.91/14.51 thf(type_def_179, type, option4927543243414619207at_nat: $tType).
% 54.91/14.51 thf(type_def_180, type, option2860828798490689354et_nat: $tType).
% 54.91/14.51 thf(type_def_181, type, option5190343406534369742et_nat: $tType).
% 54.91/14.51 thf(type_def_182, type, option4624381673175914239nt_int: $tType).
% 54.91/14.51 thf(type_def_183, type, option3972171592325465343uint32: $tType).
% 54.91/14.51 thf(type_def_184, type, option_int: $tType).
% 54.91/14.51 thf(type_def_185, type, option_num: $tType).
% 54.91/14.51 thf(type_def_186, type, option_rat: $tType).
% 54.91/14.51 thf(type_def_187, type, option_real: $tType).
% 54.91/14.51 thf(type_def_188, type, char: $tType).
% 54.91/14.51 thf(type_def_189, type, heap_e7401611519738050253t_unit: $tType).
% 54.91/14.51 thf(type_def_190, type, produc7102631898165422375list_o: $tType).
% 54.91/14.51 thf(type_def_191, type, produc1186641810826059865st_int: $tType).
% 54.91/14.51 thf(type_def_192, type, produc1828647624359046049st_nat: $tType).
% 54.91/14.51 thf(type_def_193, type, produc478978216448986841t_real: $tType).
% 54.91/14.51 thf(type_def_194, type, produc823665806539077721uint32: $tType).
% 54.91/14.51 thf(type_def_195, type, produc3089554586268799851_VEBTi: $tType).
% 54.91/14.51 thf(type_def_196, type, produc9211091688327510695T_VEBT: $tType).
% 54.91/14.51 thf(type_def_197, type, produc5657529347773406293et_nat: $tType).
% 54.91/14.51 thf(type_def_198, type, produc6830853553727218525et_nat: $tType).
% 54.91/14.51 thf(type_def_199, type, produc1219242969750017639nt_int: $tType).
% 54.91/14.51 thf(type_def_200, type, produc859450856879609959at_nat: $tType).
% 54.91/14.51 thf(type_def_201, type, produc8822557026176459367uint32: $tType).
% 54.91/14.51 thf(type_def_202, type, produc8786904178792722361al_int: $tType).
% 54.91/14.51 thf(type_def_203, type, produc2422161461964618553l_real: $tType).
% 54.91/14.51 thf(type_def_204, type, produc3757001726724277373T_VEBT: $tType).
% 54.91/14.51 thf(type_def_205, type, produc7819656566062154093et_nat: $tType).
% 54.91/14.51 thf(type_def_206, type, produc334124729049499915VEBT_o: $tType).
% 54.91/14.51 thf(type_def_207, type, produc4894624898956917775BT_int: $tType).
% 54.91/14.51 thf(type_def_208, type, produc9072475918466114483BT_nat: $tType).
% 54.91/14.51 thf(type_def_209, type, produc5170161368751668367T_real: $tType).
% 54.91/14.51 thf(type_def_210, type, set_Pr3444600963470892981et_nat: $tType).
% 54.91/14.51 thf(type_def_211, type, set_Pr7928877670098842301et_nat: $tType).
% 54.91/14.51 thf(type_def_212, type, set_Pr2560585780119916871nt_int: $tType).
% 54.91/14.51 thf(type_def_213, type, set_Pr8693737435421807431at_nat: $tType).
% 54.91/14.51 thf(type_def_214, type, set_Pr3773659940955823943uint32: $tType).
% 54.91/14.51 thf(type_def_215, type, itself_Numeral_num0: $tType).
% 54.91/14.51 thf(func_def_0, type, set_Pr3444600963470892981et_nat: $tType).
% 54.91/14.51 thf(func_def_1, type, produc5657529347773406293et_nat: $tType).
% 54.91/14.51 thf(func_def_2, type, set_Pr7928877670098842301et_nat: $tType).
% 54.91/14.51 thf(func_def_3, type, produc6830853553727218525et_nat: $tType).
% 54.91/14.51 thf(func_def_4, type, option2860828798490689354et_nat: $tType).
% 54.91/14.51 thf(func_def_5, type, list_P362550909693114634et_nat: $tType).
% 54.91/14.51 thf(func_def_6, type, set_Pr8536935166611901872et_nat: $tType).
% 54.91/14.51 thf(func_def_7, type, produc2732055786443039994et_nat: $tType).
% 54.91/14.51 thf(func_def_8, type, option5190343406534369742et_nat: $tType).
% 54.91/14.51 thf(func_def_9, type, list_P2321686559999237006et_nat: $tType).
% 54.91/14.51 thf(func_def_10, type, set_Pr3286484037609594932et_nat: $tType).
% 54.91/14.51 thf(func_def_11, type, produc3925858234332021118et_nat: $tType).
% 54.91/14.51 thf(func_def_12, type, word_N3645301735248828278l_num1: $tType).
% 54.91/14.51 thf(func_def_13, type, set_Pr3773659940955823943uint32: $tType).
% 54.91/14.51 thf(func_def_14, type, produc8822557026176459367uint32: $tType).
% 54.91/14.51 thf(func_def_15, type, set_Pr8693737435421807431at_nat: $tType).
% 54.91/14.51 thf(func_def_16, type, set_Pr2560585780119916871nt_int: $tType).
% 54.91/14.51 thf(func_def_17, type, set_Pr4797120415438012619_VEBTi: $tType).
% 54.91/14.51 thf(func_def_18, type, list_P7985473006766602707_nat_o: $tType).
% 54.91/14.51 thf(func_def_19, type, set_Pr4532377907799695533_nat_o: $tType).
% 54.91/14.51 thf(func_def_20, type, set_Pr1916528119006554503T_VEBT: $tType).
% 54.91/14.51 thf(func_def_21, type, produc859450856879609959at_nat: $tType).
% 54.91/14.51 thf(func_def_22, type, produc1219242969750017639nt_int: $tType).
% 54.91/14.51 thf(func_def_23, type, list_P9062070895058802706et_nat: $tType).
% 54.91/14.51 thf(func_def_24, type, set_Pr3948176798113811640et_nat: $tType).
% 54.91/14.51 thf(func_def_25, type, produc3089554586268799851_VEBTi: $tType).
% 54.91/14.51 thf(func_def_26, type, produc9211091688327510695T_VEBT: $tType).
% 54.91/14.51 thf(func_def_27, type, set_Pr2258164808687509945uint32: $tType).
% 54.91/14.51 thf(func_def_28, type, produc3658429121746597890et_nat: $tType).
% 54.91/14.51 thf(func_def_29, type, list_P785718909624839377_VEBTi: $tType).
% 54.91/14.51 thf(func_def_30, type, set_Pr2227491710730465451_VEBTi: $tType).
% 54.91/14.51 thf(func_def_31, type, set_Pr611352295856513593t_real: $tType).
% 54.91/14.51 thf(func_def_32, type, list_P735349106241217576_VEBTi: $tType).
% 54.91/14.51 thf(func_def_33, type, list_P5988454224134618948T_VEBT: $tType).
% 54.91/14.51 thf(func_def_34, type, set_Pr3451248702717554689st_nat: $tType).
% 54.91/14.51 thf(func_def_35, type, set_Pr765067013931698361st_int: $tType).
% 54.91/14.51 thf(func_def_36, type, list_P7413028617227757229T_VEBT: $tType).
% 54.91/14.51 thf(func_def_37, type, set_Pr6192946355708809607T_VEBT: $tType).
% 54.91/14.51 thf(func_def_38, type, list_P6254988961118846195et_nat: $tType).
% 54.91/14.51 thf(func_def_39, type, set_Pr5488025237498180813et_nat: $tType).
% 54.91/14.51 thf(func_def_40, type, produc823665806539077721uint32: $tType).
% 54.91/14.51 thf(func_def_41, type, produc3777764054643897931_VEBTi: $tType).
% 54.91/14.51 thf(func_def_42, type, produc478978216448986841t_real: $tType).
% 54.91/14.51 thf(func_def_43, type, list_P8536626330812492744i_real: $tType).
% 54.91/14.51 thf(func_def_44, type, list_P7392757774524453448Ti_int: $tType).
% 54.91/14.51 thf(func_def_45, type, list_P2320588648998582380_VEBTi: $tType).
% 54.91/14.51 thf(func_def_46, type, list_P4447955379000644808_VEBTi: $tType).
% 54.91/14.51 thf(func_def_47, type, produc3625547720036274456_VEBTi: $tType).
% 54.91/14.51 thf(func_def_48, type, produc2810682830582626868T_VEBT: $tType).
% 54.91/14.51 thf(func_def_49, type, list_P2623026923184700063T_real: $tType).
% 54.91/14.51 thf(func_def_50, type, list_P877281246627933069T_VEBT: $tType).
% 54.91/14.51 thf(func_def_51, type, produc1828647624359046049st_nat: $tType).
% 54.91/14.51 thf(func_def_52, type, produc1186641810826059865st_int: $tType).
% 54.91/14.51 thf(func_def_53, type, set_Pr7765410600122031685T_real: $tType).
% 54.91/14.51 thf(func_def_54, type, set_Pr6019664923565264691T_VEBT: $tType).
% 54.91/14.51 thf(func_def_55, type, list_P7037539587688870467BT_nat: $tType).
% 54.91/14.51 thf(func_def_56, type, list_P4547456442757143711BT_int: $tType).
% 54.91/14.51 thf(func_def_57, type, list_P5647936690300460905T_VEBT: $tType).
% 54.91/14.51 thf(func_def_58, type, list_P7524865323317820941T_VEBT: $tType).
% 54.91/14.51 thf(func_def_59, type, set_Pr6227168374412355847list_o: $tType).
% 54.91/14.51 thf(func_def_60, type, produc8243902056947475879T_VEBT: $tType).
% 54.91/14.51 thf(func_def_61, type, option3972171592325465343uint32: $tType).
% 54.91/14.51 thf(func_def_62, type, set_Pr7556676689462069481BT_nat: $tType).
% 54.91/14.51 thf(func_def_63, type, set_Pr5066593544530342725BT_int: $tType).
% 54.91/14.51 thf(func_def_64, type, set_Pr8044002425091019955T_VEBT: $tType).
% 54.91/14.51 thf(func_def_65, type, produc7819656566062154093et_nat: $tType).
% 54.91/14.51 thf(func_def_66, type, produc8923325533196201883nteger: $tType).
% 54.91/14.51 thf(func_def_67, type, list_P3069071885182933823uint32: $tType).
% 54.91/14.51 thf(func_def_68, type, list_P8833571063612306856EBTi_o: $tType).
% 54.91/14.51 thf(func_def_69, type, set_Pr1773385645901665561uint32: $tType).
% 54.91/14.51 thf(func_def_70, type, list_P3126845725202233233VEBT_o: $tType).
% 54.91/14.51 thf(func_def_71, type, list_P7495141550334521929T_VEBT: $tType).
% 54.91/14.51 thf(func_def_72, type, set_Pr3175402225741728619VEBT_o: $tType).
% 54.91/14.51 thf(func_def_73, type, produc6680258955013199682i_real: $tType).
% 54.91/14.51 thf(func_def_74, type, option4927543243414619207at_nat: $tType).
% 54.91/14.51 thf(func_def_75, type, option4624381673175914239nt_int: $tType).
% 54.91/14.51 thf(func_def_76, type, list_P8689742595348180415l_real: $tType).
% 54.91/14.51 thf(func_def_77, type, set_Pr6218003697084177305l_real: $tType).
% 54.91/14.51 thf(func_def_78, type, produc8927069083091599426Ti_int: $tType).
% 54.91/14.51 thf(func_def_79, type, produc214224863196444774_VEBTi: $tType).
% 54.91/14.51 thf(func_def_80, type, produc2062302194595185346_VEBTi: $tType).
% 54.91/14.51 thf(func_def_81, type, list_P6834414599653733731al_nat: $tType).
% 54.91/14.51 thf(func_def_82, type, list_P4344331454722006975al_int: $tType).
% 54.91/14.51 thf(func_def_83, type, list_P3644420460460130531t_real: $tType).
% 54.91/14.51 thf(func_def_84, type, list_P6863124054624500543t_real: $tType).
% 54.91/14.51 thf(func_def_85, type, produc5170161368751668367T_real: $tType).
% 54.91/14.51 thf(func_def_86, type, produc3757001726724277373T_VEBT: $tType).
% 54.91/14.51 thf(func_def_87, type, set_Pr1019928272762051225al_int: $tType).
% 54.91/14.51 thf(func_def_88, type, set_Pr3538720872664544793t_real: $tType).
% 54.91/14.51 thf(func_def_89, type, produc7102631898165422375list_o: $tType).
% 54.91/14.51 thf(func_def_90, type, list_P6011104703257516679at_nat: $tType).
% 54.91/14.51 thf(func_def_91, type, list_P3521021558325789923at_int: $tType).
% 54.91/14.51 thf(func_def_92, type, list_P8198026277950538467nt_nat: $tType).
% 54.91/14.51 thf(func_def_93, type, list_P5707943133018811711nt_int: $tType).
% 54.91/14.51 thf(func_def_94, type, produc9072475918466114483BT_nat: $tType).
% 54.91/14.51 thf(func_def_95, type, produc4894624898956917775BT_int: $tType).
% 54.91/14.51 thf(func_def_96, type, produc8025551001238799321T_VEBT: $tType).
% 54.91/14.51 thf(func_def_97, type, produc1531783533982839933T_VEBT: $tType).
% 54.91/14.51 thf(func_def_98, type, set_Pr1261947904930325089at_nat: $tType).
% 54.91/14.51 thf(func_def_99, type, set_Pr7995236796853374141at_int: $tType).
% 54.91/14.51 thf(func_def_100, type, set_Pr3448869479623346877nt_nat: $tType).
% 54.91/14.51 thf(func_def_101, type, set_Pr958786334691620121nt_int: $tType).
% 54.91/14.51 thf(func_def_102, type, heap_T2636463487746394924on_nat: $tType).
% 54.91/14.51 thf(func_def_103, type, produc827990862158126777uint32: $tType).
% 54.91/14.51 thf(func_def_104, type, heap_T8145700208782473153_VEBTi: $tType).
% 54.91/14.51 thf(func_def_105, type, produc5014006835512566296EBTi_o: $tType).
% 54.91/14.51 thf(func_def_106, type, list_P3595434254542482545real_o: $tType).
% 54.91/14.51 thf(func_def_107, type, list_P5232166724548748803o_real: $tType).
% 54.91/14.51 thf(func_def_108, type, list_list_VEBT_VEBT: $tType).
% 54.91/14.51 thf(func_def_109, type, set_list_list_nat: $tType).
% 54.91/14.51 thf(func_def_110, type, list_P7333126701944960589_nat_o: $tType).
% 54.91/14.51 thf(func_def_111, type, list_P5087981734274514673_int_o: $tType).
% 54.91/14.51 thf(func_def_112, type, list_P6285523579766656935_o_nat: $tType).
% 54.91/14.51 thf(func_def_113, type, list_P3795440434834930179_o_int: $tType).
% 54.91/14.51 thf(func_def_114, type, set_list_VEBT_VEBT: $tType).
% 54.91/14.51 thf(func_def_115, type, produc334124729049499915VEBT_o: $tType).
% 54.91/14.51 thf(func_def_116, type, set_Pr903927857289325719_int_o: $tType).
% 54.91/14.51 thf(func_def_117, type, set_list_set_nat: $tType).
% 54.91/14.51 thf(func_def_118, type, set_li6976499617229504675nteger: $tType).
% 54.91/14.51 thf(func_def_119, type, produc6271795597528267376eger_o: $tType).
% 54.91/14.51 thf(func_def_120, type, set_set_VEBT_VEBT: $tType).
% 54.91/14.51 thf(func_def_121, type, set_set_set_nat: $tType).
% 54.91/14.51 thf(func_def_122, type, set_set_Code_integer: $tType).
% 54.91/14.51 thf(func_def_123, type, produc2422161461964618553l_real: $tType).
% 54.91/14.51 thf(func_def_124, type, produc8786904178792722361al_int: $tType).
% 54.91/14.51 thf(func_def_125, type, produc7716430852924023517t_real: $tType).
% 54.91/14.51 thf(func_def_126, type, produc679980390762269497t_real: $tType).
% 54.91/14.51 thf(func_def_127, type, heap_e7401611519738050253t_unit: $tType).
% 54.91/14.51 thf(func_def_128, type, product_prod_nat_nat: $tType).
% 54.91/14.51 thf(func_def_129, type, product_prod_nat_int: $tType).
% 54.91/14.51 thf(func_def_130, type, product_prod_int_nat: $tType).
% 54.91/14.51 thf(func_def_131, type, product_prod_int_int: $tType).
% 54.91/14.51 thf(func_def_132, type, list_P4002435161011370285od_o_o: $tType).
% 54.91/14.51 thf(func_def_133, type, set_list_complex: $tType).
% 54.91/14.51 thf(func_def_134, type, set_Product_prod_o_o: $tType).
% 54.91/14.51 thf(func_def_135, type, set_list_literal: $tType).
% 54.91/14.51 thf(func_def_136, type, set_set_complex: $tType).
% 54.91/14.51 thf(func_def_137, type, array_VEBT_VEBTi: $tType).
% 54.91/14.51 thf(func_def_138, type, option_set_nat: $tType).
% 54.91/14.51 thf(func_def_139, type, option_set_int: $tType).
% 54.91/14.51 thf(func_def_140, type, list_VEBT_VEBTi: $tType).
% 54.91/14.51 thf(func_def_141, type, list_list_real: $tType).
% 54.91/14.51 thf(func_def_142, type, set_VEBT_VEBTi: $tType).
% 54.91/14.51 thf(func_def_143, type, set_list_real: $tType).
% 54.91/14.51 thf(func_def_144, type, list_list_nat: $tType).
% 54.91/14.51 thf(func_def_145, type, list_list_int: $tType).
% 54.91/14.51 thf(func_def_146, type, list_VEBT_VEBT: $tType).
% 54.91/14.51 thf(func_def_147, type, heap_Time_Heap_nat: $tType).
% 54.91/14.51 thf(func_def_148, type, set_set_real: $tType).
% 54.91/14.51 thf(func_def_149, type, set_list_nat: $tType).
% 54.91/14.51 thf(func_def_150, type, set_list_int: $tType).
% 54.91/14.51 thf(func_def_151, type, product_prod_nat_o: $tType).
% 54.91/14.51 thf(func_def_152, type, product_prod_int_o: $tType).
% 54.91/14.51 thf(func_def_153, type, product_prod_o_nat: $tType).
% 54.91/14.51 thf(func_def_154, type, product_prod_o_int: $tType).
% 54.91/14.51 thf(func_def_155, type, list_set_nat: $tType).
% 54.91/14.51 thf(func_def_156, type, list_Code_integer: $tType).
% 54.91/14.51 thf(func_def_157, type, set_VEBT_VEBT: $tType).
% 54.91/14.51 thf(func_def_158, type, set_set_nat: $tType).
% 54.91/14.51 thf(func_def_159, type, set_set_int: $tType).
% 54.91/14.51 thf(func_def_160, type, set_Code_integer: $tType).
% 54.91/14.51 thf(func_def_161, type, set_Product_unit: $tType).
% 54.91/14.51 thf(func_def_162, type, set_Numeral_num0: $tType).
% 54.91/14.51 thf(func_def_163, type, option_set_o: $tType).
% 54.91/14.51 thf(func_def_164, type, list_list_o: $tType).
% 54.91/14.51 thf(func_def_165, type, itself_Numeral_num0: $tType).
% 54.91/14.51 thf(func_def_166, type, list_complex: $tType).
% 54.91/14.51 thf(func_def_167, type, list_assn: $tType).
% 54.91/14.51 thf(func_def_168, type, heap_Time_Heap_o: $tType).
% 54.91/14.51 thf(func_def_169, type, set_list_o: $tType).
% 54.91/14.51 thf(func_def_170, type, product_prod_o_o: $tType).
% 54.91/14.51 thf(func_def_171, type, list_literal: $tType).
% 54.91/14.51 thf(func_def_172, type, set_complex: $tType).
% 54.91/14.51 thf(func_def_173, type, option_real: $tType).
% 54.91/14.51 thf(func_def_174, type, list_uint32: $tType).
% 54.91/14.51 thf(func_def_175, type, filter_real: $tType).
% 54.91/14.51 thf(func_def_176, type, set_literal: $tType).
% 54.91/14.51 thf(func_def_177, type, set_set_o: $tType).
% 54.91/14.51 thf(func_def_178, type, set_uint32: $tType).
% 54.91/14.51 thf(func_def_179, type, option_rat: $tType).
% 54.91/14.51 thf(func_def_180, type, option_num: $tType).
% 54.91/14.51 thf(func_def_181, type, option_nat: $tType).
% 54.91/14.51 thf(func_def_182, type, option_int: $tType).
% 54.91/14.51 thf(func_def_183, type, filter_nat: $tType).
% 54.91/14.51 thf(func_def_184, type, vEBT_VEBTi: $tType).
% 54.91/14.51 thf(func_def_185, type, list_real: $tType).
% 54.91/14.51 thf(func_def_186, type, set_real: $tType).
% 54.91/14.51 thf(func_def_187, type, list_rat: $tType).
% 54.91/14.51 thf(func_def_188, type, list_num: $tType).
% 54.91/14.51 thf(func_def_189, type, list_nat: $tType).
% 54.91/14.51 thf(func_def_190, type, list_int: $tType).
% 54.91/14.51 thf(func_def_191, type, vEBT_VEBT: $tType).
% 54.91/14.51 thf(func_def_192, type, set_rat: $tType).
% 54.91/14.51 thf(func_def_193, type, set_num: $tType).
% 54.91/14.51 thf(func_def_194, type, set_nat: $tType).
% 54.91/14.51 thf(func_def_195, type, set_int: $tType).
% 54.91/14.51 thf(func_def_196, type, code_integer: $tType).
% 54.91/14.51 thf(func_def_197, type, extended_enat: $tType).
% 54.91/14.51 thf(func_def_198, type, list_o: $tType).
% 54.91/14.51 thf(func_def_199, type, complex: $tType).
% 54.91/14.51 thf(func_def_200, type, assn: $tType).
% 54.91/14.51 thf(func_def_201, type, literal: $tType).
% 54.91/14.51 thf(func_def_202, type, set_o: $tType).
% 54.91/14.51 thf(func_def_203, type, uint32: $tType).
% 54.91/14.51 thf(func_def_204, type, char: $tType).
% 54.91/14.51 thf(func_def_205, type, real: $tType).
% 54.91/14.51 thf(func_def_206, type, rat: $tType).
% 54.91/14.51 thf(func_def_207, type, num: $tType).
% 54.91/14.51 thf(func_def_208, type, nat: $tType).
% 54.91/14.51 thf(func_def_209, type, int: $tType).
% 54.91/14.51 thf(func_def_210, type, archim7802044766580827645g_real: real > int).
% 54.91/14.51 thf(func_def_211, type, archim3151403230148437115or_rat: rat > int).
% 54.91/14.51 thf(func_def_212, type, archim6058952711729229775r_real: real > int).
% 54.91/14.51 thf(func_def_213, type, archimedean_frac_rat: rat > rat).
% 54.91/14.51 thf(func_def_214, type, archim2898591450579166408c_real: real > real).
% 54.91/14.51 thf(func_def_215, type, rep_assn: assn > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_216, type, entails: assn > assn > $o).
% 54.91/14.51 thf(func_def_217, type, ex_ass463751140784270563_VEBTi: (list_VEBT_VEBTi > assn) > assn).
% 54.91/14.51 thf(func_def_218, type, ex_assn_VEBT_VEBT: (vEBT_VEBT > assn) > assn).
% 54.91/14.51 thf(func_def_219, type, pure_assn: $o > assn).
% 54.91/14.51 thf(func_def_220, type, snga_assn_VEBT_VEBTi: array_VEBT_VEBTi > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_221, type, times_assn_raw: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_222, type, times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o).
% 54.91/14.51 thf(func_def_223, type, bNF_re3403563459893282935_int_o: (int > int > $o) > ((int > $o) > (int > $o) > $o) > (int > int > $o) > (int > int > $o) > $o).
% 54.91/14.51 thf(func_def_224, type, bNF_re711492959462206631nt_int: (int > int > $o) > ((int > int) > (int > int) > $o) > (int > int > int) > (int > int > int) > $o).
% 54.91/14.51 thf(func_def_225, type, bNF_re3376528473927230327_nat_o: (int > int > $o) > ((nat > $o) > (nat > $o) > $o) > (int > nat > $o) > (int > nat > $o) > $o).
% 54.91/14.51 thf(func_def_226, type, bNF_re5089333283451836215nt_o_o: (int > int > $o) > ($o > $o > $o) > (int > $o) > (int > $o) > $o).
% 54.91/14.51 thf(func_def_227, type, bNF_re4712519889275205905nt_int: (int > int > $o) > (int > int > $o) > (int > int) > (int > int) > $o).
% 54.91/14.51 thf(func_def_228, type, bNF_re3715656647883201625at_nat: (int > int > $o) > (nat > nat > $o) > (int > nat) > (int > nat) > $o).
% 54.91/14.51 thf(func_def_229, type, bNF_re4785983289428654063nt_int: (nat > nat > $o) > ((int > int) > (int > int) > $o) > (nat > int > int) > (nat > int > int) > $o).
% 54.91/14.51 thf(func_def_230, type, bNF_re578469030762574527_nat_o: (nat > nat > $o) > ((nat > $o) > (nat > $o) > $o) > (nat > nat > $o) > (nat > nat > $o) > $o).
% 54.91/14.51 thf(func_def_231, type, bNF_re1345281282404953727at_nat: (nat > nat > $o) > ((nat > nat) > (nat > nat) > $o) > (nat > nat > nat) > (nat > nat > nat) > $o).
% 54.91/14.51 thf(func_def_232, type, bNF_re4705727531993890431at_o_o: (nat > nat > $o) > ($o > $o > $o) > (nat > $o) > (nat > $o) > $o).
% 54.91/14.51 thf(func_def_233, type, bNF_re6650684261131312217nt_int: (nat > nat > $o) > (int > int > $o) > (nat > int) > (nat > int) > $o).
% 54.91/14.51 thf(func_def_234, type, bNF_re5653821019739307937at_nat: (nat > nat > $o) > (nat > nat > $o) > (nat > nat) > (nat > nat) > $o).
% 54.91/14.51 thf(func_def_235, type, bNF_re8402795839162346335um_int: (num > num > $o) > ((num > int) > (num > int) > $o) > (num > num > int) > (num > num > int) > $o).
% 54.91/14.51 thf(func_def_236, type, bNF_re1822329894187522285nt_int: (num > num > $o) > (int > int > $o) > (num > int) > (num > int) > $o).
% 54.91/14.51 thf(func_def_237, type, bNF_re7364608769721783435num1_o: (word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o) > ((word_N3645301735248828278l_num1 > $o) > (word_N3645301735248828278l_num1 > $o) > $o) > (word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o) > (word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o) > $o).
% 54.91/14.51 thf(func_def_238, type, bNF_re5013357767504289739m1_o_o: (word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o) > ($o > $o > $o) > (word_N3645301735248828278l_num1 > $o) > (word_N3645301735248828278l_num1 > $o) > $o).
% 54.91/14.51 thf(func_def_239, type, binomial: nat > nat > nat).
% 54.91/14.51 thf(func_def_240, type, bit_bi6516823479961619367ts_int: (nat > $o) > int).
% 54.91/14.51 thf(func_def_241, type, bit_wf_set_bits_int: (nat > $o) > $o).
% 54.91/14.51 thf(func_def_242, type, bit_concat_bit: nat > int > int > int).
% 54.91/14.51 thf(func_def_243, type, bit_ri7632146776885996613nteger: code_integer > code_integer).
% 54.91/14.51 thf(func_def_244, type, bit_ri7919022796975470100ot_int: int > int).
% 54.91/14.51 thf(func_def_245, type, bit_ri631733984087533419it_int: nat > int > int).
% 54.91/14.51 thf(func_def_246, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_247, type, bit_se725231765392027082nd_int: int > int > int).
% 54.91/14.51 thf(func_def_248, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_249, type, bit_se3928097537394005634nteger: nat > code_integer > code_integer).
% 54.91/14.51 thf(func_def_250, type, bit_se8568078237143864401it_int: nat > int > int).
% 54.91/14.51 thf(func_def_251, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_252, type, bit_se3964402333458159761uint32: nat > uint32 > uint32).
% 54.91/14.51 thf(func_def_253, type, bit_se5176125413884933531l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1).
% 54.91/14.51 thf(func_def_254, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 54.91/14.51 thf(func_def_255, type, bit_se2159334234014336723it_int: nat > int > int).
% 54.91/14.51 thf(func_def_256, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_257, type, bit_se2119862282449309892nteger: nat > code_integer).
% 54.91/14.51 thf(func_def_258, type, bit_se2000444600071755411sk_int: nat > int).
% 54.91/14.51 thf(func_def_259, type, bit_se2002935070580805687sk_nat: nat > nat).
% 54.91/14.51 thf(func_def_260, type, bit_se1080825931792720795nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_261, type, bit_se1409905431419307370or_int: int > int > int).
% 54.91/14.51 thf(func_def_262, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_263, type, bit_se2966626333419230250uint32: uint32 > uint32 > uint32).
% 54.91/14.51 thf(func_def_264, type, bit_se7788150548672797655nteger: nat > code_integer > code_integer).
% 54.91/14.51 thf(func_def_265, type, bit_se545348938243370406it_int: nat > int > int).
% 54.91/14.51 thf(func_def_266, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_267, type, bit_se5742574853984576102uint32: nat > uint32 > uint32).
% 54.91/14.51 thf(func_def_268, type, bit_se837345729053750000l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1).
% 54.91/14.51 thf(func_def_269, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 54.91/14.51 thf(func_def_270, type, bit_se7879613467334960850it_int: nat > int > int).
% 54.91/14.51 thf(func_def_271, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_272, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 54.91/14.51 thf(func_def_273, type, bit_se2923211474154528505it_int: nat > int > int).
% 54.91/14.51 thf(func_def_274, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_275, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 54.91/14.51 thf(func_def_276, type, bit_se4203085406695923979it_int: nat > int > int).
% 54.91/14.51 thf(func_def_277, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_278, type, bit_se3222712562003087583nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_279, type, bit_se6526347334894502574or_int: int > int > int).
% 54.91/14.51 thf(func_def_280, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_281, type, bit_se9216721137139052372nteger: code_integer > nat > $o).
% 54.91/14.51 thf(func_def_282, type, bit_se1146084159140164899it_int: int > nat > $o).
% 54.91/14.51 thf(func_def_283, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 54.91/14.51 thf(func_def_284, type, bit_se5367290876889521763uint32: uint32 > nat > $o).
% 54.91/14.51 thf(func_def_285, type, bit_se6859397288646540909l_num1: word_N3645301735248828278l_num1 > nat > $o).
% 54.91/14.51 thf(func_def_286, type, bit_Sh3965577149348748681tl_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_287, type, bit_Sh2154871086232339855tr_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_288, type, bits_integer_set_bit: code_integer > code_integer > $o > code_integer).
% 54.91/14.51 thf(func_def_289, type, bits_integer_shiftl: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_290, type, bits_integer_shiftr: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_291, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 54.91/14.51 thf(func_def_292, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_293, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_294, type, code_int_of_integer: code_integer > int).
% 54.91/14.51 thf(func_def_295, type, code_integer_of_int: int > code_integer).
% 54.91/14.51 thf(func_def_296, type, code_integer_of_nat: nat > code_integer).
% 54.91/14.51 thf(func_def_297, type, code_integer_of_num: num > code_integer).
% 54.91/14.51 thf(func_def_298, type, code_nat_of_integer: code_integer > nat).
% 54.91/14.51 thf(func_def_299, type, code_negative: num > code_integer).
% 54.91/14.51 thf(func_def_300, type, code_num_of_integer: code_integer > num).
% 54.91/14.51 thf(func_def_301, type, code_positive: num > code_integer).
% 54.91/14.51 thf(func_def_302, type, complete_Inf_Inf_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_303, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 54.91/14.51 thf(func_def_304, type, complete_Sup_Sup_int: set_int > int).
% 54.91/14.51 thf(func_def_305, type, complete_Sup_Sup_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_306, type, comple1385675409528146559p_real: set_real > real).
% 54.91/14.51 thf(func_def_307, type, complex2: real > real > complex).
% 54.91/14.51 thf(func_def_308, type, has_fi5821293074295781190e_real: (real > real) > real > filter_real > $o).
% 54.91/14.51 thf(func_def_309, type, adjust_div: product_prod_int_int > int).
% 54.91/14.51 thf(func_def_310, type, adjust_mod: int > int > int).
% 54.91/14.51 thf(func_def_311, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_312, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 54.91/14.51 thf(func_def_313, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 54.91/14.51 thf(func_def_314, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 54.91/14.51 thf(func_def_315, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_316, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 54.91/14.51 thf(func_def_317, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_318, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_319, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 54.91/14.51 thf(func_def_320, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_321, type, semiri1408675320244567234ct_nat: nat > nat).
% 54.91/14.51 thf(func_def_322, type, semiri2265585572941072030t_real: nat > real).
% 54.91/14.51 thf(func_def_323, type, inverse_inverse_real: real > real).
% 54.91/14.51 thf(func_def_324, type, at_bot_real: filter_real).
% 54.91/14.51 thf(func_def_325, type, at_top_nat: filter_nat).
% 54.91/14.51 thf(func_def_326, type, at_top_real: filter_real).
% 54.91/14.51 thf(func_def_327, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 54.91/14.51 thf(func_def_328, type, eventually_real: (real > $o) > filter_real > $o).
% 54.91/14.51 thf(func_def_329, type, filterlim_nat_nat: (nat > nat) > filter_nat > filter_nat > $o).
% 54.91/14.51 thf(func_def_330, type, filterlim_nat_real: (nat > real) > filter_real > filter_nat > $o).
% 54.91/14.51 thf(func_def_331, type, filterlim_real_real: (real > real) > filter_real > filter_real > $o).
% 54.91/14.51 thf(func_def_332, type, finite_Fpow_o: set_o > set_set_o).
% 54.91/14.51 thf(func_def_333, type, finite1532502677820914807nteger: set_Code_integer > set_set_Code_integer).
% 54.91/14.51 thf(func_def_334, type, finite_Fpow_complex: set_complex > set_set_complex).
% 54.91/14.51 thf(func_def_335, type, finite_Fpow_int: set_int > set_set_int).
% 54.91/14.51 thf(func_def_336, type, finite_Fpow_nat: set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_337, type, finite_Fpow_set_nat: set_set_nat > set_set_set_nat).
% 54.91/14.51 thf(func_def_338, type, finite_card_o: set_o > nat).
% 54.91/14.51 thf(func_def_339, type, finite4902975817058060853nteger: set_Code_integer > nat).
% 54.91/14.51 thf(func_def_340, type, finite_card_complex: set_complex > nat).
% 54.91/14.51 thf(func_def_341, type, finite_card_int: set_int > nat).
% 54.91/14.51 thf(func_def_342, type, finite_card_list_o: set_list_o > nat).
% 54.91/14.51 thf(func_def_343, type, finite5823187341872139973nteger: set_li6976499617229504675nteger > nat).
% 54.91/14.51 thf(func_def_344, type, finite5120063068150530198omplex: set_list_complex > nat).
% 54.91/14.51 thf(func_def_345, type, finite_card_list_int: set_list_int > nat).
% 54.91/14.51 thf(func_def_346, type, finite7325466520557071688st_nat: set_list_list_nat > nat).
% 54.91/14.51 thf(func_def_347, type, finite_card_list_nat: set_list_nat > nat).
% 54.91/14.51 thf(func_def_348, type, finite4141703471298347796t_real: set_list_real > nat).
% 54.91/14.51 thf(func_def_349, type, finite5631907774883551598et_nat: set_list_set_nat > nat).
% 54.91/14.51 thf(func_def_350, type, finite7554361855635516162iteral: set_list_literal > nat).
% 54.91/14.51 thf(func_def_351, type, finite5915292604075114978T_VEBT: set_list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_352, type, finite_card_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_353, type, finite_card_num: set_num > nat).
% 54.91/14.51 thf(func_def_354, type, finite6454714172617411596l_num0: set_Numeral_num0 > nat).
% 54.91/14.51 thf(func_def_355, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 54.91/14.51 thf(func_def_356, type, finite_card_rat: set_rat > nat).
% 54.91/14.51 thf(func_def_357, type, finite_card_real: set_real > nat).
% 54.91/14.51 thf(func_def_358, type, finite_card_set_nat: set_set_nat > nat).
% 54.91/14.51 thf(func_def_359, type, finite_card_literal: set_literal > nat).
% 54.91/14.51 thf(func_def_360, type, finite7802652506058667612T_VEBT: set_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_361, type, finite_finite_o: set_o > $o).
% 54.91/14.51 thf(func_def_362, type, finite6017078050557962740nteger: set_Code_integer > $o).
% 54.91/14.51 thf(func_def_363, type, finite3207457112153483333omplex: set_complex > $o).
% 54.91/14.51 thf(func_def_364, type, finite_finite_int: set_int > $o).
% 54.91/14.51 thf(func_def_365, type, finite_finite_list_o: set_list_o > $o).
% 54.91/14.51 thf(func_def_366, type, finite1283093830868386564nteger: set_li6976499617229504675nteger > $o).
% 54.91/14.51 thf(func_def_367, type, finite8712137658972009173omplex: set_list_complex > $o).
% 54.91/14.51 thf(func_def_368, type, finite3922522038869484883st_int: set_list_int > $o).
% 54.91/14.51 thf(func_def_369, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 54.91/14.51 thf(func_def_370, type, finite306553202115118035t_real: set_list_real > $o).
% 54.91/14.51 thf(func_def_371, type, finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_372, type, finite_finite_nat: set_nat > $o).
% 54.91/14.51 thf(func_def_373, type, finite_finite_num: set_num > $o).
% 54.91/14.51 thf(func_def_374, type, finite_finite_rat: set_rat > $o).
% 54.91/14.51 thf(func_def_375, type, finite_finite_real: set_real > $o).
% 54.91/14.51 thf(func_def_376, type, finite_finite_set_o: set_set_o > $o).
% 54.91/14.51 thf(func_def_377, type, finite6931041176100689706nteger: set_set_Code_integer > $o).
% 54.91/14.51 thf(func_def_378, type, finite6551019134538273531omplex: set_set_complex > $o).
% 54.91/14.51 thf(func_def_379, type, finite6197958912794628473et_int: set_set_int > $o).
% 54.91/14.51 thf(func_def_380, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 54.91/14.51 thf(func_def_381, type, finite9007344921179782393t_real: set_set_real > $o).
% 54.91/14.51 thf(func_def_382, type, finite9070685783930458813T_VEBT: set_set_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_383, type, finite5847741373460823677iteral: set_literal > $o).
% 54.91/14.51 thf(func_def_384, type, finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_385, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_386, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_387, type, comp_C3531382070062128313er_num: (code_integer > code_integer) > (num > code_integer) > num > code_integer).
% 54.91/14.51 thf(func_def_388, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 54.91/14.51 thf(func_def_389, type, comp_nat_o_nat: (nat > $o) > (nat > nat) > nat > $o).
% 54.91/14.51 thf(func_def_390, type, comp_nat_nat_nat: (nat > nat) > (nat > nat) > nat > nat).
% 54.91/14.51 thf(func_def_391, type, comp_nat_real_nat: (nat > real) > (nat > nat) > nat > real).
% 54.91/14.51 thf(func_def_392, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 54.91/14.51 thf(func_def_393, type, inj_on_real_real: (real > real) > set_real > $o).
% 54.91/14.51 thf(func_def_394, type, inj_on_set_nat_nat: (set_nat > nat) > set_set_nat > $o).
% 54.91/14.51 thf(func_def_395, type, strict1292158309912662752at_nat: (nat > nat) > set_nat > $o).
% 54.91/14.51 thf(func_def_396, type, the_in5290026491893676941l_real: set_real > (real > real) > real > real).
% 54.91/14.51 thf(func_def_397, type, gcd_Gcd_int: set_int > int).
% 54.91/14.51 thf(func_def_398, type, gcd_Gcd_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_399, type, bezw: nat > nat > product_prod_int_int).
% 54.91/14.51 thf(func_def_400, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 54.91/14.51 thf(func_def_401, type, gcd_gcd_int: int > int > int).
% 54.91/14.51 thf(func_def_402, type, gcd_gcd_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_403, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 54.91/14.51 thf(func_def_404, type, semiri4256215615220890538in_int: set_int > int).
% 54.91/14.51 thf(func_def_405, type, semiri4258706085729940814in_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_406, type, generi2397576812484419408nteger: code_integer > nat > $o > code_integer).
% 54.91/14.51 thf(func_def_407, type, generi1993664874377053279uint32: uint32 > nat > $o > uint32).
% 54.91/14.51 thf(func_def_408, type, generi5268133209446125161l_num1: word_N3645301735248828278l_num1 > nat > $o > word_N3645301735248828278l_num1).
% 54.91/14.51 thf(func_def_409, type, abs_abs_Code_integer: code_integer > code_integer).
% 54.91/14.51 thf(func_def_410, type, abs_abs_int: int > int).
% 54.91/14.51 thf(func_def_411, type, abs_abs_rat: rat > rat).
% 54.91/14.51 thf(func_def_412, type, abs_abs_real: real > real).
% 54.91/14.51 thf(func_def_413, type, minus_8727706125548526216plex_o: (complex > $o) > (complex > $o) > complex > $o).
% 54.91/14.51 thf(func_def_414, type, minus_minus_int_o: (int > $o) > (int > $o) > int > $o).
% 54.91/14.51 thf(func_def_415, type, minus_1139252259498527702_nat_o: (list_nat > $o) > (list_nat > $o) > list_nat > $o).
% 54.91/14.51 thf(func_def_416, type, minus_minus_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 54.91/14.51 thf(func_def_417, type, minus_minus_real_o: (real > $o) > (real > $o) > real > $o).
% 54.91/14.51 thf(func_def_418, type, minus_6910147592129066416_nat_o: (set_nat > $o) > (set_nat > $o) > set_nat > $o).
% 54.91/14.51 thf(func_def_419, type, minus_2794559001203777698VEBT_o: (vEBT_VEBT > $o) > (vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_420, type, minus_minus_assn: assn > assn > assn).
% 54.91/14.51 thf(func_def_421, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_422, type, minus_minus_complex: complex > complex > complex).
% 54.91/14.51 thf(func_def_423, type, minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat).
% 54.91/14.51 thf(func_def_424, type, minus_minus_int: int > int > int).
% 54.91/14.51 thf(func_def_425, type, minus_minus_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_426, type, minus_minus_rat: rat > rat > rat).
% 54.91/14.51 thf(func_def_427, type, minus_minus_real: real > real > real).
% 54.91/14.51 thf(func_def_428, type, minus_minus_set_o: set_o > set_o > set_o).
% 54.91/14.51 thf(func_def_429, type, minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_430, type, minus_811609699411566653omplex: set_complex > set_complex > set_complex).
% 54.91/14.51 thf(func_def_431, type, minus_minus_set_int: set_int > set_int > set_int).
% 54.91/14.51 thf(func_def_432, type, minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat).
% 54.91/14.51 thf(func_def_433, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_434, type, minus_minus_set_num: set_num > set_num > set_num).
% 54.91/14.51 thf(func_def_435, type, minus_minus_set_rat: set_rat > set_rat > set_rat).
% 54.91/14.51 thf(func_def_436, type, minus_minus_set_real: set_real > set_real > set_real).
% 54.91/14.51 thf(func_def_437, type, minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_438, type, minus_7832829386415567259iteral: set_literal > set_literal > set_literal).
% 54.91/14.51 thf(func_def_439, type, minus_3697805406911847364_VEBTi: set_VEBT_VEBTi > set_VEBT_VEBTi > set_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_440, type, minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_441, type, minus_minus_uint32: uint32 > uint32 > uint32).
% 54.91/14.51 thf(func_def_442, type, one_one_assn: assn).
% 54.91/14.51 thf(func_def_443, type, one_one_Code_integer: code_integer).
% 54.91/14.51 thf(func_def_444, type, one_one_complex: complex).
% 54.91/14.51 thf(func_def_445, type, one_one_int: int).
% 54.91/14.51 thf(func_def_446, type, one_one_nat: nat).
% 54.91/14.51 thf(func_def_447, type, one_one_rat: rat).
% 54.91/14.51 thf(func_def_448, type, one_one_real: real).
% 54.91/14.51 thf(func_def_449, type, one_one_uint32: uint32).
% 54.91/14.51 thf(func_def_450, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_451, type, plus_plus_complex: complex > complex > complex).
% 54.91/14.51 thf(func_def_452, type, plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat).
% 54.91/14.51 thf(func_def_453, type, plus_plus_int: int > int > int).
% 54.91/14.51 thf(func_def_454, type, plus_plus_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_455, type, plus_plus_num: num > num > num).
% 54.91/14.51 thf(func_def_456, type, plus_plus_rat: rat > rat > rat).
% 54.91/14.51 thf(func_def_457, type, plus_plus_real: real > real > real).
% 54.91/14.51 thf(func_def_458, type, plus_plus_uint32: uint32 > uint32 > uint32).
% 54.91/14.51 thf(func_def_459, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 54.91/14.51 thf(func_def_460, type, sgn_sgn_int: int > int).
% 54.91/14.51 thf(func_def_461, type, sgn_sgn_rat: rat > rat).
% 54.91/14.51 thf(func_def_462, type, sgn_sgn_real: real > real).
% 54.91/14.51 thf(func_def_463, type, times_times_assn: assn > assn > assn).
% 54.91/14.51 thf(func_def_464, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_465, type, times_times_complex: complex > complex > complex).
% 54.91/14.51 thf(func_def_466, type, times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat).
% 54.91/14.51 thf(func_def_467, type, times_times_int: int > int > int).
% 54.91/14.51 thf(func_def_468, type, times_times_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_469, type, times_times_rat: rat > rat > rat).
% 54.91/14.51 thf(func_def_470, type, times_times_real: real > real > real).
% 54.91/14.51 thf(func_def_471, type, times_times_uint32: uint32 > uint32 > uint32).
% 54.91/14.51 thf(func_def_472, type, uminus1680532995456772888plex_o: (complex > $o) > complex > $o).
% 54.91/14.51 thf(func_def_473, type, uminus_uminus_int_o: (int > $o) > int > $o).
% 54.91/14.51 thf(func_def_474, type, uminus5770388063884162150_nat_o: (list_nat > $o) > list_nat > $o).
% 54.91/14.51 thf(func_def_475, type, uminus_uminus_nat_o: (nat > $o) > nat > $o).
% 54.91/14.51 thf(func_def_476, type, uminus_uminus_real_o: (real > $o) > real > $o).
% 54.91/14.51 thf(func_def_477, type, uminus6401447641752708672_nat_o: (set_nat > $o) > set_nat > $o).
% 54.91/14.51 thf(func_def_478, type, uminus2746543603091002386VEBT_o: (vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_479, type, uminus_uminus_assn: assn > assn).
% 54.91/14.51 thf(func_def_480, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 54.91/14.51 thf(func_def_481, type, uminus1482373934393186551omplex: complex > complex).
% 54.91/14.51 thf(func_def_482, type, uminus_uminus_int: int > int).
% 54.91/14.51 thf(func_def_483, type, uminus_uminus_rat: rat > rat).
% 54.91/14.51 thf(func_def_484, type, uminus_uminus_real: real > real).
% 54.91/14.51 thf(func_def_485, type, uminus_uminus_set_o: set_o > set_o).
% 54.91/14.51 thf(func_def_486, type, uminus8566677241136511917omplex: set_complex > set_complex).
% 54.91/14.51 thf(func_def_487, type, uminus1532241313380277803et_int: set_int > set_int).
% 54.91/14.51 thf(func_def_488, type, uminus3195874150345416415st_nat: set_list_nat > set_list_nat).
% 54.91/14.51 thf(func_def_489, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 54.91/14.51 thf(func_def_490, type, uminus612125837232591019t_real: set_real > set_real).
% 54.91/14.51 thf(func_def_491, type, uminus613421341184616069et_nat: set_set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_492, type, uminus8041839845116263051T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_493, type, uminus_uminus_uint32: uint32 > uint32).
% 54.91/14.51 thf(func_def_494, type, zero_z3403309356797280102nteger: code_integer).
% 54.91/14.51 thf(func_def_495, type, zero_zero_complex: complex).
% 54.91/14.51 thf(func_def_496, type, zero_z5237406670263579293d_enat: extended_enat).
% 54.91/14.51 thf(func_def_497, type, zero_zero_int: int).
% 54.91/14.51 thf(func_def_498, type, zero_zero_nat: nat).
% 54.91/14.51 thf(func_def_499, type, zero_zero_rat: rat).
% 54.91/14.51 thf(func_def_500, type, zero_zero_real: real).
% 54.91/14.51 thf(func_def_501, type, zero_zero_uint32: uint32).
% 54.91/14.51 thf(func_def_502, type, groups8507830703676809646_o_nat: ($o > nat) > set_o > nat).
% 54.91/14.51 thf(func_def_503, type, groups7872700643590313910_o_rat: ($o > rat) > set_o > rat).
% 54.91/14.51 thf(func_def_504, type, groups8691415230153176458o_real: ($o > real) > set_o > real).
% 54.91/14.51 thf(func_def_505, type, groups7241207224191747786uint32: ($o > uint32) > set_o > uint32).
% 54.91/14.51 thf(func_def_506, type, groups8024822376189712711omplex: (code_integer > complex) > set_Code_integer > complex).
% 54.91/14.51 thf(func_def_507, type, groups7234854612051535045er_int: (code_integer > int) > set_Code_integer > int).
% 54.91/14.51 thf(func_def_508, type, groups7237345082560585321er_nat: (code_integer > nat) > set_Code_integer > nat).
% 54.91/14.51 thf(func_def_509, type, groups6602215022474089585er_rat: (code_integer > rat) > set_Code_integer > rat).
% 54.91/14.51 thf(func_def_510, type, groups1270011288395367621r_real: (code_integer > real) > set_Code_integer > real).
% 54.91/14.51 thf(func_def_511, type, groups8847630953604152069uint32: (code_integer > uint32) > set_Code_integer > uint32).
% 54.91/14.51 thf(func_def_512, type, groups6621422865394947399nteger: (complex > code_integer) > set_complex > code_integer).
% 54.91/14.51 thf(func_def_513, type, groups7754918857620584856omplex: (complex > complex) > set_complex > complex).
% 54.91/14.51 thf(func_def_514, type, groups5690904116761175830ex_int: (complex > int) > set_complex > int).
% 54.91/14.51 thf(func_def_515, type, groups5693394587270226106ex_nat: (complex > nat) > set_complex > nat).
% 54.91/14.51 thf(func_def_516, type, groups5058264527183730370ex_rat: (complex > rat) > set_complex > rat).
% 54.91/14.51 thf(func_def_517, type, groups5808333547571424918x_real: (complex > real) > set_complex > real).
% 54.91/14.51 thf(func_def_518, type, groups8736914816313324502uint32: (complex > uint32) > set_complex > uint32).
% 54.91/14.51 thf(func_def_519, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 54.91/14.51 thf(func_def_520, type, groups3049146728041665814omplex: (int > complex) > set_int > complex).
% 54.91/14.51 thf(func_def_521, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 54.91/14.51 thf(func_def_522, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 54.91/14.51 thf(func_def_523, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 54.91/14.51 thf(func_def_524, type, groups8778361861064173332t_real: (int > real) > set_int > real).
% 54.91/14.51 thf(func_def_525, type, groups5712668689793887828uint32: (int > uint32) > set_int > uint32).
% 54.91/14.51 thf(func_def_526, type, groups4396056296759096172at_nat: (list_nat > nat) > set_list_nat > nat).
% 54.91/14.51 thf(func_def_527, type, groups2073611262835488442omplex: (nat > complex) > set_nat > complex).
% 54.91/14.51 thf(func_def_528, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 54.91/14.51 thf(func_def_529, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 54.91/14.51 thf(func_def_530, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 54.91/14.51 thf(func_def_531, type, groups6591440286371151544t_real: (nat > real) > set_nat > real).
% 54.91/14.51 thf(func_def_532, type, groups833757482993574392uint32: (nat > uint32) > set_nat > uint32).
% 54.91/14.51 thf(func_def_533, type, groups7713935264441627589nteger: (real > code_integer) > set_real > code_integer).
% 54.91/14.51 thf(func_def_534, type, groups5754745047067104278omplex: (real > complex) > set_real > complex).
% 54.91/14.51 thf(func_def_535, type, groups1932886352136224148al_int: (real > int) > set_real > int).
% 54.91/14.51 thf(func_def_536, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
% 54.91/14.51 thf(func_def_537, type, groups1300246762558778688al_rat: (real > rat) > set_real > rat).
% 54.91/14.51 thf(func_def_538, type, groups8097168146408367636l_real: (real > real) > set_real > real).
% 54.91/14.51 thf(func_def_539, type, groups5944083974425963860uint32: (real > uint32) > set_real > uint32).
% 54.91/14.51 thf(func_def_540, type, groups8294997508430121362at_nat: (set_nat > nat) > set_set_nat > nat).
% 54.91/14.51 thf(func_def_541, type, groups8556826181031883383nteger: (literal > code_integer) > set_literal > code_integer).
% 54.91/14.51 thf(func_def_542, type, groups8649609317433967686al_int: (literal > int) > set_literal > int).
% 54.91/14.51 thf(func_def_543, type, groups8652099787943017962al_nat: (literal > nat) > set_literal > nat).
% 54.91/14.51 thf(func_def_544, type, groups2795228986978005958l_real: (literal > real) > set_literal > real).
% 54.91/14.51 thf(func_def_545, type, groups4542640294765070598uint32: (literal > uint32) > set_literal > uint32).
% 54.91/14.51 thf(func_def_546, type, groups5748017345553531991nteger: (vEBT_VEBT > code_integer) > set_VEBT_VEBT > code_integer).
% 54.91/14.51 thf(func_def_547, type, groups1794756597179926696omplex: (vEBT_VEBT > complex) > set_VEBT_VEBT > complex).
% 54.91/14.51 thf(func_def_548, type, groups769130701875090982BT_int: (vEBT_VEBT > int) > set_VEBT_VEBT > int).
% 54.91/14.51 thf(func_def_549, type, groups771621172384141258BT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_550, type, groups136491112297645522BT_rat: (vEBT_VEBT > rat) > set_VEBT_VEBT > rat).
% 54.91/14.51 thf(func_def_551, type, groups2240296850493347238T_real: (vEBT_VEBT > real) > set_VEBT_VEBT > real).
% 54.91/14.51 thf(func_def_552, type, groups8325533452322294502uint32: (vEBT_VEBT > uint32) > set_VEBT_VEBT > uint32).
% 54.91/14.51 thf(func_def_553, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 54.91/14.51 thf(func_def_554, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 54.91/14.51 thf(func_def_555, type, groups4561878855575611511st_nat: list_nat > nat).
% 54.91/14.51 thf(func_def_556, type, the_int: (int > $o) > int).
% 54.91/14.51 thf(func_def_557, type, the_real: (real > $o) > real).
% 54.91/14.51 thf(func_def_558, type, undefi7330133036835070352uint32: (nat > uint32 > uint32) > code_integer > uint32 > uint32).
% 54.91/14.51 thf(func_def_559, type, undefi8952517107220742160uint32: (nat > uint32 > uint32) > uint32 > code_integer > uint32).
% 54.91/14.51 thf(func_def_560, type, undefi8537048349889504752uint32: (uint32 > nat > $o > uint32) > uint32 > code_integer > $o > uint32).
% 54.91/14.51 thf(func_def_561, type, undefi6981832269580975664eger_o: (uint32 > nat > $o) > uint32 > code_integer > $o).
% 54.91/14.51 thf(func_def_562, type, undefi1878487536576149250nteger: code_integer > code_integer > $o > code_integer).
% 54.91/14.51 thf(func_def_563, type, undefi8133104259855420269nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_564, type, size_a6397454172108246045_VEBTi: (vEBT_VEBTi > nat) > array_VEBT_VEBTi > nat).
% 54.91/14.51 thf(func_def_565, type, heap_Time_return_nat: nat > heap_Time_Heap_nat).
% 54.91/14.51 thf(func_def_566, type, heap_T3487192422709364219on_nat: option_nat > heap_T2636463487746394924on_nat).
% 54.91/14.51 thf(func_def_567, type, hoare_hoare_triple_o: assn > heap_Time_Heap_o > ($o > assn) > $o).
% 54.91/14.51 thf(func_def_568, type, hoare_3067605981109127869le_nat: assn > heap_Time_Heap_nat > (nat > assn) > $o).
% 54.91/14.51 thf(func_def_569, type, hoare_7629718768684598413on_nat: assn > heap_T2636463487746394924on_nat > (option_nat > assn) > $o).
% 54.91/14.51 thf(func_def_570, type, hoare_1429296392585015714_VEBTi: assn > heap_T8145700208782473153_VEBTi > (vEBT_VEBTi > assn) > $o).
% 54.91/14.51 thf(func_def_571, type, if_assn: $o > assn > assn > assn).
% 54.91/14.51 thf(func_def_572, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_573, type, if_complex: $o > complex > complex > complex).
% 54.91/14.51 thf(func_def_574, type, if_int: $o > int > int > int).
% 54.91/14.51 thf(func_def_575, type, if_list_int: $o > list_int > list_int > list_int).
% 54.91/14.51 thf(func_def_576, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 54.91/14.51 thf(func_def_577, type, if_nat: $o > nat > nat > nat).
% 54.91/14.51 thf(func_def_578, type, if_num: $o > num > num > num).
% 54.91/14.51 thf(func_def_579, type, if_option_nat: $o > option_nat > option_nat > option_nat).
% 54.91/14.51 thf(func_def_580, type, if_option_set_o: $o > option_set_o > option_set_o > option_set_o).
% 54.91/14.51 thf(func_def_581, type, if_option_set_int: $o > option_set_int > option_set_int > option_set_int).
% 54.91/14.51 thf(func_def_582, type, if_option_set_nat: $o > option_set_nat > option_set_nat > option_set_nat).
% 54.91/14.51 thf(func_def_583, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 54.91/14.51 thf(func_def_584, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_585, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 54.91/14.51 thf(func_def_586, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_587, type, if_Pro1135515155860407935uint32: $o > produc827990862158126777uint32 > produc827990862158126777uint32 > produc827990862158126777uint32).
% 54.91/14.51 thf(func_def_588, type, if_rat: $o > rat > rat > rat).
% 54.91/14.51 thf(func_def_589, type, if_real: $o > real > real > real).
% 54.91/14.51 thf(func_def_590, type, if_set_int: $o > set_int > set_int > set_int).
% 54.91/14.51 thf(func_def_591, type, if_uint32: $o > uint32 > uint32 > uint32).
% 54.91/14.51 thf(func_def_592, type, if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_593, type, infini8530281810654367211te_nat: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_594, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 54.91/14.51 thf(func_def_595, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 54.91/14.51 thf(func_def_596, type, nat2: int > nat).
% 54.91/14.51 thf(func_def_597, type, ring_1_Ints_int: set_int).
% 54.91/14.51 thf(func_def_598, type, ring_1_Ints_rat: set_rat).
% 54.91/14.51 thf(func_def_599, type, ring_1_Ints_real: set_real).
% 54.91/14.51 thf(func_def_600, type, ring_1_Ints_uint32: set_uint32).
% 54.91/14.51 thf(func_def_601, type, ring_18347121197199848620nteger: int > code_integer).
% 54.91/14.51 thf(func_def_602, type, ring_1_of_int_rat: int > rat).
% 54.91/14.51 thf(func_def_603, type, ring_1_of_int_real: int > real).
% 54.91/14.51 thf(func_def_604, type, inf_inf_assn: assn > assn > assn).
% 54.91/14.51 thf(func_def_605, type, inf_inf_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_606, type, inf_inf_set_nat: set_nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_607, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 54.91/14.51 thf(func_def_608, type, sup_sup_assn: assn > assn > assn).
% 54.91/14.51 thf(func_def_609, type, sup_sup_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_610, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_611, type, lattic1921953407002678535_Max_o: set_o > $o).
% 54.91/14.51 thf(func_def_612, type, lattic4901227151466704046nteger: set_Code_integer > code_integer).
% 54.91/14.51 thf(func_def_613, type, lattic8263393255366662781ax_int: set_int > int).
% 54.91/14.51 thf(func_def_614, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_615, type, lattic4823215512031491691ax_num: set_num > num).
% 54.91/14.51 thf(func_def_616, type, lattic7630753665789217321ax_rat: set_rat > rat).
% 54.91/14.51 thf(func_def_617, type, lattic4275903605611617917x_real: set_real > real).
% 54.91/14.51 thf(func_def_618, type, lattic1973801136483472281_Min_o: set_o > $o).
% 54.91/14.51 thf(func_def_619, type, lattic1063845414844153500nteger: set_Code_integer > code_integer).
% 54.91/14.51 thf(func_def_620, type, lattic8718645017227715691in_int: set_int > int).
% 54.91/14.51 thf(func_def_621, type, lattic8721135487736765967in_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_622, type, lattic5278467273892544601in_num: set_num > num).
% 54.91/14.51 thf(func_def_623, type, lattic8086005427650270231in_rat: set_rat > rat).
% 54.91/14.51 thf(func_def_624, type, lattic3629708407755379051n_real: set_real > real).
% 54.91/14.51 thf(func_def_625, type, lattic2140725968369957399_o_rat: ($o > rat) > set_o > $o).
% 54.91/14.51 thf(func_def_626, type, lattic8697145971487455083o_real: ($o > real) > set_o > $o).
% 54.91/14.51 thf(func_def_627, type, lattic5439806495466278992er_rat: (code_integer > rat) > set_Code_integer > code_integer).
% 54.91/14.51 thf(func_def_628, type, lattic2659822949269061924r_real: (code_integer > real) > set_Code_integer > code_integer).
% 54.91/14.51 thf(func_def_629, type, lattic1922116423962787043ex_num: (complex > num) > set_complex > complex).
% 54.91/14.51 thf(func_def_630, type, lattic4729654577720512673ex_rat: (complex > rat) > set_complex > complex).
% 54.91/14.51 thf(func_def_631, type, lattic8794016678065449205x_real: (complex > real) > set_complex > complex).
% 54.91/14.51 thf(func_def_632, type, lattic7811156612396918303nt_rat: (int > rat) > set_int > int).
% 54.91/14.51 thf(func_def_633, type, lattic2675449441010098035t_real: (int > real) > set_int > int).
% 54.91/14.51 thf(func_def_634, type, lattic6811802900495863747at_rat: (nat > rat) > set_nat > nat).
% 54.91/14.51 thf(func_def_635, type, lattic488527866317076247t_real: (nat > real) > set_nat > nat).
% 54.91/14.51 thf(func_def_636, type, lattic1613168225601753569al_num: (real > num) > set_real > real).
% 54.91/14.51 thf(func_def_637, type, lattic4420706379359479199al_rat: (real > rat) > set_real > real).
% 54.91/14.51 thf(func_def_638, type, lattic3331990488459210229BT_num: (vEBT_VEBT > num) > set_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_639, type, lattic6139528642216935859BT_rat: (vEBT_VEBT > rat) > set_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_640, type, bfun_nat_real: (nat > real) > filter_nat > $o).
% 54.91/14.51 thf(func_def_641, type, at_infinity_real: filter_real).
% 54.91/14.51 thf(func_def_642, type, append_o: list_o > list_o > list_o).
% 54.91/14.51 thf(func_def_643, type, append_int: list_int > list_int > list_int).
% 54.91/14.51 thf(func_def_644, type, append_nat: list_nat > list_nat > list_nat).
% 54.91/14.51 thf(func_def_645, type, butlast_o: list_o > list_o).
% 54.91/14.51 thf(func_def_646, type, butlast_int: list_int > list_int).
% 54.91/14.51 thf(func_def_647, type, butlast_nat: list_nat > list_nat).
% 54.91/14.51 thf(func_def_648, type, butlast_real: list_real > list_real).
% 54.91/14.51 thf(func_def_649, type, butlast_VEBT_VEBTi: list_VEBT_VEBTi > list_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_650, type, butlast_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_651, type, concat_o: list_list_o > list_o).
% 54.91/14.51 thf(func_def_652, type, concat_nat: list_list_nat > list_nat).
% 54.91/14.51 thf(func_def_653, type, concat_real: list_list_real > list_real).
% 54.91/14.51 thf(func_def_654, type, concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_655, type, count_list_o: list_o > $o > nat).
% 54.91/14.51 thf(func_def_656, type, count_3970941599679287265nteger: list_Code_integer > code_integer > nat).
% 54.91/14.51 thf(func_def_657, type, count_list_complex: list_complex > complex > nat).
% 54.91/14.51 thf(func_def_658, type, count_list_int: list_int > int > nat).
% 54.91/14.51 thf(func_def_659, type, count_list_nat: list_nat > nat > nat).
% 54.91/14.51 thf(func_def_660, type, count_list_real: list_real > real > nat).
% 54.91/14.51 thf(func_def_661, type, count_list_set_nat: list_set_nat > set_nat > nat).
% 54.91/14.51 thf(func_def_662, type, count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_663, type, distinct_o: list_o > $o).
% 54.91/14.51 thf(func_def_664, type, distin1543349897113766820nteger: list_Code_integer > $o).
% 54.91/14.51 thf(func_def_665, type, distinct_complex: list_complex > $o).
% 54.91/14.51 thf(func_def_666, type, distinct_int: list_int > $o).
% 54.91/14.51 thf(func_def_667, type, distinct_nat: list_nat > $o).
% 54.91/14.51 thf(func_def_668, type, distinct_num: list_num > $o).
% 54.91/14.51 thf(func_def_669, type, distinct_rat: list_rat > $o).
% 54.91/14.51 thf(func_def_670, type, distinct_real: list_real > $o).
% 54.91/14.51 thf(func_def_671, type, distinct_set_nat: list_set_nat > $o).
% 54.91/14.51 thf(func_def_672, type, distinct_VEBT_VEBTi: list_VEBT_VEBTi > $o).
% 54.91/14.51 thf(func_def_673, type, distinct_VEBT_VEBT: list_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_674, type, enumerate_o: nat > list_o > list_P7333126701944960589_nat_o).
% 54.91/14.51 thf(func_def_675, type, enumerate_int: nat > list_int > list_P3521021558325789923at_int).
% 54.91/14.51 thf(func_def_676, type, enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat).
% 54.91/14.51 thf(func_def_677, type, enumerate_real: nat > list_real > list_P3644420460460130531t_real).
% 54.91/14.51 thf(func_def_678, type, enumerate_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_P2320588648998582380_VEBTi).
% 54.91/14.51 thf(func_def_679, type, enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 54.91/14.51 thf(func_def_680, type, filter_nat2: (nat > $o) > list_nat > list_nat).
% 54.91/14.51 thf(func_def_681, type, foldl_assn_assn: (assn > assn > assn) > assn > list_assn > assn).
% 54.91/14.51 thf(func_def_682, type, foldl_int_int: (int > int > int) > int > list_int > int).
% 54.91/14.51 thf(func_def_683, type, foldl_nat_o: (nat > $o > nat) > nat > list_o > nat).
% 54.91/14.51 thf(func_def_684, type, foldl_nat_nat: (nat > nat > nat) > nat > list_nat > nat).
% 54.91/14.51 thf(func_def_685, type, foldl_nat_real: (nat > real > nat) > nat > list_real > nat).
% 54.91/14.51 thf(func_def_686, type, foldl_nat_VEBT_VEBT: (nat > vEBT_VEBT > nat) > nat > list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_687, type, foldl_rat_rat: (rat > rat > rat) > rat > list_rat > rat).
% 54.91/14.51 thf(func_def_688, type, foldl_real_real: (real > real > real) > real > list_real > real).
% 54.91/14.51 thf(func_def_689, type, foldl_uint32_uint32: (uint32 > uint32 > uint32) > uint32 > list_uint32 > uint32).
% 54.91/14.51 thf(func_def_690, type, foldr_o_nat: ($o > nat > nat) > list_o > nat > nat).
% 54.91/14.51 thf(func_def_691, type, foldr_nat_nat: (nat > nat > nat) > list_nat > nat > nat).
% 54.91/14.51 thf(func_def_692, type, foldr_real_nat: (real > nat > nat) > list_real > nat > nat).
% 54.91/14.51 thf(func_def_693, type, foldr_real_real: (real > real > real) > list_real > real > real).
% 54.91/14.51 thf(func_def_694, type, foldr_VEBT_VEBT_nat: (vEBT_VEBT > nat > nat) > list_VEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_695, type, last_o: list_o > $o).
% 54.91/14.51 thf(func_def_696, type, last_int: list_int > int).
% 54.91/14.51 thf(func_def_697, type, last_nat: list_nat > nat).
% 54.91/14.51 thf(func_def_698, type, last_real: list_real > real).
% 54.91/14.51 thf(func_def_699, type, last_VEBT_VEBTi: list_VEBT_VEBTi > vEBT_VEBTi).
% 54.91/14.51 thf(func_def_700, type, last_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_701, type, lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o).
% 54.91/14.51 thf(func_def_702, type, lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int).
% 54.91/14.51 thf(func_def_703, type, lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat).
% 54.91/14.51 thf(func_def_704, type, lenlex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real).
% 54.91/14.51 thf(func_def_705, type, lenlex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32).
% 54.91/14.51 thf(func_def_706, type, lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT).
% 54.91/14.51 thf(func_def_707, type, lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o).
% 54.91/14.51 thf(func_def_708, type, lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int).
% 54.91/14.51 thf(func_def_709, type, lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat).
% 54.91/14.51 thf(func_def_710, type, lex_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real).
% 54.91/14.51 thf(func_def_711, type, lex_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32).
% 54.91/14.51 thf(func_def_712, type, lex_VEBT_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr4797120415438012619_VEBTi).
% 54.91/14.51 thf(func_def_713, type, lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT).
% 54.91/14.51 thf(func_def_714, type, linord3142498349692569832_set_o: set_o > list_o).
% 54.91/14.51 thf(func_def_715, type, linord2324613341767563021nteger: set_Code_integer > list_Code_integer).
% 54.91/14.51 thf(func_def_716, type, linord2612477271533052124et_int: set_int > list_int).
% 54.91/14.51 thf(func_def_717, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 54.91/14.51 thf(func_def_718, type, linord8395671565052656842et_num: set_num > list_num).
% 54.91/14.51 thf(func_def_719, type, linord1979837681955606664et_rat: set_rat > list_rat).
% 54.91/14.51 thf(func_def_720, type, linord4252657396651189596t_real: set_real > list_real).
% 54.91/14.51 thf(func_def_721, type, linord2913955441264437540iteral: set_literal > list_literal).
% 54.91/14.51 thf(func_def_722, type, cons_o: $o > list_o > list_o).
% 54.91/14.51 thf(func_def_723, type, cons_Code_integer: code_integer > list_Code_integer > list_Code_integer).
% 54.91/14.51 thf(func_def_724, type, cons_int: int > list_int > list_int).
% 54.91/14.51 thf(func_def_725, type, cons_nat: nat > list_nat > list_nat).
% 54.91/14.51 thf(func_def_726, type, cons_num: num > list_num > list_num).
% 54.91/14.51 thf(func_def_727, type, cons_P8766293264717362397od_o_o: product_prod_o_o > list_P4002435161011370285od_o_o > list_P4002435161011370285od_o_o).
% 54.91/14.51 thf(func_def_728, type, cons_P1455986808126089405_o_int: product_prod_o_int > list_P3795440434834930179_o_int > list_P3795440434834930179_o_int).
% 54.91/14.51 thf(func_def_729, type, cons_P5633837827635286113_o_nat: product_prod_o_nat > list_P6285523579766656935_o_nat > list_P6285523579766656935_o_nat).
% 54.91/14.51 thf(func_def_730, type, cons_P7321330006258091179_int_o: product_prod_int_o > list_P5087981734274514673_int_o > list_P5087981734274514673_int_o).
% 54.91/14.51 thf(func_def_731, type, cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int).
% 54.91/14.51 thf(func_def_732, type, cons_P7512249878480867347nt_nat: product_prod_int_nat > list_P8198026277950538467nt_nat > list_P8198026277950538467nt_nat).
% 54.91/14.51 thf(func_def_733, type, cons_P9142372351690779143_nat_o: product_prod_nat_o > list_P7333126701944960589_nat_o > list_P7333126701944960589_nat_o).
% 54.91/14.51 thf(func_def_734, type, cons_P2335045147070616083at_int: product_prod_nat_int > list_P3521021558325789923at_int > list_P3521021558325789923at_int).
% 54.91/14.51 thf(func_def_735, type, cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat).
% 54.91/14.51 thf(func_def_736, type, cons_P3149448846263281007uint32: produc827990862158126777uint32 > list_P3069071885182933823uint32 > list_P3069071885182933823uint32).
% 54.91/14.51 thf(func_def_737, type, cons_rat: rat > list_rat > list_rat).
% 54.91/14.51 thf(func_def_738, type, cons_real: real > list_real > list_real).
% 54.91/14.51 thf(func_def_739, type, cons_set_nat: set_nat > list_set_nat > list_set_nat).
% 54.91/14.51 thf(func_def_740, type, cons_uint32: uint32 > list_uint32 > list_uint32).
% 54.91/14.51 thf(func_def_741, type, cons_VEBT_VEBTi: vEBT_VEBTi > list_VEBT_VEBTi > list_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_742, type, cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_743, type, nil_o: list_o).
% 54.91/14.51 thf(func_def_744, type, nil_int: list_int).
% 54.91/14.51 thf(func_def_745, type, nil_nat: list_nat).
% 54.91/14.51 thf(func_def_746, type, hd_nat: list_nat > nat).
% 54.91/14.51 thf(func_def_747, type, map_nat_o: (nat > $o) > list_nat > list_o).
% 54.91/14.51 thf(func_def_748, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 54.91/14.51 thf(func_def_749, type, map_Pr7541730621154948341_o_o_o: (product_prod_o_o > $o) > list_P4002435161011370285od_o_o > list_o).
% 54.91/14.51 thf(func_def_750, type, map_VEBT_VEBT_nat: (vEBT_VEBT > nat) > list_VEBT_VEBT > list_nat).
% 54.91/14.51 thf(func_def_751, type, map_VEBT_VEBT_real: (vEBT_VEBT > real) > list_VEBT_VEBT > list_real).
% 54.91/14.51 thf(func_def_752, type, set_Pr400311997697478754_nat_o: list_P7985473006766602707_nat_o > set_Pr4532377907799695533_nat_o).
% 54.91/14.51 thf(func_def_753, type, set_o2: list_o > set_o).
% 54.91/14.51 thf(func_def_754, type, set_Code_integer2: list_Code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_755, type, set_complex2: list_complex > set_complex).
% 54.91/14.51 thf(func_def_756, type, set_int2: list_int > set_int).
% 54.91/14.51 thf(func_def_757, type, set_list_o2: list_list_o > set_list_o).
% 54.91/14.51 thf(func_def_758, type, set_list_int2: list_list_int > set_list_int).
% 54.91/14.51 thf(func_def_759, type, set_list_nat2: list_list_nat > set_list_nat).
% 54.91/14.51 thf(func_def_760, type, set_list_real2: list_list_real > set_list_real).
% 54.91/14.51 thf(func_def_761, type, set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_762, type, set_nat2: list_nat > set_nat).
% 54.91/14.51 thf(func_def_763, type, set_num2: list_num > set_num).
% 54.91/14.51 thf(func_def_764, type, set_Pr7458301993993767461et_nat: list_P362550909693114634et_nat > set_Pr8536935166611901872et_nat).
% 54.91/14.51 thf(func_def_765, type, set_Pr364071364088684201et_nat: list_P2321686559999237006et_nat > set_Pr3286484037609594932et_nat).
% 54.91/14.51 thf(func_def_766, type, set_Product_prod_o_o2: list_P4002435161011370285od_o_o > set_Product_prod_o_o).
% 54.91/14.51 thf(func_def_767, type, set_Pr3864771053587467565et_nat: list_P9062070895058802706et_nat > set_Pr3948176798113811640et_nat).
% 54.91/14.51 thf(func_def_768, type, set_Pr8694291782656941196_int_o: list_P5087981734274514673_int_o > set_Pr903927857289325719_int_o).
% 54.91/14.51 thf(func_def_769, type, set_Pr2470121279949933262nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int).
% 54.91/14.51 thf(func_def_770, type, set_Pr6647972299459129970nt_nat: list_P8198026277950538467nt_nat > set_Pr3448869479623346877nt_nat).
% 54.91/14.51 thf(func_def_771, type, set_Pr112895574167722958t_real: list_P6863124054624500543t_real > set_Pr3538720872664544793t_real).
% 54.91/14.51 thf(func_def_772, type, set_Pr8714266321650254504T_VEBT: list_P7524865323317820941T_VEBT > set_Pr8044002425091019955T_VEBT).
% 54.91/14.51 thf(func_def_773, type, set_Pr1470767568048878706at_int: list_P3521021558325789923at_int > set_Pr7995236796853374141at_int).
% 54.91/14.51 thf(func_def_774, type, set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat).
% 54.91/14.51 thf(func_def_775, type, set_Pr8219819362198175822al_int: list_P4344331454722006975al_int > set_Pr1019928272762051225al_int).
% 54.91/14.51 thf(func_def_776, type, set_Pr5999470521830281550l_real: list_P8689742595348180415l_real > set_Pr6218003697084177305l_real).
% 54.91/14.51 thf(func_def_777, type, set_Pr8897343066327330088T_VEBT: list_P877281246627933069T_VEBT > set_Pr6019664923565264691T_VEBT).
% 54.91/14.51 thf(func_def_778, type, set_Pr9040384385603167362et_nat: list_P6254988961118846195et_nat > set_Pr5488025237498180813et_nat).
% 54.91/14.51 thf(func_def_779, type, set_Pr2418681094996576974uint32: list_P3069071885182933823uint32 > set_Pr1773385645901665561uint32).
% 54.91/14.51 thf(func_def_780, type, set_Pr7708085864119495200VEBT_o: list_P3126845725202233233VEBT_o > set_Pr3175402225741728619VEBT_o).
% 54.91/14.51 thf(func_def_781, type, set_Pr2853735649769556538BT_int: list_P4547456442757143711BT_int > set_Pr5066593544530342725BT_int).
% 54.91/14.51 thf(func_def_782, type, set_Pr7031586669278753246BT_nat: list_P7037539587688870467BT_nat > set_Pr7556676689462069481BT_nat).
% 54.91/14.51 thf(func_def_783, type, set_Pr1087130671499945274T_real: list_P2623026923184700063T_real > set_Pr7765410600122031685T_real).
% 54.91/14.51 thf(func_def_784, type, set_Pr9182192707038809660T_VEBT: list_P7413028617227757229T_VEBT > set_Pr6192946355708809607T_VEBT).
% 54.91/14.51 thf(func_def_785, type, set_rat2: list_rat > set_rat).
% 54.91/14.51 thf(func_def_786, type, set_real2: list_real > set_real).
% 54.91/14.51 thf(func_def_787, type, set_set_nat2: list_set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_788, type, set_literal2: list_literal > set_literal).
% 54.91/14.51 thf(func_def_789, type, set_uint322: list_uint32 > set_uint32).
% 54.91/14.51 thf(func_def_790, type, set_VEBT_VEBTi2: list_VEBT_VEBTi > set_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_791, type, set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_792, type, size_list_VEBT_VEBT: (vEBT_VEBT > nat) > list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_793, type, list_u6943956310655620667_nat_o: list_P7985473006766602707_nat_o > nat > (produc3658429121746597890et_nat > $o) > list_P7985473006766602707_nat_o).
% 54.91/14.51 thf(func_def_794, type, list_update_o: list_o > nat > $o > list_o).
% 54.91/14.51 thf(func_def_795, type, list_update_int: list_int > nat > int > list_int).
% 54.91/14.51 thf(func_def_796, type, list_update_nat: list_nat > nat > nat > list_nat).
% 54.91/14.51 thf(func_def_797, type, list_u1913845194572276492et_nat: list_P362550909693114634et_nat > nat > produc2732055786443039994et_nat > list_P362550909693114634et_nat).
% 54.91/14.51 thf(func_def_798, type, list_u1866171116859985808et_nat: list_P2321686559999237006et_nat > nat > produc3925858234332021118et_nat > list_P2321686559999237006et_nat).
% 54.91/14.51 thf(func_def_799, type, list_u1537252308907898773od_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o > list_P4002435161011370285od_o_o).
% 54.91/14.51 thf(func_def_800, type, list_u9060326803697358356et_nat: list_P9062070895058802706et_nat > nat > produc3658429121746597890et_nat > list_P9062070895058802706et_nat).
% 54.91/14.51 thf(func_def_801, type, list_u3002344382305578791nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int > list_P5707943133018811711nt_int).
% 54.91/14.51 thf(func_def_802, type, list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat).
% 54.91/14.51 thf(func_def_803, type, list_u2546161786664092711uint32: list_P3069071885182933823uint32 > nat > produc827990862158126777uint32 > list_P3069071885182933823uint32).
% 54.91/14.51 thf(func_def_804, type, list_u30558089781959097_VEBTi: list_P785718909624839377_VEBTi > nat > produc3777764054643897931_VEBTi > list_P785718909624839377_VEBTi).
% 54.91/14.51 thf(func_def_805, type, list_u9044509791230035014T_VEBT: list_P5988454224134618948T_VEBT > nat > produc2810682830582626868T_VEBT > list_P5988454224134618948T_VEBT).
% 54.91/14.51 thf(func_def_806, type, list_u636002643828906794_VEBTi: list_P735349106241217576_VEBTi > nat > produc3625547720036274456_VEBTi > list_P735349106241217576_VEBTi).
% 54.91/14.51 thf(func_def_807, type, list_u6961636818849549845T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT > list_P7413028617227757229T_VEBT).
% 54.91/14.51 thf(func_def_808, type, list_update_real: list_real > nat > real > list_real).
% 54.91/14.51 thf(func_def_809, type, list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat).
% 54.91/14.51 thf(func_def_810, type, list_update_uint32: list_uint32 > nat > uint32 > list_uint32).
% 54.91/14.51 thf(func_def_811, type, list_u6098035379799741383_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi > list_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_812, type, list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_813, type, listrel1_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o).
% 54.91/14.51 thf(func_def_814, type, listrel1_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int).
% 54.91/14.51 thf(func_def_815, type, listrel1_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat).
% 54.91/14.51 thf(func_def_816, type, listrel1_real: set_Pr6218003697084177305l_real > set_Pr611352295856513593t_real).
% 54.91/14.51 thf(func_def_817, type, listrel1_uint32: set_Pr1773385645901665561uint32 > set_Pr2258164808687509945uint32).
% 54.91/14.51 thf(func_def_818, type, listrel1_VEBT_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr4797120415438012619_VEBTi).
% 54.91/14.51 thf(func_def_819, type, listrel1_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT).
% 54.91/14.51 thf(func_def_820, type, nth_o: list_o > nat > $o).
% 54.91/14.51 thf(func_def_821, type, nth_int: list_int > nat > int).
% 54.91/14.51 thf(func_def_822, type, nth_nat: list_nat > nat > nat).
% 54.91/14.51 thf(func_def_823, type, nth_num: list_num > nat > num).
% 54.91/14.51 thf(func_def_824, type, nth_Pr4439495888332055232nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int).
% 54.91/14.51 thf(func_def_825, type, nth_Pr731366597535767232t_real: list_P6863124054624500543t_real > nat > produc679980390762269497t_real).
% 54.91/14.51 thf(func_def_826, type, nth_Pr5092243222550848201_VEBTi: list_P4447955379000644808_VEBTi > nat > produc2062302194595185346_VEBTi).
% 54.91/14.51 thf(func_def_827, type, nth_Pr3474266648193625910T_VEBT: list_P7524865323317820941T_VEBT > nat > produc1531783533982839933T_VEBT).
% 54.91/14.51 thf(func_def_828, type, nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o).
% 54.91/14.51 thf(func_def_829, type, nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int).
% 54.91/14.51 thf(func_def_830, type, nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_831, type, nth_Pr7767817059697521252t_real: list_P3644420460460130531t_real > nat > produc7716430852924023517t_real).
% 54.91/14.51 thf(func_def_832, type, nth_Pr3244165891152107629_VEBTi: list_P2320588648998582380_VEBTi > nat > produc214224863196444774_VEBTi).
% 54.91/14.51 thf(func_def_833, type, nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT).
% 54.91/14.51 thf(func_def_834, type, nth_Pr6139322253122866368uint32: list_P3069071885182933823uint32 > nat > produc827990862158126777uint32).
% 54.91/14.51 thf(func_def_835, type, nth_Pr3306050735993963089EBTi_o: list_P8833571063612306856EBTi_o > nat > produc5014006835512566296EBTi_o).
% 54.91/14.51 thf(func_def_836, type, nth_Pr2733638074192486473Ti_int: list_P7392757774524453448Ti_int > nat > produc8927069083091599426Ti_int).
% 54.91/14.51 thf(func_def_837, type, nth_Pr3433448822664029129i_real: list_P8536626330812492744i_real > nat > produc6680258955013199682i_real).
% 54.91/14.51 thf(func_def_838, type, nth_Pr6329974346453275474_VEBTi: list_P785718909624839377_VEBTi > nat > produc3777764054643897931_VEBTi).
% 54.91/14.51 thf(func_def_839, type, nth_Pr8725177398587324397T_VEBT: list_P5988454224134618948T_VEBT > nat > produc2810682830582626868T_VEBT).
% 54.91/14.51 thf(func_def_840, type, nth_rat: list_rat > nat > rat).
% 54.91/14.51 thf(func_def_841, type, nth_real: list_real > nat > real).
% 54.91/14.51 thf(func_def_842, type, nth_set_nat: list_set_nat > nat > set_nat).
% 54.91/14.51 thf(func_def_843, type, nth_uint32: list_uint32 > nat > uint32).
% 54.91/14.51 thf(func_def_844, type, nth_VEBT_VEBTi: list_VEBT_VEBTi > nat > vEBT_VEBTi).
% 54.91/14.51 thf(func_def_845, type, nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_846, type, remove1_o: $o > list_o > list_o).
% 54.91/14.51 thf(func_def_847, type, remove1_Code_integer: code_integer > list_Code_integer > list_Code_integer).
% 54.91/14.51 thf(func_def_848, type, remove1_int: int > list_int > list_int).
% 54.91/14.51 thf(func_def_849, type, remove1_nat: nat > list_nat > list_nat).
% 54.91/14.51 thf(func_def_850, type, remove1_num: num > list_num > list_num).
% 54.91/14.51 thf(func_def_851, type, remove1_rat: rat > list_rat > list_rat).
% 54.91/14.51 thf(func_def_852, type, remove1_real: real > list_real > list_real).
% 54.91/14.51 thf(func_def_853, type, remove1_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_854, type, removeAll_o: $o > list_o > list_o).
% 54.91/14.51 thf(func_def_855, type, removeAll_int: int > list_int > list_int).
% 54.91/14.51 thf(func_def_856, type, removeAll_nat: nat > list_nat > list_nat).
% 54.91/14.51 thf(func_def_857, type, removeAll_real: real > list_real > list_real).
% 54.91/14.51 thf(func_def_858, type, removeAll_set_nat: set_nat > list_set_nat > list_set_nat).
% 54.91/14.51 thf(func_def_859, type, removeAll_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_860, type, replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_861, type, rotate1_o: list_o > list_o).
% 54.91/14.51 thf(func_def_862, type, rotate1_nat: list_nat > list_nat).
% 54.91/14.51 thf(func_def_863, type, rotate1_real: list_real > list_real).
% 54.91/14.51 thf(func_def_864, type, rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_865, type, sorted_wrt_o: ($o > $o > $o) > list_o > $o).
% 54.91/14.51 thf(func_def_866, type, sorted710888440204495920nteger: (code_integer > code_integer > $o) > list_Code_integer > $o).
% 54.91/14.51 thf(func_def_867, type, sorted_wrt_int: (int > int > $o) > list_int > $o).
% 54.91/14.51 thf(func_def_868, type, sorted_wrt_nat: (nat > nat > $o) > list_nat > $o).
% 54.91/14.51 thf(func_def_869, type, sorted_wrt_num: (num > num > $o) > list_num > $o).
% 54.91/14.51 thf(func_def_870, type, sorted_wrt_rat: (rat > rat > $o) > list_rat > $o).
% 54.91/14.51 thf(func_def_871, type, sorted_wrt_real: (real > real > $o) > list_real > $o).
% 54.91/14.51 thf(func_def_872, type, sorted_wrt_literal: (literal > literal > $o) > list_literal > $o).
% 54.91/14.51 thf(func_def_873, type, sorted9206477368072086664_VEBTi: (vEBT_VEBTi > vEBT_VEBTi > $o) > list_VEBT_VEBTi > $o).
% 54.91/14.51 thf(func_def_874, type, sorted_wrt_VEBT_VEBT: (vEBT_VEBT > vEBT_VEBT > $o) > list_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_875, type, subseqs_o: list_o > list_list_o).
% 54.91/14.51 thf(func_def_876, type, subseqs_int: list_int > list_list_int).
% 54.91/14.51 thf(func_def_877, type, subseqs_nat: list_nat > list_list_nat).
% 54.91/14.51 thf(func_def_878, type, subseqs_real: list_real > list_list_real).
% 54.91/14.51 thf(func_def_879, type, subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_880, type, take_o: nat > list_o > list_o).
% 54.91/14.51 thf(func_def_881, type, take_int: nat > list_int > list_int).
% 54.91/14.51 thf(func_def_882, type, take_nat: nat > list_nat > list_nat).
% 54.91/14.51 thf(func_def_883, type, take_num: nat > list_num > list_num).
% 54.91/14.51 thf(func_def_884, type, take_rat: nat > list_rat > list_rat).
% 54.91/14.51 thf(func_def_885, type, take_real: nat > list_real > list_real).
% 54.91/14.51 thf(func_def_886, type, take_set_nat: nat > list_set_nat > list_set_nat).
% 54.91/14.51 thf(func_def_887, type, take_uint32: nat > list_uint32 > list_uint32).
% 54.91/14.51 thf(func_def_888, type, take_VEBT_VEBTi: nat > list_VEBT_VEBTi > list_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_889, type, take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_890, type, upt: nat > nat > list_nat).
% 54.91/14.51 thf(func_def_891, type, upto: int > int > list_int).
% 54.91/14.51 thf(func_def_892, type, upto_aux: int > int > list_int > list_int).
% 54.91/14.51 thf(func_def_893, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 54.91/14.51 thf(func_def_894, type, zip_Pr8136144321567152340et_nat: list_P7985473006766602707_nat_o > list_P2321686559999237006et_nat > list_P362550909693114634et_nat).
% 54.91/14.51 thf(func_def_895, type, zip_Pr7134870689397686104et_nat: list_P7985473006766602707_nat_o > list_P9062070895058802706et_nat > list_P2321686559999237006et_nat).
% 54.91/14.51 thf(func_def_896, type, zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 54.91/14.51 thf(func_def_897, type, zip_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 54.91/14.51 thf(func_def_898, type, zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 54.91/14.51 thf(func_def_899, type, zip_o_real: list_o > list_real > list_P5232166724548748803o_real).
% 54.91/14.51 thf(func_def_900, type, zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 54.91/14.51 thf(func_def_901, type, zip_int_o: list_int > list_o > list_P5087981734274514673_int_o).
% 54.91/14.51 thf(func_def_902, type, zip_int_int: list_int > list_int > list_P5707943133018811711nt_int).
% 54.91/14.51 thf(func_def_903, type, zip_int_nat: list_int > list_nat > list_P8198026277950538467nt_nat).
% 54.91/14.51 thf(func_def_904, type, zip_int_real: list_int > list_real > list_P6863124054624500543t_real).
% 54.91/14.51 thf(func_def_905, type, zip_int_VEBT_VEBTi: list_int > list_VEBT_VEBTi > list_P4447955379000644808_VEBTi).
% 54.91/14.51 thf(func_def_906, type, zip_int_VEBT_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT).
% 54.91/14.51 thf(func_def_907, type, zip_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o).
% 54.91/14.51 thf(func_def_908, type, zip_nat_int: list_nat > list_int > list_P3521021558325789923at_int).
% 54.91/14.51 thf(func_def_909, type, zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat).
% 54.91/14.51 thf(func_def_910, type, zip_real_o: list_real > list_o > list_P3595434254542482545real_o).
% 54.91/14.51 thf(func_def_911, type, zip_real_int: list_real > list_int > list_P4344331454722006975al_int).
% 54.91/14.51 thf(func_def_912, type, zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat).
% 54.91/14.51 thf(func_def_913, type, zip_real_real: list_real > list_real > list_P8689742595348180415l_real).
% 54.91/14.51 thf(func_def_914, type, zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT).
% 54.91/14.51 thf(func_def_915, type, zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat).
% 54.91/14.51 thf(func_def_916, type, zip_uint32_uint32: list_uint32 > list_uint32 > list_P3069071885182933823uint32).
% 54.91/14.51 thf(func_def_917, type, zip_VEBT_VEBTi_o: list_VEBT_VEBTi > list_o > list_P8833571063612306856EBTi_o).
% 54.91/14.51 thf(func_def_918, type, zip_VEBT_VEBTi_int: list_VEBT_VEBTi > list_int > list_P7392757774524453448Ti_int).
% 54.91/14.51 thf(func_def_919, type, zip_VEBT_VEBTi_real: list_VEBT_VEBTi > list_real > list_P8536626330812492744i_real).
% 54.91/14.51 thf(func_def_920, type, zip_VE793581609497812771_VEBTi: list_VEBT_VEBTi > list_VEBT_VEBTi > list_P785718909624839377_VEBTi).
% 54.91/14.51 thf(func_def_921, type, zip_VE7413257051550508102T_VEBT: list_VEBT_VEBTi > list_VEBT_VEBT > list_P5988454224134618948T_VEBT).
% 54.91/14.51 thf(func_def_922, type, zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 54.91/14.51 thf(func_def_923, type, zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 54.91/14.51 thf(func_def_924, type, zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 54.91/14.51 thf(func_def_925, type, zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real).
% 54.91/14.51 thf(func_def_926, type, zip_VE6444338338598820466_VEBTi: list_VEBT_VEBT > list_VEBT_VEBTi > list_P735349106241217576_VEBTi).
% 54.91/14.51 thf(func_def_927, type, zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 54.91/14.51 thf(func_def_928, type, biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o).
% 54.91/14.51 thf(func_def_929, type, biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o).
% 54.91/14.51 thf(func_def_930, type, bijective_int_int: set_Pr958786334691620121nt_int > $o).
% 54.91/14.51 thf(func_def_931, type, bijective_nat_nat: set_Pr1261947904930325089at_nat > $o).
% 54.91/14.51 thf(func_def_932, type, biject2923219584331114343uint32: set_Pr1773385645901665561uint32 > $o).
% 54.91/14.51 thf(func_def_933, type, dflt_None_set_o: set_o > option_set_o).
% 54.91/14.51 thf(func_def_934, type, dflt_None_set_int: set_int > option_set_int).
% 54.91/14.51 thf(func_def_935, type, dflt_None_set_nat: set_nat > option_set_nat).
% 54.91/14.51 thf(func_def_936, type, mergesort_remdups_o: list_o > list_o).
% 54.91/14.51 thf(func_def_937, type, merges1654122896337280797ps_int: list_int > list_int).
% 54.91/14.51 thf(func_def_938, type, merges1656613366846331073ps_nat: list_nat > list_nat).
% 54.91/14.51 thf(func_def_939, type, merges7437317189856885515ps_num: list_num > list_num).
% 54.91/14.51 thf(func_def_940, type, merges1021483306759835337ps_rat: list_rat > list_rat).
% 54.91/14.51 thf(func_def_941, type, merges7559785487730971421s_real: list_real > list_real).
% 54.91/14.51 thf(func_def_942, type, slice_o: nat > nat > list_o > list_o).
% 54.91/14.51 thf(func_def_943, type, slice_int: nat > nat > list_int > list_int).
% 54.91/14.51 thf(func_def_944, type, slice_nat: nat > nat > list_nat > list_nat).
% 54.91/14.51 thf(func_def_945, type, slice_real: nat > nat > list_real > list_real).
% 54.91/14.51 thf(func_def_946, type, slice_VEBT_VEBTi: nat > nat > list_VEBT_VEBTi > list_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_947, type, slice_VEBT_VEBT: nat > nat > list_VEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_948, type, the_default_nat: nat > option_nat > nat).
% 54.91/14.51 thf(func_def_949, type, the_de3812365490807259288at_nat: product_prod_nat_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_950, type, the_default_set_o: set_o > option_set_o > set_o).
% 54.91/14.51 thf(func_def_951, type, the_default_set_int: set_int > option_set_int > set_int).
% 54.91/14.51 thf(func_def_952, type, the_default_set_nat: set_nat > option_set_nat > set_nat).
% 54.91/14.51 thf(func_def_953, type, suc: nat > nat).
% 54.91/14.51 thf(func_def_954, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 54.91/14.51 thf(func_def_955, type, semiri4939895301339042750nteger: nat > code_integer).
% 54.91/14.51 thf(func_def_956, type, semiri1314217659103216013at_int: nat > int).
% 54.91/14.51 thf(func_def_957, type, semiri1316708129612266289at_nat: nat > nat).
% 54.91/14.51 thf(func_def_958, type, semiri681578069525770553at_rat: nat > rat).
% 54.91/14.51 thf(func_def_959, type, semiri5074537144036343181t_real: nat > real).
% 54.91/14.51 thf(func_def_960, type, semiri2565882477558803405uint32: nat > uint32).
% 54.91/14.51 thf(func_def_961, type, size_size_list_o: list_o > nat).
% 54.91/14.51 thf(func_def_962, type, size_s3445333598471063425nteger: list_Code_integer > nat).
% 54.91/14.51 thf(func_def_963, type, size_s3451745648224563538omplex: list_complex > nat).
% 54.91/14.51 thf(func_def_964, type, size_size_list_int: list_int > nat).
% 54.91/14.51 thf(func_def_965, type, size_s2710708370519433104list_o: list_list_o > nat).
% 54.91/14.51 thf(func_def_966, type, size_s3023201423986296836st_nat: list_list_nat > nat).
% 54.91/14.51 thf(func_def_967, type, size_s6660260683639930848t_real: list_list_real > nat).
% 54.91/14.51 thf(func_def_968, type, size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_969, type, size_size_list_nat: list_nat > nat).
% 54.91/14.51 thf(func_def_970, type, size_size_list_num: list_num > nat).
% 54.91/14.51 thf(func_def_971, type, size_s2624279037499656343o_real: list_P5232166724548748803o_real > nat).
% 54.91/14.51 thf(func_def_972, type, size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat).
% 54.91/14.51 thf(func_def_973, type, size_s987546567493390085real_o: list_P3595434254542482545real_o > nat).
% 54.91/14.51 thf(func_def_974, type, size_s1877336372972134351al_nat: list_P6834414599653733731al_nat > nat).
% 54.91/14.51 thf(func_def_975, type, size_s3932428310213730859l_real: list_P8689742595348180415l_real > nat).
% 54.91/14.51 thf(func_def_976, type, size_s3289364478449617953T_VEBT: list_P877281246627933069T_VEBT > nat).
% 54.91/14.51 thf(func_def_977, type, size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat).
% 54.91/14.51 thf(func_def_978, type, size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat).
% 54.91/14.51 thf(func_def_979, type, size_s5035110155006384947T_real: list_P2623026923184700063T_real > nat).
% 54.91/14.51 thf(func_def_980, type, size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat).
% 54.91/14.51 thf(func_def_981, type, size_size_list_rat: list_rat > nat).
% 54.91/14.51 thf(func_def_982, type, size_size_list_real: list_real > nat).
% 54.91/14.51 thf(func_def_983, type, size_s3254054031482475050et_nat: list_set_nat > nat).
% 54.91/14.51 thf(func_def_984, type, size_s2501651207091587910iteral: list_literal > nat).
% 54.91/14.51 thf(func_def_985, type, size_s4844771616002835472uint32: list_uint32 > nat).
% 54.91/14.51 thf(func_def_986, type, size_s7982070591426661849_VEBTi: list_VEBT_VEBTi > nat).
% 54.91/14.51 thf(func_def_987, type, size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_988, type, size_size_num: num > nat).
% 54.91/14.51 thf(func_def_989, type, size_size_option_nat: option_nat > nat).
% 54.91/14.51 thf(func_def_990, type, size_s170228958280169651at_nat: option4927543243414619207at_nat > nat).
% 54.91/14.51 thf(func_def_991, type, size_size_VEBT_VEBTi: vEBT_VEBTi > nat).
% 54.91/14.51 thf(func_def_992, type, size_size_VEBT_VEBT: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_993, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_994, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 54.91/14.51 thf(func_def_995, type, nat_set_decode: nat > set_nat).
% 54.91/14.51 thf(func_def_996, type, nat_set_encode: set_nat > nat).
% 54.91/14.51 thf(func_def_997, type, nat_triangle: nat > nat).
% 54.91/14.51 thf(func_def_998, type, root: nat > real > real).
% 54.91/14.51 thf(func_def_999, type, sqrt: real > real).
% 54.91/14.51 thf(func_def_1000, type, bitM: num > num).
% 54.91/14.51 thf(func_def_1001, type, inc: num > num).
% 54.91/14.51 thf(func_def_1002, type, neg_nu3811975205180677377ec_int: int > int).
% 54.91/14.51 thf(func_def_1003, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 54.91/14.51 thf(func_def_1004, type, neg_nu6075765906172075777c_real: real > real).
% 54.91/14.51 thf(func_def_1005, type, neg_nu965353292909893953uint32: uint32 > uint32).
% 54.91/14.51 thf(func_def_1006, type, neg_nu5851722552734809277nc_int: int > int).
% 54.91/14.51 thf(func_def_1007, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 54.91/14.51 thf(func_def_1008, type, neg_nu8295874005876285629c_real: real > real).
% 54.91/14.51 thf(func_def_1009, type, neg_nu4269007558841261821uint32: uint32 > uint32).
% 54.91/14.51 thf(func_def_1010, type, bit0: num > num).
% 54.91/14.51 thf(func_def_1011, type, bit1: num > num).
% 54.91/14.51 thf(func_def_1012, type, one: num).
% 54.91/14.51 thf(func_def_1013, type, size_num: num > nat).
% 54.91/14.51 thf(func_def_1014, type, numera6620942414471956472nteger: num > code_integer).
% 54.91/14.51 thf(func_def_1015, type, numera1916890842035813515d_enat: num > extended_enat).
% 54.91/14.51 thf(func_def_1016, type, numeral_numeral_int: num > int).
% 54.91/14.51 thf(func_def_1017, type, numeral_numeral_nat: num > nat).
% 54.91/14.51 thf(func_def_1018, type, numeral_numeral_real: num > real).
% 54.91/14.51 thf(func_def_1019, type, numera9087168376688890119uint32: num > uint32).
% 54.91/14.51 thf(func_def_1020, type, none_nat: option_nat).
% 54.91/14.51 thf(func_def_1021, type, none_P199884684680593241et_nat: option2860828798490689354et_nat).
% 54.91/14.51 thf(func_def_1022, type, none_P4972525538344268765et_nat: option5190343406534369742et_nat).
% 54.91/14.51 thf(func_def_1023, type, none_P2377608414092835994nt_int: option4624381673175914239nt_int).
% 54.91/14.51 thf(func_def_1024, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 54.91/14.51 thf(func_def_1025, type, none_P7441528354948028570uint32: option3972171592325465343uint32).
% 54.91/14.51 thf(func_def_1026, type, none_set_o: option_set_o).
% 54.91/14.51 thf(func_def_1027, type, none_set_int: option_set_int).
% 54.91/14.51 thf(func_def_1028, type, none_set_nat: option_set_nat).
% 54.91/14.51 thf(func_def_1029, type, some_int: int > option_int).
% 54.91/14.51 thf(func_def_1030, type, some_nat: nat > option_nat).
% 54.91/14.51 thf(func_def_1031, type, some_num: num > option_num).
% 54.91/14.51 thf(func_def_1032, type, some_P1630309045189364437et_nat: produc2732055786443039994et_nat > option2860828798490689354et_nat).
% 54.91/14.51 thf(func_def_1033, type, some_P750831030444334937et_nat: produc3925858234332021118et_nat > option5190343406534369742et_nat).
% 54.91/14.51 thf(func_def_1034, type, some_P4184893108420464158nt_int: product_prod_int_int > option4624381673175914239nt_int).
% 54.91/14.51 thf(func_def_1035, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 54.91/14.51 thf(func_def_1036, type, some_P6695178580830101022uint32: produc827990862158126777uint32 > option3972171592325465343uint32).
% 54.91/14.51 thf(func_def_1037, type, some_rat: rat > option_rat).
% 54.91/14.51 thf(func_def_1038, type, some_real: real > option_real).
% 54.91/14.51 thf(func_def_1039, type, some_set_o: set_o > option_set_o).
% 54.91/14.51 thf(func_def_1040, type, some_set_int: set_int > option_set_int).
% 54.91/14.51 thf(func_def_1041, type, some_set_nat: set_nat > option_set_nat).
% 54.91/14.51 thf(func_def_1042, type, case_o184042715313410164at_nat: $o > (product_prod_nat_nat > $o) > option4927543243414619207at_nat > $o).
% 54.91/14.51 thf(func_def_1043, type, case_o1383228350324149268at_nat: option_nat > (product_prod_nat_nat > option_nat) > option4927543243414619207at_nat > option_nat).
% 54.91/14.51 thf(func_def_1044, type, case_o2442805151034396888at_nat: vEBT_VEBT > (product_prod_nat_nat > vEBT_VEBT) > option4927543243414619207at_nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1045, type, size_option_nat: (nat > nat) > option_nat > nat).
% 54.91/14.51 thf(func_def_1046, type, size_o8335143837870341156at_nat: (product_prod_nat_nat > nat) > option4927543243414619207at_nat > nat).
% 54.91/14.51 thf(func_def_1047, type, the_nat: option_nat > nat).
% 54.91/14.51 thf(func_def_1048, type, bot_bo3790638025767943357_nat_o: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 54.91/14.51 thf(func_def_1049, type, bot_bo5580076615179976505_nat_o: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_1050, type, bot_bot_o_o: $o > $o).
% 54.91/14.51 thf(func_def_1051, type, bot_bot_complex_o: complex > $o).
% 54.91/14.51 thf(func_def_1052, type, bot_bot_int_int_o: int > int > $o).
% 54.91/14.51 thf(func_def_1053, type, bot_bot_int_o: int > $o).
% 54.91/14.51 thf(func_def_1054, type, bot_bot_list_nat_o: list_nat > $o).
% 54.91/14.51 thf(func_def_1055, type, bot_bot_nat_nat_o: nat > nat > $o).
% 54.91/14.51 thf(func_def_1056, type, bot_bot_nat_o: nat > $o).
% 54.91/14.51 thf(func_def_1057, type, bot_bot_real_o: real > $o).
% 54.91/14.51 thf(func_def_1058, type, bot_bot_set_nat_o: set_nat > $o).
% 54.91/14.51 thf(func_def_1059, type, bot_bo8112279147790955290nt32_o: uint32 > uint32 > $o).
% 54.91/14.51 thf(func_def_1060, type, bot_bot_VEBT_VEBT_o: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1062, type, bot_bot_assn: assn).
% 54.91/14.51 thf(func_def_1063, type, bot_bot_nat: nat).
% 54.91/14.51 thf(func_def_1064, type, bot_bot_set_o: set_o).
% 54.91/14.51 thf(func_def_1065, type, bot_bo3990330152332043303nteger: set_Code_integer).
% 54.91/14.51 thf(func_def_1066, type, bot_bot_set_complex: set_complex).
% 54.91/14.51 thf(func_def_1067, type, bot_bot_set_int: set_int).
% 54.91/14.51 thf(func_def_1068, type, bot_bot_set_list_nat: set_list_nat).
% 54.91/14.51 thf(func_def_1069, type, bot_bot_set_nat: set_nat).
% 54.91/14.51 thf(func_def_1070, type, bot_bot_set_num: set_num).
% 54.91/14.51 thf(func_def_1071, type, bot_bo5635537948650799172et_nat: set_Pr8536935166611901872et_nat).
% 54.91/14.51 thf(func_def_1072, type, bot_bo1481135142794719944et_nat: set_Pr3286484037609594932et_nat).
% 54.91/14.51 thf(func_def_1073, type, bot_bo7073875226086086771od_o_o: set_Product_prod_o_o).
% 54.91/14.51 thf(func_def_1074, type, bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int).
% 54.91/14.51 thf(func_def_1075, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 54.91/14.51 thf(func_def_1076, type, bot_bo8438649754162204037uint32: set_Pr1773385645901665561uint32).
% 54.91/14.51 thf(func_def_1077, type, bot_bo5088076668136028147T_VEBT: set_Pr6192946355708809607T_VEBT).
% 54.91/14.51 thf(func_def_1078, type, bot_bot_set_rat: set_rat).
% 54.91/14.51 thf(func_def_1079, type, bot_bot_set_real: set_real).
% 54.91/14.51 thf(func_def_1080, type, bot_bot_set_set_int: set_set_int).
% 54.91/14.51 thf(func_def_1081, type, bot_bot_set_set_nat: set_set_nat).
% 54.91/14.51 thf(func_def_1082, type, bot_bot_set_literal: set_literal).
% 54.91/14.51 thf(func_def_1083, type, bot_bot_set_uint32: set_uint32).
% 54.91/14.51 thf(func_def_1084, type, bot_bo8982466882572371071_VEBTi: set_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_1085, type, bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1086, type, ord_Least_nat: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1087, type, ord_Least_real: (real > $o) > real).
% 54.91/14.51 thf(func_def_1088, type, ord_less_int_o: (int > $o) > (int > $o) > $o).
% 54.91/14.51 thf(func_def_1089, type, ord_less_nat_o: (nat > $o) > (nat > $o) > $o).
% 54.91/14.51 thf(func_def_1090, type, ord_less_real_o: (real > $o) > (real > $o) > $o).
% 54.91/14.51 thf(func_def_1091, type, ord_less_set_nat_o: (set_nat > $o) > (set_nat > $o) > $o).
% 54.91/14.51 thf(func_def_1092, type, ord_less_VEBT_VEBT_o: (vEBT_VEBT > $o) > (vEBT_VEBT > $o) > $o).
% 54.91/14.51 thf(func_def_1093, type, ord_less_o: $o > $o > $o).
% 54.91/14.51 thf(func_def_1094, type, ord_less_assn: assn > assn > $o).
% 54.91/14.51 thf(func_def_1095, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 54.91/14.51 thf(func_def_1096, type, ord_le72135733267957522d_enat: extended_enat > extended_enat > $o).
% 54.91/14.51 thf(func_def_1097, type, ord_less_int: int > int > $o).
% 54.91/14.51 thf(func_def_1098, type, ord_less_nat: nat > nat > $o).
% 54.91/14.51 thf(func_def_1099, type, ord_less_num: num > num > $o).
% 54.91/14.51 thf(func_def_1100, type, ord_less_option_int: option_int > option_int > $o).
% 54.91/14.51 thf(func_def_1101, type, ord_less_option_nat: option_nat > option_nat > $o).
% 54.91/14.51 thf(func_def_1102, type, ord_less_option_num: option_num > option_num > $o).
% 54.91/14.51 thf(func_def_1103, type, ord_less_option_rat: option_rat > option_rat > $o).
% 54.91/14.51 thf(func_def_1104, type, ord_less_option_real: option_real > option_real > $o).
% 54.91/14.51 thf(func_def_1105, type, ord_less_rat: rat > rat > $o).
% 54.91/14.51 thf(func_def_1106, type, ord_less_real: real > real > $o).
% 54.91/14.51 thf(func_def_1107, type, ord_less_set_o: set_o > set_o > $o).
% 54.91/14.51 thf(func_def_1108, type, ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o).
% 54.91/14.51 thf(func_def_1109, type, ord_less_set_complex: set_complex > set_complex > $o).
% 54.91/14.51 thf(func_def_1110, type, ord_less_set_int: set_int > set_int > $o).
% 54.91/14.51 thf(func_def_1111, type, ord_le1190675801316882794st_nat: set_list_nat > set_list_nat > $o).
% 54.91/14.51 thf(func_def_1112, type, ord_less_set_nat: set_nat > set_nat > $o).
% 54.91/14.51 thf(func_def_1113, type, ord_less_set_num: set_num > set_num > $o).
% 54.91/14.51 thf(func_def_1114, type, ord_less_set_rat: set_rat > set_rat > $o).
% 54.91/14.51 thf(func_def_1115, type, ord_less_set_real: set_real > set_real > $o).
% 54.91/14.51 thf(func_def_1116, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 54.91/14.51 thf(func_def_1117, type, ord_less_set_literal: set_literal > set_literal > $o).
% 54.91/14.51 thf(func_def_1118, type, ord_le3480810397992357184T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1119, type, ord_less_char: char > char > $o).
% 54.91/14.51 thf(func_def_1120, type, ord_less_literal: literal > literal > $o).
% 54.91/14.51 thf(func_def_1121, type, ord_less_uint32: uint32 > uint32 > $o).
% 54.91/14.51 thf(func_def_1122, type, ord_le750835935415966154l_num1: word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o).
% 54.91/14.51 thf(func_def_1123, type, ord_le6753239538765779593_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > $o).
% 54.91/14.51 thf(func_def_1124, type, ord_le8000401564054156549_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > $o).
% 54.91/14.51 thf(func_def_1125, type, ord_le6741204236512500942_int_o: (int > int > $o) > (int > int > $o) > $o).
% 54.91/14.51 thf(func_def_1126, type, ord_less_eq_int_o: (int > $o) > (int > $o) > $o).
% 54.91/14.51 thf(func_def_1127, type, ord_le2646555220125990790_nat_o: (nat > nat > $o) > (nat > nat > $o) > $o).
% 54.91/14.51 thf(func_def_1128, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 54.91/14.51 thf(func_def_1129, type, ord_less_eq_real_o: (real > $o) > (real > $o) > $o).
% 54.91/14.51 thf(func_def_1130, type, ord_le3964352015994296041_nat_o: (set_nat > $o) > (set_nat > $o) > $o).
% 54.91/14.51 thf(func_def_1131, type, ord_le5999336846926846542nt32_o: (uint32 > uint32 > $o) > (uint32 > uint32 > $o) > $o).
% 54.91/14.51 thf(func_def_1132, type, ord_le418104280809901481VEBT_o: (vEBT_VEBT > $o) > (vEBT_VEBT > $o) > $o).
% 54.91/14.51 thf(func_def_1133, type, ord_less_eq_o: $o > $o > $o).
% 54.91/14.51 thf(func_def_1134, type, ord_less_eq_assn: assn > assn > $o).
% 54.91/14.51 thf(func_def_1135, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 54.91/14.51 thf(func_def_1136, type, ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o).
% 54.91/14.51 thf(func_def_1137, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 54.91/14.51 thf(func_def_1138, type, ord_le4104064031414453916r_real: filter_real > filter_real > $o).
% 54.91/14.51 thf(func_def_1139, type, ord_less_eq_int: int > int > $o).
% 54.91/14.51 thf(func_def_1140, type, ord_less_eq_nat: nat > nat > $o).
% 54.91/14.51 thf(func_def_1141, type, ord_less_eq_num: num > num > $o).
% 54.91/14.51 thf(func_def_1142, type, ord_le1736525451366464988on_int: option_int > option_int > $o).
% 54.91/14.51 thf(func_def_1143, type, ord_le5914376470875661696on_nat: option_nat > option_nat > $o).
% 54.91/14.51 thf(func_def_1144, type, ord_le6622620407824499402on_num: option_num > option_num > $o).
% 54.91/14.51 thf(func_def_1145, type, ord_le2406147912482264968on_rat: option_rat > option_rat > $o).
% 54.91/14.51 thf(func_def_1146, type, ord_le353528952715127954et_int: option_set_int > option_set_int > $o).
% 54.91/14.51 thf(func_def_1147, type, ord_less_eq_rat: rat > rat > $o).
% 54.91/14.51 thf(func_def_1148, type, ord_less_eq_real: real > real > $o).
% 54.91/14.51 thf(func_def_1149, type, ord_less_eq_set_o: set_o > set_o > $o).
% 54.91/14.51 thf(func_def_1150, type, ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o).
% 54.91/14.51 thf(func_def_1151, type, ord_le211207098394363844omplex: set_complex > set_complex > $o).
% 54.91/14.51 thf(func_def_1152, type, ord_less_eq_set_int: set_int > set_int > $o).
% 54.91/14.51 thf(func_def_1153, type, ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o).
% 54.91/14.51 thf(func_def_1154, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 54.91/14.51 thf(func_def_1155, type, ord_less_eq_set_num: set_num > set_num > $o).
% 54.91/14.51 thf(func_def_1156, type, ord_le4763372923235995152et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > $o).
% 54.91/14.51 thf(func_def_1157, type, ord_le5966269811547037844et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > $o).
% 54.91/14.51 thf(func_def_1158, type, ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o).
% 54.91/14.51 thf(func_def_1159, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 54.91/14.51 thf(func_def_1160, type, ord_le6429528607962791097uint32: set_Pr1773385645901665561uint32 > set_Pr1773385645901665561uint32 > $o).
% 54.91/14.51 thf(func_def_1161, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 54.91/14.51 thf(func_def_1162, type, ord_less_eq_set_real: set_real > set_real > $o).
% 54.91/14.51 thf(func_def_1163, type, ord_le4403425263959731960et_int: set_set_int > set_set_int > $o).
% 54.91/14.51 thf(func_def_1164, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 54.91/14.51 thf(func_def_1165, type, ord_le9131159989063066194et_nat: set_set_set_nat > set_set_set_nat > $o).
% 54.91/14.51 thf(func_def_1166, type, ord_le7307670543136651348iteral: set_literal > set_literal > $o).
% 54.91/14.51 thf(func_def_1167, type, ord_le6592769550269828683_VEBTi: set_VEBT_VEBTi > set_VEBT_VEBTi > $o).
% 54.91/14.51 thf(func_def_1168, type, ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1169, type, ord_less_eq_char: char > char > $o).
% 54.91/14.51 thf(func_def_1170, type, ord_less_eq_uint32: uint32 > uint32 > $o).
% 54.91/14.51 thf(func_def_1171, type, ord_le3335648743751981014l_num1: word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1 > $o).
% 54.91/14.51 thf(func_def_1172, type, ord_max_o: $o > $o > $o).
% 54.91/14.51 thf(func_def_1173, type, ord_max_assn: assn > assn > assn).
% 54.91/14.51 thf(func_def_1174, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_1175, type, ord_max_int: int > int > int).
% 54.91/14.51 thf(func_def_1176, type, ord_max_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_1177, type, ord_max_num: num > num > num).
% 54.91/14.51 thf(func_def_1178, type, ord_max_rat: rat > rat > rat).
% 54.91/14.51 thf(func_def_1179, type, ord_max_real: real > real > real).
% 54.91/14.51 thf(func_def_1180, type, ord_max_set_o: set_o > set_o > set_o).
% 54.91/14.51 thf(func_def_1181, type, ord_max_set_int: set_int > set_int > set_int).
% 54.91/14.51 thf(func_def_1182, type, ord_max_set_nat: set_nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_1183, type, ord_min_Code_integer: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_1184, type, ord_min_int: int > int > int).
% 54.91/14.51 thf(func_def_1185, type, ord_min_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_1186, type, order_Greatest_nat: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1187, type, ordering_top_assn: (assn > assn > $o) > (assn > assn > $o) > assn > $o).
% 54.91/14.51 thf(func_def_1188, type, ordering_top_nat: (nat > nat > $o) > (nat > nat > $o) > nat > $o).
% 54.91/14.51 thf(func_def_1189, type, ordering_top_set_o: (set_o > set_o > $o) > (set_o > set_o > $o) > set_o > $o).
% 54.91/14.51 thf(func_def_1190, type, ordering_top_set_int: (set_int > set_int > $o) > (set_int > set_int > $o) > set_int > $o).
% 54.91/14.51 thf(func_def_1191, type, ordering_top_set_nat: (set_nat > set_nat > $o) > (set_nat > set_nat > $o) > set_nat > $o).
% 54.91/14.51 thf(func_def_1192, type, top_top_assn: assn).
% 54.91/14.51 thf(func_def_1193, type, top_top_set_o: set_o).
% 54.91/14.51 thf(func_def_1194, type, top_top_set_int: set_int).
% 54.91/14.51 thf(func_def_1195, type, top_top_set_nat: set_nat).
% 54.91/14.51 thf(func_def_1196, type, top_to3689904424835650196l_num0: set_Numeral_num0).
% 54.91/14.51 thf(func_def_1197, type, top_to1996260823553986621t_unit: set_Product_unit).
% 54.91/14.51 thf(func_def_1198, type, top_top_set_real: set_real).
% 54.91/14.51 thf(func_def_1199, type, top_top_set_literal: set_literal).
% 54.91/14.51 thf(func_def_1200, type, power_power_assn: assn > nat > assn).
% 54.91/14.51 thf(func_def_1201, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 54.91/14.51 thf(func_def_1202, type, power_power_complex: complex > nat > complex).
% 54.91/14.51 thf(func_def_1203, type, power_power_int: int > nat > int).
% 54.91/14.51 thf(func_def_1204, type, power_power_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_1205, type, power_power_rat: rat > nat > rat).
% 54.91/14.51 thf(func_def_1206, type, power_power_real: real > nat > real).
% 54.91/14.51 thf(func_def_1207, type, power_power_uint32: uint32 > nat > uint32).
% 54.91/14.51 thf(func_def_1208, type, produc2245416461498447860et_nat: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > produc2732055786443039994et_nat).
% 54.91/14.51 thf(func_def_1209, type, produc5001842942810119800et_nat: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > produc3925858234332021118et_nat).
% 54.91/14.51 thf(func_def_1210, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 54.91/14.51 thf(func_def_1211, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 54.91/14.51 thf(func_def_1212, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 54.91/14.51 thf(func_def_1213, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 54.91/14.51 thf(func_def_1214, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_1215, type, produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > set_nat > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_1216, type, product_Pair_int_o: int > $o > product_prod_int_o).
% 54.91/14.51 thf(func_def_1217, type, product_Pair_int_int: int > int > product_prod_int_int).
% 54.91/14.51 thf(func_def_1218, type, product_Pair_int_nat: int > nat > product_prod_int_nat).
% 54.91/14.51 thf(func_def_1219, type, produc801115645435158769t_real: int > real > produc679980390762269497t_real).
% 54.91/14.51 thf(func_def_1220, type, produc4497823428076633978_VEBTi: int > vEBT_VEBTi > produc2062302194595185346_VEBTi).
% 54.91/14.51 thf(func_def_1221, type, produc3329399203697025711T_VEBT: int > vEBT_VEBT > produc1531783533982839933T_VEBT).
% 54.91/14.51 thf(func_def_1222, type, produc8435520187683070743list_o: list_o > list_o > produc7102631898165422375list_o).
% 54.91/14.51 thf(func_def_1223, type, produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int).
% 54.91/14.51 thf(func_def_1224, type, produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat).
% 54.91/14.51 thf(func_def_1225, type, produc1408950526243324945t_real: list_real > list_real > produc478978216448986841t_real).
% 54.91/14.51 thf(func_def_1226, type, produc7487160679990061969uint32: list_uint32 > list_uint32 > produc823665806539077721uint32).
% 54.91/14.51 thf(func_def_1227, type, produc4384243565435462691_VEBTi: list_VEBT_VEBTi > list_VEBT_VEBTi > produc3089554586268799851_VEBTi).
% 54.91/14.51 thf(func_def_1228, type, produc3897820843166775703T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > produc9211091688327510695T_VEBT).
% 54.91/14.51 thf(func_def_1229, type, product_Pair_nat_o: nat > $o > product_prod_nat_o).
% 54.91/14.51 thf(func_def_1230, type, product_Pair_nat_int: nat > int > product_prod_nat_int).
% 54.91/14.51 thf(func_def_1231, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_1232, type, produc7837566107596912789t_real: nat > real > produc7716430852924023517t_real).
% 54.91/14.51 thf(func_def_1233, type, produc2649746096677893406_VEBTi: nat > vEBT_VEBTi > produc214224863196444774_VEBTi).
% 54.91/14.51 thf(func_def_1234, type, produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT).
% 54.91/14.51 thf(func_def_1235, type, produc1940133919992309389et_nat: produc2732055786443039994et_nat > produc2732055786443039994et_nat > produc5657529347773406293et_nat).
% 54.91/14.51 thf(func_def_1236, type, produc8599840265553166229et_nat: produc3925858234332021118et_nat > produc3925858234332021118et_nat > produc6830853553727218525et_nat).
% 54.91/14.51 thf(func_def_1237, type, produc3646306378393792727nt_int: product_prod_int_int > product_prod_int_int > produc1219242969750017639nt_int).
% 54.91/14.51 thf(func_def_1238, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 54.91/14.51 thf(func_def_1239, type, produc6884863695460953815uint32: produc827990862158126777uint32 > produc827990862158126777uint32 > produc8822557026176459367uint32).
% 54.91/14.51 thf(func_def_1240, type, produc3179012173361985393al_int: real > int > produc8786904178792722361al_int).
% 54.91/14.51 thf(func_def_1241, type, produc4511245868158468465l_real: real > real > produc2422161461964618553l_real).
% 54.91/14.51 thf(func_def_1242, type, produc6931449550656315951T_VEBT: real > vEBT_VEBT > produc3757001726724277373T_VEBT).
% 54.91/14.51 thf(func_def_1243, type, produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat).
% 54.91/14.51 thf(func_def_1244, type, produc1400373151660368625uint32: uint32 > uint32 > produc827990862158126777uint32).
% 54.91/14.51 thf(func_def_1245, type, produc8194178580519725514EBTi_o: vEBT_VEBTi > $o > produc5014006835512566296EBTi_o).
% 54.91/14.51 thf(func_def_1246, type, produc7190175284220460154Ti_int: vEBT_VEBTi > int > produc8927069083091599426Ti_int).
% 54.91/14.51 thf(func_def_1247, type, produc8457151488442208762i_real: vEBT_VEBTi > real > produc6680258955013199682i_real).
% 54.91/14.51 thf(func_def_1248, type, produc436343169921013763_VEBTi: vEBT_VEBTi > vEBT_VEBTi > produc3777764054643897931_VEBTi).
% 54.91/14.51 thf(func_def_1249, type, produc7053807326796202854T_VEBT: vEBT_VEBTi > vEBT_VEBT > produc2810682830582626868T_VEBT).
% 54.91/14.51 thf(func_def_1250, type, produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o).
% 54.91/14.51 thf(func_def_1251, type, produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int).
% 54.91/14.51 thf(func_def_1252, type, produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat).
% 54.91/14.51 thf(func_def_1253, type, produc8117437818029410057T_real: vEBT_VEBT > real > produc5170161368751668367T_real).
% 54.91/14.51 thf(func_def_1254, type, produc6084888613844515218_VEBTi: vEBT_VEBT > vEBT_VEBTi > produc3625547720036274456_VEBTi).
% 54.91/14.51 thf(func_def_1255, type, produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT).
% 54.91/14.51 thf(func_def_1256, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_1257, type, produc6197397395684419436_o_o_o: ($o > $o > $o) > product_prod_o_o > $o).
% 54.91/14.51 thf(func_def_1258, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 54.91/14.51 thf(func_def_1259, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 54.91/14.51 thf(func_def_1260, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 54.91/14.51 thf(func_def_1261, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 54.91/14.51 thf(func_def_1262, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 54.91/14.51 thf(func_def_1263, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 54.91/14.51 thf(func_def_1264, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 54.91/14.51 thf(func_def_1265, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 54.91/14.51 thf(func_def_1266, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 54.91/14.51 thf(func_def_1267, type, produc2484365769952853102on_nat: (nat > nat > option_nat) > product_prod_nat_nat > option_nat).
% 54.91/14.51 thf(func_def_1268, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_1269, type, produc3169358591047799142T_VEBT: (nat > nat > vEBT_VEBT) > product_prod_nat_nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1270, type, produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer).
% 54.91/14.51 thf(func_def_1271, type, produc1824681642469235216et_nat: produc3658429121746597890et_nat > heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_1272, type, product_fst_int_int: product_prod_int_int > int).
% 54.91/14.51 thf(func_def_1273, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 54.91/14.51 thf(func_def_1274, type, produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer).
% 54.91/14.51 thf(func_def_1275, type, produc8586169260539613262et_nat: produc3658429121746597890et_nat > set_nat).
% 54.91/14.51 thf(func_def_1276, type, product_snd_int_int: product_prod_int_int > int).
% 54.91/14.51 thf(func_def_1277, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 54.91/14.51 thf(func_def_1278, type, normalize: product_prod_int_int > product_prod_int_int).
% 54.91/14.51 thf(func_def_1279, type, real_V1022390504157884413omplex: complex > real).
% 54.91/14.51 thf(func_def_1280, type, refine_Imp_refines_o: heap_Time_Heap_o > heap_Time_Heap_o > $o).
% 54.91/14.51 thf(func_def_1281, type, refine7594492741263601813on_nat: heap_T2636463487746394924on_nat > heap_T2636463487746394924on_nat > $o).
% 54.91/14.51 thf(func_def_1282, type, refine5565527176597971370_VEBTi: heap_T8145700208782473153_VEBTi > heap_T8145700208782473153_VEBTi > $o).
% 54.91/14.51 thf(func_def_1283, type, total_on_o: set_o > set_Product_prod_o_o > $o).
% 54.91/14.51 thf(func_def_1284, type, total_on_int: set_int > set_Pr958786334691620121nt_int > $o).
% 54.91/14.51 thf(func_def_1285, type, total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 54.91/14.51 thf(func_def_1286, type, total_on_real: set_real > set_Pr6218003697084177305l_real > $o).
% 54.91/14.51 thf(func_def_1287, type, total_on_set_nat: set_set_nat > set_Pr5488025237498180813et_nat > $o).
% 54.91/14.51 thf(func_def_1288, type, total_on_uint32: set_uint32 > set_Pr1773385645901665561uint32 > $o).
% 54.91/14.51 thf(func_def_1289, type, total_on_VEBT_VEBT: set_VEBT_VEBT > set_Pr6192946355708809607T_VEBT > $o).
% 54.91/14.51 thf(func_def_1290, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_1291, type, divide_divide_int: int > int > int).
% 54.91/14.51 thf(func_def_1292, type, divide_divide_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_1293, type, divide_divide_real: real > real > real).
% 54.91/14.51 thf(func_def_1294, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 54.91/14.51 thf(func_def_1295, type, dvd_dvd_int: int > int > $o).
% 54.91/14.51 thf(func_def_1296, type, dvd_dvd_nat: nat > nat > $o).
% 54.91/14.51 thf(func_def_1297, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 54.91/14.51 thf(func_def_1298, type, modulo_modulo_int: int > int > int).
% 54.91/14.51 thf(func_def_1299, type, modulo_modulo_nat: nat > nat > nat).
% 54.91/14.51 thf(func_def_1300, type, zero_n2684676970156552555ol_int: $o > int).
% 54.91/14.51 thf(func_def_1301, type, zero_n2687167440665602831ol_nat: $o > nat).
% 54.91/14.51 thf(func_def_1302, type, suminf_real: (nat > real) > real).
% 54.91/14.51 thf(func_def_1303, type, summable_real: (nat > real) > $o).
% 54.91/14.51 thf(func_def_1304, type, sums_real: (nat > real) > real > $o).
% 54.91/14.51 thf(func_def_1305, type, collect_o: ($o > $o) > set_o).
% 54.91/14.51 thf(func_def_1306, type, collect_Code_integer: (code_integer > $o) > set_Code_integer).
% 54.91/14.51 thf(func_def_1307, type, collect_complex: (complex > $o) > set_complex).
% 54.91/14.51 thf(func_def_1308, type, collect_int: (int > $o) > set_int).
% 54.91/14.51 thf(func_def_1309, type, collect_list_o: (list_o > $o) > set_list_o).
% 54.91/14.51 thf(func_def_1310, type, collec3483841146883906114nteger: (list_Code_integer > $o) > set_li6976499617229504675nteger).
% 54.91/14.51 thf(func_def_1311, type, collect_list_complex: (list_complex > $o) > set_list_complex).
% 54.91/14.51 thf(func_def_1312, type, collect_list_int: (list_int > $o) > set_list_int).
% 54.91/14.51 thf(func_def_1313, type, collec5989764272469232197st_nat: (list_list_nat > $o) > set_list_list_nat).
% 54.91/14.51 thf(func_def_1314, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 54.91/14.51 thf(func_def_1315, type, collect_list_real: (list_real > $o) > set_list_real).
% 54.91/14.51 thf(func_def_1316, type, collect_list_set_nat: (list_set_nat > $o) > set_list_set_nat).
% 54.91/14.51 thf(func_def_1317, type, collect_list_literal: (list_literal > $o) > set_list_literal).
% 54.91/14.51 thf(func_def_1318, type, collec5608196760682091941T_VEBT: (list_VEBT_VEBT > $o) > set_list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1319, type, collect_nat: (nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_1320, type, collect_num: (num > $o) > set_num).
% 54.91/14.51 thf(func_def_1321, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 54.91/14.51 thf(func_def_1322, type, collect_rat: (rat > $o) > set_rat).
% 54.91/14.51 thf(func_def_1323, type, collect_real: (real > $o) > set_real).
% 54.91/14.51 thf(func_def_1324, type, collec574505750873337192nteger: (set_Code_integer > $o) > set_set_Code_integer).
% 54.91/14.51 thf(func_def_1325, type, collect_set_complex: (set_complex > $o) > set_set_complex).
% 54.91/14.51 thf(func_def_1326, type, collect_set_int: (set_int > $o) > set_set_int).
% 54.91/14.51 thf(func_def_1327, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 54.91/14.51 thf(func_def_1328, type, collect_literal: (literal > $o) > set_literal).
% 54.91/14.51 thf(func_def_1329, type, collect_VEBT_VEBT: (vEBT_VEBT > $o) > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1330, type, pow_nat: set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1331, type, image_o_o: ($o > $o) > set_o > set_o).
% 54.91/14.51 thf(func_def_1332, type, image_o_int: ($o > int) > set_o > set_int).
% 54.91/14.51 thf(func_def_1333, type, image_o_nat: ($o > nat) > set_o > set_nat).
% 54.91/14.51 thf(func_def_1334, type, image_o_VEBT_VEBT: ($o > vEBT_VEBT) > set_o > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1335, type, image_4470545334726330049nteger: (code_integer > code_integer) > set_Code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_1336, type, image_3397630267976458002omplex: (code_integer > complex) > set_Code_integer > set_complex).
% 54.91/14.51 thf(func_def_1337, type, image_948535463418740880er_int: (code_integer > int) > set_Code_integer > set_int).
% 54.91/14.51 thf(func_def_1338, type, image_951025933927791156er_nat: (code_integer > nat) > set_Code_integer > set_nat).
% 54.91/14.51 thf(func_def_1339, type, image_315895873841295420er_rat: (code_integer > rat) > set_Code_integer > set_rat).
% 54.91/14.51 thf(func_def_1340, type, image_7738145705984076560r_real: (code_integer > real) > set_Code_integer > set_real).
% 54.91/14.51 thf(func_def_1341, type, image_1994230757181692690nteger: (complex > code_integer) > set_complex > set_Code_integer).
% 54.91/14.51 thf(func_def_1342, type, image_1468599708987790691omplex: (complex > complex) > set_complex > set_complex).
% 54.91/14.51 thf(func_def_1343, type, image_complex_int: (complex > int) > set_complex > set_int).
% 54.91/14.51 thf(func_def_1344, type, image_complex_nat: (complex > nat) > set_complex > set_nat).
% 54.91/14.51 thf(func_def_1345, type, image_complex_rat: (complex > rat) > set_complex > set_rat).
% 54.91/14.51 thf(func_def_1346, type, image_complex_real: (complex > real) > set_complex > set_real).
% 54.91/14.51 thf(func_def_1347, type, image_932796090930683071T_VEBT: (complex > vEBT_VEBT) > set_complex > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1348, type, image_int_o: (int > $o) > set_int > set_o).
% 54.91/14.51 thf(func_def_1349, type, image_1587234942943678608nteger: (int > code_integer) > set_int > set_Code_integer).
% 54.91/14.51 thf(func_def_1350, type, image_int_complex: (int > complex) > set_int > set_complex).
% 54.91/14.51 thf(func_def_1351, type, image_int_int: (int > int) > set_int > set_int).
% 54.91/14.51 thf(func_def_1352, type, image_int_nat: (int > nat) > set_int > set_nat).
% 54.91/14.51 thf(func_def_1353, type, image_int_real: (int > real) > set_int > set_real).
% 54.91/14.51 thf(func_def_1354, type, image_int_literal: (int > literal) > set_int > set_literal).
% 54.91/14.51 thf(func_def_1355, type, image_int_VEBT_VEBT: (int > vEBT_VEBT) > set_int > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1356, type, image_list_o_set_o: (list_o > set_o) > set_list_o > set_set_o).
% 54.91/14.51 thf(func_def_1357, type, image_3606813740839090725et_int: (list_int > set_int) > set_list_int > set_set_int).
% 54.91/14.51 thf(func_def_1358, type, image_list_nat_nat: (list_nat > nat) > set_list_nat > set_nat).
% 54.91/14.51 thf(func_def_1359, type, image_1775855109352712557et_nat: (list_nat > set_nat) > set_list_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1360, type, image_6239767680843085477t_real: (list_real > set_real) > set_list_real > set_set_real).
% 54.91/14.51 thf(func_def_1361, type, image_6463372868993444447T_VEBT: (list_VEBT_VEBT > set_VEBT_VEBT) > set_list_VEBT_VEBT > set_set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1362, type, image_nat_o: (nat > $o) > set_nat > set_o).
% 54.91/14.51 thf(func_def_1363, type, image_1215581382706833972nteger: (nat > code_integer) > set_nat > set_Code_integer).
% 54.91/14.51 thf(func_def_1364, type, image_nat_complex: (nat > complex) > set_nat > set_complex).
% 54.91/14.51 thf(func_def_1365, type, image_nat_int: (nat > int) > set_nat > set_int).
% 54.91/14.51 thf(func_def_1366, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 54.91/14.51 thf(func_def_1367, type, image_nat_rat: (nat > rat) > set_nat > set_rat).
% 54.91/14.51 thf(func_def_1368, type, image_nat_real: (nat > real) > set_nat > set_real).
% 54.91/14.51 thf(func_def_1369, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1370, type, image_nat_literal: (nat > literal) > set_nat > set_literal).
% 54.91/14.51 thf(func_def_1371, type, image_nat_VEBT_VEBTi: (nat > vEBT_VEBTi) > set_nat > set_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_1372, type, image_nat_VEBT_VEBT: (nat > vEBT_VEBT) > set_nat > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1373, type, image_rat_rat: (rat > rat) > set_rat > set_rat).
% 54.91/14.51 thf(func_def_1374, type, image_4958697645175560720nteger: (real > code_integer) > set_real > set_Code_integer).
% 54.91/14.51 thf(func_def_1375, type, image_real_complex: (real > complex) > set_real > set_complex).
% 54.91/14.51 thf(func_def_1376, type, image_real_int: (real > int) > set_real > set_int).
% 54.91/14.51 thf(func_def_1377, type, image_real_nat: (real > nat) > set_real > set_nat).
% 54.91/14.51 thf(func_def_1378, type, image_real_real: (real > real) > set_real > set_real).
% 54.91/14.51 thf(func_def_1379, type, image_real_VEBT_VEBT: (real > vEBT_VEBT) > set_real > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1380, type, image_set_o_set_o: (set_o > set_o) > set_set_o > set_set_o).
% 54.91/14.51 thf(func_def_1381, type, image_524474410958335435et_int: (set_int > set_int) > set_set_int > set_set_int).
% 54.91/14.51 thf(func_def_1382, type, image_4702325430467532143et_nat: (set_int > set_nat) > set_set_int > set_set_nat).
% 54.91/14.51 thf(func_def_1383, type, image_set_nat_int: (set_nat > int) > set_set_nat > set_int).
% 54.91/14.51 thf(func_def_1384, type, image_set_nat_nat: (set_nat > nat) > set_set_nat > set_nat).
% 54.91/14.51 thf(func_def_1385, type, image_3739036796817536367et_int: (set_nat > set_int) > set_set_nat > set_set_int).
% 54.91/14.51 thf(func_def_1386, type, image_7916887816326733075et_nat: (set_nat > set_nat) > set_set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1387, type, image_6725021117256019401et_nat: (set_nat > set_set_nat) > set_set_nat > set_set_set_nat).
% 54.91/14.51 thf(func_def_1388, type, image_2436557299294012491t_real: (set_real > set_real) > set_set_real > set_set_real).
% 54.91/14.51 thf(func_def_1389, type, image_7884819252390400639et_nat: (set_set_nat > set_set_nat) > set_set_set_nat > set_set_set_nat).
% 54.91/14.51 thf(func_def_1390, type, image_1661326939266726661T_VEBT: (set_VEBT_VEBT > set_VEBT_VEBT) > set_set_VEBT_VEBT > set_set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1391, type, image_4442872163159017964nteger: (literal > code_integer) > set_literal > set_Code_integer).
% 54.91/14.51 thf(func_def_1392, type, image_5274195009022015549omplex: (literal > complex) > set_literal > set_complex).
% 54.91/14.51 thf(func_def_1393, type, image_literal_nat: (literal > nat) > set_literal > set_nat).
% 54.91/14.51 thf(func_def_1394, type, image_8195128725298311301iteral: (literal > literal) > set_literal > set_literal).
% 54.91/14.51 thf(func_def_1395, type, image_uint32_uint32: (uint32 > uint32) > set_uint32 > set_uint32).
% 54.91/14.51 thf(func_def_1396, type, image_VEBT_VEBTi_int: (vEBT_VEBTi > int) > set_VEBT_VEBTi > set_int).
% 54.91/14.51 thf(func_def_1397, type, image_VEBT_VEBTi_nat: (vEBT_VEBTi > nat) > set_VEBT_VEBTi > set_nat).
% 54.91/14.51 thf(func_def_1398, type, image_6202559892754154600i_real: (vEBT_VEBTi > real) > set_VEBT_VEBTi > set_real).
% 54.91/14.51 thf(func_def_1399, type, image_7547481670047419768T_VEBT: (vEBT_VEBTi > vEBT_VEBT) > set_VEBT_VEBTi > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1400, type, image_VEBT_VEBT_o: (vEBT_VEBT > $o) > set_VEBT_VEBT > set_o).
% 54.91/14.51 thf(func_def_1401, type, image_2092689629700589388nteger: (vEBT_VEBT > code_integer) > set_VEBT_VEBT > set_Code_integer).
% 54.91/14.51 thf(func_def_1402, type, image_3793382806556112285omplex: (vEBT_VEBT > complex) > set_VEBT_VEBT > set_complex).
% 54.91/14.51 thf(func_def_1403, type, image_VEBT_VEBT_int: (vEBT_VEBT > int) > set_VEBT_VEBT > set_int).
% 54.91/14.51 thf(func_def_1404, type, image_VEBT_VEBT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > set_nat).
% 54.91/14.51 thf(func_def_1405, type, image_VEBT_VEBT_real: (vEBT_VEBT > real) > set_VEBT_VEBT > set_real).
% 54.91/14.51 thf(func_def_1406, type, image_3375948659692109573T_VEBT: (vEBT_VEBT > vEBT_VEBT) > set_VEBT_VEBT > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1407, type, insert_o: $o > set_o > set_o).
% 54.91/14.51 thf(func_def_1408, type, insert_Code_integer: code_integer > set_Code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_1409, type, insert_complex: complex > set_complex > set_complex).
% 54.91/14.51 thf(func_def_1410, type, insert_int: int > set_int > set_int).
% 54.91/14.51 thf(func_def_1411, type, insert_list_nat: list_nat > set_list_nat > set_list_nat).
% 54.91/14.51 thf(func_def_1412, type, insert_nat: nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_1413, type, insert_num: num > set_num > set_num).
% 54.91/14.51 thf(func_def_1414, type, insert6201435330877294327od_o_o: product_prod_o_o > set_Product_prod_o_o > set_Product_prod_o_o).
% 54.91/14.51 thf(func_def_1415, type, insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 54.91/14.51 thf(func_def_1416, type, insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 54.91/14.51 thf(func_def_1417, type, insert4454361187789264009uint32: produc827990862158126777uint32 > set_Pr1773385645901665561uint32 > set_Pr1773385645901665561uint32).
% 54.91/14.51 thf(func_def_1418, type, insert494605675473494903T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > set_Pr6192946355708809607T_VEBT).
% 54.91/14.51 thf(func_def_1419, type, insert_rat: rat > set_rat > set_rat).
% 54.91/14.51 thf(func_def_1420, type, insert_real: real > set_real > set_real).
% 54.91/14.51 thf(func_def_1421, type, insert_set_nat: set_nat > set_set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1422, type, insert_literal: literal > set_literal > set_literal).
% 54.91/14.51 thf(func_def_1423, type, insert_uint32: uint32 > set_uint32 > set_uint32).
% 54.91/14.51 thf(func_def_1424, type, insert_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > set_VEBT_VEBTi).
% 54.91/14.51 thf(func_def_1425, type, insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1426, type, is_singleton_o: set_o > $o).
% 54.91/14.51 thf(func_def_1427, type, is_singleton_complex: set_complex > $o).
% 54.91/14.51 thf(func_def_1428, type, is_singleton_int: set_int > $o).
% 54.91/14.51 thf(func_def_1429, type, is_sin2641923865335537900st_nat: set_list_nat > $o).
% 54.91/14.51 thf(func_def_1430, type, is_singleton_nat: set_nat > $o).
% 54.91/14.51 thf(func_def_1431, type, is_singleton_real: set_real > $o).
% 54.91/14.51 thf(func_def_1432, type, is_singleton_set_nat: set_set_nat > $o).
% 54.91/14.51 thf(func_def_1433, type, is_singleton_literal: set_literal > $o).
% 54.91/14.51 thf(func_def_1434, type, is_sin24926331636114728T_VEBT: set_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1435, type, remove_o: $o > set_o > set_o).
% 54.91/14.51 thf(func_def_1436, type, remove_int: int > set_int > set_int).
% 54.91/14.51 thf(func_def_1437, type, remove_nat: nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_1438, type, remove_real: real > set_real > set_real).
% 54.91/14.51 thf(func_def_1439, type, remove_set_nat: set_nat > set_set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1440, type, remove_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1441, type, the_elem_o: set_o > $o).
% 54.91/14.51 thf(func_def_1442, type, the_elem_int: set_int > int).
% 54.91/14.51 thf(func_def_1443, type, the_elem_nat: set_nat > nat).
% 54.91/14.51 thf(func_def_1444, type, the_elem_set_nat: set_set_nat > set_nat).
% 54.91/14.51 thf(func_def_1445, type, the_elem_VEBT_VEBT: set_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1446, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 54.91/14.51 thf(func_def_1447, type, set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_1448, type, set_or1266510415728281911st_int: int > int > set_int).
% 54.91/14.51 thf(func_def_1449, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 54.91/14.51 thf(func_def_1450, type, set_or1222579329274155063t_real: real > real > set_real).
% 54.91/14.51 thf(func_def_1451, type, set_or7139685690850216873Than_o: $o > $o > set_o).
% 54.91/14.51 thf(func_def_1452, type, set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_1453, type, set_or4662586982721622107an_int: int > int > set_int).
% 54.91/14.51 thf(func_def_1454, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 54.91/14.51 thf(func_def_1455, type, set_or1222409239386451017an_num: num > num > set_num).
% 54.91/14.51 thf(func_def_1456, type, set_or4029947393144176647an_rat: rat > rat > set_rat).
% 54.91/14.51 thf(func_def_1457, type, set_or66887138388493659n_real: real > real > set_real).
% 54.91/14.51 thf(func_def_1458, type, set_or8585797421378605585et_int: set_int > set_int > set_set_int).
% 54.91/14.51 thf(func_def_1459, type, set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1460, type, set_ord_atMost_int: int > set_int).
% 54.91/14.51 thf(func_def_1461, type, set_ord_atMost_nat: nat > set_nat).
% 54.91/14.51 thf(func_def_1462, type, set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_1463, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 54.91/14.51 thf(func_def_1464, type, set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer).
% 54.91/14.51 thf(func_def_1465, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 54.91/14.51 thf(func_def_1466, type, set_or1633881224788618240n_real: real > real > set_real).
% 54.91/14.51 thf(func_def_1467, type, set_ord_lessThan_o: $o > set_o).
% 54.91/14.51 thf(func_def_1468, type, set_ord_lessThan_int: int > set_int).
% 54.91/14.51 thf(func_def_1469, type, set_ord_lessThan_nat: nat > set_nat).
% 54.91/14.51 thf(func_def_1470, type, set_ord_lessThan_num: num > set_num).
% 54.91/14.51 thf(func_def_1471, type, set_ord_lessThan_rat: rat > set_rat).
% 54.91/14.51 thf(func_def_1472, type, set_or5984915006950818249n_real: real > set_real).
% 54.91/14.51 thf(func_def_1473, type, set_or890127255671739683et_nat: set_nat > set_set_nat).
% 54.91/14.51 thf(func_def_1474, type, signed6292675348222524329lo_int: int > int > int).
% 54.91/14.51 thf(func_def_1475, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 54.91/14.51 thf(func_def_1476, type, time_TBOUND_o: heap_Time_Heap_o > nat > $o).
% 54.91/14.51 thf(func_def_1477, type, time_TBOUND_nat: heap_Time_Heap_nat > nat > $o).
% 54.91/14.51 thf(func_def_1478, type, time_T8353473612707095248on_nat: heap_T2636463487746394924on_nat > nat > $o).
% 54.91/14.51 thf(func_def_1479, type, time_T5737551269749752165_VEBTi: heap_T8145700208782473153_VEBTi > nat > $o).
% 54.91/14.51 thf(func_def_1480, type, time_htt_o: assn > heap_Time_Heap_o > ($o > assn) > nat > $o).
% 54.91/14.51 thf(func_def_1481, type, time_htt_nat: assn > heap_Time_Heap_nat > (nat > assn) > nat > $o).
% 54.91/14.51 thf(func_def_1482, type, time_htt_option_nat: assn > heap_T2636463487746394924on_nat > (option_nat > assn) > nat > $o).
% 54.91/14.51 thf(func_def_1483, type, time_htt_VEBT_VEBTi: assn > heap_T8145700208782473153_VEBTi > (vEBT_VEBTi > assn) > nat > $o).
% 54.91/14.51 thf(func_def_1484, type, time_time_VEBT_VEBTi: heap_T8145700208782473153_VEBTi > heap_e7401611519738050253t_unit > nat).
% 54.91/14.51 thf(func_def_1485, type, topolo6980174941875973593q_real: (nat > real) > $o).
% 54.91/14.51 thf(func_def_1486, type, topolo2177554685111907308n_real: real > set_real > filter_real).
% 54.91/14.51 thf(func_def_1487, type, topolo2815343760600316023s_real: real > filter_real).
% 54.91/14.51 thf(func_def_1488, type, topolo4055970368930404560y_real: (nat > real) > $o).
% 54.91/14.51 thf(func_def_1489, type, arccos: real > real).
% 54.91/14.51 thf(func_def_1490, type, arcosh_real: real > real).
% 54.91/14.51 thf(func_def_1491, type, arcsin: real > real).
% 54.91/14.51 thf(func_def_1492, type, arctan: real > real).
% 54.91/14.51 thf(func_def_1493, type, artanh_real: real > real).
% 54.91/14.51 thf(func_def_1494, type, cos_real: real > real).
% 54.91/14.51 thf(func_def_1495, type, cos_coeff: nat > real).
% 54.91/14.51 thf(func_def_1496, type, cosh_real: real > real).
% 54.91/14.51 thf(func_def_1497, type, cot_real: real > real).
% 54.91/14.51 thf(func_def_1498, type, exp_real: real > real).
% 54.91/14.51 thf(func_def_1499, type, ln_ln_real: real > real).
% 54.91/14.51 thf(func_def_1500, type, log: real > real > real).
% 54.91/14.51 thf(func_def_1501, type, pi: real).
% 54.91/14.51 thf(func_def_1502, type, powr_real: real > real > real).
% 54.91/14.51 thf(func_def_1503, type, sin_real: real > real).
% 54.91/14.51 thf(func_def_1504, type, sin_coeff: nat > real).
% 54.91/14.51 thf(func_def_1505, type, sinh_real: real > real).
% 54.91/14.51 thf(func_def_1506, type, tan_real: real > real).
% 54.91/14.51 thf(func_def_1507, type, tanh_real: real > real).
% 54.91/14.51 thf(func_def_1508, type, transitive_trancl_o: set_Product_prod_o_o > set_Product_prod_o_o).
% 54.91/14.51 thf(func_def_1509, type, transi6261509568448316235cl_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 54.91/14.51 thf(func_def_1510, type, transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 54.91/14.51 thf(func_def_1511, type, transi5221092739591632921et_nat: set_Pr3444600963470892981et_nat > set_Pr3444600963470892981et_nat).
% 54.91/14.51 thf(func_def_1512, type, transi3145040225084697757et_nat: set_Pr7928877670098842301et_nat > set_Pr7928877670098842301et_nat).
% 54.91/14.51 thf(func_def_1513, type, transi6288783178788033498nt_int: set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int).
% 54.91/14.51 thf(func_def_1514, type, transi243908449541399842at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 54.91/14.51 thf(func_def_1515, type, transi5456044692924788698uint32: set_Pr3773659940955823943uint32 > set_Pr3773659940955823943uint32).
% 54.91/14.51 thf(func_def_1516, type, transi1789104906590519371l_real: set_Pr6218003697084177305l_real > set_Pr6218003697084177305l_real).
% 54.91/14.51 thf(func_def_1517, type, transi3114468042090999947uint32: set_Pr1773385645901665561uint32 > set_Pr1773385645901665561uint32).
% 54.91/14.51 thf(func_def_1518, type, transi2803566869205510612_VEBTi: set_Pr2227491710730465451_VEBTi > set_Pr2227491710730465451_VEBTi).
% 54.91/14.51 thf(func_def_1519, type, transi8906537157094044885T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr6192946355708809607T_VEBT).
% 54.91/14.51 thf(func_def_1520, type, type_l4264026598287037464l_num0: itself_Numeral_num0 > nat).
% 54.91/14.51 thf(func_def_1521, type, type_d8366093980585677751er_int: (code_integer > int) > (int > code_integer) > set_int > $o).
% 54.91/14.51 thf(func_def_1522, type, div0_uint32: uint32 > uint32).
% 54.91/14.51 thf(func_def_1523, type, mod0_uint32: uint32 > uint32).
% 54.91/14.51 thf(func_def_1524, type, set_bits_aux_uint32: (nat > $o) > nat > uint32 > uint32).
% 54.91/14.51 thf(func_def_1525, type, signed489701013188660438uint32: nat > uint32 > uint32).
% 54.91/14.51 thf(func_def_1526, type, rep_uint32: uint32 > word_N3645301735248828278l_num1).
% 54.91/14.51 thf(func_def_1527, type, uint32_divmod: uint32 > uint32 > produc827990862158126777uint32).
% 54.91/14.51 thf(func_def_1528, type, uint32_sdiv: uint32 > uint32 > uint32).
% 54.91/14.51 thf(func_def_1529, type, uint32_set_bit: uint32 > code_integer > $o > uint32).
% 54.91/14.51 thf(func_def_1530, type, uint32_shiftl: uint32 > code_integer > uint32).
% 54.91/14.51 thf(func_def_1531, type, uint32_shiftr: uint32 > code_integer > uint32).
% 54.91/14.51 thf(func_def_1532, type, uint32_sshiftr: uint32 > code_integer > uint32).
% 54.91/14.51 thf(func_def_1533, type, uint32_test_bit: uint32 > code_integer > $o).
% 54.91/14.51 thf(func_def_1534, type, vEBT_T_i_n_s_e_r_t: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1535, type, vEBT_T_i_n_s_e_r_t2: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1536, type, vEBT_T5076183648494686801_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1537, type, vEBT_T9217963907923527482_t_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1538, type, vEBT_T_m_a_x_t: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1539, type, vEBT_T_m_a_x_t_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1540, type, vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1541, type, vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1542, type, vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1543, type, vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1544, type, vEBT_T_m_i_n_N_u_l_l: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1545, type, vEBT_T5462971552011256508_l_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1546, type, vEBT_T_m_i_n_t: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1547, type, vEBT_T_m_i_n_t_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1548, type, vEBT_T_p_r_e_d: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1549, type, vEBT_T_p_r_e_d2: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1550, type, vEBT_T_p_r_e_d_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1551, type, vEBT_T_p_r_e_d_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1552, type, vEBT_T_s_u_c_c: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1553, type, vEBT_T_s_u_c_c2: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1554, type, vEBT_T_s_u_c_c_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1555, type, vEBT_T_s_u_c_c_rel2: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1556, type, vEBT_V441764108873111860ildupi: nat > nat).
% 54.91/14.51 thf(func_def_1557, type, vEBT_V9176841429113362141ildupi: nat > int).
% 54.91/14.51 thf(func_def_1558, type, vEBT_V3352910403632780892pi_rel: nat > nat > $o).
% 54.91/14.51 thf(func_def_1559, type, vEBT_V2957053500504383685pi_rel: nat > nat > $o).
% 54.91/14.51 thf(func_def_1560, type, vEBT_VEBT_Tb: nat > int).
% 54.91/14.51 thf(func_def_1561, type, vEBT_VEBT_Tb2: nat > nat).
% 54.91/14.51 thf(func_def_1562, type, vEBT_VEBT_Tb_rel: nat > nat > $o).
% 54.91/14.51 thf(func_def_1563, type, vEBT_VEBT_Tb_rel2: nat > nat > $o).
% 54.91/14.51 thf(func_def_1564, type, vEBT_VEBT_highi: nat > nat > heap_Time_Heap_nat).
% 54.91/14.51 thf(func_def_1565, type, vEBT_VEBT_lowi: nat > nat > heap_Time_Heap_nat).
% 54.91/14.51 thf(func_def_1566, type, vEBT_VEBT_minNulli: vEBT_VEBTi > heap_Time_Heap_o).
% 54.91/14.51 thf(func_def_1567, type, vEBT_V739175172307565963ildupi: nat > heap_T8145700208782473153_VEBTi).
% 54.91/14.51 thf(func_def_1568, type, vEBT_V3964819847710782039nserti: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi).
% 54.91/14.51 thf(func_def_1569, type, vEBT_V854960066525838166emberi: vEBT_VEBT > vEBT_VEBTi > nat > heap_Time_Heap_o).
% 54.91/14.51 thf(func_def_1570, type, vEBT_Leafi: $o > $o > vEBT_VEBTi).
% 54.91/14.51 thf(func_def_1571, type, vEBT_Nodei: option4927543243414619207at_nat > nat > array_VEBT_VEBTi > vEBT_VEBTi > vEBT_VEBTi).
% 54.91/14.51 thf(func_def_1572, type, vEBT_size_VEBTi: vEBT_VEBTi > nat).
% 54.91/14.51 thf(func_def_1573, type, vEBT_vebt_assn_raw: vEBT_VEBT > vEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1574, type, vEBT_v8524038756793281170aw_rel: produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o).
% 54.91/14.51 thf(func_def_1575, type, vEBT_vebt_buildupi: nat > heap_T8145700208782473153_VEBTi).
% 54.91/14.51 thf(func_def_1576, type, vEBT_vebt_inserti: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi).
% 54.91/14.51 thf(func_def_1577, type, vEBT_vebt_maxti: vEBT_VEBTi > heap_T2636463487746394924on_nat).
% 54.91/14.51 thf(func_def_1578, type, vEBT_vebt_maxti_rel: vEBT_VEBTi > vEBT_VEBTi > $o).
% 54.91/14.51 thf(func_def_1579, type, vEBT_vebt_memberi: vEBT_VEBTi > nat > heap_Time_Heap_o).
% 54.91/14.51 thf(func_def_1580, type, vEBT_vebt_minti: vEBT_VEBTi > heap_T2636463487746394924on_nat).
% 54.91/14.51 thf(func_def_1581, type, vEBT_vebt_minti_rel: vEBT_VEBTi > vEBT_VEBTi > $o).
% 54.91/14.51 thf(func_def_1582, type, vEBT_Leaf: $o > $o > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1583, type, vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1584, type, vEBT_size_VEBT: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1585, type, vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1586, type, vEBT_VEBT_high: nat > nat > nat).
% 54.91/14.51 thf(func_def_1587, type, vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1588, type, vEBT_VEBT_low: nat > nat > nat).
% 54.91/14.51 thf(func_def_1589, type, vEBT_VEBT_membermima: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1590, type, vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1591, type, vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1592, type, vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1593, type, vEBT_VEBT_valid: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1594, type, vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1595, type, vEBT_invar_vebt: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1596, type, vEBT_set_vebt: vEBT_VEBT > set_nat).
% 54.91/14.51 thf(func_def_1597, type, vEBT_vebt_buildup: nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1598, type, vEBT_v4011308405150292612up_rel: nat > nat > $o).
% 54.91/14.51 thf(func_def_1599, type, vEBT_V1365221501068881998eletei: vEBT_VEBT > vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi).
% 54.91/14.51 thf(func_def_1600, type, vEBT_vebt_deletei: vEBT_VEBTi > nat > heap_T8145700208782473153_VEBTi).
% 54.91/14.51 thf(func_def_1601, type, vEBT_T_d_e_l_e_t_e: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1602, type, vEBT_T8441311223069195367_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1603, type, vEBT_V1232361888498592333_e_t_e: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1604, type, vEBT_V6368547301243506412_e_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1605, type, vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1606, type, vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1607, type, vEBT_VEBT_height: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1608, type, vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1609, type, vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1610, type, vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1611, type, vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1612, type, vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1613, type, vEBT_Intf_vebt_assn: nat > set_nat > vEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1614, type, vEBT_L6286945158656146733_VEBTi: set_nat > ($o > vEBT_VEBTi > assn) > list_o > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1615, type, vEBT_L1319876754960170684T_VEBT: set_nat > ($o > vEBT_VEBT > assn) > list_o > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1616, type, vEBT_L3563379889750563018_int_o: set_nat > (int > $o > assn) > list_int > list_o > assn).
% 54.91/14.51 thf(func_def_1617, type, vEBT_L8888932350013902202nt_int: set_nat > (int > int > assn) > list_int > list_int > assn).
% 54.91/14.51 thf(func_def_1618, type, vEBT_L8891422820522952478nt_nat: set_nat > (int > nat > assn) > list_int > list_nat > assn).
% 54.91/14.51 thf(func_def_1619, type, vEBT_L7077748017936769786t_real: set_nat > (int > real > assn) > list_int > list_real > assn).
% 54.91/14.51 thf(func_def_1620, type, vEBT_L114188773329725699_VEBTi: set_nat > (int > vEBT_VEBTi > assn) > list_int > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1621, type, vEBT_L2018189785592951398T_VEBT: set_nat > (int > vEBT_VEBT > assn) > list_int > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1622, type, vEBT_L7489483478785760935_VEBTi: set_nat > (nat > vEBT_VEBTi > assn) > list_nat > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1623, type, vEBT_L8511957252848910786T_VEBT: set_nat > (nat > vEBT_VEBT > assn) > list_nat > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1624, type, vEBT_L7851252805511451907_VEBTi: set_nat > (real > vEBT_VEBTi > assn) > list_real > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1625, type, vEBT_L3095048238742455910T_VEBT: set_nat > (real > vEBT_VEBT > assn) > list_real > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1626, type, vEBT_L3328983362619735041EBTi_o: set_nat > (vEBT_VEBTi > $o > assn) > list_VEBT_VEBTi > list_o > assn).
% 54.91/14.51 thf(func_def_1627, type, vEBT_L2806540629473551875Ti_int: set_nat > (vEBT_VEBTi > int > assn) > list_VEBT_VEBTi > list_int > assn).
% 54.91/14.51 thf(func_def_1628, type, vEBT_L2809031099982602151Ti_nat: set_nat > (vEBT_VEBTi > nat > assn) > list_VEBT_VEBTi > list_nat > assn).
% 54.91/14.51 thf(func_def_1629, type, vEBT_L7728200936804140803i_real: set_nat > (vEBT_VEBTi > real > assn) > list_VEBT_VEBTi > list_real > assn).
% 54.91/14.51 thf(func_def_1630, type, vEBT_L886525131989349516_VEBTi: set_nat > (vEBT_VEBTi > vEBT_VEBTi > assn) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1631, type, vEBT_L2497118539674116125T_VEBT: set_nat > (vEBT_VEBTi > vEBT_VEBT > assn) > list_VEBT_VEBTi > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1632, type, vEBT_L8650695023172932196BT_nat: set_nat > (vEBT_VEBT > nat > assn) > list_VEBT_VEBT > list_nat > assn).
% 54.91/14.51 thf(func_def_1633, type, vEBT_L1528199826722428489_VEBTi: set_nat > (vEBT_VEBT > vEBT_VEBTi > assn) > list_VEBT_VEBT > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1634, type, vEBT_L3204528365124325536T_VEBT: set_nat > (vEBT_VEBT > vEBT_VEBT > assn) > list_VEBT_VEBT > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1635, type, vEBT_L4725278957065240257o_real: ($o > real > assn) > list_o > list_real > assn).
% 54.91/14.51 thf(func_def_1636, type, vEBT_L1750719106661372127T_VEBT: ($o > vEBT_VEBT > assn) > list_o > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1637, type, vEBT_L74593716426352029nt_int: (int > int > assn) > list_int > list_int > assn).
% 54.91/14.51 thf(func_def_1638, type, vEBT_L77084186935402305nt_nat: (int > nat > assn) > list_int > list_nat > assn).
% 54.91/14.51 thf(func_def_1639, type, vEBT_L6235239671944049190_VEBTi: (int > vEBT_VEBTi > assn) > list_int > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1640, type, vEBT_L1664421287176695555T_VEBT: (int > vEBT_VEBT > assn) > list_int > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1641, type, vEBT_L6102073776069194049t_real: (nat > real > assn) > list_nat > list_real > assn).
% 54.91/14.51 thf(func_def_1642, type, vEBT_L8158188754432654943T_VEBT: (nat > vEBT_VEBT > assn) > list_nat > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1643, type, vEBT_L6234343332106409831real_o: (real > $o > assn) > list_real > list_o > assn).
% 54.91/14.51 thf(func_def_1644, type, vEBT_L1930518968523514909l_real: (real > real > assn) > list_real > list_real > assn).
% 54.91/14.51 thf(func_def_1645, type, vEBT_L4595930785310033027T_VEBT: (real > vEBT_VEBT > assn) > list_real > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1646, type, vEBT_L8927591528087875366Ti_int: (vEBT_VEBTi > int > assn) > list_VEBT_VEBTi > list_int > assn).
% 54.91/14.51 thf(func_def_1647, type, vEBT_L8930081998596925642Ti_nat: (vEBT_VEBTi > nat > assn) > list_VEBT_VEBTi > list_nat > assn).
% 54.91/14.51 thf(func_def_1648, type, vEBT_L1891944875198410415_VEBTi: (vEBT_VEBTi > vEBT_VEBTi > assn) > list_VEBT_VEBTi > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1649, type, vEBT_L7265847600308530106T_VEBT: (vEBT_VEBTi > vEBT_VEBT > assn) > list_VEBT_VEBTi > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1650, type, vEBT_L7489408758114837031VEBT_o: (vEBT_VEBT > $o > assn) > list_VEBT_VEBT > list_o > assn).
% 54.91/14.51 thf(func_def_1651, type, vEBT_L8296926524756676353BT_nat: (vEBT_VEBT > nat > assn) > list_VEBT_VEBT > list_nat > assn).
% 54.91/14.51 thf(func_def_1652, type, vEBT_L5781919052683127133T_real: (vEBT_VEBT > real > assn) > list_VEBT_VEBT > list_real > assn).
% 54.91/14.51 thf(func_def_1653, type, vEBT_L6296928887356842470_VEBTi: (vEBT_VEBT > vEBT_VEBTi > assn) > list_VEBT_VEBT > list_VEBT_VEBTi > assn).
% 54.91/14.51 thf(func_def_1654, type, vEBT_L1279224858307276611T_VEBT: (vEBT_VEBT > vEBT_VEBT > assn) > list_VEBT_VEBT > list_VEBT_VEBT > assn).
% 54.91/14.51 thf(func_def_1655, type, vEBT_VEBT_bit_concat: nat > nat > nat > nat).
% 54.91/14.51 thf(func_def_1656, type, vEBT_VEBT_minNull: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1657, type, vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1658, type, vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat).
% 54.91/14.51 thf(func_def_1659, type, vEBT_vebt_member: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1660, type, vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1661, type, vEBT_VEBT_add: option_nat > option_nat > option_nat).
% 54.91/14.51 thf(func_def_1662, type, vEBT_VEBT_greater: option_nat > option_nat > $o).
% 54.91/14.51 thf(func_def_1663, type, vEBT_VEBT_less: option_nat > option_nat > $o).
% 54.91/14.51 thf(func_def_1664, type, vEBT_VEBT_lesseq: option_nat > option_nat > $o).
% 54.91/14.51 thf(func_def_1665, type, vEBT_VEBT_max_in_set: set_nat > nat > $o).
% 54.91/14.51 thf(func_def_1666, type, vEBT_VEBT_min_in_set: set_nat > nat > $o).
% 54.91/14.51 thf(func_def_1667, type, vEBT_VEBT_mul: option_nat > option_nat > option_nat).
% 54.91/14.51 thf(func_def_1668, type, vEBT_V4262088993061758097ft_nat: (nat > nat > nat) > option_nat > option_nat > option_nat).
% 54.91/14.51 thf(func_def_1669, type, vEBT_VEBT_power: option_nat > option_nat > option_nat).
% 54.91/14.51 thf(func_def_1670, type, vEBT_vebt_maxt: vEBT_VEBT > option_nat).
% 54.91/14.51 thf(func_def_1671, type, vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1672, type, vEBT_vebt_mint: vEBT_VEBT > option_nat).
% 54.91/14.51 thf(func_def_1673, type, vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1674, type, vEBT_is_pred_in_set: set_nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1675, type, vEBT_vebt_pred: vEBT_VEBT > nat > option_nat).
% 54.91/14.51 thf(func_def_1676, type, vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1677, type, vEBT_V8646137997579335489_i_l_d: nat > nat).
% 54.91/14.51 thf(func_def_1678, type, vEBT_V8346862874174094_d_u_p: nat > nat).
% 54.91/14.51 thf(func_def_1679, type, vEBT_V1247956027447740395_p_rel: nat > nat > $o).
% 54.91/14.51 thf(func_def_1680, type, vEBT_V5144397997797733112_d_rel: nat > nat > $o).
% 54.91/14.51 thf(func_def_1681, type, vEBT_VEBT_cnt: vEBT_VEBT > real).
% 54.91/14.51 thf(func_def_1682, type, vEBT_VEBT_cnt2: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1683, type, vEBT_VEBT_cnt_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1684, type, vEBT_VEBT_cnt_rel2: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1685, type, vEBT_VEBT_space: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1686, type, vEBT_VEBT_space2: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1687, type, vEBT_VEBT_space_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1688, type, vEBT_VEBT_space_rel2: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1689, type, vEBT_VEBT_vebt_predi: vEBT_VEBT > vEBT_VEBTi > nat > heap_T2636463487746394924on_nat).
% 54.91/14.51 thf(func_def_1690, type, vEBT_VEBT_vebt_succi: vEBT_VEBT > vEBT_VEBTi > nat > heap_T2636463487746394924on_nat).
% 54.91/14.51 thf(func_def_1691, type, vEBT_vebt_predi: vEBT_VEBTi > nat > heap_T2636463487746394924on_nat).
% 54.91/14.51 thf(func_def_1692, type, vEBT_vebt_succi: vEBT_VEBTi > nat > heap_T2636463487746394924on_nat).
% 54.91/14.51 thf(func_def_1693, type, vEBT_is_succ_in_set: set_nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1694, type, vEBT_vebt_succ: vEBT_VEBT > nat > option_nat).
% 54.91/14.51 thf(func_def_1695, type, vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1696, type, vEBT_V6289311342943941716sTrans: vEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1697, type, accp_nat: (nat > nat > $o) > nat > $o).
% 54.91/14.51 thf(func_def_1698, type, accp_P1862375125659990705et_nat: (produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o) > produc2732055786443039994et_nat > $o).
% 54.91/14.51 thf(func_def_1699, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 54.91/14.51 thf(func_def_1700, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 54.91/14.51 thf(func_def_1701, type, accp_P2887432264394892906BT_nat: (produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o) > produc9072475918466114483BT_nat > $o).
% 54.91/14.51 thf(func_def_1702, type, accp_P7675410724331315407_VEBTi: (produc3625547720036274456_VEBTi > produc3625547720036274456_VEBTi > $o) > produc3625547720036274456_VEBTi > $o).
% 54.91/14.51 thf(func_def_1703, type, accp_VEBT_VEBTi: (vEBT_VEBTi > vEBT_VEBTi > $o) > vEBT_VEBTi > $o).
% 54.91/14.51 thf(func_def_1704, type, accp_VEBT_VEBT: (vEBT_VEBT > vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1705, type, signed5000768011106662067l_num1: nat > word_N3645301735248828278l_num1 > word_N3645301735248828278l_num1).
% 54.91/14.51 thf(func_def_1706, type, member6576561426505652726_nat_o: (produc3658429121746597890et_nat > $o) > set_Pr4532377907799695533_nat_o > $o).
% 54.91/14.51 thf(func_def_1707, type, member_o: $o > set_o > $o).
% 54.91/14.51 thf(func_def_1708, type, member_Code_integer: code_integer > set_Code_integer > $o).
% 54.91/14.51 thf(func_def_1709, type, member_complex: complex > set_complex > $o).
% 54.91/14.51 thf(func_def_1710, type, member_int: int > set_int > $o).
% 54.91/14.51 thf(func_def_1711, type, member_list_o: list_o > set_list_o > $o).
% 54.91/14.51 thf(func_def_1712, type, member_list_nat: list_nat > set_list_nat > $o).
% 54.91/14.51 thf(func_def_1713, type, member_list_real: list_real > set_list_real > $o).
% 54.91/14.51 thf(func_def_1714, type, member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1715, type, member_nat: nat > set_nat > $o).
% 54.91/14.51 thf(func_def_1716, type, member_num: num > set_num > $o).
% 54.91/14.51 thf(func_def_1717, type, member6124377750444531601et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > $o).
% 54.91/14.51 thf(func_def_1718, type, member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o).
% 54.91/14.51 thf(func_def_1719, type, member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o).
% 54.91/14.51 thf(func_def_1720, type, member6260224972018164377et_nat: produc3658429121746597890et_nat > set_Pr3948176798113811640et_nat > $o).
% 54.91/14.51 thf(func_def_1721, type, member4489920277610959864_int_o: product_prod_int_o > set_Pr903927857289325719_int_o > $o).
% 54.91/14.51 thf(func_def_1722, type, member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o).
% 54.91/14.51 thf(func_def_1723, type, member216504246829706758nt_nat: product_prod_int_nat > set_Pr3448869479623346877nt_nat > $o).
% 54.91/14.51 thf(func_def_1724, type, member2744130022092475746t_real: produc679980390762269497t_real > set_Pr3538720872664544793t_real > $o).
% 54.91/14.51 thf(func_def_1725, type, member2056185340421749780T_VEBT: produc1531783533982839933T_VEBT > set_Pr8044002425091019955T_VEBT > $o).
% 54.91/14.51 thf(func_def_1726, type, member4159035015898711888list_o: produc7102631898165422375list_o > set_Pr6227168374412355847list_o > $o).
% 54.91/14.51 thf(func_def_1727, type, member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o).
% 54.91/14.51 thf(func_def_1728, type, member7340969449405702474st_nat: produc1828647624359046049st_nat > set_Pr3451248702717554689st_nat > $o).
% 54.91/14.51 thf(func_def_1729, type, member6584958104391596930t_real: produc478978216448986841t_real > set_Pr611352295856513593t_real > $o).
% 54.91/14.51 thf(func_def_1730, type, member2333554998283850498uint32: produc823665806539077721uint32 > set_Pr2258164808687509945uint32 > $o).
% 54.91/14.51 thf(func_def_1731, type, member4173000155140927252_VEBTi: produc3089554586268799851_VEBTi > set_Pr4797120415438012619_VEBTi > $o).
% 54.91/14.51 thf(func_def_1732, type, member4439316823752958928T_VEBT: produc9211091688327510695T_VEBT > set_Pr1916528119006554503T_VEBT > $o).
% 54.91/14.51 thf(func_def_1733, type, member4262671552274231302at_int: product_prod_nat_int > set_Pr7995236796853374141at_int > $o).
% 54.91/14.51 thf(func_def_1734, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 54.91/14.51 thf(func_def_1735, type, member6341495586645257982et_nat: produc5657529347773406293et_nat > set_Pr3444600963470892981et_nat > $o).
% 54.91/14.51 thf(func_def_1736, type, member4763271486408492550et_nat: produc6830853553727218525et_nat > set_Pr7928877670098842301et_nat > $o).
% 54.91/14.51 thf(func_def_1737, type, member8566619992076573584nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > $o).
% 54.91/14.51 thf(func_def_1738, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 54.91/14.51 thf(func_def_1739, type, member4724532482705224080uint32: produc8822557026176459367uint32 > set_Pr3773659940955823943uint32 > $o).
% 54.91/14.51 thf(func_def_1740, type, member1627681773268152802al_int: produc8786904178792722361al_int > set_Pr1019928272762051225al_int > $o).
% 54.91/14.51 thf(func_def_1741, type, member7849222048561428706l_real: produc2422161461964618553l_real > set_Pr6218003697084177305l_real > $o).
% 54.91/14.51 thf(func_def_1742, type, member7262085504369356948T_VEBT: produc3757001726724277373T_VEBT > set_Pr6019664923565264691T_VEBT > $o).
% 54.91/14.51 thf(func_def_1743, type, member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o).
% 54.91/14.51 thf(func_def_1744, type, member8027108493173000802uint32: produc827990862158126777uint32 > set_Pr1773385645901665561uint32 > $o).
% 54.91/14.51 thf(func_def_1745, type, member660371905731732212_VEBTi: produc3777764054643897931_VEBTi > set_Pr2227491710730465451_VEBTi > $o).
% 54.91/14.51 thf(func_def_1746, type, member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o).
% 54.91/14.51 thf(func_def_1747, type, member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o).
% 54.91/14.51 thf(func_def_1748, type, member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o).
% 54.91/14.51 thf(func_def_1749, type, member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o).
% 54.91/14.51 thf(func_def_1750, type, member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o).
% 54.91/14.51 thf(func_def_1751, type, member_rat: rat > set_rat > $o).
% 54.91/14.51 thf(func_def_1752, type, member_real: real > set_real > $o).
% 54.91/14.51 thf(func_def_1753, type, member_set_o: set_o > set_set_o > $o).
% 54.91/14.51 thf(func_def_1754, type, member_set_int: set_int > set_set_int > $o).
% 54.91/14.51 thf(func_def_1755, type, member_set_nat: set_nat > set_set_nat > $o).
% 54.91/14.51 thf(func_def_1756, type, member_set_real: set_real > set_set_real > $o).
% 54.91/14.51 thf(func_def_1757, type, member_set_set_nat: set_set_nat > set_set_set_nat > $o).
% 54.91/14.51 thf(func_def_1758, type, member_set_VEBT_VEBT: set_VEBT_VEBT > set_set_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1759, type, member_literal: literal > set_literal > $o).
% 54.91/14.51 thf(func_def_1760, type, member_uint32: uint32 > set_uint32 > $o).
% 54.91/14.51 thf(func_def_1761, type, member_VEBT_VEBTi: vEBT_VEBTi > set_VEBT_VEBTi > $o).
% 54.91/14.51 thf(func_def_1762, type, member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1763, type, a: heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_1764, type, b: set_nat).
% 54.91/14.51 thf(func_def_1765, type, n: nat).
% 54.91/14.51 thf(func_def_1766, type, r: vEBT_VEBTi).
% 54.91/14.51 thf(func_def_1767, type, s: set_nat).
% 54.91/14.51 thf(func_def_1768, type, t: vEBT_VEBT).
% 54.91/14.51 thf(func_def_1769, type, x: nat).
% 54.91/14.51 thf(func_def_1770, type, xa: nat).
% 54.91/14.51 thf(func_def_1789, type, sP0: option_nat > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1790, type, sP1: nat > nat > nat > nat > list_VEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1791, type, sP2: vEBT_VEBT > $o > $o).
% 54.91/14.51 thf(func_def_1792, type, sP3: vEBT_VEBT > $o > $o).
% 54.91/14.51 thf(func_def_1793, type, sP4: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1794, type, sP5: nat > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1795, type, sP6: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 54.91/14.51 thf(func_def_1796, type, sP7: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 54.91/14.51 thf(func_def_1797, type, sP8: nat > list_VEBT_VEBT > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1798, type, sP9: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1799, type, sP10: vEBT_VEBT > list_VEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1800, type, sP11: nat > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1801, type, sP12: nat > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1802, type, sP13: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1803, type, sP14: nat > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1804, type, sP15: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 54.91/14.51 thf(func_def_1805, type, sP16: nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1806, type, sP17: nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1807, type, sP18: nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1808, type, sP19: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 54.91/14.51 thf(func_def_1809, type, sP20: $o > $o > nat > $o).
% 54.91/14.51 thf(func_def_1810, type, sP21: $o > $o > $o > nat > $o).
% 54.91/14.51 thf(func_def_1811, type, sP22: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 54.91/14.51 thf(func_def_1812, type, sP23: $o > nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 54.91/14.51 thf(func_def_1813, type, sP24: $o > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1814, type, sP25: vEBT_VEBT > $o > nat > $o).
% 54.91/14.51 thf(func_def_1815, type, sP26: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1816, type, sP27: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1817, type, sP28: set_nat > (set_nat > $o) > $o).
% 54.91/14.51 thf(func_def_1818, type, sP29: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1819, type, sP30: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > $o).
% 54.91/14.51 thf(func_def_1820, type, sP31: nat > nat > set_nat > set_nat > $o).
% 54.91/14.51 thf(func_def_1821, type, sP32: nat > nat > set_nat > set_nat > $o).
% 54.91/14.51 thf(func_def_1822, type, sP33: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 54.91/14.51 thf(func_def_1823, type, sP34: vEBT_VEBT > list_VEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1824, type, sP35: vEBT_VEBT > option_nat > $o).
% 54.91/14.51 thf(func_def_1825, type, sP36: $o > $o > nat > $o).
% 54.91/14.51 thf(func_def_1826, type, sK37: nat > nat > nat).
% 54.91/14.51 thf(func_def_1827, type, sK38: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_1828, type, sK39: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_1829, type, sK40: set_nat > set_nat > nat).
% 54.91/14.51 thf(func_def_1830, type, sK41: set_nat > set_nat > nat).
% 54.91/14.51 thf(func_def_1831, type, sK42: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_1832, type, sK43: produc3925858234332021118et_nat > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_1833, type, sK44: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1834, type, sK45: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1835, type, sK46: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1836, type, sK47: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1837, type, sK48: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_1838, type, sK49: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_1839, type, sK50: nat > nat > nat).
% 54.91/14.51 thf(func_def_1840, type, sK51: nat > nat).
% 54.91/14.51 thf(func_def_1841, type, sK52: (produc2732055786443039994et_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_1842, type, sK53: (produc2732055786443039994et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_1843, type, sK54: (produc2732055786443039994et_nat > $o) > heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_1844, type, sK55: (produc2732055786443039994et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_1845, type, sK56: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_1846, type, sK57: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_1847, type, sK58: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1848, type, sK59: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1849, type, sK60: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1850, type, sK61: vEBT_VEBT > option4927543243414619207at_nat).
% 54.91/14.51 thf(func_def_1851, type, sK62: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1852, type, sK63: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1853, type, sK64: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1854, type, sK65: nat > nat).
% 54.91/14.51 thf(func_def_1855, type, sK66: (nat > $o) > set_nat > nat).
% 54.91/14.51 thf(func_def_1856, type, sK67: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1857, type, sK68: (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_1858, type, sK69: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_1859, type, sK70: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_1860, type, sK71: (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1861, type, sK72: (nat > $o) > nat > nat > nat).
% 54.91/14.51 thf(func_def_1862, type, sK73: nat > nat).
% 54.91/14.51 thf(func_def_1863, type, sK74: set_nat > set_nat).
% 54.91/14.51 thf(func_def_1864, type, sK75: set_nat > nat).
% 54.91/14.51 thf(func_def_1865, type, sK76: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_1866, type, sK77: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_1867, type, sK78: nat > nat).
% 54.91/14.51 thf(func_def_1868, type, sK79: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1869, type, sK80: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_1870, type, sK81: produc3658429121746597890et_nat > set_nat).
% 54.91/14.51 thf(func_def_1871, type, sK82: produc3658429121746597890et_nat > heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_1872, type, sK83: list_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1873, type, sK84: list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1874, type, sK85: list_VEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1875, type, sK86: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1876, type, sK87: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1877, type, sK88: set_nat > nat).
% 54.91/14.51 thf(func_def_1878, type, sK89: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1879, type, sK90: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1880, type, sK91: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1881, type, sK92: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1882, type, sK93: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1883, type, sK94: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1884, type, sK95: option_nat > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1885, type, sK96: option_nat > vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1886, type, sK97: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1887, type, sK98: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1888, type, sK99: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1889, type, sK100: vEBT_VEBT > option_nat > nat).
% 54.91/14.51 thf(func_def_1890, type, sK101: vEBT_VEBT > option_nat > nat).
% 54.91/14.51 thf(func_def_1891, type, sK102: vEBT_VEBT > option_nat > nat).
% 54.91/14.51 thf(func_def_1892, type, sK103: vEBT_VEBT > option_nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1893, type, sK104: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1894, type, sK105: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1895, type, sK106: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1896, type, sK107: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1897, type, sK108: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1898, type, sK109: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1899, type, sK110: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1900, type, sK111: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1901, type, sK112: vEBT_VEBT > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_1902, type, sK113: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1903, type, sK114: (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1904, type, sK115: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1905, type, sK116: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1906, type, sK117: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1907, type, sK118: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1908, type, sK119: vEBT_VEBT > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_1909, type, sK120: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1910, type, sK121: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1911, type, sK122: nat > vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1912, type, sK123: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1913, type, sK124: nat > vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1914, type, sK125: vEBT_VEBT > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_1915, type, sK126: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1916, type, sK127: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1917, type, sK128: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1918, type, sK129: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1919, type, sK130: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1920, type, sK131: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_1921, type, sK132: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_1922, type, sK133: produc2732055786443039994et_nat > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_1923, type, sK134: nat > nat).
% 54.91/14.51 thf(func_def_1924, type, sK135: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1925, type, sK136: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1926, type, sK137: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1927, type, sK138: nat > vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1928, type, sK139: nat > vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1929, type, sK140: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1930, type, sK141: vEBT_VEBT > nat > $o).
% 54.91/14.51 thf(func_def_1931, type, sK142: set_nat > nat).
% 54.91/14.51 thf(func_def_1932, type, sK143: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_1933, type, sK144: option4927543243414619207at_nat > nat).
% 54.91/14.51 thf(func_def_1934, type, sK145: option4927543243414619207at_nat > nat).
% 54.91/14.51 thf(func_def_1935, type, sK146: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_1936, type, sK147: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1937, type, sK148: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1938, type, sK149: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_1939, type, sK150: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1940, type, sK151: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1941, type, sK152: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1942, type, sK153: list_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1943, type, sK154: list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1944, type, sK155: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1945, type, sK156: nat > list_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1946, type, sK157: assn > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_1947, type, sK158: assn > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_1948, type, sK159: (nat > rat) > (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_1949, type, sK160: (nat > rat) > (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_1950, type, sK161: (nat > $o) > nat > nat > nat).
% 54.91/14.51 thf(func_def_1951, type, sK162: assn > assn > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_1952, type, sK163: assn > assn > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_1953, type, sK164: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1954, type, sK165: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1955, type, sK166: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1956, type, sK167: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1957, type, sK168: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_1958, type, sK169: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_1959, type, sK170: nat > nat).
% 54.91/14.51 thf(func_def_1960, type, sK171: vEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1961, type, sK172: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 54.91/14.51 thf(func_def_1962, type, sK173: vEBT_VEBT > nat > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1963, type, sK174: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1964, type, sK175: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1965, type, sK176: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1966, type, sK177: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_1967, type, sK178: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_1968, type, sK179: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1969, type, sK180: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1970, type, sK181: nat > vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1971, type, sK182: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1972, type, sK183: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1973, type, sK184: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1974, type, sK185: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1975, type, sK186: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1976, type, sK187: nat > vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1977, type, sK188: vEBT_VEBT > nat > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1978, type, sK189: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1979, type, sK190: vEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1980, type, sK191: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1981, type, sK192: vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_1982, type, sK193: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1983, type, sK194: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1984, type, sK195: nat > vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1985, type, sK196: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1986, type, sK197: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1987, type, sK198: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1988, type, sK199: nat > vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1989, type, sK200: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1990, type, sK201: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1991, type, sK202: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1992, type, sK203: nat > vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_1993, type, sK204: nat > vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_1994, type, sK205: nat > list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1995, type, sK206: nat > list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_1996, type, sK207: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1997, type, sK208: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_1998, type, sK209: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_1999, type, sK210: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_2000, type, sK211: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_2001, type, sK212: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2002, type, sK213: (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2003, type, sK214: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2004, type, sK215: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2005, type, sK216: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2006, type, sK217: (nat > $o) > nat > nat > nat).
% 54.91/14.51 thf(func_def_2007, type, sK218: nat > (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_2008, type, sK219: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2009, type, sK220: (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2010, type, sK221: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2011, type, sK222: (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2012, type, sK223: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2013, type, sK224: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2014, type, sK225: assn > $o > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_2015, type, sK226: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_2016, type, sK227: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2017, type, sK228: produc3925858234332021118et_nat > set_nat).
% 54.91/14.51 thf(func_def_2018, type, sK229: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2019, type, sK230: produc3925858234332021118et_nat > heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_2020, type, sK231: nat > nat).
% 54.91/14.51 thf(func_def_2021, type, sK232: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2022, type, sK233: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2023, type, sK234: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2024, type, sK235: vEBT_VEBT > $o > nat > $o).
% 54.91/14.51 thf(func_def_2025, type, sK236: vEBT_VEBT > $o > nat > $o).
% 54.91/14.51 thf(func_def_2026, type, sK237: vEBT_VEBT > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_2027, type, sK238: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2028, type, sK239: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2029, type, sK240: vEBT_VEBT > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_2030, type, sK241: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2031, type, sK242: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2032, type, sK243: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2033, type, sK244: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2034, type, sK245: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2035, type, sK246: vEBT_VEBT > nat > $o > nat).
% 54.91/14.51 thf(func_def_2036, type, sK247: vEBT_VEBT > nat > $o > nat).
% 54.91/14.51 thf(func_def_2037, type, sK248: vEBT_VEBT > nat > $o > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2038, type, sK249: vEBT_VEBT > nat > $o > nat).
% 54.91/14.51 thf(func_def_2039, type, sK250: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2040, type, sK251: nat > nat > nat).
% 54.91/14.51 thf(func_def_2041, type, sK252: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_2042, type, sK253: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_2043, type, sK254: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2044, type, sK255: produc2732055786443039994et_nat > produc3925858234332021118et_nat).
% 54.91/14.51 thf(func_def_2045, type, sK256: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2046, type, sK257: produc3925858234332021118et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2047, type, sK258: produc3925858234332021118et_nat > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_2048, type, sK259: (nat > nat > $o) > set_nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2049, type, sK260: (nat > nat > $o) > set_nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2050, type, sK261: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2051, type, sK262: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2052, type, sK263: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2053, type, sK264: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2054, type, sK265: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2055, type, sK266: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2056, type, sK267: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2057, type, sK268: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2058, type, sK269: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2059, type, sK270: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2060, type, sK271: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2061, type, sK272: assn > $o > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_2062, type, sK273: list_VEBT_VEBT > vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_2063, type, sK274: list_VEBT_VEBT > vEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_2064, type, sK275: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 54.91/14.51 thf(func_def_2065, type, sK276: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 54.91/14.51 thf(func_def_2066, type, sK277: list_VEBT_VEBT > nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2067, type, sK278: list_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2068, type, sK279: list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2069, type, sK280: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2070, type, sK281: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2071, type, sK282: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2072, type, sK283: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2073, type, sK284: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2074, type, sK285: (produc2732055786443039994et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2075, type, sK286: (produc2732055786443039994et_nat > $o) > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_2076, type, sK287: (produc2732055786443039994et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2077, type, sK288: (produc3925858234332021118et_nat > $o) > heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_2078, type, sK289: (produc3925858234332021118et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2079, type, sK290: (produc3925858234332021118et_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2080, type, sK291: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_2081, type, sK292: nat > nat).
% 54.91/14.51 thf(func_def_2082, type, sK293: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2083, type, sK294: produc2732055786443039994et_nat > produc3925858234332021118et_nat).
% 54.91/14.51 thf(func_def_2084, type, sK295: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2085, type, sK296: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2086, type, sK297: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2087, type, sK298: nat > nat).
% 54.91/14.51 thf(func_def_2088, type, sK299: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2089, type, sK300: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2090, type, sK301: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2091, type, sK302: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2092, type, sK303: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2093, type, sK304: (nat > nat > $o) > nat).
% 54.91/14.51 thf(func_def_2094, type, sK305: set_nat > (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2095, type, sK306: set_nat > (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2096, type, sK307: set_nat > nat).
% 54.91/14.51 thf(func_def_2097, type, sK308: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2098, type, sK309: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_2099, type, sK310: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_2100, type, sK311: product_prod_nat_nat > nat).
% 54.91/14.51 thf(func_def_2101, type, sK312: product_prod_nat_nat > nat).
% 54.91/14.51 thf(func_def_2102, type, sK313: nat > nat > nat).
% 54.91/14.51 thf(func_def_2103, type, sK314: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2104, type, sK315: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2105, type, sK316: (produc3925858234332021118et_nat > $o) > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_2106, type, sK317: (produc3925858234332021118et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2107, type, sK318: nat > nat).
% 54.91/14.51 thf(func_def_2108, type, sK319: nat > nat > nat).
% 54.91/14.51 thf(func_def_2109, type, sK320: produc2732055786443039994et_nat > heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_2110, type, sK321: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2111, type, sK322: produc2732055786443039994et_nat > set_nat).
% 54.91/14.51 thf(func_def_2112, type, sK323: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2113, type, sK324: nat > nat).
% 54.91/14.51 thf(func_def_2114, type, sK325: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2115, type, sK326: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2116, type, sK327: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2117, type, sK328: vEBT_VEBT > option4927543243414619207at_nat).
% 54.91/14.51 thf(func_def_2118, type, sK329: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2119, type, sK330: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2120, type, sK331: (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2121, type, sK332: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2122, type, sK333: nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_2123, type, sK334: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2124, type, sK335: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2125, type, sK336: (nat > $o) > (nat > $o) > set_nat > nat).
% 54.91/14.51 thf(func_def_2126, type, sK337: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2127, type, sK338: (nat > $o) > (nat > $o) > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2128, type, sK339: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2129, type, sK340: nat > (nat > $o) > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2130, type, sK341: nat > nat > set_nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_2131, type, sK342: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_2132, type, sK343: nat > nat).
% 54.91/14.51 thf(func_def_2133, type, sK344: nat > nat).
% 54.91/14.51 thf(func_def_2134, type, sK345: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2135, type, sK346: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2136, type, sK347: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2137, type, sK348: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2138, type, sK349: vEBT_VEBT > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_2139, type, sK350: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2140, type, sK351: nat > nat).
% 54.91/14.51 thf(func_def_2141, type, sK352: set_int > (nat > int > $o) > set_nat > int).
% 54.91/14.51 thf(func_def_2142, type, sK353: set_int > (nat > int > $o) > set_nat > nat).
% 54.91/14.51 thf(func_def_2143, type, sK354: product_prod_nat_nat > nat).
% 54.91/14.51 thf(func_def_2144, type, sK355: product_prod_nat_nat > nat).
% 54.91/14.51 thf(func_def_2145, type, sK356: (nat > $o) > set_nat > nat).
% 54.91/14.51 thf(func_def_2146, type, sK357: (nat > nat) > nat).
% 54.91/14.51 thf(func_def_2147, type, sK358: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2148, type, sK359: nat > nat).
% 54.91/14.51 thf(func_def_2149, type, sK360: set_nat > nat).
% 54.91/14.51 thf(func_def_2150, type, sK361: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2151, type, sK362: vEBT_VEBT > product_prod_nat_nat).
% 54.91/14.51 thf(func_def_2152, type, sK363: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2153, type, sK364: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2154, type, sK365: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2155, type, sK366: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2156, type, sK367: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2157, type, sK368: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2158, type, sK369: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2159, type, sK370: (produc2732055786443039994et_nat > $o) > produc3925858234332021118et_nat).
% 54.91/14.51 thf(func_def_2160, type, sK371: (produc2732055786443039994et_nat > $o) > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2161, type, sK372: (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2162, type, sK373: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2163, type, sK374: (product_prod_nat_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2164, type, sK375: (product_prod_nat_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2165, type, sK376: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_2166, type, sK377: nat > nat).
% 54.91/14.51 thf(func_def_2167, type, sK378: nat > set_nat > set_nat).
% 54.91/14.51 thf(func_def_2168, type, sK379: vEBT_VEBT > list_VEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_2169, type, sK380: vEBT_VEBT > list_VEBT_VEBT > nat > nat).
% 54.91/14.51 thf(func_def_2170, type, sK381: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 54.91/14.51 thf(func_def_2171, type, sK382: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 54.91/14.51 thf(func_def_2172, type, sK383: list_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2173, type, sK384: list_VEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2174, type, sK385: nat > list_VEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2175, type, sK386: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_2176, type, sK387: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2177, type, sK388: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2178, type, sK389: assn > assn > produc3658429121746597890et_nat).
% 54.91/14.51 thf(func_def_2179, type, sK390: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2180, type, sK391: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2181, type, sK392: nat > nat).
% 54.91/14.51 thf(func_def_2182, type, sK393: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_2183, type, sK394: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2184, type, sK395: nat > nat).
% 54.91/14.51 thf(func_def_2185, type, sK396: nat).
% 54.91/14.51 thf(func_def_2186, type, sK397: nat).
% 54.91/14.51 thf(func_def_2187, type, sK398: nat > nat).
% 54.91/14.51 thf(func_def_2188, type, sK399: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2189, type, sK400: vEBT_VEBT > $o).
% 54.91/14.51 thf(func_def_2190, type, sK401: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_2191, type, sK402: nat > set_nat > nat).
% 54.91/14.51 thf(func_def_2192, type, sK403: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2193, type, sK404: (nat > $o) > nat > nat).
% 54.91/14.51 thf(func_def_2194, type, sK405: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_2195, type, sK406: vEBT_VEBT > option_nat > $o).
% 54.91/14.51 thf(func_def_2196, type, sK407: vEBT_VEBT > option_nat > $o).
% 54.91/14.51 thf(func_def_2197, type, sK408: vEBT_VEBT > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2198, type, sK409: vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2199, type, sK410: vEBT_VEBT > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2200, type, sK411: vEBT_VEBT > option_nat > nat).
% 54.91/14.51 thf(func_def_2201, type, sK412: vEBT_VEBT > option_nat > nat).
% 54.91/14.51 thf(func_def_2202, type, sK413: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 54.91/14.51 thf(func_def_2203, type, sK414: vEBT_VEBT > option_nat > nat).
% 54.91/14.51 thf(func_def_2204, type, sK415: vEBT_VEBT > option_nat > vEBT_VEBT).
% 54.91/14.51 thf(func_def_2205, type, sK416: nat > nat).
% 54.91/14.51 thf(func_def_2206, type, sK417: set_nat > nat > nat).
% 54.91/14.51 thf(func_def_2207, type, sK418: (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2208, type, sK419: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2209, type, sK420: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2210, type, sK421: (set_nat > $o) > nat).
% 54.91/14.51 thf(func_def_2211, type, sK422: (set_nat > $o) > set_nat).
% 54.91/14.51 thf(func_def_2212, type, sK423: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2213, type, sK424: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2214, type, sK425: nat > vEBT_VEBT > nat).
% 54.91/14.51 thf(func_def_2215, type, sK426: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2216, type, sK427: nat > (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2217, type, sK428: (nat > $o) > nat).
% 54.91/14.51 thf(func_def_2218, type, sK429: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2219, type, sK430: produc2732055786443039994et_nat > produc3658429121746597890et_nat > $o).
% 54.91/14.51 thf(func_def_2220, type, sK431: produc2732055786443039994et_nat > heap_e7401611519738050253t_unit).
% 54.91/14.51 thf(func_def_2221, type, sK432: produc2732055786443039994et_nat > set_nat).
% 54.91/14.51 thf(func_def_2222, type, sK433: nat > nat > nat).
% 54.91/14.51 thf(func_def_2224, type, ph435: !>[X0: $tType]:(X0)).
% 54.91/14.51 thf(f28893,plain,(
% 54.91/14.51 $false),
% 54.91/14.51 inference(avatar_sat_refutation,[status(thm)],[f28804,f28892])).
% 54.91/14.51 thf(f28892,plain,(
% 54.91/14.51 spl434_3),
% 54.91/14.51 inference(avatar_split_clause,[status(thm)],[f28891,f28696])).
% 54.91/14.51 thf(f28696,definition,(
% 54.91/14.51 spl434_3 <=> ! [X0 : nat] : ((vEBT_invar_vebt @ t @ X0) != $true)),
% 54.91/14.51 introduced(definition,[new_symbols(naming,[spl434_3])],[avatar_definition])).
% 54.91/14.51 thf(f28891,plain,(
% 54.91/14.51 ( ! [X0 : nat] : (((vEBT_invar_vebt @ t @ X0) != $true)) )),
% 54.91/14.51 inference(subsumption_resolution,[status(thm)],[f28890,f25951])).
% 54.91/14.51 thf(f25951,plain,(
% 54.91/14.51 (x != xa)),
% 54.91/14.51 inference(cnf_transformation,[status(thm)],[f24225])).
% 54.91/14.51 thf(f24225,plain,(
% 54.91/14.51 (x != xa)),
% 54.91/14.51 inference(flattening,[status(thm)],[f9151])).
% 54.91/14.51 thf(f9151,negated_conjecture,(
% 54.91/14.51 ~(x = xa)),
% 54.91/14.51 inference(negated_conjecture,[status(cth)],[f9150])).
% 54.91/14.51 thf(f9150,conjecture,(
% 54.91/14.51 (x = xa)),
% 54.91/14.51 file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_5)).
% 54.91/14.51 thf(f28890,plain,(
% 54.91/14.51 ( ! [X0 : nat] : ((x = xa) | ((vEBT_invar_vebt @ t @ X0) != $true)) )),
% 54.91/14.51 inference(subsumption_resolution,[status(thm)],[f28888,f28677])).
% 54.91/14.51 thf(f28677,plain,(
% 54.91/14.51 ((vEBT_V8194947554948674370ptions @ t @ xa) = $true)),
% 54.91/14.51 inference(superposition,[status(thm)],[f26940,f28664])).
% 54.91/14.51 thf(f28664,plain,(
% 54.91/14.51 ((member_nat @ xa @ (collect_nat @ (vEBT_V8194947554948674370ptions @ t))) = $true)),
% 54.91/14.51 inference(beta_eta_normalization,[status(thm)],[f27502])).
% 54.91/14.51 thf(f27502,plain,(
% 54.91/14.51 ((member_nat @ xa @ ((^[Y0 : vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ Y0))) @ t)) = $true)),
% 54.91/14.51 inference(definition_unfolding,[status(thm)],[f26533,f27027])).
% 54.91/14.51 thf(f27027,plain,(
% 54.91/14.51 (vEBT_set_vebt = (^[Y0 : vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ Y0))))),
% 54.91/14.51 inference(cnf_transformation,[status(thm)],[f23040])).
% 54.91/14.51 thf(f23040,plain,(
% 54.91/14.51 (vEBT_set_vebt = (^[Y0 : vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ Y0))))),
% 54.91/14.51 inference(fool_elimination,[status(thm)],[f23039])).
% 54.91/14.51 thf(f23039,plain,(
% 54.91/14.51 ((^[X0 : vEBT_VEBT] : (collect_nat @ (vEBT_V8194947554948674370ptions @ X0))) = vEBT_set_vebt)),
% 54.91/14.51 inference(rectify,[status(thm)],[f6534])).
% 54.91/14.51 thf(f6534,axiom,(
% 54.91/14.51 ((^[X117 : vEBT_VEBT] : (collect_nat @ (vEBT_V8194947554948674370ptions @ X117))) = vEBT_set_vebt)),
% 54.91/14.51 file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',fact_6533_set__vebt__def)).
% 54.91/14.51 thf(f26533,plain,(
% 54.91/14.51 ((member_nat @ xa @ (vEBT_set_vebt @ t)) = $true)),
% 54.91/14.51 inference(cnf_transformation,[status(thm)],[f19631])).
% 54.91/14.51 thf(f19631,plain,(
% 54.91/14.51 ((member_nat @ xa @ (vEBT_set_vebt @ t)) = $true)),
% 54.91/14.51 inference(fool_elimination,[status(thm)],[f19630])).
% 54.91/14.51 thf(f19630,plain,(
% 54.91/14.51 (member_nat @ xa @ (vEBT_set_vebt @ t))),
% 54.91/14.51 inference(rectify,[status(thm)],[f9148])).
% 54.91/14.51 thf(f9148,axiom,(
% 54.91/14.51 (member_nat @ xa @ (vEBT_set_vebt @ t))),
% 54.91/14.51 file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_3)).
% 54.91/14.51 thf(f26940,plain,(
% 54.91/14.51 ( ! [X0 : nat,X1 : nat > $o] : (((X1 @ X0) = (member_nat @ X0 @ (collect_nat @ X1)))) )),
% 54.91/14.51 inference(cnf_transformation,[status(thm)],[f24248])).
% 54.91/14.51 thf(f24248,plain,(
% 54.91/14.51 ! [X0 : nat,X1 : nat > $o] : ((X1 @ X0) = (member_nat @ X0 @ (collect_nat @ X1)))),
% 54.91/14.51 inference(rectify,[status(thm)],[f61])).
% 54.91/14.51 thf(f61,axiom,(
% 54.91/14.51 ! [X12 : nat,X21 : nat > $o] : ((member_nat @ X12 @ (collect_nat @ X21)) = (X21 @ X12))),
% 54.91/14.51 file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',fact_60_mem__Collect__eq)).
% 54.91/14.51 thf(f28888,plain,(
% 54.91/14.51 ( ! [X0 : nat] : (((vEBT_V8194947554948674370ptions @ t @ xa) != $true) | (x = xa) | ((vEBT_invar_vebt @ t @ X0) != $true)) )),
% 54.91/14.51 inference(trivial_inequality_removal,[status(thm)],[f28887])).
% 54.91/14.51 thf(f28887,plain,(
% 54.91/14.51 ( ! [X0 : nat] : (((vEBT_V8194947554948674370ptions @ t @ xa) != $true) | (x = xa) | ((vEBT_invar_vebt @ t @ X0) != $true) | ($true != $true)) )),
% 54.91/14.51 inference(superposition,[status(thm)],[f28742,f26941])).
% 54.91/14.51 thf(f26941,plain,(
% 54.91/14.51 ( ! [X2 : nat,X3 : nat,X0 : vEBT_VEBT,X1 : nat] : (((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1) = $true) | ((vEBT_invar_vebt @ X0 @ X3) != $true) | (X1 = X2) | ((vEBT_V8194947554948674370ptions @ X0 @ X1) != $true)) )),
% 54.91/14.51 inference(cnf_transformation,[status(thm)],[f25758])).
% 54.91/14.51 thf(f25758,plain,(
% 54.91/14.51 ! [X0 : vEBT_VEBT,X1 : nat,X2 : nat,X3 : nat] : (((vEBT_invar_vebt @ X0 @ X3) != $true) | ((((X1 != X2) & ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true)) | ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1) != $true)) & (((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1) = $true) | (X1 = X2) | ((vEBT_V8194947554948674370ptions @ X0 @ X1) != $true))))),
% 54.91/14.51 inference(flattening,[status(thm)],[f25757])).
% 54.91/14.51 thf(f25757,plain,(
% 54.91/14.51 ! [X0 : vEBT_VEBT,X1 : nat,X2 : nat,X3 : nat] : (((vEBT_invar_vebt @ X0 @ X3) != $true) | ((((X1 != X2) & ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true)) | ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1) != $true)) & (((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1) = $true) | ((X1 = X2) | ((vEBT_V8194947554948674370ptions @ X0 @ X1) != $true)))))),
% 54.91/14.51 inference(nnf_transformation,[status(thm)],[f24878])).
% 54.91/14.51 thf(f24878,plain,(
% 54.91/14.51 ! [X0 : vEBT_VEBT,X1 : nat,X2 : nat,X3 : nat] : (((vEBT_invar_vebt @ X0 @ X3) != $true) | (((X1 != X2) & ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true)) <=> ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1) = $true)))),
% 54.91/14.51 inference(ennf_transformation,[status(thm)],[f22872])).
% 54.91/14.51 thf(f22872,plain,(
% 54.91/14.51 ! [X0 : vEBT_VEBT,X1 : nat,X2 : nat,X3 : nat] : (((vEBT_invar_vebt @ X0 @ X3) = $true) => (((X1 != X2) & ((vEBT_V8194947554948674370ptions @ X0 @ X1) = $true)) <=> ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1) = $true)))),
% 54.91/14.51 inference(fool_elimination,[status(thm)],[f22871])).
% 54.91/14.51 thf(f22871,plain,(
% 54.91/14.51 ! [X0 : vEBT_VEBT,X1 : nat,X2 : nat,X3 : nat] : ((vEBT_invar_vebt @ X0 @ X3) => ((X1 != X2) & (vEBT_V8194947554948674370ptions @ X0 @ X1) = (vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X1)))),
% 54.91/14.51 inference(rectify,[status(thm)],[f24])).
% 54.91/14.51 thf(f24,axiom,(
% 54.91/14.51 ! [X0 : vEBT_VEBT,X7 : nat,X2 : nat,X1 : nat] : ((vEBT_invar_vebt @ X0 @ X1) => ((X2 != X7) & (vEBT_V8194947554948674370ptions @ X0 @ X7) = (vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ X0 @ X2) @ X7)))),
% 54.91/14.51 file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',fact_23_dele__bmo__cont__corr)).
% 54.91/14.51 thf(f28742,plain,(
% 54.91/14.51 ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ t @ x) @ xa) != $true)),
% 54.91/14.51 inference(superposition,[status(thm)],[f28663,f26940])).
% 54.91/14.51 thf(f28663,plain,(
% 54.91/14.51 ((member_nat @ xa @ (collect_nat @ (vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ t @ x)))) != $true)),
% 54.91/14.51 inference(beta_eta_normalization,[status(thm)],[f27399])).
% 54.91/14.51 thf(f27399,plain,(
% 54.91/14.51 ((member_nat @ xa @ ((^[Y0 : vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ Y0))) @ (vEBT_vebt_delete @ t @ x))) != $true)),
% 54.91/14.51 inference(definition_unfolding,[status(thm)],[f26344,f27027])).
% 54.91/14.51 thf(f26344,plain,(
% 54.91/14.51 ((member_nat @ xa @ (vEBT_set_vebt @ (vEBT_vebt_delete @ t @ x))) != $true)),
% 54.91/14.51 inference(cnf_transformation,[status(thm)],[f24226])).
% 54.91/14.51 thf(f24226,plain,(
% 54.91/14.51 ((member_nat @ xa @ (vEBT_set_vebt @ (vEBT_vebt_delete @ t @ x))) != $true)),
% 54.91/14.51 inference(flattening,[status(thm)],[f14171])).
% 54.91/14.51 thf(f14171,plain,(
% 54.91/14.51 ~((member_nat @ xa @ (vEBT_set_vebt @ (vEBT_vebt_delete @ t @ x))) = $true)),
% 54.91/14.51 inference(fool_elimination,[status(thm)],[f14170])).
% 54.91/14.51 thf(f14170,plain,(
% 54.91/14.51 ~(member_nat @ xa @ (vEBT_set_vebt @ (vEBT_vebt_delete @ t @ x)))),
% 54.91/14.51 inference(rectify,[status(thm)],[f9149])).
% 54.91/14.51 thf(f9149,axiom,(
% 54.91/14.51 ~(member_nat @ xa @ (vEBT_set_vebt @ (vEBT_vebt_delete @ t @ x)))),
% 54.91/14.51 file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_4)).
% 54.91/14.51 thf(f28804,plain,(
% 54.91/14.51 ~spl434_3),
% 54.91/14.51 inference(avatar_contradiction_clause,[status(thm)],[f28803])).
% 54.91/14.51 thf(f28803,plain,(
% 54.91/14.51 $false | ~spl434_3),
% 54.91/14.51 inference(trivial_inequality_removal,[status(thm)],[f28772])).
% 54.91/14.51 thf(f28772,plain,(
% 54.91/14.51 ($true != $true) | ~spl434_3),
% 54.91/14.51 inference(superposition,[status(thm)],[f28697,f26119])).
% 54.91/14.51 thf(f26119,plain,(
% 54.91/14.51 ((vEBT_invar_vebt @ t @ n) = $true)),
% 54.91/14.51 inference(cnf_transformation,[status(thm)],[f20679])).
% 54.91/14.51 thf(f20679,plain,(
% 54.91/14.51 ((vEBT_invar_vebt @ t @ n) = $true)),
% 54.91/14.51 inference(fool_elimination,[status(thm)],[f20678])).
% 54.91/14.51 thf(f20678,plain,(
% 54.91/14.51 (vEBT_invar_vebt @ t @ n)),
% 54.91/14.51 inference(rectify,[status(thm)],[f9146])).
% 54.91/14.51 thf(f9146,axiom,(
% 54.91/14.51 (vEBT_invar_vebt @ t @ n)),
% 54.91/14.51 file('/export/starexec/sandbox/tmp/tmp.HjxjlsJ7Tt/DTF2THF_8220.p',conj_1)).
% 54.91/14.51 thf(f28697,plain,(
% 54.91/14.51 ( ! [X0 : nat] : (((vEBT_invar_vebt @ t @ X0) != $true)) ) | ~spl434_3),
% 54.91/14.51 inference(avatar_component_clause,[status(thm)],[f28696])).
% 54.91/14.51 % SZS output end Proof for DTF2THF_8220
% 54.91/14.51 % (8497)------------------------------
% 54.91/14.51 % (8497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.91/14.51 % (8497)Termination reason: Refutation
% 54.91/14.51
% 54.91/14.51 % (8497)Memory used [KB]: 39146
% 54.91/14.51 % (8497)Time elapsed: 1.225 s
% 54.91/14.51 % (8497)Instructions burned: 2368 (million)
% 54.91/14.51 % (8497)------------------------------
% 54.91/14.51 % (8497)------------------------------
% 54.91/14.51 % (8359)Success in time 6.65 s
%------------------------------------------------------------------------------